corrugated web steel beam · 3.1 bending capacity – laterally supported 3-1 3.2 bending capacity...

SIN BEAM

TECHNICAL GUIDE Corrugated Web Steel Beam

STEELCONSTEELCONSTEELCONSTEELCON Fabrication Inc.

62 Progress Crt, Brampton, Ontario

416-798-3343 - steelcon.ca

TECHNICAL GUIDE

SEPTEMBER 2016 (V0.9) PAGE I

Table of Contents

1 GENERAL 1-1

1.1 General Description 1-1

1.2 Basis for Calculation 1-1

1.3 Product Range and Designation 1-2

1.4 Material 1-4

1.5 Tolerances 1-4

1.6 Corrosion Protection / Painting 1-4

1.7 Quality Monitoring 1-5

1.8 List of Symbols / Abbreviations 1-5

2 TECHNICAL SECTION 2-7

2.1 Bending Capacity 2-7

2.2 Shear Capacity 2-8

2.3 Axial Capacity 2-10

2.4 Web Crippling 2-11

2.5 Web Openings 2-11

2.6 Sectional Properties Calculation 2-12

2.7 Sample Calculation 2-12

3 TABLES 3-1

3.1 Bending Capacity – Laterally Supported 3-1

3.2 Bending Capacity – Laterally Unsupported 3-1

3.3 Shear Capacity 3-1

3.4 Axial Capacity 3-1

3.5 Concentrated Load / Web Crippling Capacity 3-1

3.6 M/D and W/D ratios for ULC Calculation 3-1

4 SAMPLE DETAILS 4-1

4.1 Shear Connections 4-1

4.2 Moment Connections 4-1

4.3 Miscellaneous Details 4-1

5 REFERENCES / CERTIFICATION 5-1

5.1 CWB Certification for Steelcon - SIN Beam Welding 5-1

5.2 European Code 1993-1-5:2005 Annex D Plate Girders with Corrugated Webs 5-1

5.3 Annex D – Commentary 5-1

5.4 Flange Buckling Behavior of H-Shaped Member with Sinusoidal Webs - 2008 5-1

5.5 Plate Girders with Corrugated Webs from the Journal for Civil Engineering and

Management – 2010 5-1

5.6 Pages from CAN S136 – North American Specification for Design of Cold Formed

Steel Members 5-1

5.7 Shear Load Testing Results of WT0330 beams 5-1

TECHNICAL GUIDE

SEPTEMBER 2016 (V0.9) PAGE 1-1

1 GENERAL

1.1 General Description

The SIN beam is a corrugated web welded wide flange steel beam with a corrugated steel web

welded to flat steel flanges.

SIN Beams may be used as flexural members such as roof or floor beams, as components

subjected to axial loads such as columns, or as combined bending and axial members such as in

moment frames or wind columns. The optimal application for the SIN beam is as an alternate

to a rolled or welded wide flange shape or a joist or joist girder section with a depth between

300mm and 1800mm.

Traditionally the shear capacity of a thin web steel beam has always been governed by the loss

of stability and buckling of the web. Web stiffeners can be used to avoid web bucking but are

costly to install. The sinusoidal shape of the SIN beam web prevents buckling, eliminating the

need for web stiffeners, and allowing the web steel material to reach is full shear capacity.

Figure 1: Corrugated Web Steel Beam

1.2 Basis for Calculation

The resistance of the SIN beam to bending, axial and shear forces is described in detail in

Section 2 of this guide. The bending and axial capacity of the SIN beam is based on the

formula provided in CSA S16 “Design of Steel Structures”. The web of the SIN beam is cold

formed steel therefore the shear capacity is calculated based on CSA S136 “North American

Specification for the Design of Cold-Formed Steel Structural Members”.

Due to the sinusoidal shape, the web has a negligible contribution to the axial capacity of the

SIN beam flanges. The axial forces in the beam (due to axial load or a bending moment

TECHNICAL GUIDE


couple) are carried solely by the SIN beam flanges. The corrugated web resists the beam shear

forces and stabilizes the flanges. In this way the SIN beam behaves similar to a truss or joist,

where the axial and bending forces are carried by the chords (flanges) and the shear forces are

carried by the web diagonals (corrugated web).

The SIN beam capacity is backed up by a number of experimental results and expert opinions,

some of which are included in part 6 of this document.

1.3 Product Range and Designation

Standard SIN beam members are composed of a uniform height corrugated steel web and two

flat steel flanges of equal size. Other configurations, including different top and bottom flanges

or tapered webs, are also available. The standard configurations and designations are

described in this section.

1.3.1 Beam Components

1.3.1.1 Web:

The SIN beam web is manufactured from steel coil material which is cold formed into the

corrugated shape. The standard coil widths used to manufacture SIN beam webs are 60”

(1524mm). Each of these coils is available in thickness ranging from 16ga (1.52mm) to 11ga

(3.04mm).

These standard coils can be split to create the following standard web heights:

• 13” (333mm)

• 19.7” (500mm)

• 24” (610mm)

• 29.5” (750mm)

• 39.4” (1000mm)

• 48” (1219mm)

• 59” (1500mm)

The web thickness and associated designations are as follows:

• 0 : 16ga (1.52mm) – Note 16ga is not commonly used because the welding process

involves additional time and quality control requirements.

• A : 14ga (1.90mm)

• B : 12ga (2.66mm)

• C : 11ga (3.04mm)

The corrugated web follows a sinusoidal shape with a wave length of 155mm and an amplitude

of 40mm (43mm for the 3mm web), see figure 1. The web is continuously fillet welded to both

beam flanges by robotic welding equipment, on one side of the web.

TECHNICAL GUIDE


1.3.1.2 Flange:

The flanges are fabricated of flat stock material or de-stressed coil material with thickness

ranging from ¼” (6.4mm) to 1 ½” (38mm) and in widths between 5” (127mm) and 17.7”

(450mm). For all standard size SIN beams the ratio of the flange width to thickness has been

established to ensure that the beam flange is considered Class 3 or better by CSA S16. A list of

standard sizes is included in Part 3 of this document.

Due to the availability of materials flanges thicker than 1” (25.4mm) and longer than 20’ (6m)

will be spliced with full penetration welds.

1.3.2 Parallel Flange Beam:

The standard SIN beam member is a parallel flange configuration where the web height is

constant along the length of the member. Parallel flange SIN beam sections can be

manufactured in lengths anywhere between 13’ (4m) and 50’ (15m). For spans longer than 50’

(15m) members must be fabricated in multiple pieces to suit both manufacturing and

transportation limitations, once on site members can be connected using bolted moment splices

to achieve spans over 50’ (15m).

1.3.2.1 Designation:

The standard designation for a parallel flange SIN beam is:

WT [web_thickness] [web_height] / [flange_width] x [flange_thickness] – [weight]

Example: WTA 610 / 203x16 – 61.7

A – 14ga (1.90mm) thick web

610 – 24” (610mm) tall web

203 – 8” (203mm) wide top and bottom flange

16 – 5/8” (16mm) thick top and bottom flange

61.7 – 61.7 kg / m beam weight.

SIN beam sizes are always shown in metric units.

1.3.2.2 Differing Top and Bottom flanges

Parallel flange beams can be manufactured with different upper and lower flanges. For

manufacturing reasons either the flange widths should be the same while the flange thickness

may vary or the flange thicknesses should be the same and the flange width may vary by +/-

50mm.

The designation for parallel flange SIN beams with differing upper and lower flanges is:

WT [web_thickness] [web_height] /

[upper_flange_width] x [upper_flange_thickness] /

[lower_flange_width] x [lower_flange_thickness]

Example: WTB 1000 / 229x16 / 229x10

12ga x 1000mm web

TECHNICAL GUIDE


229mm x 16mm upper flange

229mm x 10mm bottom flange

1.3.3 Trapezoidal Corrugated Web Beam

SIN beams can be manufactured with a trapezoidal / tapered configuration, where the web

height varies linearly from one end to the other. To avoid scrap two trapezoidal beams are

manufactured from a standards height beam. Using a cutting torch the beam web is cut at an

angle to the flanges and then new flanges are welded in to create two identical trapezoidal

beams.

Due to manufacturing limits the maximum length of a trapezoidal beam is 12,000mm and the

web height must be between 250mm and 1250mm.

1.3.3.1 Designation:

The designation for a trapezoidal web SIN beam follows the same convention as the parallel

flange beams (the upper flange designates the flange which is orthogonal to the web):

WT [web_thickenss] [web_height_max – web_height_min]

/ [upper_flange_width] x [upper_flange_thickness]

/ [lower_flange_width,LF] x [lower_flange_thickness]

Example: WTA 1000 – 500 / 300x15 / 320x12

A : 2.0mm thick corrugated web

1000 – 500 : web height 1000mm at one end to 500mm at the other

300x15 : 300mm x 15mm flange welded orthogonal to the web

300x12 : 300mm x 12mm flange welded along the sloped side of the web

Different upper and lower flanges are possible. For manufacturing reasons, the flange widths

should be the same, while the thicknesses may vary.

1.4 Material

The standard material for both flange and web steel is W350 in accordance with

G40.20/G40.21. Other steel grades can also be used but would be considered a special order

and would require longer procurement times, minimum order quantities and premium pricing.

1.5 Tolerances

SIN beam members are fabricated to the tolerances given in CSA G40.21 for rolled or welded

wide flange steel shapes.

All welding is W47.1 compliant and done by procedures approved by the Canadian Welding

Bureau (CWB).

1.6 Corrosion Protection / Painting

SIN beam members are available in any of the following conditions:

TECHNICAL GUIDE


1.6.1 Raw Steel

If further fabrication will be required or a special coating will be applied elsewhere the SIN

beam member can be shipped as raw steel without any coating.

The corrugated web is welded to the flanges using a continuous fillet weld on one side of the

web. It is recommended that a zinc rich primer be applied to the non-welded side of the web in

the area where the web contacts the flanges (i.e. opposite the throat of the fillet weld) or other

corrosion control measures used to protect this area of the beam.

1.6.2 Standard Shop Paint

The standard SIN beam is coated with a shop primer. Other primers, colors or coatings may be

available as a special order.

1.6.3 Hot Dip Galvanized

SIN beam members can easily be Hot Dip Galvanized.

1.7 Quality Monitoring

The manufacturing process is subject to constant and documented internal monitoring. All

welding is W47.1 compliant and done by procedures approved by the Canadian Welding Bureau

(CWB).

The quality of the original materials is verified through mill test certificates which are available

upon request.

All SIN Beam members are manufactured to meet the same or stricter tolerances than those

given for either welded or rolled wide flange steel shapes in CAN / CSA G40.20.

1.8 List of Symbols / Abbreviations

� a3 – the amplitude of the SIN beam web corrugation (see 1.1)

� Aw – web area

� bel – width of compression element (see 2.1.1)

� bf (U) or (L) – width of the SIN beam flange (Upper or Lower)

� Cr – Factored compressive resistance

� Cw – warping torsional constant

� CWB – Canadian Welding Bureau

� d – overall depth of a SIN beam member

� E – Steel elastic modulus, Young’s Modulus (200,000 MPa)

� EN 1993-1-5 – European code for plated steel elements

� Fy – specified minimum steel yield strength

� G40.20/G40.21 – CSA Standard for the requirements for rolled or welded structural steel

� hw – height of the SIN beam web (i.e. between the flanges)

� Ix, Iy – Moment of inertial about the strong axis / weak axis

� J – St. Venant torsional constant

TECHNICAL GUIDE


� Lu – longest unbraced length where the beam will reach its full moment resistance

� M/D – mass over heated perimeter (kg / m / m) per ULC

� Mr – factored moment resistance

� N – length of bearing for an applied load

� rx – radius of gyration with respect to the strong axis

� ry – radius of gyration with respect to the weak axis

� s – unfolded length of half of a single wave of the SIN beam corrugation

� S16 – CSA Standard for Structural Steel

� S136 – CSA Standard for Cold Formed Steel

� Sx – elastic section modulus

� tf (U) or (L) – thickness of the SIN beam flange (Upper or Lower)

� tw – SIN beam web thickness

� ULC – Underwriters Laboratory of Canada

� Vr – factored shear resistance

� w – length of half of a single wave of the SIN beam corrugation

� W/D – weight over heated perimeter (lb / ft / ft) per ULC

� W47.1 – CSA Standard for fusion welding

� WTA, WTB, WTC – SIN Beam web thickness designation (see 1.3.1.1)

� Zx – plastic section modulus

� � – poisson’s ratio

� ��,� / �,� – reduction factor for local and global buckling

TECHNICAL GUIDE


2 TECHNICAL SECTION

2.1 Bending Capacity

2.1.1 Laterally Supported Members

The SIN beam bending moment capacity can be calculated based on the formula given in CSA

S16, Clause 13.5. Due to the nature of the corrugated beam web the web material has an

insignificant contribution to the bending capacity of the member and should be ignored.

Because only the beam flanges contribute to the bending section modulus there is little

difference between the elastic (Sx) and plastic (Zx) section modulus therefore the elastic

section modulus (Sx) is used for all bending capacity calculations.

S16 requires that for flanges of flexural members the following ratio of flange width to thickness

be maintained �

� ≤ �� (Cl 11.2). Based on testing and published research it is considered

conservative to determine the effective flange width for a SIN beam member as

�� = �� (��) . All standard SIN beam sections (published in Part 3 of this document) have been

determined to ensure that the flanges meet this criteria and are therefore considered Class 1, 2,

or 3 in bending.

Standard SIN beam sectional properties and Laterally Supported Moment capacity are given

Section 3.1 of this document in both Metric and Imperial units.

2.1.2 Laterally Unsupported Members

The capacity of laterally unsupported flexural members can also be calculated based on the

formula given in CSA S16, Clause 13.6. Again the bending sectional properties are calculated

based on the flanges only, neglecting any contribution of the web. For standard SIN beam

sections all of the member properties (�� , �� , �, � ) required to use the formula given in Clause

13.6 are given in Section 3.1 of this document, and the moment capacity for various

unsupported lengths is given in Section 3.2, in both metric and imperial units.

There is research that suggests that the nature of the corrugated web provides enhanced

resistance to lateral torsional buckling (over a standard wide flange shape). There are currently

no proposed design formula that takes this enhanced stability into effect so the formula of S16

can be used knowing that they will be conservative.

TECHNICAL GUIDE


2.1.3 Deflection Calculations

Because of the thin and deep web of the SIN beam member, shear deformations may be

significant and should be considered for accurate deflection calculations. The beam shear area

for each web height and thickness is included in Section 3.3, and can be used to calculate the

shear deformation of the SIN beam.

The Shear Deflection calculation has been included in the sample MathCAD calculations included

in section 2.7 of this report. For common beam sizes i.e. less than 36in (914mm) in depth and

typical beam spans the shear deflections typical increase the deflection by 5 to 15%. However

for deep sections i.e. over 36in (914mm) in depth particularly with low span to depth ratios this

ratio will increase.

2.2 Shear Capacity

The SIN beam web material is cold formed steel therefore the shear design of the beam is

governed by CSA S136.

There are two clauses in CSA S136 for the shear design of beams, clause C3.2 covers the

design of flat web beams, while clause C3.7 applies to stiffened beams. The corrugated shape

of the SIN beam will stiffen the web of the beam however none of the stiffened cases covered

in C3.7 are directly applicable to the SIN beam configuration. Clause C3.7.4 covers non-

conforming stiffeners and indicates that the capacity of such beams shall be determined by

either tests in accordance with Chapter F or rational engineering analysis in accordance with

Section A1.2b.

2.2.1 Shear Capacity – Rational Engineering Analysis

CSA S136 allows for the calculation of shear capacity for a beam with non-conforming

stiffeners, such as the SIN beam, to be carried out by rational engineering analysis in

accordance with S136 Section A1.2b. For the calculation of the SIN beam shear capacity we

will use the formula from the European code (which is more conservative than S136 or S16)

multiplied by a material resistance factor of 0.75 per S136.

First the following is a brief look at the Canadian Codes (S136 and S16) and their approach to

shear design, followed by a comparison to the European Code (EN 1993-1-5:2005 Annex D).

All three codes follow similar design approaches, neither S136 nor S16 account for the stiffening

effect of the corrugated web, while the European Code was developed specifically for a

corrugated web beam. The shear capacity of a steel beam web is governed by either material

yielding or by buckling of the beam web.

2.2.1.1 CSA S136 Approach

CSA S136, clause C3.2 contains formula for the analysis of flat web steel beams. The formula

for the shear capacity is given as:

!" = #$ %& , where F( = 0.60 F, or a reduced value to allow for web buckling

TECHNICAL GUIDE


2.2.1.2 CSA S16 Approach

CSA S16, clause 13.4 contains formula for the analysis of flat web steel beams. The formula for

the shear capacity is given as:

!" = #$ %-, where %- = 0.66 %� or a reduced value to allow for web buckling

2.2.1.3 EN 1993-1-5:2005 Annex D Approach

The European steel design code EN 1993-1-5:2005 includes Annex D entitled “Plate Girders with

Corrugated Webs” which has been developed specifically to design corrugated web steel beams.

Annex D provides formula for the shear design of corrugated web beams which accounts for the

yielding, local buckling, or global buckling of a corrugated web. The basic shear formula of the

European Code and Annex D is:

!" = �� .�/0�√3 ℎ 4

�� is a reduction factor to account for local or global buckling

/0� is the partial factor equal to 1.0 (we are using a material resistance factor below) ��√5 = .577 .� is similar and slightly more conservative than %- = 0.66 %� used in S16 or

F( = 0.60 F, used in S136

ℎ 4 = $ is the area of the web

In the European code material resistance factors are left up to each country and not

included in the code formula.

For the calculations in this document the above formula has been multiplied by a limit states

material resistance factor of #- = 0.75 as per the requirements of CSA S136 Clause A1.2b.

Therefore the factored shear capacity for the SIN beam to comply with CSA S136 is given by:

!" = #- �� √5 ℎ 4

Where:

#- = 0.75 - Material resistance factor based on CSA S136

�� - is the lesser of the local or global buckling coefficient ��,� or ��,�

Local Buckling

��,� = �.�8�.9:;<=,� ≤ 1.0

?̅�,� = A ��B=C,� ∙ √5

E�",� = F5.34 + IJKLM �MN OPQ

��(�RSP) F�M- N�

T5 - Web amplitude

TECHNICAL GUIDE


� - unfolded length of one half wave

U – Young’s modulus

� – Poisson’s Ratio

Global Buckling

��,� = �.8�.8:;<=,VP ≤ 1.0

?̅�,� = A ��B=C,V ∙ √5

E�",� = 5�.W�M LMP AX� XY5Z

X� = Q �J��(�RSP)

-

XY = Q [\

] - length of one half wave

�Y - second moment of area of one corrugation of length w

%� – Web steel yield strength

ℎ 4 - The height and thickness of the corrugated steel web

2.2.2 Shear Capacity – Load Testing

S136, Chapter F provides an outline of the testing regime required to determine member

capacities based on load testing alone. This process would require a minimum of 3 load tests

for every possible web thickness and depth, which would be a long and restrictive process as

SIN beam members can be produced in a range of sizes and web thicknesses.

Steelcon has conducted shear load testing, based on S136 Chapter F, of a selection of SIN

beam members to ensure that the shear formula based on EN-1993-1-5 is conservative. A

report of the shear load testing is included in section 6 of this guide. As the shear load testing

has shown that the EN-1993-1-5 formula are conservative, but not overly conservative, all SIN

Beam shear capacities are determined based the above formula.

2.2.3 Combined Shear and Moment

Both CSA S16 and S136 include clauses to limit combined bending and shear. This is not

required for the SIN beam design as any contribution of the web material to the flexural

capacity is ignored.

2.3 Axial Capacity

The axial capacity of a SIN beam section can be determined by formula contained in S16 clause

13.3, or 13.8 for combined compression and bending. Similar to the flexural resistance the

TECHNICAL GUIDE


axial resistance is provided solely by the steel area of the flanges (neglecting any contribution

of the web). All of the parameters required to calculate the axial capacity of the SIN beam

members are indicated in the table 3.1. Table 3.4 includes the compressive resistance of SIN

beam members for various unsupported lengths calculated based on S16 clause 13.3.

2.4 Web Crippling

Testing has been done in Europe that indicates that the European code formula given in

EN1993-1-8:2005 clause 6.2.6.2 is conservative for the calculation of bearing resistance / web

crippling, %�, �,^_ = `∙aM=∙bb,=,M=∙�M=∙��,M=cde where ��,�, � = 4� + 2√2T + 5(4�� + g). A number of

these variables in these formulas can be eliminated because they are equal to unity or zero and

the formula rearranged using the common S16 variable names to read h" = 4 ij + 54�k%�.

This formula is more conservative than the S16 formula in 14.3.2 for interior loads. Table 3.5

summarizes the web crippling capacity for common SIN beam sizes using this formula and

applying a material resistance factor of #l = 0.80.

When the bearing resistance of the web is exceeded, or for any concentrated loads located at

the end of a SIN beam member bearing stiffeners shall be used.

2.5 Web Openings

Openings can be cut into the web of the SIN beam members during the manufacturing process.

The equipment used to manufacture the SIN beam member is equipped with a plasma cutting

device to cut holes in the web of the members. The following rules are to be followed for web

openings:

• No holes within 200mm of the top or bottom flange of the member. (the equipment

cannot cut close to the flange and the web material is required to stabilize the

compression flange of the beam)

• Holes only where the shear utilization ratio is less than 67%

• Holes should be located as near to mid depth of the beam as possible.

2.5.1 Hole Reinforcing

The following reinforcing is generally recommended for web openings:

Hole diameter Reinforcing Required

<1/10 Web Depth No Reinforcing

1/10 to ¼ web depth Weld pipe into hole

¼ to ½ web depth Full height vertical stiffeners and horizontal stiffeners above and below the opening

TECHNICAL GUIDE


2.6 Sectional Properties Calculation

Part 3 of this document contains member sectional properties for standard size SIN beams. All

of these sections are based on constant depth beams with equal top and bottom flanges. The

following formula were used to calculate the SIN beam properties:

• $noT = 2 ∙ �� ∙ 4� (Area of Flanges for Axial load or bending)

• �ℎoTn $noT = ℎ 4 - (Area to be used for shear distortion calculations)

• pqonTrr Xos4ℎ t = ℎ + 2 ∗ 4�

• �� = 2 v �� ∙ �� ∙ 4�5 + �� ∙ 4� ∙ (�

� ℎ + �� 4�)�w or �� = �

�� ∙ �� ∙ t5 − �� ∙ �� ∙ ℎ 5

• �� = [yzP_

• �� = �� ∙ 2 ∙ 4� ∙ ��5

• �� = [�zPb

• � = �∙b∙�bJ5 (Galambos 1968 based on Flange only)

• � = (_R�b)P∙bJ∙�b�W (Galambos 1968, Picard and Beaulieu 1991 based on Flange only)

• {" = ∅ ∙ ��%� (CSA S16 Cl 13.5)

2.7 Sample Calculation

Attached is a sample calculation for the bending, shear capacity and deflection (including shear

deformations) of a typical SIN beam flexural member using PTC Mathcad. A digital (editable)

copy of this calculation is available on request, and PTC Mathcad Express can be downloaded

for free from www.ptc.com.

Project:Description:

Sample CalculationSIN Beam Capacity

Date: Sept 16, 2016

Sample Calculation for a SIN Beam WTA 750/230x9.5

Beam Properties

≔hw 762 mmmmmmmm ≔bflange 203 mmmmmmmm Web ThicknessWT0 = 1.519 mmWTA = 1.897 mmWTB = 2.657 mmWTC = 3.038 mm

≔tweb 1.897 mmmmmmmm ≔tflange 9.5 mmmmmmmm

≔aweb 40 mmmmmmmm

Material Properties

≔Fy_Flange 350 MPaMPaMPaMPa ≔Fy_Web 350 MPaMPaMPaMPa ≔ϕs 0.9

≔ν 0.3 Poissons Ratio ≔E 200 GPaGPaGPaGPa ≔G 77 GPaGPaGPaGPa ≔ϕs.shear 0.75

Calculated Section Properties

≔A =⋅⋅2 bflange tflange 3857 mmmmmmmm2

≔d =+hw ⋅2 tflange 781 mmmmmmmm

≔Ix =−⋅⋅―1

12bflange d

3 ⋅⋅―1

12bflange hw

3 ⎛⎝ ⋅573.962 106 ⎞⎠ mmmmmmmm4

≔Sx =――Ix

⋅―1

2d

⎛⎝ ⋅1.47 106 ⎞⎠ mmmmmmmm3 ≔Zx =――――――Ix

+⋅―1

2hw ―

1

2tflange

⎛⎝ ⋅1.488 106 ⎞⎠ mmmmmmmm3

≔Iy =−⋅⋅―1

12bflange

3d ⋅⋅―

1

12bflange

3hw

⎛⎝ ⋅13.245 106 ⎞⎠ mmmmmmmm4

≔Sy =―――Iy

⋅―1

2bflange

⎛⎝ ⋅130.495 103 ⎞⎠ mmmmmmmm3

≔J =――――――⋅⋅2 bflange tflange

3

3⎛⎝ ⋅116.031 103 ⎞⎠ mmmmmmmm4

≔Cw =―――――――――⋅⋅⎛⎝ −d tflange⎞⎠

2

bflange3tflange

24⎛⎝ ⋅1.971 1012⎞⎠ mmmmmmmm6



Date: Sept 16, 2016

CSA S16-09 - Moment Calculation

Flange Classification per Clause 11.2

< 145 = Class 1< 170 = Class 2< 200 = Class 3

=⋅―――

―1

2bflange

tflange

‾‾‾‾‾‾‾2

―――Fy_Flange

1 MPaMPaMPaMPa199.883

Moment Capacty per 13.5 - Laterally Supported

≔Mr =⋅⋅ϕs Fy_Flange Sx 462.991 ⋅kNkNkNkN mmmm Elastic Capacity is generally used because it is very close to the plastic capacity≔Mr =⋅⋅ϕs Fy_Flange Zx 468.693 ⋅kNkNkNkN mmmm

Moment Capacity 13.6 - Laterally UnSupported

full unsupported for 6m

≔My ⋅Fy_Flange Sx

≔ω2 1.0 this is to match what is shown in S16 design tables actual value could be calculated based on S16 if requried

=Cw⎛⎝ ⋅1.971 1012⎞⎠ mmmmmmmm6

=J ⎛⎝ ⋅116.031 103 ⎞⎠ mmmmmmmm4

≔L 6000 mmmmmmmm

≔Mu =⋅――⋅ω2 ππππ

L

‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾

+⋅⋅⋅E Iy G J ⋅⋅⎛⎜⎝――⋅ππππ E

L

⎞⎟⎠

2

Iy Cw 291.503 ⋅kNkNkNkN mmmm

=<Mu ⋅0.67 My 1 ≔Mr =⋅ϕs Mu 262.352 ⋅kNkNkNkN mmmm



Date: Sept 16, 2016

Shear Capacity - Per CSA S136 / EN 1993-1-5:2006 Annex D clause 2.2

≔tw tweb ≔a3 aweb ≔fyw Fy_Web ≔w ――155

2mmmmmmmm

≔γm1 1.0 Partial Factor EN1993-1-1:2005 cl 6.1

≔s =―1

2

⌠⎮⎮⎮⌡

d

0

2 w

‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾

+1⎛⎜⎝

⋅――⋅a3 ππππ

2 wsin

⎛⎜⎝―――

⋅⋅2 ππππ x

2 w

⎞⎟⎠

⎞⎟⎠

2

x 88.985 mmmmmmmm =2 s 177.97 mmmmmmmm

≔Iz =―1

2

⌠⎮⎮⌡

d

0

2 w

⎛⎜⎜⎝

+⋅―1

12tw

3 ⋅tw⎛⎜⎝

⋅―a3

2sin

⎛⎜⎝―――

⋅⋅2 ππππ x

2 w

⎞⎟⎠

⎞⎟⎠

2 ⎞⎟⎟⎠x 2.945 cmcmcmcm4

≔τcr.l =⋅⋅⎛⎜⎝

+5.34 ―――⋅aweb s

⋅hw tw

⎞⎟⎠――――

⋅ππππ2 E

⋅12 ⎛⎝ −1 ν2 ⎞⎠

⎛⎜⎝―tw

s

⎞⎟⎠

2

⎛⎝ ⋅640.964 103 ⎞⎠ kPakPakPakPa

≔λc.l =‾‾‾‾‾‾‾―――fyw

⋅τcr.l ‾‾3⋅561.483 10−3

≔χc.l =min⎛⎜⎝,1 ―――

1.15

+0.9 λc.l

⎞⎟⎠

⋅786.872 10−3

≔Dz =――⋅E Iz

w75.994 ⋅kNkNkNkN mmmm

≔Dx =⋅――――⋅E tw

3

⋅12 ⎛⎝ −1 ν2 ⎞⎠

―w

s⎛⎝ ⋅108.891 10−3⎞⎠ ⋅kNkNkNkN mmmm

≔τcr.g =⋅―――32.4

⋅tw hw2

‾‾‾‾‾‾4⋅Dx Dz

3 ⎛⎝ ⋅434.91 103 ⎞⎠ kPakPakPakPa

≔λc.g =‾‾‾‾‾‾‾‾―――fyw

⋅τcr.g ‾‾3⋅681.638 10−3

≔χc.g =min⎛⎜⎝

,――――1.5

+0.5 λc.g2

1⎞⎟⎠

1

≔χc =min ⎛⎝ ,χc.l χc.g⎞⎠ ⋅786.872 10−3

≔V =⋅⋅⋅χc ―――fyw

⋅γm1 ‾‾3hw tw 229.844 kNkNkNkN

≔Vr =⋅ϕs.shear V 172.383 kNkNkNkN



Date: Sept 16, 2016

Deflection Calculation - Including Shear Deformations

≔wload ⋅4.8 kPakPakPakPa 6 mmmm ≔l 12000 mmmmmmmm

≔∆flexure =⋅――5

384―――

⋅wload l4

⋅E Ix67.74 mmmmmmmm

≔G 77 GPaGPaGPaGPa ≔b =bflange 203 mmmmmmmm

≔d1 =hw 762 mmmmmmmm ≔t =⋅tweb ―w

s1.652 mmmmmmmm

≔α ⋅A ―――――――+−⋅b d2 ⋅b d1

2 ⋅t d12

⋅⋅8 Ix t

≔∆shear =――――⋅⋅wload l

2α

⋅⋅8 A G6.133 mmmmmmmm

≔∆total =+∆flexure ∆shear 73.873 mmmmmmmm =――∆shear

∆total⋅83.021 10−3

For A Point Load

≔P 200 kNkNkNkN ≔L 10000 mmmmmmmm

≔∆flexure =―――⋅P L3

⋅⋅48 E Ix36.297 mmmmmmmm

≔∆shear =―――⋅⋅P L α

⋅⋅4 A G5.915 mmmmmmmm

≔∆total =+∆flexure ∆shear 42.213 mmmmmmmm =――∆shear

∆total⋅140.13 10−3

TECHNICAL GUIDE


3 TABLES

3.1 Common SIN Beam Sizes

1 Page – Combined Metric and Imperial

3.2 Bending Capacity – Laterally Supported

8 Pages – Metric

8 Pages - Imperial

3.3 Bending Capacity – Laterally Unsupported

7 Pages – Metric

7 Pages – Imperial

3.4 Shear Capacity

1 Page – Metric

1 Page – Imperial

3.5 Axial Capacity

7 Pages – Metric

7 Pages – Imperial

3.6 Concentrated Load / Web Crippling Capacity

1 Page – Metric

1 Page – Imperial

3.7 M/D and W/D ratios for ULC Calculation

8 pages – Combined Metric and Imperial

Common SIN Beam Sizes

ga mm in mm in t (mm) W (mm) t (in) W (in)

