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Steel Frame Design ManualAPI RP 2A WSD 21st

API RP 2A-WSD 21st Steel Frame Design Manual

for

ISO SAP102816M10 Rev. 0 October 2016 Proudly developed in the United States of America

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THIS PRODUCT IS A PRACTICAL AND POWERFUL TOOL FOR STRUCTURAL DESIGN. HOWEVER, THE USER MUST EXPLICITLY UNDERSTAND THE BASIC ASSUMPTIONS OF THE SOFTWARE MODELING, ANALYSIS, AND DESIGN ALGORITHMS AND COMPENSATE FOR THE ASPECTS THAT ARE NOT ADDRESSED.

THE INFORMATION PRODUCED BY THE SOFTWARE MUST BE CHECKED BY A QUALIFIED AND EXPERIENCED ENGINEER. THE ENGINEER MUST INDEPENDENTLY VERIFY THE RESULTS AND TAKE PROFESSIONAL RESPONSIBILITY FOR THE INFORMATION THAT IS USED.

Contents

1 Introduction 1

1.1 Units 1

1.2 Axes Notation 1

1.3 Symbols 1

2 Member Design 4

2.1 Safety Factors 4

2.2 Tension Check 4

2.3 Compression Check 5

2.4 Flexure Check 5

2.5 Shear Check 6

2.6 Hoop Buckling Check 6

2.7 Axial Tension and Bending Check 7

2.8 Axial Compression and Bending Check 7

3 Joint Design 9

3.1 Joint Geometry 9

3.2 Punching Shear Method 10

3.2.1 Design Loads 10 3.2.2 Allowable Stresses 10 3.2.3 Axial and Bending Check 11 3.2.4 Overlapping Joints 12

3.3 Nominal Load Method 12

i

Steel Frame Design API RP 2A-WSD 21st Introduction

3.3.1 Allowable Capacities 12 3.3.2 Axial and Bending Check 13 3.3.3 Overlapping Joints 13

4 Supplements 2 and 3 14

4.1 Joint Design 14

4.1.1 Allowable Capacities 14 4.1.2 Axial and Bending Check 16 4.1.3 Overlapping Joints 16

5 References 17

Units ii

1 Introduction

This manual describes the steel frame design algorithms in the software for API Recommended Practice 2A-WSD 21st Edition (American Petroleum Institute, 2000). The design algorithms in the software for API RP 2A-WSD 21st cover allowable stress checks for typical structural elements used in offshore steel structures, as detailed in this manual. Such elements are tubular members and tubular joints. For other types of structural elements, the software uses AISC ASD 9th Edition. Requirements of the code not documented in this manual should be considered using other methods.

This manual documents the design details for cylindrical sections having thickness t ≥ 6mm, D/t < 300. Members of other section shapes are designed in accordance with AISC ASD 9th Edition (American Institute of Steel Construction, 1989).

It is important to read this entire manual before using the design algorithms to become familiar with any limitations of the algorithms or assumptions that have been made.

1.1 Units

The API RP 2A-WSD design code is based on kip, inch, and second units and as such, so is this manual, unless noted otherwise. Any units, imperial, metric, or MKS may be used in the software in conjunction with API RP 2A-WSD design.

1.2 Axes Notation

The software analysis results refer to the member local axes system, which consists of the 2-2 axis and the 3-3 axis. The API RP 2A-WSD design code refers to x-x and y-y axes, which are equivalent to the software 3-3 and 2-2 axes, respectively. These notations may be used interchangeably in the design algorithms, although every effort has been made to use the design code convention where possible.

1.3 Symbols

The following table provides a list of the symbols used in this manual, along with a short

Units 1


description. Where possible, the same symbol from the design code is used in this manual.

