steel roof truss optimization

8/9/2019 Steel Roof Truss Optimization

http://slidepdf.com/reader/full/steel-roof-truss-optimization 1/98

INFORMATION TO USERS

This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some

thesis and dissertation copies are in typewriter face, while others may be

from any type o f computer printer.

The quality of this reproduction is dependent upon the quality of the

copy submitted. Broken or indistinct print, colored or poor quality

illustrations and photographs, print bleedthrough, substandard margins,

and improper alignment can adversely affect reproduction.

In the unlikely event that the author did not send UMI a complete

manuscript and there are missing pages, these will be noted. Also, if

unauthorized copyright material had to be removed, a note will indicate

the deletion.

Oversize materials (e.g., maps, drawings, charts) are reproduced by

sectioning the original, beginning at the upper left-hand comer and

continuing from left to right in equal sections with small overlaps. Each

original is also photographed in one exposure and is included in reduced

form at the back o f the book.

Photographs included in the original manuscript have been reproduced

xerographically in this copy. Higher quality 6” x 9” black and white

photographic prints are available for any photographs or illustrations

appearing in this copy for an additional charge. Contact UMI directly to

order.

UMIA Bell & Howell Information Company

300 North Zeefo Road, Ann Arbor MI 48106-1346 USA

313/761-4700 800/S21-0600

pro du ced with perm ission of the copyright owner. Further reproduction prohibited without permission .


http://slidepdf.com/reader/full/steel-roof-truss-optimization 2/98roduced with permission of the copyright owner. Further reproduction prohibited without permission.



STEEL ROOF TRUSS OPTIMIZATION

by

Min Shuai

A Thesis Presented to the

FACULTY OF THE SCHOOL OF ARCHITECTURE

UNIVERSITY OF SOUTHERN CALIFORNIA

In Partial Fulfillment of the

Requirements for the Degree

MASTER OF BUILDING SCIENCE

(Architecture)

May 1998

Copyright 1998 Min Shuai

ep rodu ced with perm ission o f the copyright owner. Further reproduction prohibited without permission .



UMI Number: 1391099

UMI Microform 1391099 Copyright 1998, by UMI Company. All rights reserved.

This microform edition is protected against unauthorized

copying under Title 17, United States Code.

UMI300 North Zeeb Road

Ann Arbor, MI 48103

prod uced with perm ission of the copyright owner. Further reproduction prohibited without permission.



UNIVERSITY OF SOUTHERN CALIFORNIA

SCHOOL OF ARCHITECTURE

UNIVERSITY PARK

LOS ANGELES, CA 90089-0291

This thesis, written 6y J Min Shuai

under the direction o f h er ____ Thesis Committee,

andapproved 6y off its members, has 6een presented

to and accepted 6y the (Dean o f The SchooC o f

Architecture in partiaCfuCfiKment of the requirements

fo r the degree of

MASTER- OF BUILDING SCIENCE

K[. ~

(Dean

(Date.3 O ^ 3

T H E S I S C O M M I T T E E

\ L \ U

rodu ced with perm ission o f the copyright owner. Further reproduction prohibited without permission.



ACKNOWLEDGMENTS

This thesis is based on my studies undertaken in Building Science Program.

School of Architecture at University of Southern California from fall of 1995 to summer

of 1998.1would like to thank all the individuals within USC as well as others who were

encouraging and helpful during this long time of study. However, they are too numerous

to be mentioned individually. So. I just take this opportunity to express my sincere

gratitude to the following people:

Prof. Goetz Schierle. my chief advisor, for his expert ideas and clear guidance

for the development o f my thesis;

Prof. Dimitry Vergun for his extensive experience and invaluable suggestions,

which led me throughout the entire study;

Prof. Marc Schiler. who read my manuscript so carefully and offered

suggestions as well as criticism and whose support during a difficult period in my life

will be treasured forever.

I am grateful to the school for the financial aid. without which my study would

have been much more difficult. My love goes to my husband. Mingsong Yin, for his

unceasing support and encouragement.

Finally, my heart surrendered to God Almighty. Who answers my prayers and

gives me a new life in this New Land.

ii

pro du ced with perm ission of the copyright owne r. Further reproduction prohibited without perm ission.