WT0 16 1.519 0.060 333 13.11 6 127 1/4 5

WTA 14 1.897 0.075 500 19.69 6 152 1/4 6

WTB 12 2.657 0.105 610 24.00 10 127 3/8 5

WTC 11 3.038 0.120 750 29.53 10 152 3/8 6

1000 39.37 10 178 3/8 7

1219 48.00 10 203 3/8 8

1500 59.06 10 229 3/8 9

16 152 5/8 6

16 178 5/8 7

Designation is WebThickness WebHeight / FlangeW x FlangeT 16 203 5/8 8

i.e.WTA610/203x10 16 229 5/8 9

‐ 2.0mm thick web 16 254 5/8 10

‐ 610mm tall web 16 279 5/8 11

‐ 203 x 10 mm flanges 16 305 5/8 12

16 330 5/8 13

16 356 5/8 14

25 203 1 8

25 229 1 9

25 254 1 10

25 279 1 11

25 305 1 12

2016‐02‐02

Web Thicknesses Web Height Flange Size

Each SIN beam can be any combination of Web Thickness, WebHeight and

FlangeSize

The length of the sin wave is constantly 155mm

The magnitude of the sin wave is 40mm for the WTA, and WTB but 43mm

for the WTC

25 305 1 12

25 330 1 13

25 356 1 14

25 406 1 16

25 450 1 17.7

32 305 1 1/4 12

32 330 1 1/4 13

32 356 1 1/4 14

32 406 1 1/4 16

32 450 1 1/4 17.7

mm in

WT0 1.847 0.073

WTA 2.307 0.091

WTB 3.231 0.127

WTC 3.694 0.145

Web Thicknesses (for weigth calculation)

For Tekla Modeling with a flat web beam

use an increased web thickness to achive

the proper beam weigth

Table 3.2a (metric)

SIN Beam Bending PropertiesDepth of Overall

Web Width Thickness Area Depth Torsion Warpinghw bf tf d Ix Sx Iy Sy J Cw Mr Lu WT0 WTA WTB WTC

(mm) (mm) (mm) (mm2) (mm) 106 mm4 103 mm3 106 mm4 103 mm3 103 mm4 109 mm6 kN m mm kg / m kg / m kg / m kg / ma b c d e f g h i j k l m n 0 p q r

333 127 x 6 1612.9 346 46.44 268.7 2.17 34.1 21.7 62.4 84.6 1910 17.5 18.7 21.1 22.3127 x 10 2419.4 352 70.98 403.2 3.25 51.2 73.2 95.4 127.0 1950 23.8 25.0 27.4 28.6152 x 2903.2 352 85.18 483.9 5.62 73.7 87.8 164.8 152.4 2340 27.6 28.8 31.2 32.4178 x 3387.1 352 99.37 564.5 8.92 100.4 102.4 261.7 177.8 2740 31.4 32.6 35.0 36.2203 x 3871 352 113.57 645.2 13.32 131.1 117.1 390.7 203.2 3130 35.2 36.4 38.8 40.0152 x 16 4838.7 365 147.34 807.9 9.37 122.9 406.5 285.0 254.5 2480 42.8 44.0 46.4 47.6178 x 5645.2 365 171.89 942.5 14.87 167.3 474.2 452.5 296.9 2890 49.1 50.3 52.8 54.0203 x 6451.6 365 196.45 1077.2 22.20 218.5 542.0 675.5 339.3 3300 55.5 56.7 59.1 60.3229 x 7258.1 365 221.00 1211.8 31.61 276.5 609.7 961.8 381.7 3720 61.8 63.0 65.4 66.6254 x 8064.5 365 245.56 1346.5 43.36 341.4 677.5 1319.3 424.1 4130 68.1 69.3 71.8 73.0279 x 8871 365 270.12 1481.1 57.71 413.1 745.2 1756.0 466.5 4540 74.5 75.7 78.1 79.3305 x 9677.4 365 294.67 1615.7 74.92 491.6 813.0 2279.7 509.0 4960 80.8 82.0 84.4 85.6330 x 10484 365 319.23 1750.4 95.26 577.0 880.7 2898.5 551.4 5370 87.1 88.3 90.7 92.0203 x 25 10323 384 332.04 1730.3 35.52 349.6 2219.9 1140.6 545.0 3720 85.9 87.1 89.5 90.7229 x 11613 384 373.54 1946.6 50.57 442.5 2497.4 1624.0 613.2 4180 96.0 97.2 99.6 100.8254 x 12903 384 415.05 2162.8 69.37 546.2 2774.9 2227.7 681.3 4650 106.1 107.3 109.7 110.9279 x 14194 384 456.55 2379.1 92.33 660.9 3052.4 2965.1 749.4 5110 116.2 117.5 119.9 121.1305 x 15484 384 498.06 2595.4 119.87 786.6 3329.9 3849.5 817.6 5580 126.4 127.6 130.0 131.2330 x 16774 384 539.56 2811.7 152.41 923.1 3607.3 4894.3 885.7 6040 136.5 137.7 140.1 141.3356 x 18064 384 581.07 3028.0 190.36 1070.6 3884.8 6112.8 953.8 6510 146.6 147.8 150.3 151.5406 x 20645 384 664.08 3460.5 284.15 1398.4 4439.8 9124.7 1090.1 7440 166.9 168.1 170.5 171.7450 x 22860 384 735.32 3831.8 385.76 1714.5 4916.1 12387.9 1207.0 8230 184.3 185.5 187.9 189.1305 x 32 19355 397 645.38 3255.4 149.84 983.2 6503.6 4983.9 1025.4 6130 156.8 158.0 160.4 161.6330 x 20968 397 699.16 3526.7 190.51 1153.9 7045.6 6336.6 1110.9 6640 169.4 170.6 173.0 174.3356 x 22581 397 752.94 3797.9 237.95 1338.3 7587.6 7914.2 1196.4 7160 182.1 183.3 185.7 186.9406 x 25806 397 860.51 4340.5 355.18 1748.0 8671.5 11813.7 1367.3 8180 207.4 208.6 211.0 212.2450 x 28575 397 952.82 4806.2 482.20 2143.1 9601.8 16038.4 1513.9 9060 229.1 230.3 232.8 234.0

Depth WT0 WTA WTB WTCaa bb cc dd ee

333 60.5 80.2 121.8 143.5

Mass

Factored Shear Resistance Vr (kN)

MetricFlange

Strong Axis Weak AxisSection Properties Moment

Resistance

SIN Properties - v0.08 | 2016-09-26

Table 3.2a (metric)




MassMetric

FlangeStrong Axis Weak Axis

Section Properties MomentResistance



500 87.2 116.4 178.7 211.0



Table 3.2a (metric)




MassMetric





610 104.4 139.9 215.8 255.0



Table 3.2a (metric)




MassMetric



750 127 x 6 1612.9 763 230.68 604.9 2.17 34.1 21.7 310.0 190.5 1890 26.2 31.7 34.4127 x 10 2419.4 769 348.94 907.4 3.25 51.2 73.2 469.0 285.8 1900 32.6 38.0 40.7152 x 2903.2 769 418.72 1088.9 5.62 73.7 87.8 810.4 343.0 2280 36.4 41.8 44.5178 x 3387.1 769 488.51 1270.4 8.92 100.4 102.4 1286.9 400.2 2660 40.2 45.6 48.3203 x 3871 769 558.30 1451.9 13.32 131.1 117.1 1920.9 457.4 3040 44.0 49.4 52.1152 x 16 4838.7 782 709.65 1815.6 9.37 122.9 406.5 1373.3 571.9 2310 51.6 57.0 59.7178 x 5645.2 782 827.93 2118.1 14.87 167.3 474.2 2180.8 667.2 2690 57.9 63.3 66.1203 x 6451.6 782 946.21 2420.7 22.20 218.5 542.0 3255.3 762.5 3080 64.2 69.7 72.4229 x 7258.1 782 1064.48 2723.3 31.61 276.5 609.7 4635.0 857.8 3460 70.6 76.0 78.7254 x 8064.5 782 1182.76 3025.9 43.36 341.4 677.5 6358.0 953.2 3850 76.9 82.3 85.1279 x 8871 782 1301.03 3328.5 57.71 413.1 745.2 8462.5 1048.5 4230 83.2 88.7 91.4305 x 9677.4 782 1419.31 3631.1 74.92 491.6 813.0 10986.6 1143.8 4620 89.6 95.0 97.7330 x 10484 782 1537.58 3933.7 95.26 577.0 880.7 13968.5 1239.1 5010 95.9 101.3 104.0203 x 25 10323 801 1552.15 3876.5 35.52 349.6 2219.9 5338.8 1221.1 3170 94.6 100.1 102.8229 x 11613 801 1746.17 4361.1 50.57 442.5 2497.4 7601.6 1373.7 3560 104.7 110.2 112.9254 x 12903 801 1940.19 4845.6 69.37 546.2 2774.9 10427.4 1526.4 3960 114.9 120.3 123.0279 x 14194 801 2134.21 5330.2 92.33 660.9 3052.4 13878.8 1679.0 4360 125.0 130.4 133.2305 x 15484 801 2328.23 5814.8 119.87 786.6 3329.9 18018.5 1831.6 4750 135.1 140.6 143.3330 x 16774 801 2522.25 6299.3 152.41 923.1 3607.3 22909.0 1984.3 5150 145.3 150.7 153.4356 x 18064 801 2716.27 6783.9 190.36 1070.6 3884.8 28612.7 2136.9 5550 155.4 160.8 163.6406 x 20645 801 3104.30 7753.0 284.15 1398.4 4439.8 42710.6 2442.2 6340 175.6 181.1 183.8450 x 22860 801 3437.35 8584.8 385.76 1714.5 4916.1 57984.5 2704.2 7020 193.0 198.5 201.2305 x 32 19355 814 2958.72 7274.0 149.84 983.2 6503.6 22893.6 2291.3 4870 165.5 171.0 173.7330 x 20968 814 3205.28 7880.2 190.51 1153.9 7045.6 29107.1 2482.3 5280 178.2 183.6 186.3356 x 22581 814 3451.83 8486.4 237.95 1338.3 7587.6 36354.1 2673.2 5680 190.8 196.3 199.0406 x 25806 814 3944.95 9698.7 355.18 1748.0 8671.5 54266.2 3055.1 6500 216.2 221.6 224.3450 x 28575 814 4368.18 10739.2 482.20 2143.1 9601.8 73672.6 3382.9 7190 237.9 243.3 246.1

Depth WTA WTB WTCaa cc dd ee

750 169.9 263.2 311.3



Table 3.2a (metric)




MassMetric





1000 222.9 347.3 411.2



Table 3.2a (metric)




MassMetric





1219 269.1 420.9 498.7



Table 3.2a (metric)




MassMetric





1500 290.1 433.2 577.8



Table 3.2a (metric)




MassMetric



Notes

- SIN Beam sizes are indicated as WT[WEB THICKNESS] [WEB DEPTH] / [FLANGE WIDTH] x [FLANGE THICKNESS] - [WEIGHT]i.e. For a 914mm x 2.5mm web with 254mm x 16mm Flanges and a Weight of 86.5 kg/m the designation is WTB915 / 254x16 - 86.5

- Flanges and Webs are all fabricated from W350 Material (Fy = 350MPa)- Flanges of over 16mm in thickness will include a premium due to the required splicing of the flat bar

a Depth of the Beam web, i.e. Inside of flangesb Width of top and bottom flanged Thickess of top and bottom flangee Cross sectionional area of flanges only (web is neglected)f Overall depth of sectiong Strong Axis Moment of Inertia computed using flange properties onlyh Strong Axis Section Modulas computed using flange properties onlyi Weak Axis Moment of Inertia computed using flange properties onlyj Weak Axis Section Modulas computed using flange properties onlyk Torsional Constant J computed using flange properties onlyl Warping Constant Cw - computed using flange properties only

m Strong Axis Factored Moment Restance assuming compression flange is fully braced based on CSA S16-09n Maximum unbraced lenght for which Mr is applicableo Mass of member per unit length with a web thickess of 16 ga (1.519mm)p Mass of member per unit length with a web thickess of 14ga (1.897mm)q Mass of member per unit length with a web thickess of 12 ga (2.657mm)r Mass of member per unit length with a web thickess of 11ga (3.038mm)

aa Depth of Beam webbb Shear Capacity for a 16 ga (1.519mm) webaa Shear Capacity for a 14ga (1.897mm) webbb Shear Capacity for a 12 ga (2.657mm) webaa Shear Capacity for a 11ga (3.038mm) web


Table 3.2b (imperial)

SIN Beam Bending PropertiesSIN Size Depth Overall

of Web Width Thickness Area Depth Torsion Warpinghw bf tf d Ix Sx Iy Sy J Cw Mr Lu WT0 WTA WTB WTCin in in in2 in in4 in3 in4 in3 in4 in6 kip ft in lb / ft lb / ft lb / ft lb / ft

- a b c d e f g h i j k l m n o p q r

WT_ 333/127x6 13.1 5.0 x 0.250 2.50 13.61 129 16.4 6.0 2.1 0.052 289 62.4 75 11.7 12.5 14.2 15.0WT_ 333/127x10 5.0 x 0.375 3.75 13.86 197 24.6 9.0 3.1 0.176 441 93.7 77 16.0 16.8 18.4 19.2WT_ 333/152x10 6.0 x 4.50 13.86 236 29.5 15.6 4.5 0.211 762 112.4 92 18.5 19.3 20.9 21.8WT_ 333/178x10 7.0 x 5.25 13.86 276 34.4 24.8 6.1 0.246 1210 131.2 107 21.1 21.9 23.5 24.3WT_ 333/203x10 8.0 x 6.00 13.86 315 39.4 37.0 8.0 0.281 1806 149.9 123 23.6 24.4 26.0 26.9WT_ 333/152x16 6.0 x 0.625 7.50 14.36 409 49.3 26.0 7.5 0.977 1318 187.7 97 28.7 29.5 31.1 31.9WT_ 333/178x16 7.0 x 8.75 14.36 477 57.5 41.3 10.2 1.139 2092 219.0 113 33.0 33.8 35.4 36.2WT_ 333/203x16 8.0 x 10.00 14.36 545 65.7 61.6 13.3 1.302 3123 250.3 130 37.2 38.0 39.6 40.4WT_ 333/229x16 9.0 x 11.25 14.36 613 73.9 87.7 16.9 1.465 4447 281.5 146 41.4 42.2 43.9 44.7WT_ 333/254x16 10.0 x 12.50 14.36 682 82.2 120.3 20.8 1.628 6100 312.8 162 45.7 46.5 48.1 48.9WT_ 333/279x16 11.0 x 13.75 14.36 750 90.4 160.2 25.2 1.790 8119 344.1 179 49.9 50.7 52.4 53.2WT_ 333/305x16 12.0 x 15.00 14.36 818 98.6 207.9 30.0 1.953 10541 375.4 195 54.2 55.0 56.6 57.4WT_ 333/330x16 13.0 x 16.25 14.36 886 106.8 264.4 35.2 2.116 13402 406.7 211 58.4 59.2 60.8 61.7WT_ 333/203x25 8.0 x 1.000 16.00 15.11 922 105.6 98.6 21.3 5.333 5274 402.0 146 57.6 58.4 60.0 60.8WT_ 333/229x25 9.0 x 18.00 15.11 1037 118.8 140.4 27.0 6.000 7509 452.2 164 64.4 65.2 66.8 67.6WT_ 333/254x25 10.0 x 20.00 15.11 1152 132.0 192.5 33.3 6.667 10301 502.5 183 71.2 72.0 73.6 74.4WT_ 333/279x25 11.0 x 22.00 15.11 1267 145.2 256.3 40.3 7.333 13710 552.7 201 78.0 78.8 80.4 81.2WT_ 333/305x25 12.0 x 24.00 15.11 1382 158.4 332.7 48.0 8.000 17799 603.0 219 84.7 85.5 87.2 88.0WT_ 333/330x25 13.0 x 26.00 15.11 1498 171.6 423.0 56.3 8.667 22630 653.2 238 91.5 92.3 94.0 94.8WT_ 333/356x25 14.0 x 28.00 15.11 1613 184.8 528.3 65.3 9.333 28265 703.5 256 98.3 99.1 100.8 101.6WT_ 333/406x25 16.0 x 32.00 15.11 1843 211.2 788.6 85.3 10.667 42191 804.0 292 111.9 112.7 114.3 115.1WT_ 333/450x25 17.7 x 35.43 15.11 2041 233.8 1070.7 104.6 11.811 57280 890.3 324 123.6 124.4 126.0 126.8WT_ 333/305x32 12.0 x 1.250 30.00 15.61 1791 198.7 415.9 60.0 15.625 23045 756.3 241 105.1 105.9 107.5 108.4WT_ 333/330x32 13.0 x 32.50 15.61 1940 215.2 528.8 70.4 16.927 29299 819.4 261 113.6 114.4 116.0 116.8WT_ 333/356x32 14.0 x 35.00 15.61 2090 231.8 660.4 81.7 18.229 36594 882.4 281 122.1 122.9 124.5 125.3WT_ 333/406x32 16.0 x 40.00 15.61 2388 264.9 985.8 106.7 20.833 54625 1008.4 322 139.1 139.9 141.5 142.3WT_ 333/450x32 17.7 x 44.29 15.61 2645 293.3 1338.3 130.8 23.068 74159 1116.6 356 153.7 154.5 156.1 156.9


13.1 13.6 18.0 27.4 32.3

ImperialMass

Factored Shear Resistance Vr (kips)

Strong Axis Weak Axis ResistanceFlange Section Properties Moment






ImperialMass




19.7 19.6 26.2 40.2 47.4







ImperialMass




24.0 23.5 31.5 48.5 57.3







ImperialMass


WT_ 750/127x6 29.5 5.0 x 0.250 2.50 30.03 640 36.9 6.0 2.1 0.052 1434 140.5 74 17.6 21.2 23.1WT_ 750/127x10 5.0 x 0.375 3.75 30.28 968 55.4 9.0 3.1 0.176 2168 210.8 74 21.8 25.5 27.3WT_ 750/152x10 6.0 x 4.50 30.28 1162 66.5 15.6 4.5 0.211 3747 253.0 89 24.4 28.0 29.9WT_ 750/178x10 7.0 x 5.25 30.28 1356 77.5 24.8 6.1 0.246 5950 295.2 104 26.9 30.6 32.4WT_ 750/203x10 8.0 x 6.00 30.28 1550 88.6 37.0 8.0 0.281 8882 337.3 119 29.5 33.1 35.0WT_ 750/152x16 6.0 x 0.625 7.50 30.78 1970 110.8 26.0 7.5 0.977 6350 421.8 91 34.6 38.2 40.1WT_ 750/178x16 7.0 x 8.75 30.78 2298 129.3 41.3 10.2 1.139 10084 492.1 106 38.8 42.5 44.3WT_ 750/203x16 8.0 x 10.00 30.78 2626 147.7 61.6 13.3 1.302 15052 562.4 121 43.1 46.7 48.5WT_ 750/229x16 9.0 x 11.25 30.78 2954 166.2 87.7 16.9 1.465 21431 632.7 136 47.3 51.0 52.8WT_ 750/254x16 10.0 x 12.50 30.78 3283 184.7 120.3 20.8 1.628 29398 703.0 151 51.6 55.2 57.0WT_ 750/279x16 11.0 x 13.75 30.78 3611 203.1 160.2 25.2 1.790 39129 773.3 166 55.8 59.5 61.3WT_ 750/305x16 12.0 x 15.00 30.78 3939 221.6 207.9 30.0 1.953 50800 843.6 182 60.0 63.7 65.5WT_ 750/330x16 13.0 x 16.25 30.78 4268 240.0 264.4 35.2 2.116 64588 913.9 197 64.3 67.9 69.8WT_ 750/203x25 8.0 x 1.000 16.00 31.53 4308 236.6 98.6 21.3 5.333 24686 900.6 124 63.4 67.1 68.9WT_ 750/229x25 9.0 x 18.00 31.53 4846 266.1 140.4 27.0 6.000 35148 1013.2 140 70.2 73.9 75.7WT_ 750/254x25 10.0 x 20.00 31.53 5385 295.7 192.5 33.3 6.667 48215 1125.8 156 77.0 80.7 82.5WT_ 750/279x25 11.0 x 22.00 31.53 5923 325.3 256.3 40.3 7.333 64174 1238.4 171 83.8 87.5 89.3WT_ 750/305x25 12.0 x 24.00 31.53 6462 354.8 332.7 48.0 8.000 83315 1351.0 187 90.6 94.3 96.1WT_ 750/330x25 13.0 x 26.00 31.53 7000 384.4 423.0 56.3 8.667 105928 1463.5 202 97.4 101.1 102.9WT_ 750/356x25 14.0 x 28.00 31.53 7539 414.0 528.3 65.3 9.333 132301 1576.1 218 104.2 107.8 109.7WT_ 750/406x25 16.0 x 32.00 31.53 8616 473.1 788.6 85.3 10.667 197487 1801.3 249 117.8 121.4 123.3WT_ 750/450x25 17.7 x 35.43 31.53 9540 523.9 1070.7 104.6 11.811 268111 1994.5 276 129.4 133.1 134.9WT_ 750/305x32 12.0 x 1.250 30.00 32.03 8212 443.9 415.9 60.0 15.625 105856 1690.0 191 111.0 114.6 116.5WT_ 750/330x32 13.0 x 32.50 32.03 8896 480.9 528.8 70.4 16.927 134587 1830.8 207 119.5 123.1 125.0WT_ 750/356x32 14.0 x 35.00 32.03 9580 517.9 660.4 81.7 18.229 168096 1971.7 223 128.0 131.6 133.4WT_ 750/406x32 16.0 x 40.00 32.03 10949 591.9 985.8 106.7 20.833 250919 2253.3 255 145.0 148.6 150.4WT_ 750/450x32 17.7 x 44.29 32.03 12124 655.3 1338.3 130.8 23.068 340651 2495.1 283 159.5 163.2 165.0


29.5 38.2 59.2 70.0







ImperialMass




39.4 50.1 78.1 92.4







ImperialMass




48.0 60.5 94.6 112.1







ImperialMass




59.1 65.2 97.4 129.9







ImperialMass


Notes

- SIN Beam sizes are indicated as WT[WEB THICKNESS] [WEB DEPTH] / [FLANGE WIDTH] x [FLANGE THICKNESS] - [WEIGHT]SIN Beam sizes are always indicated in Metric unitsi.e. For a 36in x 12ga web with 10in x 5/8in Flanges and a Weight of 58 lb/ft the designation is WTB915 / 254x16 - 86.5

- Flanges and Webs are all fabricated from W350 Material (Fy = 350MPa)- Flanges of over 5/8in (16mm) in thickness will include a premium due to the required splicing of the flat bar

a Depth of the Beam web, i.e. Inside of flangesb Width of top and bottom flanged Thickess of top and bottom flangee Cross sectionional area of flanges only (web is neglected)f Overall depth of sectiong Strong Axis Moment of Inertia computed using flange properties onlyh Strong Axis Section Modulas computed using flange properties onlyi Weak Axis Moment of Inertia computed using flange properties onlyj Weak Axis Section Modulas computed using flange properties onlyk Torsional Constant J computed using flange properties onlyl Warping Constant Cw - computed using flange properties only

m Strong Axis Factored Moment Restance assuming compression flange is fully braced based on CSA S16-09n Maximum unbraced lenght for which Mr is applicableo Mass of member per unit length with a web thickess of 16 ga (1.519mm)p Mass of member per unit length with a web thickess of 14ga (1.897mm)q Mass of member per unit length with a web thickess of 12 ga (2.657mm)r Mass of member per unit length with a web thickess of 11ga (3.038mm)

aa Depth of Beam webbb Shear Capacity for a 16 ga (1.519mm) webaa Shear Capacity for a 14ga (1.897mm) webbb Shear Capacity for a 12 ga (2.657mm) webaa Shear Capacity for a 11ga (3.038mm) web


Table 3.3a(metric)

SIN Beam Bending Capacity - Laterally UnsupportedDepth of

Web Width Thicknesshw bf tf

(mm) (mm) (mm) 1500 2000 2500 3000 3500 4000 5000 6000 7000 8000 9000 10000 11000 12000 14000a b c d e f g h i j k l m n o p q r s

333 127 x 6 - 83.6 76.1 67.3 57.3 45.1 30.2 22.1 17.2 14.0 11.7 10.0 8.8 7.8 6.4127 x 10 - 126.2 116.0 104.1 91.0 75.2 52.3 39.6 31.7 26.4 22.6 19.8 17.6 15.8 13.2152 x - - 149.6 139.1 127.4 114.6 84.3 62.8 49.6 40.8 34.6 30.0 26.5 23.7 19.6178 x - - - 172.9 162.3 150.7 124.7 93.9 73.3 59.6 50.1 43.2 37.9 33.7 27.7203 x - - - - 196.1 185.5 161.5 134.2 103.7 83.7 69.8 59.7 52.0 46.1 37.5152 x 16 - - 254.0 239.9 224.8 209.0 176.5 139.7 114.3 96.8 84.1 74.4 66.7 60.5 51.1178 x - - - 294.0 279.8 264.8 233.1 200.4 163.0 136.9 118.1 104.0 92.9 84.0 70.6203 x - - - - 334.1 319.8 289.3 257.2 223.5 186.3 159.7 139.8 124.4 112.1 93.7229 x - - - - - 374.1 344.8 313.6 281.2 246.0 209.6 182.5 161.7 145.3 120.8254 x - - - - - - 399.8 369.5 337.7 305.1 268.6 232.8 205.5 183.9 152.1279 x - - - - - - 454.1 424.8 393.8 361.7 329.0 291.4 256.1 228.5 188.0305 x - - - - - - 507.9 479.7 449.6 418.1 385.8 353.0 314.3 279.4 228.7330 x - - - - - - - 534.1 504.8 474.0 442.2 409.7 376.9 337.3 274.6203 x 25 - - - - - 535.8 502.6 469.2 436.0 403.1 370.5 331.4 298.3 271.3 229.9229 x - - - - - - 586.2 552.8 519.5 486.4 453.5 420.9 382.4 347.1 293.4254 x - - - - - - 669.8 636.6 603.1 569.8 536.7 503.9 471.3 433.7 365.5279 x - - - - - - - 720.2 686.8 653.4 620.2 587.1 554.3 521.7 446.7305 x - - - - - - - 803.8 770.5 737.1 703.8 670.5 637.5 604.7 537.3330 x - - - - - - - - 854.2 820.8 787.4 754.1 720.9 687.9 622.4356 x - - - - - - - - 937.7 904.5 871.1 837.7 804.4 771.3 705.5406 x - - - - - - - - - 1071.7 1038.5 1005.1 971.7 938.3 872.0450 x - - - - - - - - - - 1182.0 1148.8 1115.4 1082.0 1015.3305 x 32 - - - - - - - - 996.4 962.9 929.7 896.7 863.9 831.3 766.7330 x - - - - - - - - 1099.1 1065.5 1032.1 998.9 965.9 933.1 868.2356 x - - - - - - - - - 1168.1 1134.6 1101.2 1068.1 1035.1 969.8406 x - - - - - - - - - - 1339.8 1306.2 1272.8 1239.6 1173.6450 x - - - - - - - - - - - 1482.4 1448.8 1415.4 1349.0