A Cross sectional area, in2

C Critical elastic buckling coefficient

Ch Critical hoop buckling coefficient

Cm Reduction factor

D Outside diameter, in

E Young’s modulus of elasticity, ksi

fa Design tensile stress, ksi

Fa Allowable compressive stress, ksi

fb Design bending stress, ksi

Fb Allowable bending stress, ksi

Fe’ Euler stress, ksi

fh Hoop stress due to hydrostatic pressure, ksi

Fhc Critical hoop buckling stress, ksi

Fhe Elastic hoop buckling stress, ksi

Ft Allowable tensile stress, ksi

fv Design beam shear stress, ksi

Fv Allowable beam shear stress, ksi

fvt Design torsional shear stress, ksi

Fvt Allowable torsional shear stress, ksi

fx Design compressive stress, ksi

Fxc Inelastic local buckling stress, ksi

Fxe Elastic local buckling stress, ksi

Fy Yield strength, ksi

g Gap distance, in

Ip Polar moment of inertia, in4

K Effective length factor

l Unbraced length, in

l Circumference of brace contact with chord, neglecting overlap, in

L Length between stiffening rings, diaphragms, or end connections, in

l1 Circumference of brace portion that contacts the chord, in

l2 Projected chord length of overlapping weld, in

M Bending moment, kip-in

M Geometric parameter

Symbols 2


Ma Allowable brace bending moment, kip-in

Mt Torsional moment, kip-in

p Hydrostatic pressure, ksi

P Axial force, kip

Pa Allowable brace axial load, kip

Pper Brace axial load component perpendicular to the chord, kip

P⊥ Allowable axial load component perpendicular to the chord, kip

Qf Chord load factor

Qg Gap factor

Qu Ultimate strength factor

Qβ Geometric factor

r Radius of gyration, in

SFb Safety factor for bending

SFh Safety factor against hydrostatic collapse

SFx Safety factor for axial force

t Wall thickness, in

tw Minimum of the weld throat thickness and thinner brace thickness, i V Transverse shear force, kip

vp Acting punching shear stress, ksi

Vp Acting punching shear, kip

vpa Allowable punching shear stress, ksi

vwa Allowable shear stress of weld between braces, ksi

ν Poisson’s ratio

θ Angle between the chord and the brace

Symbols 3

2 Member Design

This chapter provides the details of the structural steel design and stress check algorithms that are used for cylindrical member design and checking at each output station in accordance with API RP 2A-WSD.

Cylindrical members subjected solely to axial tension, axial compression, bending, shear, or hydrostatic pressure are designed in accordance with API RP 2A-WSD Sections 3.2.1 to 3.2.5, respectively. Cylindrical members subjected to combined loads without hydrostatic pressure are designed in accordance with API RP 2A-WSD Sections 3.3.1 and 3.3.2. Cylindrical members subjected to combined loads with hydrostatic pressure are designed in accordance with API RP 2A-WSD Sections 3.3.3 and 3.3.4.

2.1 Safety Factors

The safety factors used in calculating allowable stresses in the following sections are defined as:

Table 1 - Safety factors

Loading

Design Condition Axial Tension

Axial Compression

Bending Hoop Compression

Basic allowable stresses 1.67 2.0 𝐹𝐹𝑦𝑦 𝐹𝐹𝑏𝑏⁄ 2.0 One-third increase in allowable

stresses is permitted 1.25 1.5 𝐹𝐹𝑦𝑦 (1.33𝐹𝐹𝑏𝑏)⁄ 1.5

2.2 Tension Check

Members subjected to axial tension are checked for the following condition:

𝑓𝑓𝑎𝑎𝐹𝐹𝑡𝑡≤ 1.0 [API 3.2.1]

The allowable tensile stress, Ft, is defined as:

Safety Factors 4

Steel Frame Design API RP 2A-WSD 21st Member Design

𝐹𝐹𝑡𝑡 = 0.6𝐹𝐹𝑦𝑦 [API Eq. 3.2.1-1]

2.3 Compression Check

Members subjected to axial compression are checked for the following condition:

𝑓𝑓𝑎𝑎𝐹𝐹𝑎𝑎≤ 1.0 [API 3.2.2]

The allowable compressive stress, Fa, is defined as:

𝐹𝐹𝑎𝑎 =

⎩⎪⎪⎨

⎪⎪⎧ �1 − (𝐾𝐾𝐾𝐾 𝑟𝑟⁄ )2

2𝐶𝐶𝑐𝑐2�𝐹𝐹𝑦𝑦

5 3⁄ + 3(𝐾𝐾𝐾𝐾 𝑟𝑟⁄ )8𝐶𝐶𝑐𝑐

− (𝐾𝐾𝐾𝐾 𝑟𝑟⁄ )38𝐶𝐶𝑐𝑐3

for 𝐾𝐾𝐾𝐾 𝑟𝑟⁄ < 𝐶𝐶𝑐𝑐

12𝜋𝜋2𝐸𝐸23(𝐾𝐾𝐾𝐾 𝑟𝑟⁄ )2 for 𝐾𝐾𝐾𝐾 𝑟𝑟⁄ ≥ 𝐶𝐶𝑐𝑐

[API Eq. 3.2.2-1]

where,

𝐶𝐶𝑐𝑐 = �2𝜋𝜋2𝐸𝐸𝐹𝐹𝑦𝑦

�1 2⁄

𝐹𝐹𝑦𝑦 = �𝐹𝐹𝑦𝑦 for 𝐷𝐷 𝑡𝑡⁄ ≤ 60min(𝐹𝐹𝑥𝑥𝑥𝑥 ,𝐹𝐹𝑥𝑥𝑐𝑐) for 𝐷𝐷 𝑡𝑡⁄ > 60

For members with D/t > 60, the yield strength, Fy, in the above equations is replaced by the critical local buckling stress, defined as the minimum of Fxe or Fxc.