Table of Contents

Acknowledgments

List o f Figures

List of Charts

I. Objective of Roof Truss Study

II. Basic Concepts of Trusses

1. From Beam to Truss - Definition o f Trusses

2. Loads on Trusses

3. Stability and Determinacy

4. Common Types o f Ro of Trusses

5. Materials for Trusses

6. Construction Concern: Joint

III. Comparative Truss Analysis by Computer

1. Computer Program: MultiFrame

2. Prototypes of Trusses to be Studied

3. Simulation Assumptions

4. Static Loads

5. Comparing Self-Weight o f Trusses of Different

Configurations

5.1. Design of Steel Compressive Members

5.2. Design of Steel Tensile Members

e pro duc ed with permissio n of the copyright own er. Further reproduction prohibited without permissio n.



5.3. Comparison o f Truss Self-Weight and Deflection 28

5.4. Conclusions 33

6. Comparing TS Construction with the WT&DL 34

6.1. Design of TS Trusses 35

6.2. Comparing with the WT&DL Construction 38

6.3. Conclusions 40

7. Comparing Combined Stresses with Axial Stresses for

200ft-Span Cases 42

7.1. Design for Combined Stresses 42

7.2. Comparison and Conclusions 46

8. Comparing Different H/L Ratios for 200ft-Span Cases 47

8.1. R atiosof 1/5. 1/8. 1/10. 1/12.5 and 1/15 47


9. Comparing Different Panel Sizes for 200ft-Span Cases 56

9.1. Panel Sizes o f L/4. L/6. L/8. L/10 and L/12 56


IV. Conclusions and Recommendations 65

Appendix Design o f Trusses 67

Reference 87

iv




List of Figures

Figure 2-1 A Simple Beam j

Figure 2-2 A Simple Spanning Truss j

Figure 2-3 Genesis of the Truss from the Beam 4

Figure 2-4 Elements o f a Planar Truss 6

Figure 2-5 Typical R oof Truss Profiles 9

Figure 2-6 Basic Truss Patterns 10

Figure 2-7 Typical Steel Trusses 12

Figure 2-8

%Arrangement o f Truss Joints 13

Figure 3-1 Prototypes o f Trusses to be Studied 15

Figure 3-2 Overall Study Schedule 17

Figure 3-3 Roof Truss Arrangement 17

Figure 3-4 Critical Bars at Quick Design 20

Figure 3-5 Internal Axial Force Diagrams of 200-ft Span Trusses 24

Figure 3-6 Trusses of Combined Stresses 43

Figure 3-7 Trusses at Different H/L Ratios 48-52

Figure 3-8 Trusses of Different Panel Sizes 57-61

p rodu ced with permission of the copyright owner. Further reproduction prohibited without permission.



List of Charts

Chart 3-1 Truss Weight Assumption 22

Chart 3-2 Comparison of Self-Weights of Trusses @ Different Spans 29

Chart 3-3 Comparison o f Truss Weights with Assumptions 31

Chart 3-4 Comparison o f Top/Bottom Chords with Web Members 31

Chart 3-5 Truss Deflection 32

Chart 3-6 Comparison of Self-Weights of Tube Trusses @ Different Spans 39

Chart 3-7 Comparison of TB Trusses with WT&DL Trusses 41

Chart 3-8 Comparison of Top/Bottom Chords with Web Members 41

Chart 3-9 Comparison o f Trusses Loaded Differently 46

Chart 3-10 Comparison of Self-Weights of Trusses @ Different H/L Ratios 54-55

Chart 3-11 Comparison of Self-Weights of Trusses o f Different Panel Sizes 63 -64

V I

p rodu ced with p ermission of the copyright owner. Further reproduction prohibited without permission.



I . O bjective o f R oof Tru ss Study

Trusses have been used extensively for roof structure of many spans. Truss

configuration has a significant impact on both a building’s exterior appearance and

interior space.

However, in current practice, there is a lack of guidelines for optimum truss

design for architects and engineers. The usual design routine is that architects first

design, o r even jus t draw , a truss profile and pattern for some sort o f architectural

concerns without enough structural knowiedge. The design is then given to structural

engineers to calculate without regard of optimum, because of time and profit concerns.

As a result, the most efficient design is seldom achieved.

The objective o f this study is to set up a guideline for preliminary design. The

study is to compare the self-weight o f steel roof trusses of different configurations at

different spans. Constructions of Tee & double angle (WT&DL) and tube (TS) trusses

are compared. Different loading conditions, height-to-span ratio and panel size have

also been studied to see how they affect the design of roof trusses.