333 60.5 80.2 121.8 143.5

Flange Factored Moment Resistance Mr' (kN m)

Unbraced Length (mm)


Metric


Table 3.3a(metric)






Metric

500 127 x 6 - 125.0 113.4 99.4 82.5 63.8 41.9 29.9 22.7 18.0 14.7 12.4 10.6 9.3 7.4127 x 10 - 188.2 171.5 151.7 129.0 101.4 68.1 49.8 38.7 31.4 26.3 22.6 19.7 17.5 14.3152 x - - 222.8 205.8 186.2 164.2 113.0 81.7 62.7 50.3 41.7 35.4 30.7 27.1 21.9178 x - - - 257.3 240.1 220.7 174.9 125.3 95.3 75.8 62.2 52.5 45.2 39.6 31.6203 x - - - - 291.7 274.4 234.0 182.7 138.0 109.0 88.9 74.5 63.8 55.5 43.9152 x 16 - - 375.4 350.1 321.9 291.4 219.6 165.0 131.3 108.7 92.7 80.8 71.6 64.4 53.6178 x - - - 433.9 408.4 380.5 318.7 244.8 192.5 157.8 133.4 115.4 101.7 90.9 75.1203 x - - - - 492.5 466.8 409.3 345.4 270.8 220.0 184.5 158.6 139.0 123.6 101.2229 x - - - - - 550.9 497.4 437.2 368.5 297.1 247.5 211.4 184.2 163.1 132.5254 x - - - - - 633.3 583.5 526.7 464.5 391.0 323.7 275.0 238.4 210.1 169.5279 x - - - - - - 667.8 614.3 555.1 491.5 414.7 350.5 302.5 265.5 212.6305 x - - - - - - 750.7 700.2 643.9 582.9 518.2 439.1 377.5 330.0 262.6330 x - - - - - - - 784.6 731.1 672.7 610.3 542.0 464.2 404.5 319.8203 x 25 - - - - 805.6 772.6 702.4 629.2 554.8 467.7 402.1 352.9 314.6 284.0 238.1229 x - - - - - 902.2 834.7 763.1 689.4 614.8 526.2 459.6 408.1 367.2 306.3254 x - - - - - - 965.7 896.0 823.4 749.4 672.6 584.6 517.2 463.8 385.0279 x - - - - - - 1095.5 1027.9 956.8 883.7 809.5 729.8 643.1 574.9 474.7305 x - - - - - - - 1158.9 1089.4 1017.4 943.9 869.5 787.3 701.6 576.4330 x - - - - - - - 1288.8 1221.1 1150.5 1077.8 1004.0 929.5 845.0 690.7356 x - - - - - - - 1417.7 1352.0 1282.8 1211.2 1138.1 1064.1 989.5 818.5406 x - - - - - - - - 1611.1 1545.1 1476.1 1404.9 1332.2 1258.5 1109.5450 x - - - - - - - - - 1767.9 1701.3 1632.0 1560.9 1488.3 1340.6305 x 32 - - - - - - - 1479.7 1406.5 1332.1 1257.1 1182.1 1107.2 1032.7 861.7330 x - - - - - - - 1638.7 1566.7 1492.8 1418.1 1343.1 1268.1 1193.3 1026.6356 x - - - - - - - - 1726.3 1653.3 1579.0 1504.1 1429.1 1354.1 1204.8406 x - - - - - - - - - 1972.9 1900.0 1825.9 1751.2 1676.1 1526.2450 x - - - - - - - - - 2245.7 2174.3 2101.3 2027.2 1952.5 1802.5


500 87.2 116.4 178.7 211.0



Table 3.3a(metric)






Metric

610 127 x 6 - 152.3 137.9 120.6 99.2 76.5 49.8 35.3 26.5 20.8 16.9 14.1 12.0 10.4 8.1127 x 10 - 229.0 208.1 183.1 154.0 119.7 79.3 57.3 43.9 35.2 29.1 24.8 21.5 18.9 15.3152 x - - 271.0 249.7 225.1 197.2 133.1 95.2 72.2 57.3 47.0 39.5 34.0 29.7 23.6178 x - - - 312.9 291.4 266.9 207.4 147.3 111.0 87.4 71.1 59.4 50.7 44.1 34.7203 x - - - - 354.7 333.0 282.0 216.2 162.1 126.9 102.7 85.4 72.5 62.6 48.7152 x 16 - - 455.3 422.7 385.8 345.3 249.1 184.1 144.4 118.0 99.6 86.0 75.6 67.5 55.6178 x - - - 526.1 493.2 456.6 374.1 277.1 214.8 173.9 145.3 124.5 108.8 96.5 78.8203 x - - - - 596.8 563.6 488.0 398.1 305.9 245.5 203.6 173.3 150.4 132.7 107.3229 x - - - - - 667.4 597.9 517.9 420.5 335.2 276.2 233.6 201.7 177.1 141.9254 x - - - - - 768.7 704.5 630.0 546.9 445.2 364.8 306.9 263.7 230.4 183.2279 x - - - - - - 808.6 739.0 660.8 575.3 471.2 394.6 337.6 293.8 231.9305 x - - - - - - 910.6 845.4 771.7 690.6 597.2 498.3 424.6 368.3 288.7330 x - - - - - - - 949.7 880.1 803.1 719.6 619.2 526.0 454.7 354.4203 x 25 - - - - 971.6 926.8 829.3 724.9 604.4 499.7 425.5 370.4 328.1 294.6 244.9229 x - - - - - 1087.6 995.1 894.4 788.7 664.5 562.1 486.7 429.0 383.7 317.0254 x - - - - - - 1158.5 1061.8 959.0 852.4 725.2 624.6 548.1 488.3 401.0279 x - - - - - - 1319.6 1227.0 1127.5 1023.3 916.0 786.3 687.0 609.7 497.6305 x - - - - - - 1478.7 1390.2 1294.1 1192.6 1087.3 974.0 847.6 749.5 608.1330 x - - - - - - - 1551.5 1458.9 1360.2 1257.2 1151.2 1031.6 909.1 733.3356 x - - - - - - - 1711.0 1621.9 1526.2 1425.7 1321.6 1214.9 1090.0 874.4406 x - - - - - - - - 1943.2 1853.6 1758.3 1658.6 1555.4 1449.7 1208.8450 x - - - - - - - - - 2130.0 2039.2 1943.5 1843.9 1741.1 1528.8305 x 32 - - - - - - - 1770.0 1666.1 1558.5 1448.8 1338.1 1220.4 1088.4 895.4330 x - - - - - - - 1967.6 1866.2 1760.4 1652.0 1541.9 1431.1 1309.8 1072.3356 x - - - - - - - 2163.7 2065.0 1961.4 1854.4 1745.3 1635.0 1524.0 1269.8406 x - - - - - - - - 2459.1 2360.0 2256.6 2150.2 2041.6 1931.8 1710.0450 x - - - - - - - - - 2698.8 2598.8 2495.1 2388.7 2280.3 2060.2


610 104.4 139.9 215.8 255.0



Table 3.3a(metric)






Metric

750 127 x 6 - 187.2 169.4 147.8 120.9 93.0 60.2 42.4 31.6 24.7 19.9 16.4 13.9 11.9 9.2127 x 10 - 281.3 255.2 223.6 185.6 143.6 94.2 67.3 51.0 40.4 33.1 27.8 23.9 20.9 16.6152 x - - 332.8 306.2 275.1 239.7 159.4 113.0 85.0 66.8 54.2 45.2 38.5 33.4 26.2178 x - - - 384.2 357.2 326.4 250.0 176.3 131.9 103.0 83.1 68.9 58.4 50.3 39.0203 x - - - - 435.4 408.2 343.9 260.1 193.8 150.7 121.2 100.0 84.3 72.3 55.5152 x 16 - - 557.9 516.1 468.1 414.7 289.3 210.6 162.7 131.3 109.4 93.5 81.5 72.2 58.7178 x - - - 644.4 602.1 554.6 445.5 321.1 245.7 196.4 162.2 137.5 119.0 104.7 84.2203 x - - - - 730.7 688.1 589.4 466.0 353.9 280.8 230.3 194.0 166.8 145.9 116.2229 x - - - - 855.6 817.0 727.2 622.0 490.9 387.2 315.9 264.5 226.2 196.9 155.4254 x - - - - - 942.5 860.1 763.1 653.2 518.6 421.0 350.9 298.8 259.0 202.7279 x - - - - - - 989.4 899.5 797.0 677.5 548.0 455.1 386.0 333.3 259.1305 x - - - - - - 1115.8 1032.2 936.3 829.4 698.9 578.6 489.3 421.1 325.4330 x - - - - - - - 1161.7 1071.8 971.1 860.7 723.3 610.1 523.7 402.5203 x 25 - - - - 1184.7 1124.5 990.4 842.9 668.9 545.7 459.4 396.1 348.0 310.3 255.2229 x - - - - - 1325.5 1200.2 1060.3 907.0 734.3 613.9 526.1 459.8 408.0 333.0254 x - - - - - 1522.7 1405.6 1273.1 1129.0 963.2 800.3 682.1 593.1 524.1 424.7279 x - - - - - - 1607.1 1481.7 1344.0 1196.9 1022.2 866.8 750.3 660.3 531.3305 x - - - - - - 1805.3 1686.7 1555.3 1413.7 1264.3 1083.1 933.7 818.5 654.4330 x - - - - - - - 1888.5 1763.1 1627.0 1482.5 1331.3 1145.4 1000.7 795.1356 x - - - - - - - 2087.5 1967.8 1837.2 1697.5 1550.7 1388.0 1208.8 955.0406 x - - - - - - - - 2369.3 2248.9 2118.9 1980.8 1836.0 1685.7 1337.7450 x - - - - - - - - - 2594.6 2472.3 2341.6 2203.6 2059.5 1740.4305 x 32 - - - - - - 2275.6 2140.5 1994.1 1839.7 1679.7 1510.8 1315.7 1164.2 945.5330 x - - - - - - - 2388.2 2247.0 2096.8 1940.2 1779.0 1600.3 1411.2 1139.6356 x - - - - - - - 2633.3 2497.3 2351.5 2198.5 2040.2 1878.2 1691.2 1358.2406 x - - - - - - - - 2990.8 2854.0 2708.8 2557.0 2400.1 2239.6 1875.7450 x - - - - - - - - - 3278.5 3140.1 2994.3 2842.5 2686.2 2363.7


750 169.9 263.2 311.3



Table 3.3a(metric)






Metric

1000 127 x 6 - 249.4 225.4 196.3 159.7 122.6 79.0 55.3 41.0 31.7 25.4 20.8 17.4 14.9 11.3127 x 10 - 374.5 339.1 296.1 243.0 187.2 121.6 85.9 64.3 50.3 40.7 33.8 28.7 24.8 19.3152 x - - 443.0 406.9 364.5 316.1 207.5 145.9 108.7 84.5 68.0 56.1 47.3 40.6 31.2178 x - - - 511.3 474.7 432.8 327.0 229.2 170.2 131.9 105.6 86.8 72.8 62.2 47.3203 x - - - - 579.4 542.5 454.7 339.7 251.7 194.5 155.3 127.2 106.4 90.6 68.5152 x 16 - - 741.0 683.0 615.7 539.6 364.7 261.0 198.3 157.3 129.1 108.8 93.5 81.8 65.2178 x - - - 855.6 796.9 730.2 568.2 403.8 304.5 239.9 195.4 163.4 139.6 121.3 95.5203 x - - - - 969.9 910.7 771.7 592.3 444.2 348.0 281.9 234.4 199.1 172.2 134.2229 x - - - - 1137.3 1084.2 958.7 809.5 622.3 485.5 391.5 324.2 274.2 236.0 182.4254 x - - - - - 1252.5 1138.4 1002.0 843.4 655.9 527.2 435.0 366.7 314.5 241.4279 x - - - - - - 1312.4 1187.0 1041.9 863.0 691.9 569.3 478.5 409.3 312.4305 x - - - - - - 1482.1 1366.1 1231.4 1079.3 888.4 729.4 611.7 522.0 396.5330 x - - - - - - 1648.3 1540.5 1415.0 1272.8 1114.9 917.7 768.1 654.2 495.0203 x 25 - - - - 1565.3 1477.8 1277.6 1037.9 796.2 638.1 528.5 449.1 389.5 343.3 277.1229 x - - - - 1830.2 1750.5 1566.7 1355.0 1095.9 872.3 717.9 606.4 522.9 458.6 366.8254 x - - - - - 2016.7 1847.2 1650.1 1429.8 1159.7 949.3 797.6 684.5 597.6 474.2279 x - - - - - - 2120.7 1936.8 1729.7 1502.9 1227.3 1026.8 877.4 762.9 601.0305 x - - - - - - 2388.6 2216.6 2021.6 1806.7 1556.8 1297.5 1104.7 957.2 749.0330 x - - - - - - - 2490.7 2306.7 2102.9 1881.7 1613.7 1369.5 1183.0 920.3356 x - - - - - - - 2759.8 2586.1 2392.6 2181.6 1955.4 1675.0 1442.9 1116.7406 x - - - - - - - - 3130.6 2955.5 2763.2 2555.3 2333.6 2075.8 1592.5450 x - - - - - - - - 3586.1 3424.6 3246.4 3052.7 2845.0 2624.8 2098.8305 x 32 - - - - - - 3002.8 2800.7 2575.5 2331.5 2072.7 1756.6 1509.8 1320.1 1050.3330 x - - - - - - - 3138.6 2924.3 2690.6 2441.1 2168.2 1856.8 1617.9 1279.3356 x - - - - - - - 3471.5 3267.5 3043.7 2803.4 2549.4 2255.0 1958.8 1540.1406 x - - - - - - - - 3939.6 3734.3 3511.6 3274.1 3024.1 2763.6 2166.3450 x - - - - - - - - 4504.1 4313.0 4104.4 3880.4 3643.1 3394.4 2827.0


1000 222.9 347.3 411.2



Table 3.3a(metric)






Metric

1219 127 x 6 - 303.9 274.6 238.9 193.9 148.7 95.6 66.8 49.4 38.1 30.3 24.8 20.7 17.6 13.2127 x 10 - 456.3 412.8 359.9 293.8 225.9 146.0 102.6 76.4 59.4 47.8 39.4 33.2 28.5 21.8152 x - - 539.7 495.3 443.2 383.3 250.2 175.2 130.0 100.7 80.5 66.1 55.4 47.3 35.9178 x - - - 622.8 577.9 526.3 395.3 276.2 204.4 157.8 125.9 103.0 86.1 73.2 55.2203 x - - - - 705.8 660.4 552.3 410.4 303.2 233.7 186.0 151.8 126.6 107.4 80.5152 x 16 - - 901.9 829.9 745.8 650.3 433.2 307.4 231.4 181.9 147.9 123.5 105.3 91.4 71.7178 x - - - 1041.1 968.2 885.0 678.7 479.1 358.6 280.3 226.5 187.9 159.2 137.4 106.6203 x - - - - 1180.0 1106.5 932.6 706.3 526.6 409.8 329.7 272.3 229.7 197.2 151.6229 x - - - - 1384.7 1318.9 1162.7 975.4 741.1 575.0 461.0 379.4 319.0 272.9 208.3254 x - - - - - 1524.7 1383.1 1212.7 1008.0 780.3 624.1 512.3 429.4 366.4 278.1279 x - - - - - - 1596.2 1440.1 1258.3 1030.2 822.4 673.6 563.5 479.7 362.4305 x - - - - - - 1803.8 1659.7 1491.7 1300.5 1059.4 866.4 723.5 614.7 462.7330 x - - - - - - 2006.9 1873.3 1717.2 1539.2 1338.7 1093.3 911.7 773.6 580.5203 x 25 - - - - 1900.1 1788.9 1531.2 1208.0 916.7 726.7 595.7 501.3 430.7 376.5 299.4229 x - - - - 2224.9 2124.4 1889.9 1615.3 1272.5 1003.0 817.6 684.2 584.8 508.6 400.9254 x - - - - - 2450.8 2236.1 1982.8 1695.5 1344.0 1090.4 908.4 773.0 669.5 523.5279 x - - - - - - 2572.6 2338.0 2070.3 1756.7 1420.0 1178.5 999.2 862.2 669.5305 x - - - - - - 2901.4 2683.3 2433.1 2153.8 1812.1 1499.2 1267.2 1090.1 841.4330 x - - - - - - - 3020.5 2785.9 2523.0 2234.3 1875.1 1580.7 1356.2 1041.3356 x - - - - - - - 3351.1 3130.5 2882.4 2609.1 2310.7 1943.5 1663.7 1271.7406 x - - - - - - - - 3800.1 3577.7 3331.3 3062.5 2773.0 2416.1 1833.3450 x - - - - - - - - 4358.7 4154.8 3928.1 3679.8 3411.3 3124.1 2434.3305 x 32 - - - - - - 3642.3 3381.7 3086.8 2762.2 2388.9 1993.0 1698.5 1473.1 1154.9330 x - - - - - - - 3798.7 3520.3 3212.3 2878.6 2476.7 2103.9 1819.0 1417.6356 x - - - - - - - 4208.5 3945.3 3652.6 3334.0 2992.8 2571.3 2216.9 1718.7406 x - - - - - - - - 4774.1 4508.9 4217.9 3903.9 3569.4 3185.1 2447.3450 x - - - - - - - - 5467.7 5222.9 4953.0 4660.0 4346.3 4014.0 3222.0


1219 269.1 420.9 498.7



Table 3.3a(metric)






Metric

1500 127 x 6 - 373.8 337.7 293.6 237.8 182.3 117.0 81.6 60.2 46.3 36.8 30.0 25.0 21.1 15.8127 x 10 - 561.1 507.3 441.7 359.3 275.9 177.7 124.4 92.3 71.4 57.1 46.8 39.3 33.5 25.4152 x - - 663.6 608.7 544.1 469.8 305.4 213.3 157.7 121.7 97.0 79.3 66.2 56.2 42.3178 x - - - 765.7 710.2 646.2 483.3 337.0 248.8 191.6 152.3 124.3 103.5 87.7 65.6203 x - - - - 867.7 811.6 677.5 501.4 369.8 284.4 225.8 183.9 152.9 129.3 96.3152 x 16 - - 1108.1 1018.3 913.1 792.9 522.7 368.4 275.3 214.8 173.3 143.5 121.4 104.5 80.8178 x - - - 1278.9 1188.0 1083.9 822.4 577.5 429.8 333.9 268.0 220.9 185.9 159.3 121.9203 x - - - - 1449.5 1357.7 1139.8 854.7 634.3 491.2 393.0 322.7 270.7 231.0 175.5229 x - - - - 1701.8 1619.9 1424.8 1189.4 896.0 692.3 552.6 452.6 378.6 322.2 243.4254 x - - - - - 1873.6 1697.2 1483.8 1222.0 942.7 751.1 614.0 512.5 435.3 327.4279 x - - - - - - 1960.2 1765.2 1536.9 1247.7 992.8 810.4 675.4 572.7 429.2305 x - - - - - - 2216.2 2036.6 1826.2 1585.8 1282.1 1045.3 870.1 736.8 550.6330 x - - - - - - 2657.7 2574.5 2477.0 2365.4 2240.1 2101.6 1950.2 1786.5 1387.0203 x 25 - - - - 2686.6 2651.3 2568.8 2471.5 2361.2 2239.8 2108.8 1969.9 1824.3 1673.5 1325.5229 x - - - - 3050.0 3018.3 2943.6 2855.1 2754.0 2641.8 2519.8 2389.3 2251.5 2107.7 1795.8254 x - - - - - 3407.1 3352.7 3287.9 3213.4 3130.2 3039.2 2941.2 2837.1 2727.7 2495.9279 x - - - - - - 3740.2 3690.4 3633.0 3568.5 3497.6 3420.9 3339.0 3252.5 3067.7305 x - - - - - - 4115.6 4076.2 4030.4 3978.9 3922.0 3860.1 3793.8 3723.4 3572.1330 x - - - - - - 4483.9 4451.8 4414.4 4372.2 4325.5 4274.4 4219.5 4161.1 4034.7356 x - - - - - - - 4820.9 4789.8 4754.5 4715.4 4672.6 4626.3 4576.9 4469.7406 x - - - - - - - - 5505.4 5474.0 5439.1 5400.6 5358.9 5314.1 5216.1450 x - - - - - - - - 6117.2 6088.6 6056.6 6021.3 5982.9 5941.6 5850.7305 x 32 - - - - - - 5172.8 5135.6 5093.0 5045.5 4993.6 4937.9 4878.8 4816.9 4686.1330 x - - - - - - - 5582.9 5543.0 5498.2 5449.1 5396.2 5339.7 5280.3 5154.0356 x - - - - - - - 6029.1 5991.5 5949.3 5902.8 5852.4 5798.5 5741.5 5619.7406 x - - - - - - - - 6885.4 6847.5 6805.5 6759.8 6710.5 6658.1 6545.0450 x - - - - - - - - 7649.8 7615.0 7576.4 7534.1 7488.4 7439.6 7333.4


1500 290.1 433.2 577.8



Table 3.3b(imperial)

SIN Beam Bending Capacity - Laterally UnsupportedDepth of Depth

Web of Web Width Thicknesshw bf tfin in in 5 6 8 10 12 14 16 20 25 30 35 40 45 50

- a b c d e f g h i j k l m n o p q rWT_ 333/127x6 13.1 5.0 x 0.250 - - 56.9 49.0 39.2 29.6 23.3 15.9 11.1 8.4 6.8 5.6 4.8 4.2

WT_ 333/127x10 5.0 x 0.375 - - 86.5 75.9 64.0 49.8 40.1 28.5 20.8 16.3 13.5 11.5 10.0 8.9WT_ 333/152x10 6.0 x - - 111.2 101.8 91.1 79.2 64.8 45.2 32.3 25.0 20.3 17.2 14.9 13.1WT_ 333/178x10 7.0 x - - - 126.8 117.1 106.3 94.5 67.5 47.4 36.1 29.1 24.4 20.9 18.4WT_ 333/203x10 8.0 x - - - - 142.3 132.4 121.5 96.3 66.7 50.3 40.1 33.3 28.4 24.8WT_ 333/152x16 6.0 x 0.625 - - - 175.9 162.2 147.8 133.2 100.9 75.8 60.9 50.9 43.8 38.5 34.4WT_ 333/178x16 7.0 x - - - 215.9 203.0 189.2 174.9 145.2 107.5 85.4 71.0 60.8 53.3 47.4WT_ 333/203x16 8.0 x - - - - 243.2 230.0 216.2 187.4 146.7 115.4 95.2 81.2 70.8 62.8WT_ 333/229x16 9.0 x - - - - - 270.4 257.1 229.0 192.3 151.3 124.0 105.1 91.3 80.8WT_ 333/254x16 10.0 x - - - - - 310.2 297.5 270.3 234.2 193.8 157.7 133.0 115.0 101.4WT_ 333/279x16 11.0 x - - - - - - 337.5 311.2 275.9 239.2 196.8 165.1 142.2 125.0WT_ 333/305x16 12.0 x - - - - - - - 351.7 317.3 281.1 241.8 201.8 173.1 151.7WT_ 333/330x16 13.0 x - - - - - - - 391.9 358.4 322.7 286.0 243.4 208.0 181.6WT_ 333/203x25 8.0 x 1.000 - - - - - 388.7 373.7 343.7 306.5 269.8 227.5 196.7 173.3 155.0WT_ 333/229x25 9.0 x - - - - - 450.3 435.4 405.4 368.0 331.0 291.9 251.6 221.2 197.6WT_ 333/254x25 10.0 x - - - - - - 497.0 467.1 429.6 392.4 355.6 314.2 275.7 245.8WT_ 333/279x25 11.0 x - - - - - - - 528.8 491.3 453.9 416.8 380.2 337.1 300.0WT_ 333/305x25 12.0 x - - - - - - - 590.5 553.0 515.5 478.3 441.4 404.8 360.3WT_ 333/330x25 13.0 x - - - - - - - 652.0 614.8 577.2 539.8 502.7 465.9 426.9WT_ 333/356x25 14.0 x - - - - - - - - 676.5 639.0 601.5 564.2 527.2 490.5WT_ 333/406x25 16.0 x - - - - - - - - 799.7 762.4 724.9 687.4 650.1 613.0WT_ 333/450x25 17.7 x - - - - - - - - - 868.3 830.8 793.3 755.8 718.5WT_ 333/305x32 12.0 x 1.250 - - - - - - - - 719.6 682.2 645.2 608.5 572.2 536.1WT_ 333/330x32 13.0 x - - - - - - - - 795.3 757.7 720.5 683.6 647.1 610.9WT_ 333/356x32 14.0 x - - - - - - - - 871.0 833.3 795.9 758.8 722.1 685.7WT_ 333/406x32 16.0 x - - - - - - - - - 984.6 946.9 909.6 872.5 835.7WT_ 333/450x32 17.7 x - - - - - - - - - 1114.6 1076.8 1039.2 1001.9 964.8


13.1 13.6 18.0 27.4 32.3

Flange Factored Moment Resistance Mr' (kip ft)

Unbraced Length (ft)


Imperial








Imperial

WT_ 500/127x6 19.7 5.0 x 0.250 - - 84.8 72.2 55.9 41.6 32.4 21.4 14.4 10.6 8.2 6.7 5.6 4.8WT_ 500/127x10 5.0 x 0.375 - - 128.1 110.3 88.2 66.5 52.5 35.8 25.0 19.0 15.2 12.7 10.9 9.5WT_ 500/152x10 6.0 x - - 165.7 150.5 132.4 111.5 87.2 58.6 40.2 30.0 23.7 19.5 16.6 14.4WT_ 500/178x10 7.0 x - - - 188.6 172.7 154.5 134.0 89.8 60.7 44.7 35.0 28.5 24.0 20.7WT_ 500/203x10 8.0 x - - - - 211.3 195.0 176.5 130.9 87.5 63.8 49.4 40.0 33.4 28.6WT_ 500/152x16 6.0 x 0.625 - - 279.0 256.3 230.5 202.4 168.6 118.8 85.8 66.9 54.9 46.6 40.5 35.8WT_ 500/178x16 7.0 x - - - 318.3 294.9 268.9 240.9 176.1 125.0 96.2 78.1 65.7 56.8 50.0WT_ 500/203x16 8.0 x - - - - 357.4 333.5 307.4 249.9 174.9 133.0 106.9 89.3 76.6 67.2WT_ 500/229x16 9.0 x - - - - 418.5 396.4 372.0 318.0 236.8 178.2 142.0 117.7 100.4 87.6WT_ 500/254x16 10.0 x - - - - - 457.9 435.2 384.2 312.4 232.9 184.0 151.5 128.5 111.6WT_ 500/279x16 11.0 x - - - - - - 497.1 449.0 380.6 298.1 233.8 191.3 161.4 139.5WT_ 500/305x16 12.0 x - - - - - - 557.9 512.6 447.4 374.8 292.1 237.6 199.5 171.6WT_ 500/330x16 13.0 x - - - - - - - 575.1 512.9 443.3 359.7 291.0 243.2 208.3WT_ 500/203x25 8.0 x 1.000 - - - - 586.6 556.3 524.6 458.9 367.8 290.8 240.7 205.6 179.7 159.7WT_ 500/229x25 9.0 x - - - - - 652.6 622.0 557.6 474.4 380.1 312.6 265.7 231.4 205.0WT_ 500/254x25 10.0 x - - - - - 747.8 718.4 655.8 573.6 485.5 396.6 335.5 290.9 257.1WT_ 500/279x25 11.0 x - - - - - - 813.9 753.2 672.4 589.1 493.8 415.6 359.0 316.2WT_ 500/305x25 12.0 x - - - - - - - 849.9 770.8 688.3 604.5 506.9 436.1 383.0WT_ 500/330x25 13.0 x - - - - - - - 945.9 868.6 787.2 703.8 610.1 523.0 457.8WT_ 500/356x25 14.0 x - - - - - - - 1041.1 965.8 885.6 803.0 719.3 620.1 541.1WT_ 500/406x25 16.0 x - - - - - - - - 1158.4 1081.2 1000.5 917.7 834.0 735.6WT_ 500/450x25 17.7 x - - - - - - - - 1322.0 1247.6 1168.8 1087.3 1004.4 920.6WT_ 500/305x32 12.0 x 1.250 - - - - - - - 1086.2 1003.4 919.2 835.0 749.9 651.1 575.8WT_ 500/330x32 13.0 x - - - - - - - 1203.6 1121.9 1038.0 953.7 869.5 776.1 684.6WT_ 500/356x32 14.0 x - - - - - - - - 1240.0 1156.7 1072.4 988.1 904.2 805.0WT_ 500/406x32 16.0 x - - - - - - - - 1475.3 1393.5 1309.9 1225.6 1141.3 1057.3WT_ 500/450x32 17.7 x - - - - - - - - - 1596.0 1513.4 1429.5 1345.2 1260.9