The elastic local buckling stress, Fxe, is defined as:

𝐹𝐹𝑥𝑥𝑥𝑥 = 2𝐶𝐶𝐸𝐸 𝑡𝑡 𝐷𝐷⁄ [API Eq. 3.2.2-3]

where the critical elastic buckling coefficient, C = 0.3.

The inelastic local buckling stress, Fxc, is defined as:

𝐹𝐹𝑥𝑥𝑐𝑐 = 𝐹𝐹𝑦𝑦�1.64− 0.23(𝐷𝐷 𝑡𝑡⁄ )1 4⁄ � ≤ 𝐹𝐹𝑥𝑥𝑥𝑥 [API Eq. 3.2.2-4]

2.4 Flexure Check

Members subjected to bending are checked for the following condition:

𝑓𝑓𝑏𝑏𝐹𝐹𝑏𝑏

≤ 1.0 [API 3.2.3]

Compression Check 5


The allowable bending stress, Fb, is defined as:

𝐹𝐹𝑏𝑏 =

⎩⎪⎪⎨

⎪⎪⎧0.75𝐹𝐹𝑦𝑦 for

𝐷𝐷𝑡𝑡≤

1500𝐹𝐹𝑦𝑦

�0.84− 1.74𝐹𝐹𝑦𝑦𝐷𝐷𝐸𝐸𝑡𝑡 �

𝐹𝐹𝑦𝑦 for1500𝐹𝐹𝑦𝑦

<𝐷𝐷𝑡𝑡≤

3000𝐹𝐹𝑦𝑦

�0.72− 0.58𝐹𝐹𝑦𝑦𝐷𝐷𝐸𝐸𝑡𝑡 �

𝐹𝐹𝑦𝑦 for3000𝐹𝐹𝑦𝑦

<𝐷𝐷𝑡𝑡≤ 300

[API Eq. 3.2.3-1a, 1b, and 1c]

2.5 Shear Check

Members subjected to beam shear are checked for the following condition:

𝑓𝑓𝑣𝑣𝐹𝐹𝑣𝑣≤ 1.0 [API 3.2.4a]

The maximum beam shear stress, fv, and the allowable beam shear stress Fv are defined as:

𝑓𝑓𝑣𝑣 =𝑉𝑉

0.5𝐴𝐴 [API Eq. 3.2.4-1]

𝐹𝐹𝑣𝑣 = 0.4𝑓𝑓𝑦𝑦 [API Eq. 3.2.4-2]

2.6 Hoop Buckling Check

Members subjected to external pressure are checked for the following condition:

𝑓𝑓ℎ ≤ 𝐹𝐹ℎ𝑐𝑐 𝑆𝑆𝐹𝐹ℎ⁄ [API Eq. 3.2.5-1]

The hoop stress due to hydrostatic pressure, fh, is defined as:

𝑓𝑓ℎ = 𝑝𝑝𝐷𝐷 2𝑡𝑡⁄ [API Eq. 3.2.5-2]

The critical hoop buckling stress, Fhc, is defined as:

𝐹𝐹ℎ𝑐𝑐 =

⎩⎪⎨

⎪⎧𝐹𝐹ℎ𝑥𝑥 for 𝐹𝐹ℎ𝑥𝑥 ≤ 0.55𝐹𝐹𝑦𝑦0.45𝐹𝐹𝑦𝑦 + 0.18𝐹𝐹ℎ𝑥𝑥 for 0.55𝐹𝐹𝑦𝑦 < 𝐹𝐹ℎ𝑥𝑥 ≤ 1.6𝐹𝐹𝑦𝑦

1.31𝐹𝐹𝑦𝑦1.15 + �𝐹𝐹𝑦𝑦 𝐹𝐹ℎ𝑥𝑥⁄ �

for 1.6𝐹𝐹𝑦𝑦 < 𝐹𝐹ℎ𝑥𝑥 ≤ 6.2𝐹𝐹𝑦𝑦

𝐹𝐹𝑦𝑦 for 𝐹𝐹ℎ𝑥𝑥 > 6.2𝐹𝐹𝑦𝑦

[API Eq. 3.2.5-6]