Basic concepts o f trusses need to be reviewed first.

pro du ced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.



II. Basic Concepts of Trusses

1. From Beam to Truss—D efinition o f Tru sses

1.1. What is a Beam?

A beam is a linear structural elem ent that is primarily subjected to transverse

loading. Bending and shear stresses are developed to resist loads. Figure 2-1 are shear-

and bending- diagrams o f a simply supported beam with a uniformly distributed load vt

along its span. As shown in the graph, the stresses are not evenly distributed along the

span of the beam, and the deflection o f the beam increases with the 4th power of its

span under uniform load. Certainly, the beam will collapse under its own weight when

its span goes beyond a certain limit.

1.2. What is a Truss?

A truss is a framework of triangular formation of linear elements. Just like a

beam, a s imple spanning truss carries superimposed loads to its supports. However,

because inefficient stresses such as bending and shear are eliminated and only

compression and tension are developed in its members to resist loads, a truss is more

efficient than an equivalent beam earn ing the same load over an equal span (Figure 2-

2 ).

pro du ced with perm ission of the copyright owne r. Further reproduction prohibited without permission .



Sp an = L

Simple Beam-Uniformly Distributed Load: w

, L / 6 , L / 6 , 1 / 6 , L / 6 t L / 6 , L / 6 f

Simple Spuming Tim-Concentrated Load at Joints:

P = wL/6

wL/2

Shear Ditgnm

wL/2

*L’ / 8

Moment Ditgnm

2.5P

I I.5P

I 0.5P

^OlP |

-2.5P

(2/3)PL_S ^)E L( 5 / t 2 ) P L ^ > '

Shear St Moment Diagrams-The truss viewed os o beam

as a whole

Deflection5 w L'/38 4E !

F ig u re MA Simple Beam

' n J

Tv h x J N s

s s s

l 'h

Internal Axial Force DiagramContinuous line - Compression

Dashed line - Tension

Deflection

Figure 2-2A S im ple S pann ing Truss

rod uced with permission of the copyright owner. Further reproduction prohibited without permission .



The genesis o f the truss from the beam is interpreted by Michele Melaragno as

the following two steps (Melaragno: 1981. p.86.):

1) Removing some o f the material along the neutral axis where the bending stress

is small, but leaving enough material to resist shear (horizontal and vertical):

2) Moving the remaining material farther aw ay from the neutral axis to increase

its flexu ral resistance. (Figure 2-3)

a.

/REMOVEDMATERIAL

b.

SHEAR

c.

Fi gu re 2-3 The Ge nes is o f the T russ f rom t he

as a Proces ~ t imiza t ion(Meioragno: w u i. p .ts/.

Beam

a. The beam action in bending.

b. Removal of inefficient material in the 2one near the neutral axis.

c. Expanding the remaining m aterial away from the neutral axis, thu s increasing

and generation of t he truss.the resisting moment

4




1.3. Single Planar Truss

A single planar truss, as its name indicates, has all members lying in one single

plane. It is a thin structure and the compression chords of the truss tend to move out of

plane throughout its span if there is no bracing in the direction perpendicular to the

plane o f the truss.

In practice, roof and ceiling constructions normally provide enough bracing for

roof trusses. If not. other means, such as a vertical plane o f X-bracing at each truss joint

or horizontal planes of X-bracing at the level of the bottom chords, could be utilized.

The method of bracing for trusses is actually beyond the scope o f this study. The

purpose of mentioning it here is to restrict the following study to single planar trusses

only. The basic assumption is that all necessary bracing has been provided and loads

have been included in roof dead load.

1.4. Terminology of a Truss

The top and bottom perimetric members of a truss are chord members--

top/upper and bottom/lower chords. They are analogous to the top and bottom flanges of

a steel beam. The interior members of the truss are web members. All truss members are

ordinarily called bars. The connection of members or bars are called joints.




Most trusses have a pattern that consists of some repetitive, modular unit. This

unit is referred to as the panel of the truss. Join ts sometimes are called panel points.