19.7 19.6 26.2 40.2 47.4









Imperial

WT_ 610/127x6 24.0 5.0 x 0.250 - - 103.2 87.6 67.2 49.8 38.5 25.3 16.8 12.1 9.3 7.5 6.2 5.3WT_ 610/127x10 5.0 x 0.375 - - 155.6 133.1 104.5 78.2 61.2 41.1 28.1 21.0 16.6 13.6 11.6 10.0WT_ 610/152x10 6.0 x - - 201.6 182.6 159.8 132.2 102.8 68.2 45.9 33.7 26.3 21.4 18.0 15.4WT_ 610/178x10 7.0 x - - - 229.3 209.5 186.4 160.4 105.5 70.3 51.0 39.4 31.7 26.4 22.5WT_ 610/203x10 8.0 x - - - - 256.8 236.3 213.0 154.7 102.3 73.6 56.3 45.0 37.1 31.5WT_ 610/152x16 6.0 x 0.625 - - 338.5 309.3 275.4 237.7 191.7 132.4 93.6 71.8 58.1 48.8 42.1 37.0WT_ 610/178x16 7.0 x - - - 385.8 355.5 321.3 283.8 199.0 138.4 104.7 83.8 69.7 59.7 52.2WT_ 610/203x16 8.0 x - - - - 432.7 401.6 367.2 285.7 196.0 146.5 116.1 95.7 81.4 70.7WT_ 610/229x16 9.0 x - - - - 507.8 479.4 447.7 376.0 268.3 198.6 155.9 127.6 107.7 93.1WT_ 610/254x16 10.0 x - - - - - 555.1 525.9 459.0 357.1 262.1 204.1 165.9 139.2 119.7WT_ 610/279x16 11.0 x - - - - - - 602.2 539.8 448.8 338.3 261.7 211.4 176.4 150.9WT_ 610/305x16 12.0 x - - - - - - 677.0 618.6 532.7 428.5 329.6 264.8 219.8 187.2WT_ 610/330x16 13.0 x - - - - - - - 695.8 614.5 521.6 408.7 326.7 270.0 229.0WT_ 610/203x25 8.0 x 1.000 - - - - 706.5 665.0 620.8 527.1 394.6 307.2 251.5 213.1 185.0 163.7WT_ 610/229x25 9.0 x - - - - 823.6 784.7 742.8 652.4 526.3 405.6 329.4 277.4 239.7 211.2WT_ 610/254x25 10.0 x - - - - - 902.6 862.8 776.0 658.8 522.8 421.4 352.7 303.4 266.4WT_ 610/279x25 11.0 x - - - - - - 981.2 898.2 784.3 660.9 528.9 440.2 376.9 329.6WT_ 610/305x25 12.0 x - - - - - - 1098.2 1018.8 908.5 790.6 653.4 540.7 460.8 401.5WT_ 610/330x25 13.0 x - - - - - - - 1138.0 1031.3 916.2 796.2 655.5 556.2 482.8WT_ 610/356x25 14.0 x - - - - - - - 1255.9 1153.0 1040.6 922.4 785.5 663.7 574.0WT_ 610/406x25 16.0 x - - - - - - - - 1392.8 1286.4 1172.7 1054.1 918.7 789.2WT_ 610/450x25 17.7 x - - - - - - - - 1595.3 1494.1 1384.7 1269.4 1150.1 1012.1WT_ 610/305x32 12.0 x 1.250 - - - - - - - 1298.3 1179.9 1056.9 932.1 786.4 677.4 595.4WT_ 610/330x32 13.0 x - - - - - - - 1444.2 1328.4 1206.8 1082.7 945.9 811.7 711.2WT_ 610/356x32 14.0 x - - - - - - - 1589.1 1476.0 1356.2 1233.0 1108.3 961.9 840.2WT_ 610/406x32 16.0 x - - - - - - - - 1768.9 1653.2 1532.5 1409.2 1284.5 1140.6WT_ 610/450x32 17.7 x - - - - - - - - 2017.6 1905.9 1788.0 1666.4 1542.7 1418.0


24.0 23.5 31.5 48.5 57.3









Imperial

WT_ 750/127x6 29.5 5.0 x 0.250 - - 126.7 107.3 81.7 60.4 46.6 30.3 19.9 14.2 10.8 8.6 7.0 5.9WT_ 750/127x10 5.0 x 0.375 - - 190.8 162.5 125.8 93.7 72.8 48.2 32.4 23.8 18.5 15.0 12.6 10.8WT_ 750/152x10 6.0 x - - 247.7 223.8 195.0 159.4 123.3 80.9 53.7 38.9 29.9 24.0 19.9 16.9WT_ 750/178x10 7.0 x - - - 281.6 256.6 227.5 193.5 126.2 83.1 59.6 45.4 36.1 29.7 25.1WT_ 750/203x10 8.0 x - - - 337.1 315.1 289.4 260.0 186.1 121.8 86.8 65.6 51.9 42.4 35.6WT_ 750/152x16 6.0 x 0.625 - - 415.0 377.4 333.3 283.3 223.1 151.2 104.6 78.8 62.8 52.1 44.5 38.8WT_ 750/178x16 7.0 x - - - 472.5 433.4 388.8 339.2 230.3 157.0 116.7 91.9 75.5 63.9 55.4WT_ 750/203x16 8.0 x - - - - 529.4 489.3 444.4 334.0 225.1 165.5 129.1 105.1 88.3 76.0WT_ 750/229x16 9.0 x - - - - 622.4 586.1 545.1 450.8 311.2 226.7 175.4 141.7 118.2 101.1WT_ 750/254x16 10.0 x - - - - - 680.0 642.5 555.5 417.4 302.0 232.0 186.2 154.4 131.3WT_ 750/279x16 11.0 x - - - - - 771.8 737.2 656.6 536.7 392.9 300.1 239.4 197.5 167.2WT_ 750/305x16 12.0 x - - - - - - 829.9 754.9 642.6 500.9 380.7 302.3 248.2 209.2WT_ 750/330x16 13.0 x - - - - - - - 850.9 745.4 622.5 475.1 375.8 307.3 258.0WT_ 750/203x25 8.0 x 1.000 - - - - 860.2 804.1 743.3 610.8 433.0 331.2 267.5 224.2 193.1 169.6WT_ 750/229x25 9.0 x - - - - 1006.2 954.2 897.3 771.7 584.3 442.2 354.0 294.6 252.2 220.6WT_ 750/254x25 10.0 x - - - - - 1101.3 1048.0 929.1 763.5 576.1 457.4 378.1 321.9 280.2WT_ 750/279x25 11.0 x - - - - - - 1195.9 1083.5 924.7 735.2 579.4 476.0 403.1 349.4WT_ 750/305x25 12.0 x - - - - - - 1341.5 1235.1 1083.1 916.2 722.0 589.6 496.9 428.8WT_ 750/330x25 13.0 x - - - - - - - 1384.4 1239.0 1077.7 886.8 720.4 604.2 519.3WT_ 750/356x25 14.0 x - - - - - - - 1531.6 1392.5 1236.7 1068.9 869.7 726.3 621.8WT_ 750/406x25 16.0 x - - - - - - - - 1693.4 1548.5 1390.1 1221.7 1018.7 866.0WT_ 750/450x25 17.7 x - - - - - - - - 1946.1 1810.0 1659.6 1498.1 1326.7 1122.0WT_ 750/305x32 12.0 x 1.250 - - - - - - 1689.9 1568.7 1400.7 1221.6 1014.0 840.0 716.5 624.7WT_ 750/330x32 13.0 x - - - - - - - 1751.8 1589.3 1414.1 1231.4 1017.7 864.2 750.7WT_ 750/356x32 14.0 x - - - - - - - 1933.0 1776.0 1605.0 1425.2 1218.9 1030.7 892.1WT_ 750/406x32 16.0 x - - - - - - - - 2144.2 1982.0 1809.0 1628.8 1425.3 1225.4WT_ 750/450x32 17.7 x - - - - - - - - 2455.2 2300.8 2134.1 1958.8 1777.6 1570.3


29.5 38.2 59.2 70.0









Imperial

WT_ 1000/127x6 39.4 5.0 x 0.250 - - 168.7 142.5 107.9 79.6 61.2 39.5 25.7 18.2 13.6 10.7 8.6 7.2WT_ 1000/127x10 5.0 x 0.375 - - 253.6 215.1 164.4 121.8 94.1 61.5 40.6 29.2 22.3 17.8 14.7 12.4WT_ 1000/152x10 6.0 x - - 329.7 297.3 258.1 208.5 160.6 104.4 68.3 48.7 36.8 29.1 23.8 20.0WT_ 1000/178x10 7.0 x - - - 374.7 340.8 301.1 253.3 163.9 106.7 75.6 56.8 44.6 36.2 30.2WT_ 1000/203x10 8.0 x - - - 448.9 419.2 384.2 344.1 242.9 157.5 111.1 83.1 64.9 52.4 43.5WT_ 1000/152x16 6.0 x 0.625 - - 551.3 499.3 437.1 362.2 281.8 187.1 126.2 92.8 72.4 58.9 49.5 42.6WT_ 1000/178x16 7.0 x - - - 627.1 572.9 510.0 439.4 289.2 192.9 140.2 108.2 87.2 72.7 62.0WT_ 1000/203x16 8.0 x - - - - 702.2 646.2 582.8 424.0 280.4 202.1 154.7 123.7 102.2 86.7WT_ 1000/229x16 9.0 x - - - - 827.0 776.7 719.5 585.6 391.8 280.6 213.3 169.4 139.2 117.3WT_ 1000/254x16 10.0 x - - - - - 903.0 850.9 728.5 530.0 377.7 285.6 225.7 184.3 154.6WT_ 1000/279x16 11.0 x - - - - - 1026.1 978.3 865.8 695.2 495.4 373.1 293.5 238.7 199.4WT_ 1000/305x16 12.0 x - - - - - - 1102.7 998.6 840.2 636.0 477.3 374.1 303.2 252.3WT_ 1000/330x16 13.0 x - - - - - - - 1127.9 980.1 801.3 599.7 468.7 378.7 314.2WT_ 1000/203x25 8.0 x 1.000 - - - - 1134.9 1052.8 961.7 744.6 509.7 380.3 300.6 247.6 210.1 182.5WT_ 1000/229x25 9.0 x - - - - 1332.1 1257.2 1173.5 983.5 698.6 516.0 404.3 330.4 278.5 240.4WT_ 1000/254x25 10.0 x - - - - - 1456.2 1379.0 1202.2 930.7 681.8 530.1 430.1 360.4 309.5WT_ 1000/279x25 11.0 x - - - - - - 1579.5 1414.6 1173.6 881.0 680.4 548.7 457.2 390.6WT_ 1000/305x25 12.0 x - - - - - - 1776.1 1621.8 1394.4 1116.9 857.7 688.0 570.4 485.1WT_ 1000/330x25 13.0 x - - - - - - - 1824.7 1609.8 1363.5 1064.4 849.8 701.4 594.0WT_ 1000/356x25 14.0 x - - - - - - - 2023.9 1820.5 1585.7 1303.0 1036.0 851.7 718.6WT_ 1000/406x25 16.0 x - - - - - - - - 2230.5 2016.6 1776.5 1489.1 1216.0 1019.4WT_ 1000/450x25 17.7 x - - - - - - - - 2572.7 2374.5 2150.3 1903.8 1604.0 1338.6WT_ 1000/305x32 12.0 x 1.250 - - - - - - 2231.8 2050.4 1789.5 1499.3 1168.6 950.5 798.0 686.4WT_ 1000/330x32 13.0 x - - - - - - - 2300.4 2051.5 1773.1 1438.9 1164.2 972.8 833.4WT_ 1000/356x32 14.0 x - - - - - - - 2546.7 2309.2 2041.3 1749.2 1408.6 1172.0 1000.1WT_ 1000/406x32 16.0 x - - - - - - - - 2813.4 2565.5 2292.6 1999.1 1650.8 1398.8WT_ 1000/450x32 17.7 x - - - - - - - - 3236.2 3004.1 2746.2 2467.5 2156.4 1817.9


39.4 50.1 78.1 92.4









Imperial

WT_ 1219/127x6 48.0 5.0 x 0.250 - - 205.5 173.5 131.0 96.5 74.1 47.7 30.9 21.7 16.2 12.6 10.1 8.3WT_ 1219/127x10 5.0 x 0.375 - - 308.8 261.3 198.7 146.8 113.1 73.4 48.0 34.2 25.9 20.4 16.7 14.0WT_ 1219/152x10 6.0 x - - 401.7 361.9 313.6 252.0 193.8 125.3 81.5 57.6 43.2 33.9 27.5 22.8WT_ 1219/178x10 7.0 x - - - 456.4 414.8 365.8 306.3 197.5 127.9 90.1 67.2 52.4 42.2 34.9WT_ 1219/203x10 8.0 x - - - 547.0 510.5 467.5 418.1 293.4 189.5 133.0 99.0 76.8 61.7 50.8WT_ 1219/152x16 6.0 x 0.625 - - 671.1 606.5 528.8 432.7 335.0 220.1 146.4 106.1 81.7 65.7 54.6 46.5WT_ 1219/178x16 7.0 x - - - 763.0 695.6 616.9 525.2 342.9 226.0 162.4 123.8 98.6 81.3 68.7WT_ 1219/203x16 8.0 x - - - 913.5 854.0 784.4 705.0 505.3 331.0 236.2 178.9 141.5 115.8 97.2WT_ 1219/229x16 9.0 x - - - - 1006.7 944.3 873.0 705.0 465.0 330.2 248.7 195.7 159.2 133.0WT_ 1219/254x16 10.0 x - - - - - 1098.8 1034.2 881.3 631.6 446.7 335.1 262.6 212.7 176.9WT_ 1219/279x16 11.0 x - - - - - 1249.2 1190.1 1050.1 834.5 588.5 440.1 343.6 277.3 229.8WT_ 1219/305x16 12.0 x - - - - - - 1342.2 1213.0 1014.7 757.9 565.3 440.2 354.3 292.7WT_ 1219/330x16 13.0 x - - - - - - - 1371.4 1187.0 957.6 712.8 553.8 444.7 366.5WT_ 1219/203x25 8.0 x 1.000 - - - - 1376.6 1271.9 1154.5 865.7 582.9 427.9 333.4 271.1 227.5 195.7WT_ 1219/229x25 9.0 x - - - - 1618.6 1523.8 1416.9 1170.5 806.3 586.9 453.4 365.9 305.0 260.7WT_ 1219/254x25 10.0 x - - - - - 1768.3 1670.4 1443.2 1082.2 782.2 600.3 481.2 398.7 338.9WT_ 1219/279x25 11.0 x - - - - - 2007.1 1916.9 1706.5 1393.4 1018.1 776.9 619.3 510.4 431.7WT_ 1219/305x25 12.0 x - - - - - - 2158.1 1962.4 1669.2 1298.6 986.2 782.5 641.9 540.6WT_ 1219/330x25 13.0 x - - - - - - - 2212.2 1936.9 1615.8 1231.3 973.0 795.0 667.0WT_ 1219/356x25 14.0 x - - - - - - - 2456.9 2197.8 1893.9 1515.0 1193.1 971.6 812.3WT_ 1219/406x25 16.0 x - - - - - - - - 2703.3 2429.5 2117.7 1731.5 1402.1 1165.7WT_ 1219/450x25 17.7 x - - - - - - - - 3123.6 2871.8 2583.4 2262.1 1863.0 1543.1WT_ 1219/305x32 12.0 x 1.250 - - - - - - 2708.1 2474.4 2130.6 1714.0 1318.3 1059.1 879.2 748.7WT_ 1219/330x32 13.0 x - - - - - - - 2783.1 2458.0 2086.3 1634.7 1306.9 1080.1 916.0WT_ 1219/356x32 14.0 x - - - - - - - 3086.4 2778.5 2423.8 1999.7 1592.0 1310.4 1107.1WT_ 1219/406x32 16.0 x - - - - - - - - 3402.3 3078.6 2716.1 2285.3 1868.3 1568.1WT_ 1219/450x32 17.7 x - - - - - - - - 3923.1 3623.0 3284.1 2912.0 2461.9 2056.8


48.0 60.5 94.6 112.1









Imperial

WT_ 1500/127x6 59.1 5.0 x 0.250 - - 252.7 213.1 160.7 118.2 90.7 58.3 37.6 26.3 19.5 15.1 12.1 9.9WT_ 1500/127x10 5.0 x 0.375 - - 379.5 320.7 242.9 179.1 137.7 89.0 57.8 40.9 30.6 24.0 19.4 16.1WT_ 1500/152x10 6.0 x - - 493.9 444.7 384.8 308.1 236.6 152.5 98.6 69.4 51.7 40.2 32.4 26.7WT_ 1500/178x10 7.0 x - - - 561.1 509.6 448.9 374.5 240.9 155.4 109.0 80.9 62.7 50.3 41.3WT_ 1500/203x10 8.0 x - - - 672.7 627.5 574.3 513.1 358.4 230.8 161.5 119.6 92.5 73.9 60.5WT_ 1500/152x16 6.0 x 0.625 - - 824.6 744.1 646.7 524.3 404.5 263.6 173.3 124.2 94.4 75.0 61.6 52.0WT_ 1500/178x16 7.0 x - - - 937.3 853.1 754.5 636.8 413.1 269.9 192.0 144.9 114.2 93.1 78.0WT_ 1500/203x16 8.0 x - - - 1122.8 1048.7 961.8 862.3 611.3 397.5 281.4 211.2 165.6 134.2 111.7WT_ 1500/229x16 9.0 x - - - - 1237.0 1159.3 1070.2 859.1 560.8 395.4 295.7 230.8 186.3 154.3WT_ 1500/254x16 10.0 x - - - - - 1349.8 1269.3 1077.9 764.1 537.3 400.5 311.7 250.7 207.0WT_ 1500/279x16 11.0 x - - - - - 1535.3 1461.8 1286.8 1011.9 710.1 528.1 409.9 328.8 270.7WT_ 1500/305x16 12.0 x - - - - - - 1649.3 1488.2 1239.6 916.9 680.7 527.3 422.0 346.7WT_ 1500/330x16 13.0 x - - - - - - - 1892.4 1777.1 1638.1 1476.5 1293.5 1063.4 872.0WT_ 1500/203x25 8.0 x 1.000 - - - - 1973.7 1940.4 1902.7 1815.5 1686.9 1541.0 1381.7 1212.5 1009.3 858.8WT_ 1500/229x25 9.0 x - - - - 2242.5 2212.5 2178.5 2099.1 1980.9 1845.0 1694.9 1533.7 1364.1 1157.7WT_ 1500/254x25 10.0 x - - - - - 2503.0 2478.2 2420.1 2332.8 2231.5 2118.5 1995.9 1865.8 1729.8WT_ 1500/279x25 11.0 x - - - - - 2781.7 2762.7 2718.1 2650.7 2571.8 2483.2 2386.3 2282.6 2173.4WT_ 1500/305x25 12.0 x - - - - - - 3038.8 3003.4 2949.6 2886.3 2814.7 2735.9 2651.1 2561.1WT_ 1500/330x25 13.0 x - - - - - - - 3281.0 3237.0 3185.1 3125.9 3060.5 2989.6 2914.0WT_ 1500/356x25 14.0 x - - - - - - - 3553.6 3517.0 3473.5 3423.8 3368.5 3308.4 3243.9WT_ 1500/406x25 16.0 x - - - - - - - - 4046.5 4007.7 3963.0 3912.9 3858.0 3798.7WT_ 1500/450x25 17.7 x - - - - - - - - 4499.0 4463.5 4422.4 4376.2 4325.2 4269.9WT_ 1500/305x32 12.0 x 1.250 - - - - - - 3818.3 3785.0 3735.1 3677.3 3613.1 3543.8 3470.3 3393.8WT_ 1500/330x32 13.0 x - - - - - - - 4115.1 4068.2 4013.6 3952.5 3885.9 3815.0 3740.7WT_ 1500/356x32 14.0 x - - - - - - - 4444.4 4400.2 4348.5 4290.2 4226.4 4158.1 4085.9WT_ 1500/406x32 16.0 x - - - - - - - - 5061.4 5014.8 4961.8 4903.1 4839.6 4772.0WT_ 1500/450x32 17.7 x - - - - - - - - 5626.6 5583.7 5534.6 5480.0 5420.4 5356.6


59.1 65.2 97.4 129.9



Table 3.4

Constantsν 0.3 Poissons RatioE 200 GPa Youngs ModulasFy web 350 MPa Web Material Yield Strengthφs 0.75 Material Resistance Factor (Per CSA S136)

Physical PropertiesDesignation tw tw a3 w s Iz Dx Dz

ga mm mm mm mm mm4 kN m kN m

WT0 16 1.52 40 77.5 89 23250 0.056 60.0WTA 14 1.90 40 77.5 89 31050 0.109 80.1WTB 12 2.66 40 77.5 89 38850 0.299 100.3WTC 11 3.04 43 77.5 91.5 53900 0.439 139.1

Shear CapacityDesignation Web tw Shear Shear

Depth Distortion τcr.l λcr.l χcr.l τcr.g λcr.g χcr.g ResistanceArea Vr

mm mm mm2 MPa MPa kNa b c d e f g h i j k

WT0333 333 1.52 440 651.7 0.557 0.79 2016.4 0.317 1.00 60.5WTA333 333 1.90 550 901.6 0.473 0.84 2369.4 0.292 1.00 80.2WTB333 333 2.66 770 1508.4 0.366 0.91 2576.8 0.280 1.00 121.8WTC333 333 3.04 857 1867.9 0.329 0.94 3171.4 0.252 1.00 143.5WT0500 500 1.52 661 527.9 0.619 0.76 894.4 0.475 1.00 87.2WTA500 500 1.90 826 747.0 0.520 0.81 1051.0 0.438 1.00 116.4WTB500 500 2.66 1157 1291.9 0.395 0.89 1143.0 0.420 1.00 178.7WTC500 500 3.04 1287 1606.5 0.355 0.92 1406.7 0.379 1.00 211.0WT0610 610 1.52 806 483.6 0.646 0.74 601.7 0.580 1.00 104.4WTA610 610 1.90 1007 691.6 0.541 0.80 707.0 0.535 1.00 139.9WTB610 610 2.66 1410 1214.3 0.408 0.88 768.9 0.513 1.00 215.8WTC610 610 3.04 1569 1512.8 0.365 0.91 946.3 0.462 1.00 255.0WTA750 750 1.90 1239 644.2 0.560 0.79 467.1 0.658 1.00 169.9WTB750 750 2.66 1735 1148.0 0.420 0.87 508.0 0.631 1.00 263.2WTC750 750 3.04 1930 1432.7 0.376 0.90 625.2 0.569 1.00 311.3

WTA1000 1000 1.90 1652 592.9 0.584 0.78 262.7 0.877 1.00 222.9WTB1000 1000 2.66 2314 1076.0 0.433 0.86 285.7 0.841 1.00 347.3WTC1000 1000 3.04 2573 1345.9 0.387 0.89 351.7 0.758 1.00 411.2WTA1219 1219 1.90 2014 565.1 0.598 0.77 176.8 1.069 0.91 269.1WTB1219 1219 2.66 2821 1037.2 0.441 0.86 192.2 1.025 0.97 420.9WTC1219 1219 3.04 3137 1299.0 0.394 0.89 236.6 0.924 1.00 498.7WTA1500 1500 1.90 2478 541.5 0.611 0.76 116.8 1.315 0.67 290.1WTB1500 1500 2.66 3470 1004.1 0.449 0.85 127.0 1.261 0.72 433.2WTC1500 1500 3.04 3860 1259.0 0.401 0.88 156.3 1.137 0.84 577.8

Local Buckling (EN) Global Buckling

SIN Beam ShearMetric


Table 3.4

Constantsν 0.3 Poissons RatioE 29008 ksi Youngs ModulasFy web 51 ksi Web Material Yield Strengthφs 0.75 Material Resistance Factor (Per CSA S136)

Physical PropertiesDesignation tw tw a3 w s Iz Dx Dz

ga in in in in in4 kip ft kip ft

WT0 16 0.060 1.57 3.05 3.50 0.0559 0.0038 4.11WTA 14 0.075 1.57 3.05 3.50 0.0746 0.0075 5.49WTB 12 0.105 1.57 3.05 3.50 0.0933 0.0205 6.87WTC 11 0.120 1.69 3.05 3.60 0.1295 0.0301 9.53

Shear CapacityDesignation Web t web Shear Shear

Depth Distortion τcr.l λcr.l χcr.l τcr.g λcr.g χcr.g ResistanceArea Vr

in in in2 ksi ksi kipa b c d e f g h i j k

WT0333 13.11 0.060 0.683 94.5 0.557 0.79 292.4 0.317 1.00 13.6WTA333 13.11 0.075 0.853 130.8 0.473 0.84 343.7 0.292 1.00 18.0WTB333 13.11 0.105 1.194 218.8 0.366 0.91 373.7 0.280 1.00 27.4WTC333 13.11 0.120 1.328 270.9 0.329 0.94 460.0 0.252 1.00 32.3WT0500 19.69 0.060 1.025 76.6 0.619 0.76 129.7 0.475 1.00 19.6WTA500 19.69 0.075 1.280 108.3 0.520 0.81 152.4 0.438 1.00 26.2WTB500 19.69 0.105 1.793 187.4 0.395 0.89 165.8 0.420 1.00 40.2WTC500 19.69 0.120 1.994 233.0 0.355 0.92 204.0 0.379 1.00 47.4WT0610 24.00 0.060 1.250 70.1 0.646 0.74 87.3 0.580 1.00 23.5WTA610 24.00 0.075 1.561 100.3 0.541 0.80 102.5 0.535 1.00 31.5WTB610 24.00 0.105 2.186 176.1 0.408 0.88 111.5 0.513 1.00 48.5WTC610 24.00 0.120 2.431 219.4 0.365 0.91 137.3 0.462 1.00 57.3WTA750 29.53 0.075 1.921 93.4 0.560 0.79 67.7 0.658 1.00 38.2WTB750 29.53 0.105 2.689 166.5 0.420 0.87 73.7 0.631 1.00 59.2WTC750 29.53 0.120 2.991 207.8 0.376 0.90 90.7 0.569 1.00 70.0

WTA1000 39.37 0.075 2.561 86.0 0.584 0.78 38.1 0.877 1.00 50.1WTB1000 39.37 0.105 3.586 156.1 0.433 0.86 41.4 0.841 1.00 78.1WTC1000 39.37 0.120 3.988 195.2 0.387 0.89 51.0 0.758 1.00 92.4WTA1219 48.00 0.075 3.122 82.0 0.598 0.77 25.6 1.069 0.91 60.5WTB1219 48.00 0.105 4.372 150.4 0.441 0.86 27.9 1.025 0.97 94.6WTC1219 48.00 0.120 4.862 188.4 0.394 0.89 34.3 0.924 1.00 112.1WTA1500 59.06 0.075 3.841 78.5 0.611 0.76 16.9 1.315 0.67 65.2WTB1500 59.06 0.105 5.379 145.6 0.449 0.85 18.4 1.261 0.72 97.4WTC1500 59.06 0.120 5.982 182.6 0.401 0.88 22.7 1.137 0.84 129.9

SIN Beam Shear

Local Buckling (EN) Global Buckling

Imperial


Table 3.5a(metric)

Depth ofWeb Width Thickness Areahw bf tf ry rx/ry 0 2000 3000 4000 5000 6000 7000 8000 9000 10000