The elastic hoop buckling stress, Fhe, is defined as:

𝐹𝐹ℎ𝑥𝑥 = 2𝐶𝐶ℎ𝐸𝐸 𝑡𝑡 𝐷𝐷⁄ [API Eq. 3.2.5-4]

Shear Check 6


The critical hoop buckling coefficient, Ch, is defined as:

𝐶𝐶ℎ =

⎩⎪⎨

⎪⎧

0.44 𝑡𝑡 𝐷𝐷⁄ for 𝑀𝑀 ≥ 1.6𝐷𝐷 𝑡𝑡⁄

0.44(𝑡𝑡 𝐷𝐷⁄ ) +0.21(𝐷𝐷 𝑡𝑡⁄ )3

𝑀𝑀4 for 0.825𝐷𝐷 𝑡𝑡⁄ ≤ 𝑀𝑀 < 1.6𝐷𝐷 𝑡𝑡⁄

0.736 (𝑀𝑀 − 0.636)⁄ for 3.5 ≤ M < 0.825𝐷𝐷 𝑡𝑡⁄0.755 (𝑀𝑀 − 0.559)⁄ for 1.5 ≤ 𝑀𝑀 < 3.50.8 for 𝑀𝑀 < 1.5

The geometric parameter, M, is defined as:

𝑀𝑀 =𝐿𝐿𝐷𝐷

(2𝐷𝐷 𝑡𝑡⁄ )1 2⁄ [API Eq. 3.2.5-5]

2.7 Axial Tension and Bending Check

Members subjected to combined axial tension and bending loads, without hydrostatic pressure, are checked for the following condition:

𝑓𝑓𝑎𝑎0.6𝐹𝐹𝑦𝑦

+�𝑓𝑓𝑏𝑏𝑥𝑥2 + 𝑓𝑓𝑏𝑏𝑦𝑦2

𝐹𝐹𝑏𝑏≤ 1.0 [API Eq. 3.3.1-2]

Members subjected to combined axial tension, bending, and hydrostatic pressure are checked for the following condition:

𝐴𝐴2 + 𝐵𝐵2 + 2𝜈𝜈|𝐴𝐴|𝐵𝐵 ≤ 1.0 [API Eq. 3.3.3-1]

where,

𝐴𝐴 =𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 − (0.5𝑓𝑓ℎ)

𝐹𝐹𝑦𝑦(𝑆𝑆𝐹𝐹𝑥𝑥)

𝐵𝐵 =𝑓𝑓ℎ𝐹𝐹ℎ𝑐𝑐

(𝑆𝑆𝐹𝐹ℎ)

2.8 Axial Compression and Bending Check

Members subjected to combined axial compression and bending, without hydrostatic pressure, are checked for the following conditions:

Axial Tension and Bending Check 7


𝑓𝑓𝑎𝑎𝐹𝐹𝑎𝑎

+

��𝐶𝐶𝑚𝑚𝑥𝑥𝑓𝑓𝑏𝑏𝑥𝑥1 − 𝑓𝑓𝑎𝑎

𝐹𝐹𝑥𝑥𝑥𝑥′�

2

+ �𝐶𝐶𝑚𝑚𝑦𝑦𝑓𝑓𝑏𝑏𝑦𝑦1 − 𝑓𝑓𝑎𝑎

𝐹𝐹𝑥𝑥𝑦𝑦′�

2

𝐹𝐹𝑏𝑏≤ 1.0

[API Eq. 3.3.1-4]

𝑓𝑓𝑎𝑎0.6𝐹𝐹𝑦𝑦


𝐹𝐹𝑏𝑏≤ 1.0 [API Eq. 3.3.1-2]

where,

𝐹𝐹𝑥𝑥′ =12𝜋𝜋2𝐸𝐸

23(𝐾𝐾𝐾𝐾 𝑟𝑟⁄ )2 [AISC H1]

The reduction factors, Cmx and Cmy are calculated according to AISC H1.