A single planar truss has dimensions of span and height/depth. The latter is referred to

as rise when its top chords slope. (Figure 2-4)

-Joints

Top Chords

Web Members

Bottom Chords

Span

Figure 2-4 Elemen ts o f a Planar Truss

2. Loads on T russes

2.1. Static loads

Trusses are subjected to both gravity and lateral loads. Gravity load includes

gravity dead and live loads. The permanent loads on a truss, caused by the weight of the

truss and everything attached to it. are all dead loads. Other loads caused by the usage of

the building are generally referred to as live loads. Both gravity dead and live loads are

considered as static load.

Wind and earthquake generate lateral loads. Lateral refers to effects having a

direction at right angles to that of gravity. They tend to push the building sideways.

p rod uce d with perm ission of the copyright owner. Further reproduction prohibited without permission .



Although wind load and earthquake load have dynamic effects on buildings, they

are normally treated as equivalent static loads in building structure design. Lateral loads

are not considered in this study.

2.2. Secondary stress

The ideal assumption is that loads are applied to truss joints, so the members are

loaded only through the joints and only direct compression or tension forces are

generated in truss members.

Since the truss weight is actually distributed along the bar span, the above

assumption is never exactly true. The small flexural stress in a real truss is called

secondary stress. Since for short to medium span trusses, the truss weight ordinarily is

not a major part o f the total design load, the usual practice is to consider units of weight

as collected at the truss joints.

Live load can be applied to the truss joints through joists. However, if roof decks

are supported by the top chords directly or ceiling load is continuously distributed along

the bottom chords, the chords are loaded with a linear uniform load and function as

beams between their end joints. Secondary stress is therefore generated. In such cases,

truss chords need to be designed for the combined effects o f the axial stress caused by

the truss action and the bending stress caused by the direct loading. One study will

compare the combined stress cases with joint loaded cases.

rod uced with permission of the copyright owner. Further reproduction prohibited without permission.



3. Stab ility and D eterm inacy

Before a given truss is analyzed, its stability and determinacy need to be

determined. When a structure can not satisfy static equilibrium, it is unstable, and

therefore unacceptable. If a structure has the minimum number of members and

supports required for its equilibrium, it is called statically determinate. A statically

determinate structure can be analyzed by means of statics alone. If a structure has more

than the necessary members and/or supports (over stabilized), it is called statically

indeterminate. A statically indeterminate structure cannot be analyzed by means of

statics, but requires also the theory of elasticity.

According to its definition, the generation of a truss from single elements can be

viewed as two steps: 1) Connection o f three bars to form a base triangle, that means

three initial bars with three initial joints: 2) More triangles are added to the first one.

that is. two bars for each additional joint. So. the total number of truss members m is

equal to the initial 3 bars of the base triangle, plus 2 members for each additional joint

{f-3):

m=3~2(j-3)=2j-3

Obviously, if m<2j-3. uhich means not enough bars, the truss is unstable. If

m>2j-3. which means there are more bars than needed, the truss is indeterminate. Only

if m=2j-3. which means enough and necessary bars are provided, is a truss internally

stable and determinate. Another effect factor is the arrangement o f bars. They have to

p rodu ced with perm ission of the copyright owner. Further reproduction prohibited without permission.



form triangles. If there are polygons, other than triangles, existing in the truss, the truss

would have “geometric instability.”

The support conditions can also affect the external s tability and determinacy of a

truss. Since the planar truss to be discussed in this study functions as a simple beam in

terms of supports, the external stability and determinacy are assumed as for beams.

4. Com m on Types o f R oof Trusses

Functioning as a solid beam in a roof structure, a sim ple spanning truss usually

takes some typical profiles, such as those shown in Figure 2-5. The arrangement of web

members must form triangles. In years o f practice, a number o f classic truss patterns

have evolved and have become standard parts of our structural vocabulary'. Some of

them are named after the engineers who first introduced them. Among the important

truss types are the Howe truss, the Pratt truss, and the Warren truss (Figure 2-6).

Flit Truss Truss with Sloping Top Chords

u . _____________ i ^ — _____________

Cumbered Truss Arched Top Chord Truss

Gtble Truss Gsble Truss with Cambered Bottom Chords

Figure 2-5 Typica l Ro of Truss Pro f i les

9




m zi

Howt- gtbk Pntt - gtble

AAAAAAWilTU

Figu re 2-6 Basic Truss Pat terns

The Howe truss is characterized by the fact that tension members between the

two chords are all vertical, while the diagonal compression members may be parallel to

each other in a flat Howe, but not in triangular Howe.