(mm) (mm) (mm) (mm2) (mm)a b c d e f g h i j k l m n o p q

333 127 x 6 1612.9 36.7 4.63 508.1 390.1 276.6 190.6 134.3 98.0 74.1 57.7 46.1 37.6127 x 10 2419.35 36.7 4.67 762.1 585.2 414.9 285.8 201.4 147.1 111.2 86.6 69.2 56.4152 x 2903.22 44.0 3.89 914.5 769.4 596.7 439.5 322.9 241.7 185.5 145.9 117.3 96.2178 x 3387.09 51.3 3.34 1066.9 947.6 784.1 612.4 469.0 360.9 282.0 224.4 181.9 149.9203 x 3870.96 58.7 2.92 1219.4 1120.1 970.8 795.6 633.6 501.5 399.6 322.3 263.6 218.7152 x 16 4838.7 44.0 3.97 1524.2 1282.4 994.5 732.5 538.1 402.8 309.2 243.2 195.5 160.3178 x 5645.15 51.3 3.40 1778.2 1579.3 1306.9 1020.6 781.7 601.5 470.0 374.0 303.2 249.8203 x 6451.6 58.7 2.97 2032.3 1866.8 1618.1 1326.0 1056.0 835.8 665.9 537.1 439.4 364.5229 x 7258.05 66.0 2.64 2286.3 2147.0 1923.6 1638.2 1350.8 1098.8 893.2 731.0 604.3 505.1254 x 8064.5 73.3 2.38 2540.3 2421.6 2222.1 1950.7 1657.5 1383.0 1146.9 952.8 796.5 671.4279 x 8870.95 80.7 2.16 2794.3 2691.9 2514.1 2260.1 1969.4 1681.6 1421.5 1198.9 1014.0 862.3305 x 9677.4 88.0 1.98 3048.4 2959.1 2800.3 2564.7 2282.4 1988.9 1711.6 1465.1 1253.8 1076.2330 x 10483.85 95.3 1.83 3302.4 3223.8 3081.5 2864.2 2593.7 2300.7 2012.6 1747.1 1512.7 1310.7203 x 25 10322.56 58.7 3.06 3251.6 2986.9 2588.9 2121.5 1689.7 1337.3 1065.5 859.4 703.0 583.3229 x 11612.88 66.0 2.72 3658.1 3435.2 3077.7 2621.1 2161.3 1758.1 1429.2 1169.6 966.8 808.2254 x 12903.2 73.3 2.45 4064.5 3874.5 3555.4 3121.1 2651.9 2212.8 1835.1 1524.5 1274.4 1074.2279 x 14193.52 80.7 2.22 4471.0 4307.1 4022.6 3616.1 3151.1 2690.5 2274.4 1918.3 1622.3 1379.7305 x 15483.84 88.0 2.04 4877.4 4734.5 4480.4 4103.6 3651.9 3182.3 2738.6 2344.1 2006.0 1721.9330 x 16774.16 95.3 1.88 5283.9 5158.1 4930.4 4582.7 4149.9 3681.2 3220.1 2795.4 2420.2 2097.2356 x 18064.48 102.7 1.75 5690.3 5578.7 5373.8 5053.7 4642.8 4182.1 3712.7 3265.9 2859.7 2501.4406 x 20645.12 117.3 1.53 6503.2 6413.4 6245.3 5973.9 5609.4 5177.9 4712.1 4243.1 3794.0 3379.3450 x 22860 129.9 1.38 7200.9 7125.0 6981.1 6744.6 6418.1 6018.1 5569.8 5100.1 4633.0 4186.1305 x 32 19354.8 88.0 2.08 6096.8 5918.2 5600.5 5129.5 4564.8 3977.9 3423.3 2930.2 2507.5 2152.4330 x 20967.7 95.3 1.92 6604.8 6447.7 6163.0 5728.4 5187.4 4601.4 4025.2 3494.3 3025.3 2621.5356 x 22580.6 102.7 1.78 7112.9 6973.4 6717.2 6317.1 5803.6 5227.6 4640.9 4082.3 3574.6 3126.7406 x 25806.4 117.3 1.56 8129.0 8016.8 7806.6 7467.4 7011.8 6472.3 5890.2 5303.9 4742.5 4224.1450 x 28575 129.9 1.41 9001.1 8906.2 8726.4 8430.7 8022.6 7522.7 6962.2 6375.1 5791.2 5232.7

Factored Compressive Resistance Cr (kN)Effective length (mm) with respect to least radius of gyration (ry)

Flange

SIN Beam Axial CapacityMetric


Table 3.5a(metric)




Flange





Designation Depth ofWeb Width Thickness Area

hw bf tf ry rx/ry 0 5 10 15 20 25 30 35 40 45(in) (in) (in) (in2) (in)a b c d e f g h i j k l m n o p q

WT_ 333/127x6 13.1 5.0 x 1/4 2.50 1.44 4.63 114.2 99.4 61.1 34.9 21.4 14.2 10.1 7.5 5.7 4.6WT_ 333/127x10 5.0 x 3/8 3.75 1.44 4.67 171.3 149.1 91.6 52.4 32.1 21.3 15.1 11.2 8.6 6.8WT_ 333/152x10 6.0 x 4.50 1.73 3.89 205.6 188.2 132.3 82.7 52.9 35.8 25.6 19.1 14.8 11.7WT_ 333/178x10 7.0 x 5.25 2.02 3.34 239.9 226.0 174.4 118.2 79.2 54.9 39.7 29.9 23.2 18.5WT_ 333/203x10 8.0 x 6.00 2.31 2.92 274.1 262.8 216.4 157.3 110.3 78.5 57.6 43.7 34.1 27.3WT_ 333/152x16 6.0 x 5/8 7.50 1.73 3.97 342.7 313.7 220.5 137.8 88.2 59.7 42.7 31.8 24.6 19.6WT_ 333/178x16 7.0 x 8.75 2.02 3.40 399.8 376.6 290.6 197.1 132.0 91.5 66.2 49.8 38.6 30.8WT_ 333/203x16 8.0 x 10.00 2.31 2.97 456.9 438.0 360.7 262.2 183.8 130.8 96.1 72.9 56.9 45.5WT_ 333/229x16 9.0 x 11.25 2.60 2.64 514.0 498.3 429.6 330.7 242.1 177.2 132.3 101.4 79.7 64.0WT_ 333/254x16 10.0 x 12.50 2.89 2.38 571.1 557.8 496.9 400.7 305.4 229.7 174.6 135.3 107.1 86.5WT_ 333/279x16 11.0 x 13.75 3.18 2.16 628.2 616.8 562.8 471.1 372.1 287.5 222.6 174.7 139.4 113.2WT_ 333/305x16 12.0 x 15.00 3.46 1.98 685.3 675.4 627.3 541.0 440.9 349.5 275.7 219.1 176.4 144.1WT_ 333/330x16 13.0 x 16.25 3.75 1.83 742.4 733.8 690.8 610.1 510.9 414.7 333.1 268.2 218.0 179.3WT_ 333/203x25 8.0 x 1 16.00 2.31 3.06 731.0 700.8 577.1 419.5 294.0 209.3 153.7 116.6 91.0 72.8WT_ 333/229x25 9.0 x 18.00 2.60 2.72 822.4 797.3 687.3 529.1 387.4 283.4 211.7 162.2 127.5 102.4WT_ 333/254x25 10.0 x 20.00 2.89 2.45 913.7 892.5 795.1 641.2 488.7 367.5 279.4 216.5 171.4 138.4WT_ 333/279x25 11.0 x 22.00 3.18 2.22 1005.1 986.9 900.5 753.8 595.4 460.0 356.2 279.4 223.0 181.1WT_ 333/305x25 12.0 x 24.00 3.46 2.04 1096.5 1080.7 1003.7 865.6 705.5 559.2 441.1 350.5 282.2 230.6WT_ 333/330x25 13.0 x 26.00 3.75 1.88 1187.9 1174.0 1105.2 976.2 817.4 663.5 532.9 429.1 348.8 286.9WT_ 333/356x25 14.0 x 28.00 4.04 1.75 1279.2 1267.0 1205.2 1085.2 930.0 771.5 630.6 514.6 422.3 349.8WT_ 333/406x25 16.0 x 32.00 4.62 1.53 1462.0 1452.2 1401.6 1298.4 1154.2 993.7 839.0 702.5 588.1 494.4WT_ 333/450x25 17.7 x 35.43 5.11 1.38 1618.8 1610.5 1567.3 1476.6 1343.6 1186.9 1026.7 877.8 747.3 636.7WT_ 333/305x32 12.0 x 1 1/4 30.00 3.46 2.08 1370.6 1350.9 1254.7 1082.1 881.8 699.0 551.3 438.1 352.8 288.2WT_ 333/330x32 13.0 x 32.50 3.75 1.92 1484.8 1467.5 1381.5 1220.3 1021.8 829.4 666.2 536.4 436.0 358.6WT_ 333/356x32 14.0 x 35.00 4.04 1.78 1599.0 1583.7 1506.5 1356.5 1162.5 964.3 788.3 643.2 527.8 437.2WT_ 333/406x32 16.0 x 40.00 4.62 1.56 1827.5 1815.2 1752.0 1623.0 1442.7 1242.1 1048.7 878.2 735.1 618.0WT_ 333/450x32 17.7 x 44.29 5.11 1.41 2023.5 2013.2 1959.2 1845.7 1679.5 1483.6 1283.4 1097.3 934.1 795.8

SIN Beam Axial CapacityImperial

FlangeEffective length (ft) with respect to least radius of gyration (ry)

Factored Compressive Resistance Vr (kip)


Table 3.6

ConstantsFy 350 MPa

s 0.8

Web

tw (mm)

tf (mm) 0 50 100 150 200 250 300 350 400

6.4 13.50 34.77 56.03 77.30 98.56 119.83 141.09 162.36 183.62

7.9 16.88 38.14 59.41 80.67 101.94 123.20 144.47 165.73 187.00

9.5 20.25 41.52 62.78 84.05 105.31 126.58 147.84 169.11 190.37

12.7 27.01 48.27 69.54 90.80 112.07 133.33 154.60 175.86 197.13

15.9 33.76 55.02 76.29 97.55 118.82 140.08 161.35 182.61 203.88

19.1 40.51 61.77 83.04 104.30 125.57 146.83 168.10 189.36 210.63

25.4 54.01 75.28 96.54 117.81 139.07 160.34 181.60 202.87 224.13

Web

tw (mm)

tf (mm) 0 50 100 150 200 250 300 350 400

6.4 16.87 43.43 69.99 96.56 123.12 149.68 176.25 202.81 229.37

7.9 21.08 47.65 74.21 100.77 127.34 153.90 180.46 207.03 233.59

9.5 25.30 51.86 78.43 104.99 131.55 158.12 184.68 211.24 237.81

12.7 33.74 60.30 86.86 113.43 139.99 166.55 193.12 219.68 246.24

15.9 42.17 68.73 95.30 121.86 148.42 174.99 201.55 228.11 254.68

19.1 50.60 77.17 103.73 130.29 156.86 183.42 209.98 236.55 263.11

25.4 67.47 94.03 120.60 147.16 173.72 200.29 226.85 253.41 279.98

Metric

SIN Concentrated Load

Bearing Length (mm)

1.52

WT0

WTA

1.90

Bearing Length (mm)

Concentrated Load Resistance (kN)

Web

tw (mm)

tf (mm) 0 50 100 150 200 250 300 350 400

6.4 23.62 60.82 98.01 135.21 172.40 209.60 246.79 283.99 321.19

7.9 29.52 66.72 103.92 141.11 178.31 215.50 252.70 289.89 327.09

9.5 35.43 72.62 109.82 147.02 184.21 221.41 258.60 295.80 333.00

12.7 47.24 84.43 121.63 158.83 196.02 233.22 270.41 307.61 344.80

15.9 59.05 96.24 133.44 170.64 207.83 245.03 282.22 319.42 356.61

19.1 70.86 108.05 145.25 182.45 219.64 256.84 294.03 331.23 368.42

25.4 94.48 131.67 168.87 206.06 243.26 280.46 317.65 354.85 392.04

Web

tw (mm)

tf (mm) 0 50 100 150 200 250 300 350 400

6.4 27.01 69.54 112.07 154.60 197.13 239.66 282.18 324.71 367.24

7.9 33.76 76.29 118.82 161.35 203.88 246.41 288.94 331.47 374.00

9.5 40.51 83.04 125.57 168.10 210.63 253.16 295.69 338.22 380.75

12.7 54.01 96.54 139.07 181.60 224.13 266.66 309.19 351.72 394.25

15.9 67.52 110.05 152.58 195.11 237.64 280.16 322.69 365.22 407.75

19.1 81.02 123.55 166.08 208.61 251.14 293.67 336.20 378.73 421.26

25.4 108.03 150.56 193.09 235.61 278.14 320.67 363.20 405.73 448.26

3.04

WTB

2.66

Bearing Length (mm)

WTC

Bearing Length (mm)

SIN Properties ‐ v0.06 | 2016‐02‐04

Table 3.6

ConstantsFy 50.8 ksi

s 0.8

Web

tw (in)

tf (mm) 0 2 4 6 8 10 12 14 16

1/4 3.04 7.89 12.75 17.61 22.46 27.32 32.18 37.03 41.89

5/16 3.79 8.65 13.51 18.37 23.22 28.08 32.94 37.79 42.65

3/8 4.55 9.41 14.27 19.12 23.98 28.84 33.70 38.55 43.41

1/2 6.07 10.93 15.79 20.64 25.50 30.36 35.21 40.07 44.93

5/8 7.59 12.45 17.30 22.16 27.02 31.87 36.73 41.59 46.45

3/4 9.11 13.96 18.82 23.68 28.54 33.39 38.25 43.11 47.96

1 12.14 17.00 21.86 26.71 31.57 36.43 41.28 46.14 51.00

Web

tw (in)

tf (mm) 0 2 4 6 8 10 12 14 16

1/4 3.79 9.86 15.93 21.99 28.06 34.13 40.20 46.26 52.33

5/16 4.74 10.81 16.87 22.94 29.01 35.08 41.14 47.21 53.28

3/8 5.69 11.76 17.82 23.89 29.96 36.02 42.09 48.16 54.23

1/2 7.58 13.65 19.72 25.79 31.85 37.92 43.99 50.05 56.12

5/8 9.48 15.55 21.61 27.68 33.75 39.82 45.88 51.95 58.02

3/4 11.38 17.44 23.51 29.58 35.64 41.71 47.78 53.85 59.91

1 15.17 21.24 27.30 33.37 39.44 45.50 51.57 57.64 63.71

SIN Concentrated LoadImperial

Concentrated Load Resistance (kip)

Bearing Length (in)

WT0

0.0598

Bearing Length (in)

WTA

0.0747

Web

tw (in)

tf (mm) 0 2 4 6 8 10 12 14 16

1/4 5.31 13.81 22.30 30.80 39.29 47.79 56.28 64.78 73.28

5/16 6.64 15.13 23.63 32.12 40.62 49.12 57.61 66.11 74.60

3/8 7.96 16.46 24.96 33.45 41.95 50.44 58.94 67.43 75.93

1/2 10.62 19.12 27.61 36.11 44.60 53.10 61.59 70.09 78.59

5/8 13.27 21.77 30.27 38.76 47.26 55.75 64.25 72.74 81.24

3/4 15.93 24.43 32.92 41.42 49.91 58.41 66.90 75.40 83.90

1 21.24 29.74 38.23 46.73 55.22 63.72 72.21 80.71 89.21

Web

tw (in)

tf (mm) 0 2 4 6 8 10 12 14 16

1/4 6.07 15.79 25.50 35.21 44.93 54.64 64.36 74.07 83.78

5/16 7.59 17.30 27.02 36.73 46.45 56.16 65.87 75.59 85.30

3/8 9.11 18.82 28.54 38.25 47.96 57.68 67.39 77.11 86.82

1/2 12.14 21.86 31.57 41.28 51.00 60.71 70.43 80.14 89.85

5/8 15.18 24.89 34.61 44.32 54.03 63.75 73.46 83.18 92.89

3/4 18.21 27.93 37.64 47.36 57.07 66.78 76.50 86.21 95.93

1 24.29 34.00 43.71 53.43 63.14 72.86 82.57 92.28 102.00

0.1196

Bearing Length (in)

WTB

0.1046

Bearing Length (in)

WTC


Table 3.7

Highlight W/D < 0.37 lb/ft / in Surf Area = 3 * WFlange + 4 * TFlange + 2 * DWeb * 1.216 ‐ 2 * TwebHighlight M/D < 21.72 kg/m / m The 1.216 factor is to account for the sinusoidal shape of the web

Designation

WT0 WTA WTB WTC WT0 WTA WTB WTC WT0 WTA WTB WTC

a b c d e f g h i j k l m

WT_ 333/127x6 1.213 1.212 1.211 1.210 14.416 15.417 17.430 18.442 0.246 0.263 0.297 0.314WT_ 333/152x6 1.289 1.289 1.287 1.286 15.528 16.470 18.365 19.318 0.264 0.281 0.313 0.329WT_ 333/127x10 1.226 1.225 1.224 1.223 19.430 20.424 22.423 23.427 0.331 0.348 0.382 0.399WT_ 333/152x10 1.302 1.301 1.300 1.299 21.210 22.147 24.030 24.977 0.361 0.377 0.409 0.425WT_ 333/178x10 1.378 1.378 1.376 1.375 22.794 23.679 25.460 26.355 0.388 0.403 0.434 0.449WT_ 333/203x10 1.455 1.454 1.452 1.451 24.211 25.051 26.740 27.588 0.412 0.427 0.455 0.470WT_ 333/229x10 1.531 1.530 1.528 1.528 25.487 26.286 27.892 28.698 0.434 0.448 0.475 0.489WT_ 333/152x16 1.328 1.327 1.325 1.324 32.250 33.175 35.034 35.969 0.549 0.565 0.597 0.613WT_ 333/178x16 1.404 1.403 1.401 1.401 35.009 35.885 37.647 38.532 0.596 0.611 0.641 0.656WT_ 333/203x16 1.480 1.479 1.478 1.477 37.484 38.316 39.990 40.830 0.638 0.653 0.681 0.695WT_ 333/229x16 1.556 1.555 1.554 1.553 39.717 40.509 42.103 42.903 0.676 0.690 0.717 0.731WT_ 333/254x16 1.632 1.632 1.630 1.629 41.741 42.498 44.018 44.782 0.711 0.724 0.750 0.763

length less top flangeMetric M/D Ratio (kg/m / m)

SIN Beam M/D for ULC

Imperial W/D Ratio (lb/ft / in)Surface Area (m2) per metre

WT_ 333/279x16 1.709 1.708 1.706 1.705 43.585 44.308 45.763 46.493 0.742 0.755 0.779 0.792WT_ 333/305x16 1.785 1.784 1.782 1.782 45.271 45.964 47.358 48.058 0.771 0.783 0.807 0.819WT_ 333/330x16 1.861 1.860 1.859 1.858 46.819 47.485 48.822 49.494 0.797 0.809 0.832 0.843WT_ 333/356x16 1.937 1.936 1.935 1.934 48.245 48.886 50.172 50.818 0.822 0.833 0.855 0.866WT_ 333/203x25 1.518 1.517 1.516 1.515 56.561 57.382 59.032 59.861 0.963 0.977 1.005 1.020WT_ 333/229x25 1.594 1.593 1.592 1.591 60.211 60.994 62.569 63.360 1.026 1.039 1.066 1.079WT_ 333/254x25 1.670 1.670 1.668 1.667 63.528 64.277 65.783 66.539 1.082 1.095 1.120 1.133WT_ 333/279x25 1.747 1.746 1.744 1.744 66.556 67.274 68.716 69.441 1.134 1.146 1.170 1.183WT_ 333/305x25 1.823 1.822 1.821 1.820 69.330 70.019 71.404 72.099 1.181 1.193 1.216 1.228WT_ 333/330x25 1.899 1.898 1.897 1.896 71.882 72.544 73.875 74.544 1.224 1.236 1.258 1.270WT_ 333/356x25 1.975 1.974 1.973 1.972 74.237 74.875 76.156 76.800 1.264 1.275 1.297 1.308WT_ 333/406x25 2.128 2.127 2.125 2.125 78.441 79.034 80.227 80.826 1.336 1.346 1.366 1.377WT_ 333/450x25 2.258 2.258 2.256 2.255 81.597 82.157 83.282 83.847 1.390 1.399 1.418 1.428WT_ 333/305x32 1.848 1.847 1.846 1.845 84.819 85.505 86.883 87.575 1.445 1.456 1.480 1.492WT_ 333/330x32 1.924 1.924 1.922 1.921 88.039 88.699 90.025 90.691 1.500 1.511 1.533 1.545WT_ 333/356x32 2.001 2.000 1.998 1.998 91.015 91.651 92.929 93.570 1.550 1.561 1.583 1.594WT_ 333/406x32 2.153 2.152 2.151 2.150 96.334 96.927 98.118 98.716 1.641 1.651 1.671 1.681WT_ 333/450x32 2.284 2.283 2.282 2.281 100.333 100.893 102.018 102.583 1.709 1.718 1.738 1.747


Table 3.7


Designation






WT_ 500/127x6 1.619 1.619 1.617 1.616 12.295 13.417 15.671 16.804 0.209 0.229 0.267 0.286WT_ 500/152x6 1.696 1.695 1.693 1.693 13.236 14.308 16.462 17.543 0.225 0.244 0.280 0.299WT_ 500/127x10 1.632 1.631 1.630 1.629 16.079 17.193 19.434 20.559 0.274 0.293 0.331 0.350WT_ 500/152x10 1.708 1.708 1.706 1.705 17.585 18.651 20.792 21.868 0.300 0.318 0.354 0.372WT_ 500/178x10 1.784 1.784 1.782 1.781 18.963 19.983 22.034 23.064 0.323 0.340 0.375 0.393WT_ 500/203x10 1.861 1.860 1.858 1.858 20.227 21.207 23.175 24.163 0.345 0.361 0.395 0.412WT_ 500/229x10 1.937 1.936 1.935 1.934 21.393 22.334 24.225 25.175 0.364 0.380 0.413 0.429WT_ 500/152x16 1.734 1.733 1.731 1.731 26.091 27.145 29.262 30.326 0.444 0.462 0.498 0.517WT_ 500/178x16 1.810 1.809 1.808 1.807 28.491 29.501 31.531 32.551 0.485 0.502 0.537 0.554WT_ 500/203x16 1.886 1.885 1.884 1.883 30.696 31.666 33.616 34.595 0.523 0.539 0.573 0.589WT_ 500/229x16 1.962 1.962 1.960 1.959 32.730 33.664 35.539 36.481 0.557 0.573 0.605 0.621WT_ 500/254x16 2.038 2.038 2.036 2.035 34.612 35.512 37.318 38.226 0.590 0.605 0.636 0.651WT_ 500/279x16 2.115 2.114 2.112 2.112 36.359 37.226 38.969 39.844 0.619 0.634 0.664 0.679WT_ 500/305x16 2.191 2.190 2.189 2.188 37.984 38.822 40.505 41.350 0.647 0.661 0.690 0.704WT_ 500/330x16 2.267 2.266 2.265 2.264 39.499 40.310 41.937 42.754 0.673 0.687 0.714 0.728WT_ 500/356x16 2.343 2.343 2.341 2.340 40.917 41.701 43.276 44.068 0.697 0.710 0.737 0.751WT_ 500/203x25 1.924 1.923 1.922 1.921 45.881 46.838 48.761 49.727 0.781 0.798 0.831 0.847WT_ 500/229x25 2.000 2.000 1.998 1.997 49.196 50.118 51.971 52.901 0.838 0.854 0.885 0.901WT_ 500/254x25 2.077 2.076 2.074 2.074 52.269 53.158 54.945 55.842 0.890 0.905 0.936 0.951WT_ 500/279x25 2.153 2.152 2.150 2.150 55.124 55.983 57.708 58.574 0.939 0.954 0.983 0.998WT_ 500/305x25 2.229 2.228 2.227 2.226 57.784 58.614 60.282 61.119 0.984 0.998 1.027 1.041WT_ 500/330x25 2.305 2.304 2.303 2.302 60.268 61.071 62.686 63.496 1.026 1.040 1.068 1.081WT_ 500/356x25 2.381 2.381 2.379 2.378 62.593 63.371 64.935 65.721 1.066 1.079 1.106 1.119WT_ 500/406x25 2.534 2.533 2.531 2.531 66.823 67.556 69.029 69.768 1.138 1.151 1.176 1.188WT_ 500/450x25 2.665 2.664 2.662 2.662 70.068 70.766 72.168 72.872 1.193 1.205 1.229 1.241WT_ 500/305x32 2.254 2.254 2.252 2.251 70.612 71.437 73.095 73.927 1.203 1.217 1.245 1.259WT_ 500/330x32 2.331 2.330 2.328 2.328 73.736 74.535 76.141 76.947 1.256 1.269 1.297 1.311WT_ 500/356x32 2.407 2.406 2.404 2.404 76.662 77.437 78.993 79.775 1.306 1.319 1.345 1.359WT_ 500/406x32 2.559 2.558 2.557 2.556 81.992 82.722 84.189 84.925 1.396 1.409 1.434 1.446WT_ 500/450x32 2.690 2.689 2.688 2.687 86.084 86.780 88.178 88.880 1.466 1.478 1.502 1.514


Table 3.7


Designation






WT_ 610/127x6 1.886 1.885 1.884 1.883 11.400 12.573 14.929 16.113 0.194 0.214 0.254 0.274WT_ 610/152x6 1.962 1.961 1.960 1.959 12.248 13.376 15.641 16.779 0.209 0.228 0.266 0.286WT_ 610/127x10 1.899 1.898 1.896 1.896 14.658 15.825 18.168 19.345 0.250 0.270 0.309 0.329WT_ 610/152x10 1.975 1.974 1.973 1.972 16.016 17.138 19.392 20.523 0.273 0.292 0.330 0.350WT_ 610/178x10 2.051 2.050 2.049 2.048 17.273 18.354 20.524 21.614 0.294 0.313 0.350 0.368WT_ 610/203x10 2.127 2.126 2.125 2.124 18.440 19.482 21.576 22.627 0.314 0.332 0.367 0.385WT_ 610/229x10 2.203 2.203 2.201 2.200 19.526 20.533 22.555 23.570 0.333 0.350 0.384 0.401WT_ 610/152x16 2.000 1.999 1.998 1.997 23.409 24.519 26.750 27.870 0.399 0.418 0.456 0.475WT_ 610/178x16 2.076 2.076 2.074 2.073 25.599 26.669 28.819 29.899 0.436 0.454 0.491 0.509WT_ 610/203x16 2.153 2.152 2.150 2.150 27.633 28.666 30.742 31.784 0.471 0.488 0.524 0.541WT_ 610/229x16 2.229 2.228 2.227 2.226 29.529 30.527 32.533 33.540 0.503 0.520 0.554 0.571WT_ 610/254x16 2.305 2.304 2.303 2.302 31.299 32.265 34.206 35.180 0.533 0.550 0.583 0.599WT_ 610/279x16 2.381 2.380 2.379 2.378 32.956 33.892 35.771 36.715 0.561 0.577 0.609 0.625WT_ 610/305x16 2.457 2.457 2.455 2.454 34.510 35.417 37.239 38.154 0.588 0.603 0.634 0.650WT_ 610/330x16 2.534 2.533 2.531 2.531 35.971 36.851 38.619 39.507 0.613 0.628 0.658 0.673WT_ 610/356x16 2.610 2.609 2.608 2.607 37.347 38.201 39.919 40.781 0.636 0.651 0.680 0.695WT_ 610/203x25 2.191 2.190 2.188 2.188 41.024 42.043 44.092 45.121 0.699 0.716 0.751 0.769WT_ 610/229x25 2.267 2.266 2.265 2.264 44.113 45.099 47.081 48.076 0.751 0.768 0.802 0.819WT_ 610/254x25 2.343 2.342 2.341 2.340 47.001 47.956 49.876 50.839 0.801 0.817 0.849 0.866WT_ 610/279x25 2.419 2.419 2.417 2.416 49.707 50.634 52.494 53.428 0.847 0.862 0.894 0.910WT_ 610/305x25 2.496 2.495 2.493 2.492 52.249 53.147 54.952 55.858 0.890 0.905 0.936 0.951WT_ 610/330x25 2.572 2.571 2.569 2.569 54.639 55.512 57.264 58.145 0.931 0.945 0.975 0.990WT_ 610/356x25 2.648 2.647 2.646 2.645 56.892 57.740 59.444 60.299 0.969 0.983 1.012 1.027WT_ 610/406x25 2.800 2.800 2.798 2.797 61.030 61.833 63.446 64.256 1.039 1.053 1.081 1.094WT_ 610/450x25 2.931 2.930 2.929 2.928 64.238 65.006 66.549 67.324 1.094 1.107 1.133 1.147WT_ 610/305x32 2.521 2.520 2.519 2.518 63.776 64.669 66.463 67.363 1.086 1.101 1.132 1.147WT_ 610/330x32 2.597 2.596 2.595 2.594 66.780 67.648 69.390 70.265 1.137 1.152 1.182 1.197WT_ 610/356x32 2.673 2.673 2.671 2.670 69.613 70.456 72.151 73.002 1.186 1.200 1.229 1.243WT_ 610/406x32 2.826 2.825 2.823 2.823 74.820 75.619 77.225 78.032 1.274 1.288 1.315 1.329WT_ 610/450x32 2.957 2.956 2.954 2.953 78.861 79.626 81.163 81.934 1.343 1.356 1.382 1.396