If 𝑓𝑓𝑎𝑎𝐹𝐹𝑎𝑎≤ 0.15, the previous two conditions are substituted by the following condition:

𝑓𝑓𝑎𝑎𝐹𝐹𝑎𝑎


𝐹𝐹𝑏𝑏≤ 1.0 [API Eq. 3.3.1-3]

Members subjected to combined axial compression, bending, and hydrostatic pressure are checked for the following conditions:

𝑓𝑓𝑎𝑎 + (0.5𝑓𝑓ℎ)𝐹𝐹𝑥𝑥𝑐𝑐

(𝑆𝑆𝐹𝐹𝑥𝑥) +𝑓𝑓𝑏𝑏𝐹𝐹𝑦𝑦

(𝑆𝑆𝐹𝐹𝑏𝑏) ≤ 1.0 [API Eq. 3.3.4-1]

𝑆𝑆𝐹𝐹ℎ𝑓𝑓ℎ𝐹𝐹ℎ𝑐𝑐

≤ 1.0 [API Eq. 3.3.4-2]

If 𝑓𝑓𝑥𝑥 > 0.5𝐹𝐹ℎ𝑎𝑎, the following condition is also satisfied:

𝑓𝑓𝑥𝑥 − 0.5𝐹𝐹ℎ𝑎𝑎𝐹𝐹𝑎𝑎𝑎𝑎 − 0.5𝐹𝐹ℎ𝑎𝑎

+ �𝑓𝑓ℎ𝐹𝐹ℎ𝑎𝑎

�2

≤ 1.0 [API Eq. 3.3.4-3]

where,

F𝑎𝑎𝑎𝑎 =𝐹𝐹𝑥𝑥𝑥𝑥𝑆𝑆𝐹𝐹𝑥𝑥

𝐹𝐹ℎ𝑎𝑎 =𝐹𝐹ℎ𝑥𝑥𝑆𝑆𝐹𝐹ℎ

𝑓𝑓𝑥𝑥 = 𝑓𝑓𝑎𝑎 + 𝑓𝑓𝑏𝑏 + (0.5𝑓𝑓ℎ)

Axial Compression and Bending Check 8

3 Joint Design

This chapter provides the details of the joint punching load check algorithms that are used for tubular joints in accordance with API RP 2A-WSD Sections 4.3.1 and 4.3.2.

API RP 2A-WSD allows the joints to be designed on the basis of punching shear or nominal loads in the braces. Both methods are available and documented in the following sections.

3.1 Joint Geometry

Figure 1 illustrates some of the geometric parameters used in the punching load check.

d Brace diameter, in

D Chord diameter, in

g Gap distance, in

t Brace thickness, in

T Chord thickness, in

θ Angle measured from the chord to the brace

Joint Geometry 9

Steel Frame Design API RP 2A-WSD 21st Joint Design

Figure 1 - Joint geometry

The following geometric parameters are derived from those in Figure 1.

𝛽𝛽 =𝑑𝑑𝐷𝐷

𝛾𝛾 =𝐷𝐷2𝑇𝑇

𝜏𝜏 =𝑡𝑡𝑇𝑇

3.2 Punching Shear Method

3.2.1 Design Loads

The acting punching shear, Vp, is defined as:

𝑉𝑉𝑝𝑝 = τf sin𝜃𝜃 [API Eq. 4.3.1-1]

where f is the nominal axial, in-plane bending, or out-of-plane bending stress. The acting shear is kept separate for each stress type.

3.2.2 Allowable Stresses

The allowable punching shear stress, vpa, in the chord wall is defined as:

𝑣𝑣𝑝𝑝𝑎𝑎 = 𝑄𝑄𝑞𝑞𝑄𝑄𝑓𝑓𝐹𝐹𝑦𝑦𝑐𝑐

0.6𝛾𝛾≤ 0.4𝐹𝐹𝑦𝑦𝑐𝑐 [API Eq. 4.3.1-2]

The chord load factor, Qf, can be automatically calculated or user input. When automatically calculated it is taken as 1.0 when all extreme fiber stresses in the chord are tensile, otherwise it is defined as:

T

D

g

d

t

θ

ChordBrace

Brace

Punching Shear Method 10


𝑄𝑄𝑓𝑓 = 1.0 − λγ𝐴𝐴2

where,

𝜆𝜆 = �0.030 for brace axial stress0.045 for brace in− plane bending stress0.021 for brace out− of − plane bending stress

𝐴𝐴 =�𝑓𝑓�̅�𝐴𝐴𝐴2 + 𝑓𝑓�̅�𝐼𝐼𝐼𝐼𝐼2 + 𝑓𝑓�̅�𝑂𝐼𝐼𝐼𝐼2

0.6𝐹𝐹𝑦𝑦𝑥𝑥

The factor Qq is determined based on API Table 4.3.1-1.