Just reversed from the Howe truss, in the Pratt truss, the compression members

between the two chords are all vertical, but the diagonal members are in tension and

may be parallel to each other in flat Pratt, but not parallel to each other in triangular

Pratt.

The Warren is a flat truss with all members of the top and bottom chords being

of equal lengths: all diagonal members, whether in compression or in tension, have

equal lengths. In each half of the truss, the diagonal compression members are parallel

to each other: and the diagonal tension members are also parallel to each other. The

original Warren was subdivided into equilateral triangles: the common types used

nowadays, however, may have isosceles triangles.

10

p rodu ced with permission of the copyright owner. Further reproduction prohibited without perm ission.



§. M aterials for T russes

Materials most used in the U.S. for trusses are wood and steel.

There are two categories of wood truss construction: light-frame trusses and

heavy-timber trusses. The light-frame trusses are made o f dimension lumbers for small

to medium spans. The heavy-timber trusses are made of timbers or manufactured wood

products for larger spans.

Steel trusses—the only ones to be studied in this thesis—are usually made of

standard rolled sections. The most common forms of steel trusses of small to medium

size are Tee and double-angle members, connected by rivets, bolts, or welds (Figure 2-

7a). Another form is that o f tubular members, such as round pipe and flat-sided,

rectangular tube, that are directly welded to each other (Figure 2-7b). In practice,

welding is cheaper and more quality-guaranteed when used in the fabricating shop and

high strength bolts (torque tensioned) are cheaper and easier for field connections.

In other cases, wood and steel elements are sometimes mix-used in the same

truss: this is called composite construction. The reason and benefit of this are effective

utilization of materials and effective connection achievement.

Reinforced concrete has been used extensively as truss material in Europe and

Asia but not in the USA.

p rod uced with permission of the copyright owner. Further reproduction prohibited without permission .



a. Teed Double-Angle Truss Detail

& Tube Truss Detail

Figure 2-7 Typical Steel Trusses

Some general considerations that may affect the decision about what materials to

use for a particular truss design include:

1) Cost;

2) Other structure elements;

3/ Fire Requirements;4) Local Availability. (Ambrose: 1994. p. 127.)




6. Construction Concern: Joints

The means used to achieve the connection of truss members at the truss joints

depends on a number o f considerations. The major ones are:

1) The materials o f the members;

2) The for m o f the members;

3) The size o f the members;

4) The magnitude o f forces in the members. (Ambrose: 1994. p. 129—130.)

For short- to medium-span trusses, chord members may run through two or more

panels, or even entire length o f the truss. This not only reduces the number o f individual

pieces that need to be fabricated, but also eliminates a large amount o f connecting. For

long-span or multi-span trusses, the truss pattern must be designed as the necessary

division of units that can be fabricated in the shop, then transpoted to the building site

and finally assembled into whole at the site. Figure 2-8 shows such examples.

Small Truss Joist with Continuous Chord Members

____________ Shop Fabricated Sections ____________

' Field Jo int s----------

Large Truss with Shop Fabricated Units and Reid Joints

Fi gu re 2 -8 Ar ra nge me nt o f T russ Jo in t s




III. Comparative Truss Analyses by Computer

1. C om puter Program: M ultiFram e

MultiFrame is a structural analysis and design program for Windows 95 and

Windows NT released by Formation Design Systems Pty Ltd. ''MultiFrame" and

"Section Maker" are two of several parts of the program, which are used in this study. In

MultiFrame. a structure can be first established in a ‘‘Frame” window, and load can then

be applied on the structure in a "Load” window. After analyzing, a "Plo t” window

shows results graphically and a "Result" window shows numerical results. In Section

Maker, after a section is designed/drawn and material is assigned, the properties of the

section are computed by the program automatically. However, since functions such as

editing, formatting and plotting are not yet implemented, the working process is actually

not as easy as it sounds. All the information needed can only be read from screen.