Table 3.7


Designation






WT_ 750/127x6 2.227 2.227 2.225 2.224 11.787 14.239 15.470 0.201 0.243 0.263WT_ 750/152x6 2.304 2.303 2.301 2.301 12.497 14.867 16.058 0.213 0.253 0.274WT_ 750/127x10 2.240 2.239 2.238 2.237 14.547 16.987 18.212 0.248 0.289 0.310WT_ 750/152x10 2.316 2.316 2.314 2.313 15.709 18.069 19.254 0.268 0.308 0.328WT_ 750/178x10 2.392 2.392 2.390 2.389 16.797 19.082 20.230 0.286 0.325 0.345WT_ 750/203x10 2.469 2.468 2.466 2.466 17.817 20.033 21.145 0.303 0.341 0.360WT_ 750/229x10 2.545 2.544 2.543 2.542 18.776 20.926 22.005 0.320 0.356 0.375WT_ 750/152x16 2.342 2.341 2.339 2.339 22.029 24.367 25.542 0.375 0.415 0.435WT_ 750/178x16 2.418 2.417 2.416 2.415 23.954 26.219 27.357 0.408 0.447 0.466WT_ 750/203x16 2.494 2.493 2.492 2.491 25.760 27.958 29.062 0.439 0.476 0.495WT_ 750/229x16 2.570 2.570 2.568 2.567 27.460 29.594 30.665 0.468 0.504 0.522WT_ 750/254x16 2.646 2.646 2.644 2.643 29.062 31.135 32.176 0.495 0.530 0.548WT_ 750/279x16 2.723 2.722 2.720 2.720 30.574 32.590 33.602 0.521 0.555 0.572WT_ 750/305x16 2.799 2.798 2.797 2.796 32.004 33.966 34.951 0.545 0.579 0.595WT_ 750/330x16 2.875 2.874 2.873 2.872 33.358 35.269 36.228 0.568 0.601 0.617WT_ 750/356x16 2.951 2.951 2.949 2.948 34.642 36.504 37.439 0.590 0.622 0.638WT_ 750/203x25 2.532 2.531 2.530 2.529 37.377 39.548 40.639 0.637 0.674 0.692WT_ 750/229x25 2.608 2.608 2.606 2.605 40.169 42.279 43.338 0.684 0.720 0.738WT_ 750/254x25 2.685 2.684 2.682 2.682 42.803 44.854 45.884 0.729 0.764 0.782WT_ 750/279x25 2.761 2.760 2.758 2.758 45.291 47.287 48.289 0.771 0.805 0.822WT_ 750/305x25 2.837 2.836 2.835 2.834 47.645 49.589 50.565 0.812 0.845 0.861WT_ 750/330x25 2.913 2.912 2.911 2.910 49.877 51.770 52.721 0.850 0.882 0.898WT_ 750/356x25 2.989 2.989 2.987 2.986 51.994 53.841 54.768 0.886 0.917 0.933WT_ 750/406x25 3.142 3.141 3.139 3.139 55.921 57.680 58.563 0.952 0.982 0.997WT_ 750/450x25 3.273 3.272 3.270 3.270 58.999 60.689 61.538 1.005 1.034 1.048WT_ 750/305x32 2.862 2.862 2.860 2.859 57.841 59.773 60.743 0.985 1.018 1.035WT_ 750/330x32 2.939 2.938 2.936 2.936 60.651 62.534 63.479 1.033 1.065 1.081WT_ 750/356x32 3.015 3.014 3.012 3.012 63.318 65.155 66.077 1.078 1.110 1.125WT_ 750/406x32 3.167 3.166 3.165 3.164 68.268 70.019 70.898 1.163 1.193 1.208WT_ 750/450x32 3.298 3.297 3.296 3.295 72.151 73.834 74.679 1.229 1.258 1.272


Table 3.7


Designation








TECHNICAL GUIDE


4 SAMPLE DETAILS

4.1 Shear Connections

• SK-1.01 – SIN Beam to HSS Column

• SK-1.02 – SIN Beam to Wide Flange Column

• SK-1.03 – SIN Beam to SIN Beam

4.2 Moment Connections

• SK-2.01 – SIN Beam to Wide Flange Column

• SK-2.02 – SIN Beam to SIN Beam

4.3 Miscellaneous Details

• SK-3.01 – Web Openings

TECHNICAL GUIDE


5 REFERENCES / CERTIFICATION

5.1 CWB Certification for Steelcon - SIN Beam Welding

5.2 European Code 1993-1-5:2005 Annex D Plate Girders with

Corrugated Webs

5.3 Annex D – Commentary

5.4 Flange Buckling Behavior of H-Shaped Member with Sinusoidal

Webs - 2008

5.5 Plate Girders with Corrugated Webs from the Journal for Civil

Engineering and Management – 2010

5.6 Pages from CAN S136 – North American Specification for Design of Cold Formed Steel Members

5.7 Shear Load Testing Results of WT0330 beams

*

*

, CSA G40.21 44W, 50W

May 27, 2016

*

* CSA G40.21 44W, 50W

May 27, 2016

prEN 1993-1-5 : 2005 (E)

50

Annex D [informative] – Plate girders with corrugated webs D.1 General (1) Annex D covers design rules for I-girders with trapezoidally or sinusoidally corrugated webs, see Figure D.1.

x

z

α>30°

a3

2w

2s

Figure D.1: Geometric notations D.2 Ultimate limit state D.2.1 Moment of resistance (1) The moment of resistance MRd due to bending should be taken as the minimum of the following:

+

+γ

χ

+

+γ

+

+γ

=4444 34444 214444 34444 214444 34444 21

flangencompressio

21w

1M

yw11

flangencompressio

21w

0M

r,yw11

flangetension

21w

0M

r,yw22Rd 2

tthftb

;2

tthftb

;2

tthftb

minM (D.1)

where fyw,,r is the value of yield stress reduced due to transverse moments in the flanges fy,w,r = fyw fT

( )

0M

yf

zxT f

M4,01f

γ

σ−=

σx(Mz) is the stress due to the transverse moment in the flange

χ is the reduction factor for out of plane buckling according to 6.3 of EN 1993-1-1

NOTE 1 The transverse moment Mz results from the shear flow in flanges as indicated in Figure D.2.

prEN 1993-1-5 : 2005 (E)

51

NOTE 2 For sinusoidally corrugated webs fT is 1,0.

Figure D.2: Transverse moments Mz due to shear flow introduction into the

flange (2) The effective area of the compression flange should be determined from 4.4(1) and (2) using the larger value of the slenderness parameter pλ defined in 4.4(2) and the buckling factor kσ taken as:

a) 2

ab43,0k

+=σ (D.2)

where b is the maximum width of the outstand from the toe of the weld to the free edge

41 a2aa += b) 60,0k =σ (D.3)

where 2b

b 1=

D.2.2 Shear resistance (1) The shear resistance VRd should be taken as:

ww1M

ywcRd th

3

fV

γχ= (D.4)

where cχ is the lesser of the values of reduction factors for local buckling l,cχ and global buckling g,cχ obtained from (2) and (3)

(2) The reduction factor l,cχ for local buckling should be calculated from:

0,19,0

15,1,c

,c ≤λ+

=χl

l (D.5)

where 3

f

,cr

y,c

l

l

τ=λ (D.6)

2

max

w,cr a

tE83,4

=τ l (D.7)

amax should be taken as the greater of a1 and a2.

prEN 1993-1-5 : 2005 (E)

52

For sinusoidally corrugated webs l,crτ may be obtained from

2

w2

2

ww

3l,cr s

t)1(12

Ethsa

34,5

ν−π

+=τ (D.8)

where w length of one half wave, see Figure D.1, s unfolded length of one half wave, see Figure D.1. (3) The reduction factor g,cχ for global buckling should be taken as

0,15,0

5,12

g,cg,c ≤

λ+=χ (D.9)

where 3

f

g,cr

yg,c

τ=λ (D.10)

4 3zx2

wwg,cr DD

ht4,32

=τ (D.11)

( ) sw

112tED 2

3

x ν−=

wIE

D zz =

Iz second moment of area of one corrugation of length w, see Figure D.1

NOTE 1 s and Iz are related to the actual shape of the corrugation. NOTE 2 Equation (D.11) is valid for plates that are assumed to be hinged at the edges.

D.2.3 Requirements for end stiffeners (1) Bearing stiffeners should be designed according to section 9.

Commentary to EN 1993-1-5 First edition 2007

152

13 Annex D to EN 1993-1-5 – Plate girders with corrugated webs

Bernt Johansson, Division of Steel Structures, Luleå University of Technology

13.1 Background

This section will give background and justification of the design rules for girders

with corrugated webs. The rules have been developed during the drafting of

EN 1993-1-5 and the background has not been published. For this reason this

section will be quite detailed giving the reasoning behind the choice of design

rules for shear resistance.

Girders with corrugated webs are marketed as a product from specialised

fabricators or as one-off structures. One example of the former is Ranabalken,

which has been on the Swedish market for about 40 years [1]. Its main use is as

roof girder. It has a web geometry that is fixed because of the production

restraints. A vertical section through the web is shown in Figure 13.1. The

thickness of the web is minimum 2 mm, which is governed by the welding

procedure. The welding is single sided, which is important for the

competitiveness. The maximum depth is 3 m.

In Austria the company Zeman & Co is producing similar beams named Sin-beam

but with sinusoidally corrugated webs with the web geometry also shown in

Figure 13.1. The web depth is limited to 1500 mm and the web thickness is from 2

to 3 mm. The web has single sided welds.

140 50 50

380

70 70

50 40-43

155

Figure 13.1: Geometry of web plate of Ranabalken, Sweden and Sin-beam, Austria

Corrugated webs have been used for bridges in several countries, including

France, Germany and Japan. In France at least three composite bridges have been

built of which one was doubly composite with box section. The corrugated steel

web was provided with very small flanges, just enough for fixing the shear

connectors. The concrete slabs were post-tensioned and when it is important that

the steel flanges do not offer too much resistance to the imposed strains. A similar

but larger bridge has been built at Altwipfergrund in Germany. It is a three span

bridge built by cantilevering with a central span of 115 m and the depth varies

from 2,8 m in the span to 6 m at the intermediate supports. The use of single sided

welds is not recommended for bridges as it would cause problems with the

corrosion protection and the fatigue resistance is not documented.


153

13.2 Bending moment resistance

As the web is corrugated it has no ability to sustain longitudinal stresses. The

conventional assumption is to ignore its contribution to the bending moment

resistance. This is the basis for the rules in D.2.1. For a simply supported girder

supporting a uniformly distributed load the bending resistance is simply the

smallest axial resistances of the flanges times the distance between the centroids

of the flanges. This axial resistance may be influenced by lateral torsional

buckling if the compression flange is not braced closely enough. Reference is

given to the rules in 6.3 of EN 1993-1-1. There may be a positive influence of the

corrugated web on the lateral bucking resistance compared to a flat web as the

corrugation gives the web a substantial transverse bending stiffness. This should

reduce the influence of cross sectional distortion but this influence has not been

studied in detail and there is no basis for giving rules. There is also an increase in

warping stiffness that may be utilized.

!"#$%

a4

Figure 13.2: Geometry and notations for girders with corrugated webs

If there is a substantial shear force in the cross section of maximum bending

moment there may be an influence of the flange axial resistance from lateral

bending. Rules for this have been included in the German design rules [2]. A

model for calculating these secondary bending moments is shown in Figure 13.3.

The shear flow in the web will be constant V/hw and its effect can be modelled as

shown in the lower part of Figure 13.3. The maximum transverse bending moment

Mz,max occurs where the inclined part of the web intersects the centreline of the

flange. It becomes:

3,max 1 4(2 )

4z

w

VaM a a

h& ' ( 13.1)

where V is the coexisting shear force and other notations are according to Figure

13.2.

EN 1993-1-5, D.2.1


154

a3

z z

x

y

2

31

3

aa

h

VM

ah

VF

w

z

w

y

&

&

Figure 13.3: Action model for calculating secondary lateral bending moments in a flange caused by a corrugated web

In [2] the reduction of the bending resistance is expressed by the factor:

,max 0

2

61 0,4

z M

T

yf f f

Mf

f b t

(& ) ( 13.2)

This reduction is not large and actually it has not been considered in the Austrian

and Swedish design rules. From a theoretical point of view these bending

moments are required for reasons of equilibrium. However, it is questionable how

important they actually are in real life. They have been included just as a

precaution but for sinusoidially corrugated webs the factor is put to 1,0.

In case yielding of the flange governs the bending resistance becomes:

*+

,-.

/ ''

(&

2

tth

tbffM 21

w

0M

ffTyf

Rd ( 13.3)

where bftf should be taken as the smaller of b1t1 and b2t2.

Local flange buckling is of importance for the bending resistance. It will

obviously be influenced by the geometry of the web. The question is to define the

flange outstand c to be used for calculating the slenderness. There is little

information on this question in the literature. One of few published studies is by

Johnson & Cafolla [3] who suggested that the average outstand could be used if:

14,0)2(

)(

141

341 0'

'

baa

aaa ( 13.4)

where b1 is the width of the compression flange and other notations are according

to Figure 13.2. It is not stated what to do if this criterion is not fulfilled but

presumably the idea is to use the larger outstand. The average outstand was

defined as the average of the smaller and the larger outstand each calculated from

free edge to the toe of the weld.

EN 1993-1-5, D.2.1(2)


155

b1 c

a

Figure 13.4: Notations for flange geometry

The design rules for Ranabalken states that the outstand should be taken as half

the flange width minus 30 mm. This is actually smaller than the smallest outstand,

which seems quite optimistic. The corresponding rule for the Sin-beam is half the

flange width minus 11 mm.

The flange buckling may in general take place in two different modes. One

possibility is a plate type buckling of the larger outstand and another is a torsional

buckling where the flange rotates around the centreline of the web. General rules

without restrictions on the geometry have to consider both possibilities. The first

mode may be relevant for a long corrugation in combination with a narrow flange

for which the larger outstand will govern the buckling. However, the flange will

be supported by the inclined parts of the web. Assuming an equivalent rectangular

plate supported along three edges a safe approximation of the relevant length

should be a = a1 + 2a4, see Figure 13.2 and Figure 13.4. The buckling coefficient

of such a plate assuming conservatively a hinged support along the web is

approximately [4]:

k1 = 0,43 + (c/a)2 ( 13.5)

with:

c = largest outstand from weld to free edge

a = a1 + 2a4

For a geometry with small corrugations compared to the flange width the flange

will buckle in a mode of rotation around the centreline of the web. Then c is taken

to 0,5b. A corrugated web will however give a stronger restraint than a flat web.

The buckling coefficient ranges from 0,43 for simple support to 1,3 for fixed. A

solution for elastic rotational restraint is given in [4] but it is not easy to use. A

simplification in form of a reasonably conservative value is instead suggested, which is also used in [2]:

k1 = 0,60 ( 13.6)

The rules for flange buckling in 4.4 (1) and (2) of EN 1993-1-5 are used with the

buckling coefficients given above together with the relevant outstand c. In

general, both (13.5) and (13.6) have to be checked and the most unfavourable case

governs.


156

13.3 Shear resistance

13.3.1 Introduction

The shear resistance of corrugated webs has attracted interest from many

researcher. Accordingly, there are several proposals for the shear resistance e. g.

Leiva [5], Lindner [6], Höglund [7] and Johnson & Cafolla [8]. These will be

compared with 70 test results presented in Table 13.1. The formulae for the shear

resistance actually used in EN 1993-1-5 were developed during the evaluation.

This work was done in close co-operation with Professor Torsten Höglund of the Royal Institute of Technology, Stockholm. He was in charge of the corresponding

rules in EN 1999-1-1, which are now harmonized with EN 1993-1-5.

Notations for the corrugated web are shown in Figure 13.2. For the sinusoidally

corrugated web the measures a3 and 2w are relevant and the developed length of

one full wave is denoted 2s. For the trapezoidal web the following relations and

definitions apply.

a2 = a3/sin %

a4 = a3cot

w = a1 + a4

s = a1 + a2

tw = thickness of web

hw = depth of web

amax = max(a1,a2)

There are two shear buckling modes; one local governed by the largest flat panel

and one global involving one or more corrugations. The critical stress for local

buckling is taken as that for a long plate, which can be written as:

2

max

w,cr

a

tE83,4 2

3

456

7&8

( 13.7)

For a sinusoidally corrugated web the local buckling is less likely to occur. A

formula for critical shear stress for local buckling of webs with dimension as

given in Figure 13.1 can be found in [19] and reads:

22

3, 2

5,3412(1 )

wcr l

w w

a s tE

h t s

98

:/ , / ,& '- * - *) . +. +

( 13.8)

This formula was developed for the type of corrugation used in an Austrian girder

but it has turned out that the formula is not general enough and the formula may

give large errors if the dimensions are different to those given in Figure 13.1. For

this reason sinusoidially corrugated webs have to be designed by testing with

regard to local shear buckling where dimensions other than those given in Figure

13.1 are used. There is also a possibility to calculate the critical shear stresses for

local buckling with FEM and to use it in the design rules given here.

The critical stress for global buckling is given by [9]:

4 3

zx2

ww

g,cr DDht

4,32&8 ( 13.9)

EN 1993-1-5, D.2.2


157

where:

21

41

2

3

2

3

)1(12)1(12 aa

aaEt

s

wEtD ww

x '

'

)&

)&

:: ( 13.10)

41

21

2

3 3

12 aa

aaaEt

w

EID wz

z ''

&& ( 13.11)

The first versions of the formulae (13.10) and (13.11) are relevant for sinusoidally

corrugated webs where Iz is the second moment of area of one half wave. The

second versions are relevant for trapezoidally corrugated webs.

Both critical stresses are valid for simply supported long plates. The global

buckling stress is derived from orthotropic plate theory, see e. g. [9]. Some

authors have defined Dx without the factor (1-:2) in the denominator. It is

theoretically more correct to include it as in (13.10). In [9] there is also a solution

for restrained rotation along the edge. For fully clamped edges the coefficient 32,4

in (13.9) increases to 60,4. This has been used for evaluating tests e. g. in [5] but it

is hard to believe that this corresponds to the actual conditions at tests. The

flanges are not likely to be rigid enough to provide a rotational restraint for such a

stiff plate as a corrugated web. In this evaluation (13.9) will be used throughout.

Table 13.1: Data for test girders and test results (The shading shows the governing model and VR1 and VR2 are according to the

EN 1993-1-5 as described in 13.3.6)

Test

No original ref9

hw

mm

tw

mm

fyw

MPa

% a1

mm

a3

mm

Vu

kN

;u <1 <2 Vu/VR1 Vu/VR2%

0 L1A 5 994 1,94 292 45 140 48 280 0,860 0,931 0,558 1,370 0,860

1 L1B 5 994 2,59 335 45 140 48 502 1,007 0,747 0,556 1,442 1,007

2 L2A 5 1445 1,94 282 45 140 50 337 0,737 0,915 0,774 1,164 0,737

3 L2B 5 1445 2,54 317 45 140 50 564 0,839 0,741 0,768 1,197 0,839

4 L3A 5 2005 2,01 280 45 140 48 450 0,690 0,880 1,092 1,068 0,778

5 L3B 5 2005 2,53 300 45 140 48 775 0,881 0,724 1,067 1,244 0,962

6 B1 10 600 2,1 341 45 140 50 208 0,837 0,929 0,347 1,332 0,837

7 B2 10 600 2,62 315 45 140 50 273 0,954 0,716 0,315 1,340 0,954

8 B3 10 600 2,62 317 45 140 50 246 0,854 0,718 0,316 1,202 0,854

9 B4b 10 600 2,11 364 45 140 50 217 0,815 0,956 0,358 1,315 0,815

10 M101 10 600 0,99 189 45 70 15 53 0,817 0,734 0,750 1,160 0,817

11 M102 10 800 0,99 190 45 70 15 79 0,908 0,736 1,003 1,292 0,912

12 M103 10 1000 0,95 213 45 70 15 84 0,718 0,812 1,342 1,069 1,101

13 M104 10 1200 0,99 189 45 70 15 101 0,778 0,734 1,501 1,106 1,428

14 L1 11 1000 2,1 410 30 106 50 380 0,764 0,772 0,616 1,110 0,764

15 L1 11 1000 3 450 30 106 50 610 0,782 0,566 0,590 0,996 0,782

16 L2 11 1498 2 376 30 106 50 600 0,921 0,776 0,894 1,343 0,921

17 L2 11 1498 3 402 30 106 50 905 0,867 0,535 0,836 1,081 0,867

18 1 12 850 2 355 33 102 56 275 0,788 0,731 0,459 1,118 0,788

19 2 12 850 2 349 38 91 56 265 0,773 0,642 0,466 1,036 0,773

9 ref = bibliographical reference where the test results can be found


158

Test

No original ref9

hw

mm

tw

mm

fyw

MPa

% a1

mm

a3

mm

Vu

kN

;u <1 <2 Vu/VR1 Vu/VR2%

20 V1/1 13 298 2,05 298 45 144 102 68 0,646 0,917 0,099 1,021 0,646

21 V1/2 13 298 2,1 283 45 144 102 70 0,684 0,872 0,096 1,054 0,684

22 V1/3 13 298 2 298 45 144 102 81 0,789 0,940 0,100 1,262 0,789

23 V2/3 13 600 3 279 45 144 102 235 0,810 0,606 0,175 1,060 0,810

24 CW3 8 440 3,26 284 45 250 45 171 0,726 0,976 0,218 1,184 0,726

25 CW4 8 440 2,97 222 45 250 45 154 0,918 0,947 0,198 1,475 0,918

26 CW5 8 440 2,97 222 45 250 63 141 0,841 0,947 0,156 1,350 0,841

27 I/5 14 1270 2 331 62 171 24 260 0,535 1,223 1,483 0,987 0,963

28 II/11 14 1270 2 225 62 171 24 220 0,666 0,974 1,267 1,085 0,935

29 121216A 15 305 0,64 676 45 38 25 50 0,656 1,165 0,583 1,177 0,656

30 121221A 15 305 0,63 665 55 42 33 46 0,623 1,298 0,501 1,190 0,623

31 121221B 15 305 0,78 665 55 42 33 73 0,798 1,048 0,475 1,352 0,798

32 121232A 15 305 0,64 665 63 50 51 41 0,546 1,741 0,391 1,255 0,546

33 121232B 15 305 0,78 641 63 50 51 61 0,692 1,403 0,365 1,386 0,692

34 121809A 15 305 0,71 572 50 20 14 63 0,880 0,509 0,829 1,078 0,880

35 121809C 15 305 0,63 669 50 20 14 55 0,740 0,620 0,924 0,978 0,740

36 121832B 15 305 0,92 562 63 50 51 53 0,581 1,113 0,328 1,018 0,581

37 122409A 15 305 0,71 586 50 20 14 58 0,791 0,515 0,839 0,973 0,791

38 122409C 15 305 0,66 621 50 20 14 58 0,803 0,570 0,880 1,026 0,803

39 122421A 15 305 0,68 621 55 42 33 43 0,578 1,162 0,475 1,036 0,578

40 122421B 15 305 0,78 638 55 42 33 61 0,695 1,027 0,466 1,165 0,695

41 122432B 15 305 0,78 634 63 50 51 49 0,562 1,395 0,363 1,122 0,562

42 181209A 15 457 0,56 689 50 20 14 81 0,795 0,708 1,446 1,111 1,373

43 181209C 15 457 0,61 592 50 20 14 89 0,933 0,602 1,312 1,219 1,382

44 181216C 15 457 0,76 679 45 38 25 119 0,873 0,984 0,839 1,430 0,873

45 181221A 15 457 0,61 578 55 42 33 62 0,666 1,250 0,706 1,244 0,666

46 181221B 15 457 0,76 606 55 42 33 98 0,806 1,027 0,684 1,350 0,806

47 181232A 15 457 0,6 552 63 50 51 52 0,594 1,692 0,542 1,340 0,594

48 181232B 15 457 0,75 602 63 50 51 80 0,671 1,414 0,535 1,349 0,671

49 181809A 15 457 0,61 618 50 20 14 82 0,823 0,615 1,341 1,085 1,262

50 181809C 15 457 0,62 559 50 20 14 78 0,852 0,576 1,270 1,093 1,200

51 181816A 15 457 0,63 592 45 38 25 75 0,761 1,108 0,821 1,329 0,761

52 181816C 15 457 0,74 614 45 38 25 96 0,800 0,961 0,803 1,294 0,800

53 181821A 15 457 0,63 552 55 42 33 56 0,610 1,182 0,684 1,104 0,610

54 181821B 15 457 0,74 596 55 42 33 93 0,798 1,046 0,683 1,351 0,798

55 181832A 15 457 0,61 689 63 50 51 53 0,477 1,859 0,603 1,145 0,477

56 181832B 15 457 0,75 580 63 50 51 79 0,687 1,388 0,525 1,368 0,687

57 241209A 15 610 0,62 606 50 20 14 71 0,536 0,599 1,765 0,699 1,292

58 241209C 15 610 0,63 621 50 20 14 79 0,573 0,597 1,780 0,746 1,400

59 241216A 15 610 0,63 592 45 38 25 76 0,578 1,108 1,096 1,009 0,656

60 241216B 15 610 0,79 587 45 38 25 133 0,813 0,880 1,032 1,259 0,848

61 241221A 15 610 0,61 610 55 42 33 77 0,587 1,284 0,968 1,114 0,587

62 241221B 15 610 0,76 639 55 42 33 127 0,742 1,055 0,938 1,261 0,742

63 241232A 15 610 0,62 673 63 50 51 69 0,469 1,808 0,792 1,104 0,469

64 241232B 15 610 0,76 584 63 50 51 101 0,645 1,374 0,701 1,276 0,645


159

Test

No original ref9

hw

mm

tw

mm

fyw

MPa

% a1

mm

a3

mm

Vu

kN

;u <1 <2 Vu/VR1 Vu/VR2%

65 Gauche 16 460 2 254 30,5 0 126 139 1,029 1,494 0,121 2,142 1,029

66 Droit 16 550 2 254 30,5 0 126 109 0,675 1,494 0,145 1,405 0,675

67 Sin 1 17 1502 2,1 225 2w=155 40 370 0,902 0,433 1,108 1,046 1,038

68 Sin 2 17 1501 2,1 225 2w=155 40 365 0,890 0,433 1,108 1,032 1,025

69 Sin 3 17 1505 2,1 225 2w=155 40 353 0,859 0,433 1,108 0,996 0,989

Slenderness parameters are defined by:

3

yw

i

cri

f<

8& ( 13.12)

for i = 1,2,3 there 1 and 2 refers to equations (13.8) and (13.9) and 3 to equation

(13.14) below.

Values for the slenderness parameters <1 and <2 for the test girders are given in Table 13.1. The characteristic shear resistance is represented by:

ww

yw

R th3

fV ;& ( 13.13)

where ; is the minimum of the reduction values ;i determined for <1 and <2.

The ultimate shear resistance Vu in the tests can be transformed to the non-

dimensional parameter ;u by equation (13.13) and it is also given in Table 13.1.

The parameters defined above are general and will be used throughout the

analysis. The features of the different models will now be described briefly and

evaluated.

13.3.2 Model according to Leiva [5]

Leiva does not fully develop a design model but his main concern is the

interaction between local and global buckling, which is based on observations

from tests. His idea is to consider this interaction by defining a combined critical

stress 8cr3 as:

3 1 2

1 1 1n n n

cr cr cr8 8 8& ' ( 13.14)

Leiva discussed only in case n=1 but the equation has been written more general

for later use. He also considered yielding as a limit for the component critical

stresses in an attempt to make a design formula. The idea of Leiva will not be

evaluated but it will form the basis for a model that will be presented later called

"Combined model".

13.3.3 Model according to Lindner [6]

Lindner made an evaluation of test results 0 to 23 in Table 13.1. He discussed

different options for taking the interaction between local and global buckling into

account, including using (13.14) with n=2. His conclusions were however that the


160

interaction could be taken into account implicitly by correcting <2. Lindner’s model has been introduced in German recommendations [2]. The reduction factor

for the resistance:

,

0.588i L

i

;<

& ( 13.15)

is used for both local and global buckling. <1 is as defined in (13.12) but <2 is changed according to:

2

2

2

3

y

cr

f<

8& if 0.5< 8cr1/8cr2 < 2 ( 13.16)

The model has been evaluated with results shown in Figure 13.5 and in Table 13.2

where ;L is the smallest of ;=L and ;>L according to (13.15). The right hand

diagram in Figure 13.5 shows that the model has a slight bias with respect to <2. It is an under-prediction of the resistance that increases with the slenderness for

global buckling. Further the model includes discontinuities in the prediction

because of the stepwise correction in (13.15).

Figure 13.5: Test over prediction as function of <1 and <2 according to Lindner’s model

13.3.4 Model according to Johnson [8]

The model according to Johnson involves three separate checks; one for local

buckling, one for global buckling and one for combined local and global buckling.

The check for local buckling is done with the post-buckling resistance predicted

by:

1

1

0,84J;

<& < 1,0 ( 13.17)

For the global buckling the critical stress (13.9) is used but with a coefficient 36

instead of 32,4 and without (1-:2) in the denominator of Dx which gives more or

less the same results. The design strength is taken as 0,5 times the critical stress,

which includes a partial safety factor of 1,1. Considering theses differences the

characteristic reduction factor becomes:


161

2

2

2

61,0

<; &J ( 13.18)

if <2 is defined by (13.12) and (13.9).

Finally, the interaction between local and global buckling is considered with the

critical stress 8cr3 according to (13.14) with n=1. The resistance is taken as the

critical stress with a reduction factor 0,67?1,1, which leads to the reduction factor:

2

3

3

74,0

<; &J ( 13.19)

where <3 is defined by (13.12) and (13.14) with n=1.

The evaluation is shown in Figure 13.6 and Table 13.2. ;J is taken as the lowest value from the three separate checks. The right hand diagram depicting the

combined check shows a clear bias for under-prediction for high slenderness

values, which is caused by the use of reduced critical stresses as design strength.