Table 2 – Factor, Qq

Brace Action

Joint Class Axial Tension

Axial Compression

In-plane Bending

Out-of-plane Bending

K overlap 1.8

(3.72 + 0.67 𝛽𝛽⁄ ) (1.37 + 0.67 𝛽𝛽⁄ )𝑄𝑄𝛽𝛽

K gap (1.10 + 0.20 𝛽𝛽⁄ )𝑄𝑄𝑔𝑔

T&Y (1.10 + 0.20 𝛽𝛽⁄ )

Cross w/o diaphragm (1.10 + 0.20 𝛽𝛽⁄ ) (0.75 + 0.20 𝛽𝛽⁄ )𝑄𝑄𝛽𝛽

Cross w/ diaphragm (1.10 + 0.20 𝛽𝛽⁄ )

The geometric factor, Qβ, is defined as:

𝑄𝑄𝛽𝛽 = �0.3

𝛽𝛽(1 − 0.833𝛽𝛽) for 𝛽𝛽 > 0.6

1.0 for 𝛽𝛽 ≤ 0.6 [API Table 4.3.1-1]

The gap factor, Qg, is defined as:

𝑄𝑄𝑔𝑔 = �1.8 − 0.1𝑔𝑔 𝑇𝑇⁄ ≥ 1.0 for 𝛾𝛾 ≤ 201.8 − 4𝑔𝑔 𝐷𝐷⁄ ≥ 1.0 for 𝛾𝛾 > 20 [API Table 4.3.1-1]

3.2.3 Axial and Bending Check

Joints with braces subjected to combined axial and/or bending loads are checked for the following conditions:

Punching Shear Method 11


�𝑣𝑣𝑝𝑝𝑣𝑣𝑝𝑝𝑎𝑎

�𝐼𝐼𝐼𝐼𝐼𝐼

2

+ �𝑣𝑣𝑝𝑝𝑣𝑣𝑝𝑝𝑎𝑎

�𝑂𝑂𝐼𝐼𝐼𝐼

2

≤ 1.0 [API Eq. 4.3.1-3a]

�𝑣𝑣𝑝𝑝𝑣𝑣𝑝𝑝𝑎𝑎

�𝐴𝐴𝐴𝐴

+2𝜋𝜋

arcsin��𝑣𝑣𝑝𝑝𝑣𝑣𝑝𝑝𝑎𝑎


2

+ �𝑣𝑣𝑝𝑝𝑣𝑣𝑝𝑝𝑎𝑎


2

≤ 1.0 [API Eq. 4.3.1-3b]

where the arcsin term is in radians. The subscripts AX, IPB, and OPB correspond to axial, in-plane bending, and out-of-plane bending, respectively.

3.2.4 Overlapping Joints

Joints classified as K Overlap are checked for the following condition:

𝑃𝑃𝑝𝑝𝑥𝑥𝑝𝑝𝑃𝑃 ⊥

≤ 1.0 [API 4.3.2]

where Pper is the brace axial load component perpendicular to the chord, defined as:

𝑃𝑃𝑝𝑝𝑥𝑥𝑝𝑝 = 𝑃𝑃 sin𝜃𝜃

The allowable axial load, perpendicular component is defined as:

𝑃𝑃 ⊥= �𝑣𝑣𝑝𝑝𝑎𝑎𝑇𝑇𝐾𝐾1�+ (2𝑣𝑣𝑤𝑤𝑎𝑎𝑡𝑡𝑤𝑤𝐾𝐾2) [API Eq. 4.3.2-1]

3.3 Nominal Load Method

3.3.1 Allowable Capacities

The allowable brace axial load, Pa, is defined as:

𝑃𝑃𝑎𝑎 = 𝑄𝑄𝑢𝑢𝑄𝑄𝑓𝑓𝐹𝐹𝑦𝑦𝑐𝑐𝑇𝑇2

1.7 sin𝜃𝜃 [API Eq. 4.3.1-4a]

The allowable brace bending moment, Ma, is defined as:

𝑀𝑀𝑎𝑎 = 𝑄𝑄𝑢𝑢𝑄𝑄𝑓𝑓𝐹𝐹𝑦𝑦𝑐𝑐𝑇𝑇2

1.7 sin𝜃𝜃(0.8𝑑𝑑) [API Eq. 4.3.1-4b]

These allowables are increased by 1/3 when applicable.