2. Prototypes o f Tru sses to be Studied

For the purpose of this thesis, several truss profiles—parallel top and bottom

chords, cambered top chords, parabolic-arched top chords and simple gab le—have been

selected for the study. The Pratt truss is chosen over the Howe truss since it. having

shorter compression web members, is more efficient than the Howe. The Warren truss is

also included. Figure 3-1 shows the configurations to be studied.

u

p roduc ed with permission of the copyright owner. Further reproduction prohibited without perm ission.



a Simple Pitt Pntt with Ptnllel Top dt Bottom Chords

p

? p

T

P

f P

TPT

P P

T

& Mures

P /?

■ s —

c Fist Pntt with Ctabend Top Chord

-P TV

P /2

v

d Arched Top Chord Pntt

p

i

P /2

e Simple Gtble Pntt

Span = L

Figure 31 Prototypes of Trusses to be Studied




From practical experience, a height to span ratio of 1:10 is assumed for the

parallel-chord Pratt and the Warren trusses: a ratio o f 1:8 for the cambered top and

arched top Pra tt trusses; and 1:5 for the gable truss. The average o f the height to span

ratios of ail these trusses is actually 1:10. which would make this comprehensive truss

configuration-vveight study more meaningful since a choice o f either truss for a roof of a

specific building would add no other variables to the building.

It is obvious that the roof slope o f the gable is 2:5: the slope o f the cambered

Pratt is designed as 1:10.

Panel size is assumed to be 25 feet.

The truss span ranges from 100 feet to 300 feet at a 50-foot interval. Figure 3-2

shows a complete study schedule. It needs to point out that the panel size of 100-ft span

group is not 25 feet but 12.5 feet. Except for that, all the above configuration

assumptions apply to all trusses.

An indefinite roofing plan of a grid of "Span o f Truss x 30ft " is assumed.

Therefore, the truss spacing is 30 feet on center (Figure 3-3).

p rod uced with perm ission of the copyright owner. Further reproduction prohibited without permission.



Spta

ottpppp)

A / W W \I'sNNPlA'i

100-ft Spta

ISO-ft Spta

/S7WWVAArxjxTxfxI/l/Txu-n

200-ft Spta

NT xinM^I/I/PIT I

250-ft Spta

A A 7 W W W W V \

300-ft Spta

Figure 3-3 Ro of Trus s Arrangem ent

Figure 3-2 Overall Study Schedule



3. Simulation Assumptions

The following assumptions are made for structural analysis:

• A planar truss is a rigid structure composing of straight bars that are lying in

the same plane and connected to one another through frictionless single pin

joints;

• All members are assumed to be perfectly straight and of constant cross

section: their centroidal axes coincide with the centroid of the joint:

• Bracing has been provided at panel joints in the direction perpendicular to

the plane of the truss and the load of the bracing has been included in the roof

dead load:

• Only vertical static load is considered in this study and the load is applied at

joints through ro of construction except that in combined stress study:

• Forces act in the same plane of the truss plane:

• Displacement of truss is small and hardly influences the magnitude of the

force flow.

rod uced with permission of the copyright owner. Further reproduction prohibited without permission .



4. Static Loads

As it has been mentioned before, the principal sources and types of loads on

trusses include gravity dead loads, gravity live loads, wind loads and seismic loads,

among which only vertical static loads are considered in this study.

According to the Uniform Building Code, the live load of a roof is assumed to

be 12psf since the tributary area of all trusses is over 600 square feet. For a typical metal

deck roof construction, ro of dead load is assumed as 20psf exclusive of the weight o f

the truss itself, which is a subject of this study.

Assumption of Sel f-W eight of Trusses

The flat Pratt trusses at all spans are selected for self-weight assumption study.

A 3psf is first assumed and. therefore, the concentrated load at central joints o f the truss

of 100-ft span is

P = (12-20-3) x 12.5x30 = 13.1251b = 13.125Kips;

for the trusses spanning 150-ft to 300-ft. the load is

P = (12-20-3) x 25 x 30 = 26.250lb = 26.25Kips.

The internal axial forces are calculated by MultiFrame and quick designs are

done as 1) top and bottom bars are based on mid-span critical bars: 2) vertical and

diagonal bars based on critical bars at the ends of truss span (Figure 3-4).

pr odu ced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.



F i g u r e 3 4 C r it ic a l B a n a t Q u i c k D e s ig n

Truss member selections are recorded in the following table.