The scatter in the quotient test over prediction shown in Table 13.2 is also fairly

high.

Figure 13.6: Test over prediction as function of <1 and <3 according to Johnson’s model

13.3.5 Combined model

The basic idea of this model was to define the resistance by a single reduction

factor. A reduced critical stress will be defined by (13.14) in order to take the

interaction between local and global buckling into account. This critical stress is

used to calculate the slenderness parameter <3 from (13.12). It is used in combination with the strength function:

3

1.2

0.9C; <&

'<1,0 ( 13.20)

The results for n=2 are shown in Table 13.2 and in Figure 13.7. Also n=4 has been

checked and the result is quite similar considering the statistical parameters. Both

alternatives represent a quite weak interaction and the interaction becomes weaker

the higher value of n is used. It can be seen that this model improves the

prediction. However, the model is symmetrical in the influence of local and global

buckling. It could be expected on theoretical grounds that the post-critical

resistance is more pronounced for local buckling than for global. In the latter case


162

it is questionable if there is any at all. On the other hand the influence of

imperfections in the range of medium slenderness can be expected to be smaller

than for local buckling. This became clear when the tests with sinusoidialy

corrugated webs were included in the comparisons, which was done quite late in

the work. This reasoning led to the model described in the next section.

Figure 13.7: Test over prediction as function of <" according to model Combined check, n=2

13.3.6 Model according to EN 1993-1-5

The model is based on the one proposed by Höglund [7]. It has two separate

checks, one for local and one for global buckling. It has been modified in [18] and

further modification has been done here as will be discussed below. The reduction

factors for local and global buckling, respectively, is given by:

0.19.0

15.1

1,1 0

'&

<; EN ( 13.21)

0.15.0

5.122

,2 @'

&<

; EN ( 13.22)

The reasoning behind the two checks is that the local buckling is expected to show

a post-critical strength, which should not be present in the global buckling. This is

reflected by <1 appearing linear and <2 is squared in the reduction factor. In [18] the reduction factor for local buckling has no plateau but the global buckling has

the same reduction factor as (13.17). There is however one more difference. The

restraint from the flanges to the global buckling is included in [18] and an increase

of the buckling coefficient to 40 is suggested if a certain stiffness criterion is met.

The predictions were compared with the test results in Table 13.1 and also with

some tests on aluminium girders. The prediction is marginally better than the one

using (13.21) and (13.22). The idea of increasing the global buckling coefficient

has also been discussed by Leiva and it may very well be true. It has however not

been included in the model in EN 1993-1-5 for simplicity and as an additional

safety measure. The reduction factors (13.21) and (13.22) are shown in Figure

13.9 together with the Euler curve and the von Karman curve.

There are no test results that make it possible to evaluate the length of the plateau

length for local buckling. Equation (13.21) has a plateau until <1 = 0.25, which is


163

very small compared to other buckling problems. For instance the design rules for

flat webs give < = 0.83 for the plateau length with A = 1. This question will remain unsettled until further experiments are available. It is believed that (13.21)

is conservative enough.

The evaluation results are found in Figure 13.8 and Table 13.2. The notation ;EN is the minimum of (13.21) and (13.22). The prediction is quite good with all the

results between 1 and 1,5, except for test 65, which stick out in all the evaluations.

Figure 13.8: Test over prediction according to the model in EN 1993-1-5

Figure 13.9: Reduction factors according to EN 1993-1-5; global buckling solid and local buckling dashed. As reference the Euler

curve 1/<> is shown as dash-dots and the von Karman curve 1/< as dots

Figure 13.10 shows the test results for which local buckling is supposed to govern

and Figure 13.11 there global buckling is supposed to govern. The predictions gives almost the same statistical characteristics, mean 1,22 and 1,23 with

coefficient of variation 0,15 and 0,14 for local and global buckling, respectively.


164

Figure 13.10: Reduction factor for local buckling together with 59 test results where local buckling is supposed to govern

Figure 13.11: Reduction factor for global buckling together with 11 test result where global buckling is supposed to govern

Table 13.2: Evaluation of design models showing mean value, standard deviation and coefficient of variation of the quotient

;u/;prediction

Model nLindner Johnson Combined

n=2

EN1993-1-5

Mean 1.48 1.62 1.26 1.22

Stand dev 0.34 0.65 0.19 0.18

Coeff of var 0.23 0.39 0.15 0.15


165

13.3.7 Discussion

The test data base is quite large and covers a range of parameters for instance:

190 < fy < 690 Mpa

140 < hw/tw <1200

30o < < 63

o

Most of the tests are normal I-girders tested in three or four point bending. The

exceptions are test 27 and 28, which were racking tests on container walls with an

unsymmetrical corrugation. The report included one more shear test that has been

discarded because the web was not continuously welded. Test 65 and 66 had a

triangular corrugation (a1 in Figure 13.2 equal to zero) and the girder had flanges of cold-formed channels. Test 65 showed a very high resistance compared to

prediction, which to some extent may have been influenced by the flanges

carrying some shear. However, it is not the whole truth as test 66 does not stick

out. The tests by Hamilton [15] included four more tests with the remark “support

induced failure”, which are not included in Table 13.1.

The normal procedure for dealing with buckling problems is to use the critical

stress for defining a slenderness parameter as in (13.12) and to find a reduction

factor that depends on this slenderness parameter. In all the models studied here a

post critical strength is recognized for the local buckling. It is however less

pronounced than for a flat web. This is likely to be so because the folds of the web

are less efficient in supporting tension fields than the flanges of a girder with a flat

web. One question is how small the angle between adjacent panels can be made before the fold becomes insufficient as a support for the panels. The smallest

angle in the tests is 30o. This has been taken as lower limit until further evidence

is available.

The next question is interaction between the two buckling modes. This has been

considered by most of the authors except Höglund. His reasoning is that the

interaction, if any, is so weak that two separate checks are sufficient. The

evaluation in Table 13.2 supports this opinion as the EN 1993-1-5 model based on

Höglund’s ideas, shows the lowest scatter. The suggestion of Lindner to increase

the slenderness parameter for global buckling if the critical stresses for local and

global buckling are close to each other is hard to justify and it creates an unnatural

discontinuity. Using (13.14) for defining a reduced critical stress would give a

continuous procedure that gives the highest interaction when the two critical

stresses are equal. This seems intuitively reasonable. It will however be

symmetrical in 8cr1 and 8cr2, which is not likely to be true as indicated in the discussion in 13.3.5. Because of this theoretical objection and that the prediction

of the test results is as good with the separate checks this was chosen.

For some low value of the slenderness the shear yield resistance of the web should

be reached. The test results do not indicate at which slenderness this will be safely

met. From Figure 13.10 it can be seen that the lowest slenderness there local

failure was governing is <==0.5. Judging from experiences of other plate buckling

phenomena (13.21) will be very safe with <=%= 0.25 for reaching the yield resistance as discussed in 13.3.6.

The design model presented in EN 1993-1-5 has been shown to be a step forward

compared to other existing or possible design models. It is certainly not the final


166

answer to the question of shear resistance of corrugated webs and future research

will hopefully improve the model.

13.4 Patch loading

No rules for patch loading resistance are given in EN 1993-1-5. The rules for flat

webs may be used but this is in most cases quite conservative, especially if the

loaded length is larger than one half corrugation w. The patch loading resistance

has been studied by several authors [10], [20], [21]. The results have however not

been collated and merged into a design model. In [1] the design rule for patch

loading includes only a check of the yield resistance. For sinusoidally corrugated

webs for the patch loading resistance has been studied in [22] and [23].

13.5 References

[1] Ranabalk. Produktbeskrivning och dimensioneringsregler (Specification and

design rules for Rana girder), Ranaverken AB, 2000

[2] DASt Richtlinien 015, Träger mit schlanken Stege, Stahlbau-Verlag, Köln,

1990

[3] Johnson, R., Cafolla, J., Local flange buckling in plate girders with

corrugated webs, Proceedings of the Institution of Civil Engineers

Structures & Buildings May 1997 pp 148-156.

[4] Timoshenko, S. P., Gere, J. M., Theory of elastic stability, Mc Graw-Hill,

Second edition New York 1961.

[5] Leiva, L., Skjuvbuckling av plåtbalkar med trapetsprofilerat liv. Delrapport

1. (Shear buckling of trapezoidally corrugated girder webs. Report Part 1.), Chalmers Univ. of Technology, Div. of Steel and Timber Structures Publ. S

83:3, Göteborg 1983 (In Swedish)

[6] Lindner, J:, Grenzschubtragfähigkeit von I-Trägern mit trapezförmig

profilierten Steg, Stahlbau 57 (1988) Heft 12 pp 377-380.

[7] Höglund, T., Shear Buckling Resistance of Steel and Aluminium Plate

Girders, Thin-walled Structures Vol. 29, Nos. 1-4, pp 13-30, 1997

[8] Johnson, R., Cafolla, J., Corrugated webs in plate girders for bridges,

Proceedings of the Institution of Civil Engineers Structures & Buildings

May 1997 pp 157-164.

[9] Peterson, J. M., Card, M. F., Investigation of the Buckling Strength of

Corrugated Webs in Shear, NASA Technical Note D-424, Washington 1960

(referred in [5])

[10] Bergfelt, A. , Edlund, B. & Leiva, L. , Trapezoidally corrugated girder

webs. Ing. et Architects Suisses, No.1-2, Januar 1985 pp 65-69

[11] Report No. RAT 3846 Technical Research Centre of Finland, Espoo 1983

[12] Kähönen, A., About the calculation procedure of steel I-beam with

corrugated webs. Master Thesis Lappeenranta University of Technology,

1983 (In Finnish)


167

[13] Scheer, J., Versuche an Trägern mit Trapezblechstegen, Bericht Nr. 8127,

Technische Univ. Braunschweig, Inst. für Stahlbau, Dezember 1984

[14] Leiva-Aravena, L., Trapezoidal corrugated panels, Chalmers Univ. of

Technology, Div. of Steel and Timber Structures Publ. S 87:1, Göteborg

1987

[15] Elgaaly, M., Hamilton, R., Seshadri, A., Shear strength of beams with

corrugated webs, Journal of the Structural Division, ASCE, 1996 122(4),

390-398

[16] Frey, F., Essai d´une poutre a ame plisse, Rapport interne No 64, Nov 1975,

Laboratoire de Mechanique des Materiaux et Statique de Constructions,

Université de Liège

[17] Pasternak, H., Branka, P., Zum Tragverhalten von Wellstegträgern,

Bauingenieur 73 (1988) Nr. 10, pp 437-444

[18] Ullman, R., Shear Buckling of Aluminium Girders with Corrugated Webs,

Royal Inst of Technology, Structural Engineering, TRITA-BKN Bulletin,

2002

[19] Pasternak H., Hannebauer D.: Träger mit profilierten Stegen,

Stahlbaukalender 2004, Berlin, Verlag Ernst & Sohn

[20] Leiva-Aravena, L.,Edlund, B., Buckling of Trapezoidally Corrugated Webs,

ECCS Colloqium on Stability of Plate and Shell Structures , Ghent

University, 1987.

[21] Elgaaly, M., Seshadri, A., Depicting the behaviour of girders with

corrugated webs up to failure using non-linear finite element analysis,

Advances in Engineering Software, Vol 29, No. 3-6, pp 195-208, 1998.

[22] Pasternak H., Branka P.: Zum Tragverhalten von Wellstegträgern unter

lokaler Lasteinleitung, Bauingenieur 74(1999) 219-224

[23] Novák, R., Machá ek, J., Design Resistance of Undulating Webs under

Patch loading, Proceedings of the third International Conference Coupled

Instability in Metal Stuctures CIMS´2000, Lisbon, Imperial College Press,

pp 371-378.

Fifth International Conference on Thin-Walled Structures Brisbane, Australia, 2008

FLANGE BUCKLING BEHAVIOR OF THE H-SHAPED MEMBER WITH SINUSOIDAL WEBS

Guo Yan-lin1, Zhang Qing-lin1, Walter Siokola2, Hofer Andreas2

1 Tsinghua University, Beijing, 100084, China 2Zeman GmbH, A-8811, Austrian

Abstract: This paper will present a study for structural behavior of corrugated web members in two aspects. One is to develop a computational model for sectional carrying capacity, and another is trying to find a rational limit of flange width-to-thickness ratios, which is different from H-shaped member with a flat web. Based on the sectional stress distribution obtained from FEM, it is concluded that the flanges will almost carry 100% sectional normal stresses resulting from axial forces and moments and web will almost carry 100% sectional shear force. Based on two different flange buckling modes observed from FE numerical studies in this paper, the flange buckling is also studied and a rational limit of flange width-to-thickness ratio is conducted. Finally the comparison between the results obtained from the FE analysis and the test carried out recently in Tsinghua University are given, and it is shown that both reach a good agreement.

Keywords: sinusoidal web beams, sectional stress distribution, flange buckling

1. INTRODUCTION

Corrugated web members, which are composed with flat flanges and corrugated webs through continuous welding, have shown their outstanding advantages, and they were used in civil buildings in the past years. As the corrugated web has a high critical load under shear force, even though very thin web is adopted, the H-shaped member with sinusoidal webs will still result in a significant increment of web height without local buckling. Therefore, their sectional capacity to resist moment will be increased greatly. Meanwhile, the web corrugation can greatly increase the out-of-plane stiffness of webs, which means the members have a higher out-of-plane stiffness to keep their shape unchanged during transporting and hoisting. All of these reasons come to the wide application of corrugated web members in portal frames, tier buildings and bridges, etc. H-shaped members with sinusoidal webs, the most frequently used types, considered to be more aesthetical and resistive to fatigue failure, will be introduced and studied in this paper.

Most of the scholars working on this area have laid their focus on the shear load carrying capacity of web, including Peterson and Cord(1960), Rothwell(1968), Sherman and Fisher(1971), Easley(1975), Libove(1977), Lindner(1988), Elgaaly(1990), Abbas(2006),etc. Some theoretical or semiempirical formulas were given to determine the elastic shear buckling load of the web. According to these formulas, the authors adopt some special configurations and section sizes used above, and the stress distribution on the sections will be studied. A simple approach to calculate the sectional strength of corrugated web members will be present here. Furthermore, the flange stability will be studied by finite element method and a rational limit value of flange width-to-thickness ratio will be conducted.

2. STRESS DISTRIBUTION AND SECTIONAL LOAD-CARRYING CAPACITY

2.1 Finite Element Simulations and Analysis

A finite element model of sinusoidal web member was developed by using the general purpose program ANSYS to investigate sectional stress distribution and load carrying capacity. The sectional model was used

to perform an elasto-plastic analysis. Reduced integration thin shell elements were used for the web and flanges. To exclude the effect of global member buckling, a short member, with slenderness less than 5 around the strong axis and 30 around the weak axis, was chosen. As can be noted from Fig. 1, the web configuration is sinusoidal with a half wave length l=155mm, wave magnitude f=20mm and the web thickness tw=2.5mm. The flanges are both 200mm wide by 10mm thick. The material is considered as elastic-perfectly plastic with initial elastic modulus (E) of 206,000MPa, Poisson’s ratio (v) of 0.3, and the yield stress (fy) of 300MPa. Different boundary conditions and load cases were considered to study the stress distribution.

Compared with the conventional flat web beam, H-shaped sinusoidal web members have shown distinct characteristic in stress distribution. Subjected to axial compression or bending, the sinusoidal web has a negligible longitudinal stress across the web section while the flat thin web will result in a significant stress distribution on the section, as shown in Fig. 2.

a-(I) b-(II) c -(I) d-(II) e-(I) f-(II)

longitudinal stress

under axial compression

longitudinal stress under bending

shear stress under shearing

Figure 1 Geometry of sinusoidal web beam Figure 2 stress distribution of sinusoidal web beam (I)

and conventional flat web beam (II) For the sinusoidal web member subjected to an axial compression or bending, the flanges carry over 99%

of the total load, which means the contribution of the corrugated web can be ignored. This is the most important character of stress distribution of corrugated web members. The main reason for that is due to the much smaller longitudinal stiffness of sinusoidal web compared with that of flanges. Subjected to axial forces, the sinusoidal web will produce a considerable moment at the transition part, and the rigid-body motion caused by the rotation of transition part makes the longitudinal deformation develop easily. The sinusoidal web, with the geometry as shown in Fig. 1, takes a longitudinal stiffness of only 1% of the flanges’, which can be obtained easily from FE numerical analysis.

For the flat web beam subjected to an axial compression or bending, the load carried by flanges accounts for 75% to 85% of the total, which is higher than the percentage of the flange area, 68%. Although the local buckling of the flat web occurs, it has still played a considerable part to take applied load.

When subjected to shear forces, the shear stress on the sinusoidal web is distributed uniformly, as shown in Fig. 2. e. It is much different from the flat web beam, which is as shown in Fig. 2. f. This distinct difference can be consulted as the second character of stress distribution of sinusoidal web members.

In order to determine stress distribution across the section easily, a computational model is developed as following:

When subjected to axial forces or bending moments, the sinusoidal web member can be treated as a lattice girder, in which only the flanges are available and the web can be ignored; when subjected to shear forces, only the web is available and the shear stress is distributed uniformly.

2.2 Test Investigation

A test program has been carried out, in which 6 series of total 18 tests have been finished in Tsinghua University recently. They include the axial compression tests, the eccentric compression tests, the bending tests and the shearing tests. All of these specimens were fabricated by Zeman GmbH in Austrian and transported to China by air or ship. The materials for the web and flanges are S235JR in accordance with EN 10 025 with a yield strength of 300MPa. The profiling of the web generally avoids the web failure due to loss of its stability before the plastic limit-loading is reached. All of the webs were connected to the flanges on one side of the web with continuous 3mm fillet welds automatically by robot. The designation of specimens followed the following rules:

Since the out-of-plane buckling of sinusoidal web members has been avoided by lateral braces, the

sectional ultimate strength only is considered in the analysis by using FE analysis. The applied loads listed in the Table 1 as Pcal are obtained directly from the most simplified calculated model mentioned above. Meanwhile, based on FE models with the same parameters of the test specimens, the more accurate results (PFE) will be obtained by using general purpose program ANSYS to perform a nonlinear finite element analysis. All of these results, including test results (Ptest), are listed below in Table 1, and all comparison reaches a good agreement between them.

Table 1 Comparison between tests, the simplified models and FE analysis

Load case section Length/m Ptest/kN PFE/kN Pcal/kN

1-1 WTA500-200×10 2 995a 1174 1200 Axial compression 1-2 WTA500-200×10 5 1132 1139 1200

2-1 WTA500-200×10 5 841 809 857 2-2 WTA500-200×10 5 588 577 600

Eccentric compression

2-3 WTA500-200×10 5 372 387 400 3-1 WTC500-200×10 5 165 170 172 3-point

bending 3-2 WTC750-250×12 7 248 255 259 4-1 WTA500-200×10 1.5 381 343 346 4-2 WTB500-200×10 1.5 477 431 433 4-3 WTB 750-250×12 1.5 648 643 649 4-4 WTC 750-250×12 1.5 777 766 779 4-5 WTB1000-300×12 2 857 841 866

shearing

4-6 WTC1000-300×12 2 988 1008 1039 a• the test loading head failed when the flanges still were kept perfect

As depicted in the simplified model, subjected to bending, the flexural modulus EIb of H-shaped members with sinusoidal webs can be calculated through assuming flanges to be the only effective parts. However, it must be noted that the shear stiffness of the sinusoidal web is not very high due to very thin web, therefore the effect of shearing deformation must be taken into consideration. The deflection of beam includes two parts: one deformation (b) caused by bending effects and another deformation (s) caused by shearing effects. A total elastic stiffness K0 based on a simplified calculation model reflecting both bending effect and shearing effect could be expressed by the applied load divided

0 10 20 30 40 50 60 70 800

40

80

120

160

200

Loa

d/kN

disp/mm

Test FEA total elastic stiffness K

0

bending stiffness Kb

yield

flange buckled

Figure 3: load versus deflection response.

by the total deformation value defined by b+s. The detail derivation of K0 is found in the reference [Driver(2006)].

The applied loads versus deflection curves are shown in Fig.3 where both the test results and the FEA results are included. The total elastic stiffness K0 and bending stiffness Kb are depicted in Fig.3 as slopes, too. The total elastic stiffness resulting from test and FEA results agree very well with K0 and varies a lot from bending stiffness Kb. This means that the shearing deformation could not be ignored even for long members when estimating beam deflection. The test setups and failure modes are as shown in Figure 4.

(c) bending test

(a) axial compression test (b) eccentric compression test (d) shearing test

Figure 4 test setups

2.3 Summary of Sectional Load Carrying Capacity

Many theoretical and experimental works have been done on the sectional load carrying capacity of H-shaped sinusoidal web members. The computational model proposed above is proved to be rational. Ostensibly, ignoring the web contribution to normal stress makes direct load carrying capacity of sinusoidal web beams lower than conventional flat web beams in the case of the same section sizes, but the benefit is that the sinusoidal web can make the section profile more efficient for carrying moments, namely by increasing web height even though using less web thickness. Although the theoretical comparison of sectional load carrying capacity in the case of the same section sizes between flat web and sinusoidal web can’t show the advantages of sinusoidal web members directly, the facts that such thin sinusoidal web beams can be transported and erected safely, and loaded to failure due to flanges yielding instead of web failure, can strongly prove them to be economical and efficient members.

3. STABILITY OF FLANGE

In conventional flat web beams, the flange stability can be assessed by assuming the flange to be plates simply supported on three sides. For a sinusoidal web beams, the boundary condition can not be simplified in this way. Many research works have been down on this topic these years. In BS EN 1993-1-5:2006, for trapezoidal web girders, a simple approach is proposed to determine the effective area of flange, which regards the buckling factor as the larger of 0.6 and 0.43+(b/a)2, where b is the maximum width of the outstand from the toe of the weld to the free edge and a is the distance between two adjacent peaks of corrugation. This approach certainly considers the flange stability in sinusoidal web girders to be much better than conventional flat web girders. However, Johnson (1997) has found that the critical load of flanges in trapezoidal web members may be lower than flat web member, and a function R is proposed to judge whether it is conservative to use the average outstand (the same with flat web members) to determine the critical loads.

All of these works mentioned above are based on the trapezoidal corrugated web members, and the obtained results can not be proved to be suitable for sinusoidal web beams. In this paper a simple model to investigate flange stability of sinusoidal web beams will be proposed and some suggestion about the maximum flange width-to-thickness ratio will be given.

3.1 Simplified Computational Model for Flange Buckling

Although the stiffness of sinusoidal web is neglectable in the action of longitudinal stress, the web can offer a strong support to flanges in the web depth direction, the flange can be treated as a plate simply supported on two loaded sides, only constrained at the web-flange joint in out-of-plane direction. This simplified computational model is depicted as follow in Fig. 5.

Figure 5: the simplified computational model for flange buckling

Two geometric coefficients are defined to describe the web profile, that is a coefficient of web amplitude

=f/b1, and other coefficient of web wavelength =l/b1. The general purpose program ANSYS is used to perform a parameter study of the critical load versus , and width-to-thickness ratio b1/t.

3.2 Critical Loads of Simplified Flange Model

Many numerical results reveal that whatever the web profile is, the critical loads decrease proportionally to the square of b1/t. Denoting the critical load of a plate simply supported on three sides as cr,1, and the critical load of a plate supported by the corrugated web shown in Fig. 5, as cr, the normalized critical loads cr=cr/cr,1 almost hardly change when b1/t varies alone. Because the influences of web profile and the influence b1/t to flange buckling are independent, so the effect of b1/t can be excluded when the influence of the web profile to flange buckling is only considered. This paper attempt to develop the relationship between , and cr , assuming b1/t always a constant.

(a) flange buckling mode I (b) sketch of flange buckling mode I

(c) flange buckling mode II (d) sketch of flange buckling mode II Figure 6 Two buckling modes of flanges

Two different buckling modes are observed as the web corrugation size changed. Buckling mode I is

found as shown in Fig. 6(a)(b) and described as: each longitudinal side of the flange deflects towards different directions and the deformed flange rim is like a single half-wave superimposing several small waves, which is dependant on the web corrugation size. Buckling mode II as shown in Fig. 6(c)(d) also may occur and it is similar to the buckling mode of a plate longitudinally clamped on one side. The deformed flange rim is a multi-wave profiling, generally not necessarily the same as the web corrugation wave shape.

It can be noted that for buckling mode I, the critical load decreases when the wave length of corrugation increases, regardless of the amplitude of corrugation or the whole length of the flange. The flange can be treated as a plate supported at the wave crests. The out-of-plane constrains between two adjacent wave crests

could not efficiently prevent the trend of a sinusoidal shape plate from buckling. It is to mean that, as the amplitude of corrugation increases, the flange plate loses the constrain provided by half a sinusoidal web at the other point of corrugation except two adjacent wave crest points. The flange buckles as a plate clamped at two wave crest points and free at other points, and its critical load could be calculated as:

2 2

2

12 2/

30.5

fcr

f

EI Et b

l A

(1)

In which EIf is the out-of-plane bending stiffness of the flange plate as a plate-column and Af is the area of flange.

The equation (1) is compared with the FE numerical results when =0.5, as shown in Fig. 7. When buckling mode I occurs, the results from equation (1) are quite close to the FE numerical results and a little lower. Therefore, the equation (1) could be able to evaluate the critical load of buckling mode I.

0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

cr

numerical results results from eq.(1)

buckling mode I

buckling mode I

Figure 7 comparison between Equation (1)

and FE numerical results Figure 8 comparison between Equation (3)

and FE numerical results

For buckling mode II, the flange could be equivalent to a plate supported at flange-web jointing line with a flexible rotational constrain, with the loaded sides simply supported and the other side free. The flexible constrain extent depends on web corrugation size, namely, l/f. The larger l/f, the weaker such constrain. On the other hand, comparing the critical loads of flange plates in the case of the same l/f and different , it can be noted that when l/f is big enough, the critical load is in inverse proportion to (1+)3. This is because the chosen calculation width should be taken as the maximum width of the outstand from the toe of the weld to the free edge, namely, b1(1+a), and the rotational constrain stiffness is a bit weaker. When l/f is smaller, the part of the flange width is constrained too firmly to take part in the buckling deformation, so the chosen calculation width should be taken as a smaller number, as b1(1+ a), where is a reduction factor to describe the decrease of the chosen calculation width. The value of was listed in table 2.

Table 2 value of

l/f 5 6 7 8 9 11 • 13 0 1/6 1/3 1/2 0.6 0.8 1.0

Denoting the critical load of a plate clamped on one side as cr,2, the critical load of buckling mode II is between cr,1 and cr,2, depending on the value of l/f. Considering the change of effective flange width, a fitting equation is proposed:

3 3,2 ,1 ,2 ,1

,1 ,12 2/ 1 / 11 / 1 /

cr cr cr cr

cr cr crc l f c

(2)

In which c is a constant of 0.0035. When the flange buckles, the buckling mode could be either mode I or mode II, depending on which one

has a lower corresponding critical load. Finally, the normalized critical load is

3

2

2

2.0121 / 1

min 1 /

8.56 /

cr c

(3)

The equation (3) is compared with FEA results, as shown in Fig. 8. The differences between them are less than 10% and the equation (3) is a little lower. Equation (3) is available when <=0.25 and l/f>=5, and it can be used to determine which buckling mode would occur.

3.3 Limit Ratio of Flange Width to Thickness in a Sinusoidal Web Member

As in the simplified computational model as shown in Fig.5 that is only a part of a sinusoidal web member, in reality, the boundary condition of flange is a little different from. First of all, the out-of-plane flexural rigidity of webs could offer flanges some extra rotational constrain. This may cause the flange critical load calculated by using the simplified computational model a little higher. Secondly, the web in the overall model is compressible in the direction of depth. The out-of-plane constrain offered by web is not perfectly rigid, which may cause the critical load a little lower. Finite element models of seven H-shaped members including two flanges and sinusoidal web with different web corrugations, were modeled using thin shell elements. Performing a linear buckling analysis by the program ANSYS, the critical load of these overall models were obtained and compared with the three-side simply supported plates in the case of the same b1/t, as cr,o. The normalized critical loads of the simplified models as shown in Fig.5, were obtained by FE analysis, denoted as cr,s. All of these results, together with the results from Equation (3), are listed in Table 3. These members are divided into 3 series, designated as A-*(buckling mode I controls), B-* (buckling mode II controls) and C-*(flat web).