The chord load factor, Qf, can be automatically calculated or user input. When automatically calculated it is taken as 1.0 when all extreme fiber stresses in the chord are tensile, otherwise it is defined as per Section 3.2.2 above.

The ultimate strength factor, Qu, is determined based on API Table 4.3.1-2.

Nominal Load Method 12


Table 3 – Factor, Qu

Brace Action

Joint Class Axial Tension

Axial Compression

In-plane Bending


K (3.4 + 19𝛽𝛽)𝑄𝑄𝑔𝑔

(3.4 + 19𝛽𝛽) (3.4 + 7𝛽𝛽)𝑄𝑄𝛽𝛽 T&Y (3.4 + 19𝛽𝛽)

Cross w/o diaphragm (3.4 + 19𝛽𝛽) (3.4 + 19𝛽𝛽)𝑄𝑄𝛽𝛽

Cross w/ diaphragm (3.4 + 19𝛽𝛽)

The geometric factor, Qβ, and the gap factor, Qg, are defined in Section 3.2.2 above.


Joints with braces subjected to combined axial and/or bending loads are checked for the following conditions:

�𝑀𝑀𝑀𝑀𝑎𝑎


2+ �

𝑀𝑀𝑀𝑀𝑎𝑎


2≤ 1.0 [API Eq. 4.3.1-5a]

�𝑃𝑃𝑃𝑃𝑎𝑎�+

2𝜋𝜋

arcsin��𝑀𝑀𝑀𝑀𝑎𝑎


2+ �



2≤ 1.0 [API Eq. 4.3.1-5b]

where the arcsin term is in radians. The subscripts AX, IPB, and OPB correspond to axial, in-plane bending, and out-of-plane bending, respectively.




≤ 1.0 [API 4.3.2]



The allowable axial load, perpendicular component is defined as:

𝑃𝑃 ⊥= �𝑃𝑃𝑎𝑎 sin𝜃𝜃𝐾𝐾1𝐾𝐾� + (2𝑣𝑣𝑤𝑤𝑎𝑎𝑡𝑡𝑤𝑤𝐾𝐾2) [API Eq. 4.3.2-2]

Nominal Load Method 13

4 Supplements 2 and 3

These supplements include changes to the joint punching checks as described in the following sections.

This chapter provides the details of the API RP 2A-WSD 21st Supplements 2 (American Petroleum Institute, 2005) and 3 (American Petroleum Institute, 2007), released in 2005 and 2007, respectively, which are considered when the supplement option is set to include these.

4.1 Joint Design

Joint design was changed in these supplements to follow the nominal load method described in Section 3.3 above. The following sections provide details of the punching checks as implemented for these supplements. The chord yield strength, Fyc, is limited to 0.8Fu.

4.1.1 Allowable Capacities

The allowable brace axial load, Pa, is defined as:

𝑃𝑃𝑎𝑎 = 𝑄𝑄𝑢𝑢𝑄𝑄𝑓𝑓𝐹𝐹𝑦𝑦𝑐𝑐𝑇𝑇2

𝐹𝐹𝑆𝑆 sin𝜃𝜃 [API Eq. 4.3-1a]

The allowable brace bending moment, Ma, is defined as:

𝑀𝑀𝑎𝑎 = 𝑄𝑄𝑢𝑢𝑄𝑄𝑓𝑓𝐹𝐹𝑦𝑦𝑐𝑐𝑇𝑇2𝑑𝑑𝐹𝐹𝑆𝑆 sin𝜃𝜃

[API Eq. 4.3-1b]

where the safety factor, FS = 1.60.

The chord load factor, Qf, is defined as:

𝑄𝑄𝑓𝑓 = �1 + 𝐶𝐶1 �𝐹𝐹𝑆𝑆𝑃𝑃𝑐𝑐𝑃𝑃𝑦𝑦

� − 𝐶𝐶2 �𝐹𝐹𝑆𝑆𝑀𝑀𝑖𝑖𝑝𝑝𝑏𝑏

𝑀𝑀𝑝𝑝� − 𝐶𝐶3𝐴𝐴2� [API Eq. 4.3-2]

The parameter, A, is defined as:

14

Steel Frame Design API RP 2A-WSD 21st Supplements 2 and 3

𝐴𝐴 = ��𝐹𝐹𝑆𝑆𝑃𝑃𝑐𝑐𝑃𝑃𝑦𝑦

�2

+ �𝐹𝐹𝑆𝑆𝑀𝑀𝑐𝑐

𝑀𝑀𝑝𝑝�2

�0.5

[API Eq. 4.3-3]

where the safety factor, FS = 1.20 where the 1/3 increase is applicable. Pc is the nominal axial load and Mc is the nominal bending resultant in the chord.

𝑀𝑀𝑐𝑐 = �𝑀𝑀𝑖𝑖𝑝𝑝𝑏𝑏2 + 𝑀𝑀𝑜𝑜𝑝𝑝𝑏𝑏

2 [API 4.3.4]

The coefficients, C1, C2, and C3, are determined based on API Table 4.3-2.

Table 4 – Coefficients, C1, C2, and C3

Joint Type C1 C2 C3 K axial 0.2 0.2 0.3

T&Y axial 0.3 0 0.8 X axial 𝛽𝛽 ≤ 0.9 0.2 0 0.5 X axial 𝛽𝛽 = 1.0 -0.2 0 0.2

All joints moment 0.2 0 0.4

The ultimate strength factor, Qu, is determined based on API Table 4.3-1.

Table 5 – Factor, Qu

Brace Action

Joint Class

Axial Tension

Axial Compression

In-plane Bending


K (16 + 1.2𝛾𝛾)𝛽𝛽1.2𝑄𝑄𝑔𝑔 ≤ 40𝛽𝛽1.2𝑄𝑄𝑔𝑔

(5 + 0.7𝛾𝛾)𝛽𝛽1.2 2.5+(4.5 + 0.2𝛾𝛾)𝛽𝛽2.6 T&Y

30𝛽𝛽 2.8+ (20 + 0.8𝛾𝛾)𝛽𝛽1.6

≤ 2.8 + 36𝛽𝛽1.6

X 23𝛽𝛽 for 𝛽𝛽 ≤ 0.9

20.7 + (𝛽𝛽 − 0.9)(17𝛾𝛾 − 220) for 𝛽𝛽 > 0.9

[2.8+ (12 + 0.1𝛾𝛾)𝛽𝛽]𝑄𝑄𝛽𝛽

The geometric factor, Qβ, is defined as:

𝑄𝑄𝛽𝛽 = �0.3

𝛽𝛽(1 − 0.833𝛽𝛽) for 𝛽𝛽 > 0.6

1.0 for 𝛽𝛽 ≤ 0.6 [API Table 4.3.1-1]

The gap factor, Qg, is defined as:

𝑄𝑄𝑔𝑔 = �1 + 0.2[1 − 2.8𝑔𝑔 𝐷𝐷⁄ ]3 ≥ 1.0 for 𝑔𝑔 𝐷𝐷⁄ ≥ 0.050.13 + 0.65𝜙𝜙𝛾𝛾0.5 for 𝑔𝑔 𝐷𝐷⁄ < −0.05

[API Table 4.3-1]

Joint Design 15

Steel Frame Design API RP 2A-WSD 21st Supplements 2 and 3

𝜙𝜙 = 𝑡𝑡 𝐹𝐹𝑦𝑦𝑏𝑏 �𝑇𝑇𝐹𝐹𝑦𝑦�⁄


Joints are checked for the following condition:

�𝑃𝑃𝑃𝑃𝑎𝑎�+ �


�𝑖𝑖𝑝𝑝𝑏𝑏

2+ �


�𝑜𝑜𝑝𝑝𝑏𝑏

≤ 1.0 [API Eq. 4.3-5]

The subscripts IPB and OPB correspond to in-plane bending and out-of-plane bending, respectively.




≤ 1.0 [API 4.3.2]



The allowable axial load perpendicular component is defined as:

𝑃𝑃 ⊥= �𝑃𝑃𝑎𝑎 sin𝜃𝜃𝐾𝐾1𝐾𝐾� + (2𝑣𝑣𝑤𝑤𝑎𝑎𝑡𝑡𝑤𝑤𝐾𝐾2) [API Eq. 4.3.2-2]

Joint Design 16

5 References

American Institute of Steel Construction. (1989). Manual of Steel Construction - Allowable Stress Design (9th ed.). Chicago, Illinois, USA: American Institute of Steel Construction.

American Petroleum Institute. (2000). Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms - Working Stress Design (21st ed.). Washington, District of Columbia, USA: API Publishing Services.

American Petroleum Institute. (2005). RP 2A-WSD Errata and Supplement 2 (21st ed.). Washington, District of Columbia, USA: API Publishing Services.

American Petroleum Institute. (2007). RP 2A-WSD Errata and Supplement 3 (21st ed.). Washington, District of Columbia, USA: API Publishing Services.

17

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