Table 3 Comparison between equation (3) and FE numerical results

designation A-1 A-2 A-3 B-2 B-3 B-4 C-0 0.4 0.4 0.2 0.1 0.2 0.2 6 3 3 1.5 1.5 1

flat web

cr of equation (3) 0.238 0.951 0.951 1.597 2.109 2.85 1

cr,s 0.256 1.027 1.029 1.652 2.257 3.012 1

cr,o 0.6886 1.32 1.57 1.63 2.09 2.58 0.12*

—buckling mode I€ —buckling mode II€ *the flat web buckled

8 10 12 14 16 18 20 22 24 26

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

Fu/A

ff y

b1/t

A-1 A-2 A-3 B-1 B-2 B-3 C-0

Figure 9 Relationship of ultimate strength ratios versus b1/t

Furthermore, both geometric and material nonlinear analysis was performed and the ultimate strengths Fu

of these overall models were obtained. Setting b1/t as a variable, the ultimate strength ratio Fu/Af fy versus b1/t curves are depicted in Fig.9. When b1/t is small, the ultimate strength ratios of series A, whose buckling loads are controlled by buckling mode I, are obviously lower than others. It is recommended to adopt suitable web profiling to avoid buckling mode I, namely, to satisfy equation (4):

32

2

2.0128.56 / 1 / 1

1 /c

(4)

In Euro Code EN1993-1-1 and Chinese Code GB50017-2003, the maximum width-to-thickness ratios of flanges in flat web beams are limited to 15 to ensure the flange stability, in which

235 / yf (5) The maximum flange width-to-thickness ratios of sinusoidal web beams could be expressed as

1 / (max) 15b t (6) Where means the increase factor of b1/t in sinusoidal web members compared with flat web members,

based on the same critical load.

3

2

2.0121 / 1

1 /c

(7)

However, when cr of equation (3) is very high, the actual critical load of overall model may be lower than cr because of the compressibility of web in the depth direction. A square root is taken to to consider a reduction in equation (6). Usually the value of is between 1.00~1.75, so the maximum width-to-thickness ratio could be up to 20 . When a proper web profiling is adopted, the flange stability could be significantly increased due to the effect of the sinusoidal web.

4. CONCLUSION

A computational model for sectional load carrying capacity of a sinusoidal web member was proposed and was proved to be rational by both FE numerical analysis and test investigation. The sectional load carrying capacity and the deflection of beams could be easily obtained through this sectional model. Further more, based on two different flange buckling modes observed from numerical studies, the flange buckling was also studied and a rational limit of width-to-thickness ratios of flange was conducted. The research works are still on going in Tsinghua University and further research conclusions on the overall instability of a sinusoidal web member will be obtained recently.

REFERENCES

Corrugated Web Beam, Technical Documentation. Zeman & Co Gesellschaft mbH, 1999. Vienna, Austria

Driver, R.G. Abbas, H.H., and Sause, R., Shear Behavior of Corrugated Web Bridge Girders. Journal of Structure Engneering, ASCE. February 2006

Elgaaly, M. and Dagher, H. Beams and girders with corrugated webs. Proc., The Annual Technical Session, Structural Stability Res. Council (SSRC). Lehigh Univ., Bethlehem, Pa., 37-53

Elgaaly,M., Hamilton,R.W., Seshadri, Anand. Shear Strength of Beams with Corrugated Webs. Journal of Structural Engineering. April 1996

Eurocode 3–Design of steel structures–Part 1-5: Plated structural elements. BSEN 1993-1-5:2006

GUO Yan-lin, Zhang Qing-lin. Design Method of Section Bearing Capacity of H-Type Member of Corrugated Web. Journal of Architecture and Civil Engineering. 2006, 23(4) :58-63(in Chinese)

J. T. Easley, Buckling Formulas for Corrugated Metal Shear Diaphragms. Journal of the Structural Division, ASCE, No.ST7, July 1975: 1403–1417

Johnson, R.P. and Cafolla J. Local flange buckling in plate girders with corrugated webs. Proc. Instn Civ. Engrs Sructs & Bldgs, 1997, 122, May, 148-156

Smith, D. “Behavior of corrugated plates subjected to shear.” MSc thesis, Dept. of Cive Engr. Univ. of Maine, Orono, Minnesota, 1992.

JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 2010

16(2): 166–171

PLATE GIRDERS WITH CORRUGATED WEBS

Hartmut Pasternak1, Gabriel Kubieniec2

1, 2Brandenburg University of Technology, Konrad-Wachsmann-Allee 2, 03046 Cottbus, Germany E-mail: [email protected]; [email protected]

Received 25 Sept. 2009; accepted 20 Jan. 2010

Abstract. Especially for the main frames of single-storey steel buildings the use of corrugated web beams, mainly with sinusoidal corrugation, has been increased very much during the last years. Due to the thin web of 1,5 mm to 3 mm corru-gated web beams afford a significant weight reduction compared with hot rolled profiles or welded I-sections. Buckling failure of the web is prevented by the corrugation. The buckling resistance of presently used sinusoidal corrugated webs is comparable with plane webs of 12 mm thickness or more. Due to improvements of the automatic fabrication process cor-rugated webs up to 6 mm thickness became possible. Therefore the field of application of this beam type has been ex-tended considerable. Even short span bridges are possible now. The dimensioning of corrugated web beams is ruled by the EN 1993-1-5 Annex D – it covers only web thicknesses up to 3 mm. In the last years many tests and finite element simu-lations have been carried out. Regarding this background, these EN rules will be discussed and extended. Furthermore, additional proposals for patch loading and lateral-torsional buckling of girders with sinussoidal webs will be given. Keywords: plate girder, sinusoidal corrugated web, stability.

1. Introduction

Especially for the main frames of single-storey steel buildings the use of corrugated web beams, mainly with sinusoidal corrugation, has been increased very much during the last years (Fig. 1). Due to the thin web of 2 or 3 mm, corrugated web beams afford a significant weight reduction compared with hot rolled profiles or welded I-sections. Buckling failure of the web is prevented by the corrugation. The buckling resistance of presently used sinusoidal corrugated webs is comparable with plane webs of 12 mm thickness or more.

Fig. 1. Single-storey building

When corrugated web beam have been developed during the 60ies of last century, especially the profiling of the web and the welding was hand work. Due to the pro-gress of welding technology an automatic fabrication process became possible.

Since the end of the 80ies of last century corrugated web beams with sinusoidal corrugated webs are produced by an automated production process. In 1988 the first machine for the production SIN-beams were developed by ZEMAN, Austria. These semi-automatic machines of the first generation were able to produce SIN-beams with parallel flanges and a web thickness of 2.0 mm, 2.5 mm or 3.0 mm (Siokola 1997).

2. Automatic fabrication process

The machines of latest generation are able to produce SIN-beams by a fully automated process (Pasternak et al. 2008). A more variable design of cross sections, a variety of web thickness, lower beam heights and smaller flange dimensions became possible. Furthermore tapered beams and machine-made web openings can be produced.

Actually there are around 10 production lines around the world. The automatic production (Fig. 2) of the following beam dimensions is possible:

− Web height 333, 500, 625, 750, 1000, 1250 and 1500 [mm]

− Web thickness 1.5, 2, 2.5, 3, 4, 5, 6 [mm] − Flange thickness from 6 to 30 [mm] − Flange width from 120 to 450 [mm]

The maximum beam length of 16 m corresponds to the maximum range of welding robots. Usually beam are shorter because of the limits for the transport, galvanizing etc. For tapered beams the maximum length is 12 m. Due to improvements corrugated webs up to 6 mm thickness became possible. Therefore the field of application of this beam type has been extended considerable. Even short span bridges are possible now. The web material comes

JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT ISSN 1392–3730 print / ISSN 1822–3605 online http:/www.jcem.vgtu.lt doi:10.3846/jcem.2010.17 166

mailto:[email protected]

mailto:[email protected]

Journal of Civil Engineering and Management, 2010, 16(2): 166–171 167

from a coil. It is unrolled and cut to length automatically by the machine. A so called “corrugator” forms the sheet to a corrugated web. The flanges has been already pre-pared and stored in special flange baskets. After the run-ning-in of the web and flanges into the welding station all members are moved to the correct position, are pushed together and are welded by the welding robots.

Fig. 2. Automatic production process

3. Application examples

The basic areas of use of girders with sinusoidally corru-gated web are main single- or multi-span frames consisting of columns and rafters. In addition, there are also applica-tions in heavy industrial buildings. Fig. 3 shows a crane way column and Fig. 4 a Gerber hinge, used in a multi-span frame in a mill at Katowice, Poland (Pasternak, 2004). In the Innsbruck Stadium, Austria, extended for Euro 2008, 16 m long SIN beams are used as purlins (Fig. 5). Thanks to good distribution of mass within the cross-section, those girders can be characterised by high

Fig. 3. Crane way column

Fig. 4. Gerber hinge

Fig. 5. Roof structure of Innsbruck Stadium (Wimmer 2008)

bending capacity with relatively low self weight. In com-parison with traditional hot-rolled profiles, the reduction of self weight amounts even up to 40%.

4. Present state of codes

4.1. General

Actually beams with corrugated webs are ruled by the Euro-code EN 1993-1-5, Annex D (EC-3 2006). There used to be older standards as well, e.g. the German DASt-Ri 015 from 1990. But these standards deal about beams with trapezoidal corrugated webs only (EC-3 2006). Only by consideration of additional papers (Pasternak et al. 1998) and expert opinions (Pasternak et al. 1998, 2008), it became possible to use this document for the calculation of sinusoidal corrugated webs. The EN 1993-1-5 gives rules for both trapezoidal corruga-tion and sinusoidal corrugation. Whereas the dimensioning procedure for trapezoidal corrugated webs bases on the tests results for sinusoidal corrugated webs, the latest test results are not considered by the given rules. Therefore the calcula-tion procedure according to EN is comparatively conservati-ve. The bearing behaviour of a beam with corrugated web is comparable with a lattice girder. Normal force and bending moment are carried by the flanges only. Due to the corruga-tion the web is not able to carry any normal stresses in the longitudinal direction of the beam. Therefore the web is loaded by shear force only.

H. Pasternak, G. Kubieniec. Plate girders with corrugated webs 168

4.2. Bending moment resistance of flanges

To verify the bending moment capacity of a beam, the resistance of flanges against yielding and global and local buckling for the compression flange has to be taken into account. Lateral-torsional buckling of beam is verified by global out-of-plane buckling of the compression flange. The verification is a conservative assumption because the torsional stiffness is neglected. Local buckling of the flange (cross section class 4) is considered by the determi-nation of a reduced flange width. A reduced yield strength fyf.r considers the influence of transverse bending moments. These moments are caused by the shear flow longitudinal to the joint of flange / corrugated web. It has to be taken into account for trapezoidal corrugated webs. Actually produced sinusoidal corrugated webs have a small corruga-tion height compared with the width of flanges. Therefore the influence of transverse bending moments is negligible.

4.3. Shear force resistance of web

The web loaded by shear force can fail due to yielding, local buckling and global buckling. The EN 1993-1-5 defines the reduction factor for global web buckling as follows (Fig. 6):

12,5,0

5,1, ≤

λ+=χ

gcgc , (1)

where: is the reduction factor and gc,χ gc,λ the refer-ence slenderness for global web buckling.

Fig. 6. Global buckling curve: a – test, b – curve and results according to (Pasternak et al. 1996, 1998, 2008)

For local buckling the following reduction factor is defined:

1,9,0

15,1, ≤

λ+=χ

lclc , (2)

where: lc,χ is the reduction factor and lc,λ the reference slenderness for local web buckling.

5. Global and local buckling of web

For global web buckling the given rule matches the test results very well (Fig. 6). It was found by testing and FEM (e.g. Pasternak et al. 1998) that no local buckling occurs for all actually produced beams with sinusoidal corrugated webs. That means any reduction should be necessary for a reference slenderness smaller than 0,74 (area I of Fig. 7). A second reason for further research is the probably to large reduction factors for a reference slenderness greater than 1,5 (area II of Fig. 7). The reduc-tion curve shows overcritical reserves of bearing capac-ity. This behaviour is typical for plate buckling and there-fore understandable for trapezoidal corrugated webs that consist of plate elements. However, a sinusoidal corru-gated web is mainly a shell structure. The overcritical reserve of the reduction curve of EN 1993-1-5 has to be proved.

Fig. 7. Reduction curve for local buckling EN 1993-1-5

6. Lateral-torsional buckling

Concerning lateral-torsional buckling four tests and a large amount of FE simulations have been carried out (Hannebauer 2008). Tests and FE results in comparison with European buckling curves are given in Fig. 8.

7. Patch loading

In the parameter study girders with various forms of cor-rugation the patch load was investigated, the length and the amplitude of the wave were varied (Pasternak et al. 1989, 2004) (Fig. 9). From many series of FE simulations a simple approach of the ultimate load was developed

dyel

ult ftftI

WF ,

4,02

/10 ⋅⋅⋅⎟

⎠⎞

⎜⎝⎛= ⋅ , (3)


Fig. 8. Lateral-torsional buckling: a – test girder V6c, b – test and FEM in comparison with European buckling curves

where: Wel – effective section modulus of the flange; I – moment of inertia of a full wave about the horizontal axis of symmetry; t – web thickness; 2f, q– amplitude and length of the wave

12,2

3 2158,0 ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅=

qfqtI . (4)

The domain of definition is limited to 3 mm web thick-ness and 100 mm load distribution length. Analyzing a failure state (Kozlowski 2007), this formula gives reason-able ultimate loads. An extension of this formula to web thicknesses of 6 mm is necessary. 8. Interaction

First interaction diagrams between the bending moment and shear force resp. patch load are given in (Pasternak et al. 2004). 9. Present research

At the Universities of Technology in Cottbus and Braun-schweig there is carried out a research programme within the frame work of a national research project (AIF 2008). The main aim of the study is to describe influence of weld-ing process on carrying capacity of girder with sinusoidally corrugated web. The analysed girder was 7 m long beam

Fig. 9. Patch loading: a – test, b – FEM

Fig. 10. Welding simulation with flanges 25×200 [mm] and webs 3×500 [mm] (Fig. 10), loaded by two concentrated forces, each placed in distance 465 mm from a vertical axis of symmetry of girder. Two areas of investigations are distinguished i.e. local focused on welding simulations and global designed to describe behaviour of whole girder. The welding simu-lations showed that the average thickness of weld joining web and flange is about 2.8 mm and is accompanied by penetration of thermal source at width about 4 mm in every direction (Fig. 11). The residual stresses coming from wel-ding process are important parameter especially in nonlin-ear analysis that is why it should be carefully analysed. Strain gauge measurements (Fig. 12) showed highly non-linear normal stress distribution across the cross-section of flange especially in area of welding zone. This nonlinearity is much more visible in tension flange than in compression one, and can be an evidence of existing residual stresses coming from welding process which are superimposed with those from bending (Fig. 13 and 14). The comparison of diagrams representing dependence of normal stresses on

a) a)

b)

b)

H. Pasternak, G. Kubieniec. Plate girders with corrugated webs 170

Fig. 11. Test specimen

Fig. 12. Layout of gauges on flange (a) and web (b)

Fig. 13. Normal stress distribution in top flange

load for example in points 1 and 3 (Fig. 15) showed that in case of point 1 the curves run together parallel while in point 3 are clearly diverse. This can be a result of influ-ence of thermal residual stresses. Moreover there was described the width of web along which exist high normal stresses coming from bending. This width was estimated at 5 cm below the connection of the web and the flange (Fig. 16). That means that in very close vicinity of weld i.e. 50 mm there can be a superposition of normal stresses caused by welding and bending. The resultant normal stresses interact with those caused by shear force and there is a suggestion to subtract this area from shear area in design calculations. Additionally it has to be underli-ned that two effects i.e. increase of yield strength of ma-terial of web due to cold-forming process and existence of high normal stresses in mentioned above areas of web are not considered in actual design.

Fig. 14. Normal stress distribution in bottom flange

Fig. 15. Comparison of load-normal stress curve


Hannebauer, D. 2008. Zur Querschnitts- und Stabtragfähigkeit von Trägern mit profilierten Stegen. Dissertation, BTU Cottbus.

Kozlowski, A. 2007. Failure state of roof structure with corru-gated web´s girders. Awarie budowlane, Szczecin (in Po-lish).

Pasternak, H. 1996. Gutachterliche Stellungnahme zur Quer-krafttragfähigkeit von Wellstegträgern. Braunschweig/ Cottbus.

Pasternak, H.; Branka, P. 1998. Zum Tragverhalten von Wellstegträgern, Bauingenieur 73: 437–444.

Pasternak, H.; Branka, P. 1999. Tragverhalten von Wellsteg-trägern unter lokaler Last einleitung, Bauingenieur 74: 219–224.

Fig. 16. Normal stress in web Pasternak, H; Hannebauer, D. 2004. Träger mit profilierten Stegen, Stahlbau-Kalender 2004. Berlin, Verlag Ernst & Sohn, 449–492.

10. Conclusion

Pasternak, H.; Robra, J.; Bachmann, V. 2008a. Corrugated web beams with increased web thickness, in Proceedings 5thEuropea Conference on Steel and Composite Struc-tures, Graz, Austria 2008, 1161–1166.

EN 1993-1-5 Annex D rules have been discussed for actu-ally produced sinusiodal girders. For those girders do not appear local buckling effects before the web reaches its yielding shear capacity. The buckling curve should be improved. Furthermore, additional proposals for patch loading and lateral-torsional buckling of girders with si-nussoidal webs were given. Moreover tests showed nonlin-ear stress-strain relationship. This is a consequence of exis-tence of thermal fields and initial stresses coming from welding of web to flanges and also from cold-forming process of web. These aspects are studied in a national research project, carried out in Cottbus and Braunschweig.

Pasternak, H. 2008b. 2nd expert opinion on the shear capacity of girders with sinusoidally corrugated web. Braunschweig/ Cottbus 2008.

Siokola, W. 1997. Wellstegträger. Herstellung und Anwendung von Trägern mit profiliertem Steg, Stahlbau 66: 595–605.

Wimmer, A., et al. 2008. Stadion Innsbruck „Tivoli neu“ für Euro 2008 erweitert, Bauingenieur 83: 405–409.

Yan-lin, G.; Qing-lin, Z.; Siokola, W.; Hofer, A. 2008. Flange buckling behaviour of the H-shaped member with sinu-soidal webs, in Fifth International Conference on Thin-Walled Structures, Brisbane, Australia, 2008.

References

Eurocode 3 – Design of steel structures – Part 1–5: Plated structural elements, Annex D, European committee for standardisation (CEN): 2006.

AIF Einsatz der Schweißsimulation zur systematischen Entwicklung verbesserter Modelle für die Berechnung der Tragfähigkeit komplexer Stahlleichtbaustrukturen P 785/ 08/2008 / IGF-Nr. 287 ZBG.

SUDĖTINĖS SIJOS SU GOFRUOTĄJA SIENELE

H. Pasternak, G. Kubienec

S a n t r a u k a

Pastaruoju metu ypač vienaukščių pastatų plieniniams rėmams imtos plačiai naudoti sijos su pagal sinusoidę banguota sie-nele. Dėl plonų 1,5–3,0 mm storio gofruotųjų sijų sienelių jų masė gerokai sumažėja, palyginti su karštai valcuotomis arba virintinėmis dvitėjo skerspjūvio sijomis. Sijos sienelės klumpamosios irties išvengiama dėl sienelės bangavimo. Šiuo metu naudojamų pagal sinusoidę subanguotų sienelių klumpamoji galia yra lygintina su 12 mm arba didesnio storio plokščių sienelių galia. Patobulinus automatinį gaminimo procesą gofruotąją sienelę galima padaryti iki 6 mm storio. Todėl labai išsiplečia šių sijų naudojimo sritys. Sijos gali būti naudojamos nedidelio tarpatramio tiltams. Banguotasienių sijų projek-tavimo metodika aprašyta EN 1993-1-5 D priede, tačiau ji galioja tik sijoms, kurių sienelės storis neviršija 3 mm. Pastarai-siais metais atlikta daug bandymų ir skaitinių eksperimentų baigtinių elementų metodu. Todėl šios EN projektavimo nuo-statos bus aptariamos ir išplėstos. Be to, straipsnyje pateiktos papildomos rekomendacijos, kaip vertinti sijų su pagal sinusoidę banguota sienele uždėtąją apkrovą ir lenkiamąjį sukamąjį klupumą.

Reikšminiai žodžiai: sudėtinės sijos, pagal sinusoidę banguota sienelė, pastovumas.

Prof. Hartmut PASTERNAK is involved in teaching, research and design of steel structures for more than 20 years. He is member in several National and International Committees (e.g.full member of the ECCS Technical Committee 8 “Structural Stability”, member of German subcommittee DASt-Ri015 “Girders with thin webs”, member of COST C25 action “Sustainability of Constructions”, member of the working group Eurocode 3 “Cranesupporting structures”). He has participated in numerous research projects (e.g. on thin-walled members and sheeting). Under his supervision 8 PhD´s were completed. He has several publications in Journals and at Conferences (more than 100) and is co-author of books in German (4) and English (1) on steel structures. Moreover he is the editor of the journal “Bauingenieur” for steel structures.

Gabriel KUBIENIEC is a scientific assistant at the Brandenburg University of Technology Cottbus in Germany since 2009. He got PhD in 2009. His research interests include the behavior of thin-walled steel structures. He has 12 publica-tions in Journals and at Conferences.

63 Coe Dr Ajax, Ontario L1T 3J1

November 18, 2015

Steelcon Fabrication

Re: SIN Beam Shear Testing

1 INTRODUCTION

The SIN beam is welded wide flange steel beam with a sinusoidal corrugated web.

Over the past 20 years extensive testing has been done on corrugated web beams including the

SIN beam worldwide but the product is new to Canada. The purpose of this testing wa

the shear capacity formula provided in EN

for the design of corrugated web plate girders.

2 DESIGN PROCEDURE

Details on the shear design procedure

Technical Guide.

Based on S136 Rational Engineering

calculated using the shear design formula found in the European steel code (which does not

include a safety factor) and then multiplied by a material resistance factor of 0.75

A1.2b).

A WT0 330 /152x12 beam was chosen

the beam will fail in shear before

attached to this document and results in the following beam shear capacity

�� 0.75

Based on this calculation the anticipated shear capacity

the beam will fail) is 94.7 kN [21.3 kip]

3 TESTING

Testing was done in the Aucren Lab in Mississauga, Ontario, on September 15, 2015.

The load testing was done using a Riehle Universal Testing Machine which can exert 120,000lbf

of force between the upper and lower portions of the machine. In order to

a shear failure a 6’ long W8 support beam was placed across the base of the testing machi

support the SIN beam member. The SIN beam flanges were sized to ensure that the beam

63 Coe Dr Ajax, Ontario L1T 3J1 416-659-2222 [email protected]

STRUCTURAL CONSULTING | VANEEENGINEERING.CA

SIN Beam Shear Testing



SIN beam worldwide but the product is new to Canada. The purpose of this testing wa

the shear capacity formula provided in EN-1993-1-5 Annex D the European steel design code

for the design of corrugated web plate girders.

procedure / formula used by Steelcon is contained in

ngineering Analysis the shear capacity of the SIN beam can be


include a safety factor) and then multiplied by a material resistance factor of 0.75

WT0 330 /152x12 beam was chosen for testing. The test parameters were setup such that

before it fails in bending. The detailed shear design

d to this document and results in the following beam shear capacity:

75 ∗ 94.70��21.29�� 71.0��15.97��

Based on this calculation the anticipated shear capacity of the beam (i.e. the beam shear at which

is 94.7 kN [21.3 kip].


ne using a Riehle Universal Testing Machine which can exert 120,000lbf

of force between the upper and lower portions of the machine. In order to load the beam

a 6’ long W8 support beam was placed across the base of the testing machi


[email protected]


15022



SIN beam worldwide but the product is new to Canada. The purpose of this testing was to verify

5 Annex D the European steel design code

/ formula used by Steelcon is contained in the SIN beam

f the SIN beam can be


include a safety factor) and then multiplied by a material resistance factor of 0.75 (S136 Section

eters were setup such that

The detailed shear design calculation is

(i.e. the beam shear at which


ne using a Riehle Universal Testing Machine which can exert 120,000lbf

load the beam to get

a 6’ long W8 support beam was placed across the base of the testing machine to


November 18, 2015


would fail in shear before failing in bending. The testing configuration is indicated in attached

sketch SK01 and Photo-01.

The load was applied through 2

were provided at the loading point as well as

During testing the beam was loaded to failure. A dial gauge was used to measure the beam

deflection during testing and readings were taken every 5000 lbs

loading the beam continued to deflect and resist approximately 75% of the maximum load but no

further measurements were recorded.

The maximum loads supported by the 3 beams

way the beam is loaded the maximum beam shear is ½ of the load supported.

Beam 1

Beam 2

Beam 3

Average

Full testing results and additional

testing report attached to this document.


416-659-2222 [email protected]



The load was applied through 2-8”x8” plates on top of the SIN beam and additional

were provided at the loading point as well as the supports to resist any local / bearing failures.


deflection during testing and readings were taken every 5000 lbs. After reaching the maximum


further measurements were recorded.

imum loads supported by the 3 beams are given in the following table. Because of the


Load Supported Beam Shear

48538 lbf 24.27 kip [107.95 kN]

48449 lbf 24.22 kip [107.76 kN]

44074 lbf 22.04 kip [98.03 kN]

23.51 kip [104.58 kN]

additional photos of the beam shear failure are included in the Acuren

testing report attached to this document.

Sketch SK01 – Testing Setup

Page 2 of 3


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additional stiffeners

supports to resist any local / bearing failures.


After reaching the maximum


are given in the following table. Because of the


are included in the Acuren

November 18, 2015


4 CONCLUSIONS

Each of the three test results had a shear capacity which exceeded the

The average test result was 110%

minimum test result was 104% of the calculated shear capacity (

Based on the testing results the European code formula for the shear capacity

web steel beam is an accurate calculation of the beam

not however overly conservative such that

design shear resistance if additional testing were done for each beam size and web thickness.

Sincerely,

Van Ee Engineering Inc.

Derek Van Ee, P.Eng.

Encl: Acuren Testing Report

WT0 330 Shear Design Calculation


416-659-2222 [email protected]


Photo 01 – Testing Setup

Each of the three test results had a shear capacity which exceeded the European code formula

The average test result was 110% of the calculated shear capacity (104.6kN vs

104% of the calculated shear capacity (98.0kN vs 94.7

testing results the European code formula for the shear capacity

web steel beam is an accurate calculation of the beam shear capacity. The European formula is

conservative such that there would be a significant increase in


WT0 330 Shear Design Calculation

Page 3 of 3


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CONSULTING | VANEEENGINEERING.CA

European code formula.

kN vs 94.7kN). The

vs 94.7kN).

testing results the European code formula for the shear capacity of a corrugated

The European formula is

increase in the beam


2015Nov18


SIN Beam Shear TestWT0 330 Shear Design

Project No:Date:

150222015-11-02

Shear Capacity - Per CSA S136 / EN 1993-1-5:2006 Annex D clause 2.2

≔hw 330 ≔tw 1.519 ≔a3 40 ≔fyw 350 ≔w ――155

2≔E 200 ≔ν 0.3 ≔ϕs.shear 0.75≔γm1 1.0 Partial Factor EN1993-1-1:2005 cl 6.1

≔s =―1

2

⌠⎮⎮⌡

d

0

2 w

‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾

+1⎛⎜⎝

⋅――⋅a3

2 wsin

⎛⎜⎝―――

⋅⋅2 x

2 w

⎞⎟⎠

⎞⎟⎠

2

x 88.985 =2 s 177.97

≔Iz =―1

2

⌠⎮⎮⌡

d

0

2 w

⎛⎜⎝

+⋅―1

12tw

3⋅tw⎛⎜⎝

⋅―a3

2sin

⎛⎜⎝―――

⋅⋅2 x

2 w

⎞⎟⎠

⎞⎟⎠

2 ⎞⎟⎠x 2.357

4

≔τcr.l =⋅⋅⎛⎜⎝

+5.34 ――⋅a3 s

⋅hw tw

⎞⎟⎠

――――⋅

2E

⋅12 ⎛⎝ −1 ν2 ⎞⎠

⎛⎜⎝―tw

s

⎞⎟⎠

2

⎛⎝ ⋅655.292 103 ⎞⎠

≔λc.l =‾‾‾‾‾‾‾―――fyw

⋅τcr.l ‾‾3⋅555.311 10

−3

≔χc.l =min⎛⎜⎝

,1 ―――――1.0

⎛⎝ +0.5 λc.l⎞⎠1.25

⎞⎟⎠

⋅934.92 10−3

≔Dz =――⋅E Izw

60.818 ⋅

≔Dx =⋅――――⋅E tw

3

⋅12 ⎛⎝ −1 ν2 ⎞⎠

―w

s

⎛⎝ ⋅55.907 10−3⎞⎠ ⋅

≔τcr.g =⋅―――32.4

⋅tw hw2

‾‾‾‾‾‾4

⋅Dx Dz3 ⎛⎝ ⋅2.074 10

6 ⎞⎠

≔λc.g =‾‾‾‾‾‾‾‾―――fyw

⋅τcr.g ‾‾3⋅312.124 10

−3

≔χc.g =min⎛⎜⎝

,――――1.5

+0.5 λc.g2

1⎞⎟⎠

1

≔χc =min ⎛⎝ ,χc.l χc.g⎞⎠ ⋅934.92 10−3

≔V =⋅⋅⋅χc ―――fyw

⋅γm1 ‾‾3hw tw 94.701 =V 21.29

≔Vr =⋅ϕs.shear V 71.026 =Vr 15.967

corrugated web steel beam · 3.1 bending capacity – laterally supported 3-1 3.2 bending capacity...

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