Table 3-1 Quick Design o f Flat Pratt Trusses o f 3psf Self-Weight A ssumption

Truss Top Chord Bottom Chord Vertical Bar Diagonal Bar

Par-100 WT7X30.5 WT5X19.5 DL3.5X3.5X3/8 DL3X3X5/16

Par-150 WT10.5X55.5 WT 12X27.5 DL5X5X3/8 DL5X5X5/16

Par-200 W T12X73 WT7X4I DL6X6X5/8 DL6X6X3/8

Par-250 WT 15X86.5 WT7X49.5 DL8X8X1/2 DL6X6X3/8

Par-300 WT 15X95.5 WT 10.5X61 DL8X8X3/4 DL8X8X1/2

The design result shows that the assumption of 3psf is only true for the 100-ft

span truss and the self-weights o f all others are far beyond the assumption (Chart 3-1 -1).

So different assumptions have to be made for trusses of different spans separately

according to the first trial as follows: 5psf for 150-ft span. 7psf for 200-ft span. 9psf for

250-ft span and 13psf for 300-ft span. The concentrated loads at central joints for the

trusses of 100-ft to 300-ft spans are calculated as follows:

:o

ro du ced with perm ission of the copyright owner . Further reproduction prohibited without perm ission.



Prziooj, = (12+20+3) x 12.5* 30 = 13,1251b = 13.125K ip;

Paisof t = (12+20 +5 ) x 25 x 3 0 = 27,7501b = 2 7. 75K ip;

P<3200 ft = (12+ 20+ 7) x 2 5 x 3 0 = 29.2501b = 29.75Kip:

Pa250ft = (1 2+2 0+9 ) X 25 X 3 0 = 30.7501b = 30.75Kip;

P 3300 /, = (12+20+13) x 25 x 30 = 33.7501b = 33.75Kip.

A second series of designs is recorded in Table 3-2 and results prove that the

assumptions of the trusses from 150-ft to 250-ft span are good enough and that o f the

300-ft span truss seems slightly lower than the result (Chart 3-1-2). In light of the fact

that, in these quick design, truss chord internal force reductions along their span are not

considered, which will be considered in the later study, the assumption of 13psf of 300-

ft span truss is taken as acceptable.

Table 3-2 Quick Design of Flat Pratt Truss o f Different Self-Weight Assumptions

Truss Top Chord Bottom Chord Vertical Bar Diagonal Bar

Par-100 WT7X30.5 WT5XI9.5 DL3.5X3.5X3/8 DL3X3X5/I6

Par-150 WT12X58.5 WT9X30 DL6X6X3/8 DL5X5X3/8

Par-200 WT 13.5X80.5 WT9X43 DL6X6X5/8 DL6X6X3/8

Par-250 WT 15X95.5 WTI5X58 DL8X8X1/2 DL6X6X12

Par-300 WTI6.5X120.5 WT 18X80 DL8X8X1 DL8X8X1/2

All further studies are. therefore, based on these assumptions.

pro duc ed with perm ission o f the copyright owner. Further reproduction prohibited without perm ission.



Chart 3-1-1 Truss Weight Assumption - Trial One

1 2

10

M

5* 6

I«L® 4

CO

I Self-Weight

-A s s u m p t i o n

P a r -1 0 0 P a r -1 5 0 P a r -2 0 0 P a r -2 5 0 P a r -3 0 0

Span (ft.)

Chart 3-1-2 Truss Weight Assumption - Trial Two

14

12

10

Mar 8£CD

| 6a>

CO

I Self-Weight

-A s s u m p t i o n

P a r -1 0 0 P a r -1 5 0 P a r -2 0 0 P a r -2 5 0

Span (ft.)

P a r - 3 0 0

e pro du ced with perm ission of the copyright owner. Further reproduction prohibited without permission.



5. Com paring Self-W eight of Trusses o f Different Con figurations

The purpose o f this study is to compare the self-weights o f trusses o f different

configurations/types at different spans. A typical construction o f structural Tees for top

and bottom chords and equal-leg double angles for web members (Figure 2-7a) is

selected for the study.

Two series o f loading conditions are simulated -symm etric loading o f roof live

load applied through out the span of trusses and asymmetric loading of roof live load

applied on the right half of the whole span. Structural analyses are performed by the

MultiFrame and internal axial forces of all truss members are given by the program.

Figure 3-5 is a reproduction of internal axial force diagrams of the 200-ft spam

trusses. For the symmetric loading situation, critical compressive and tensile forces (C

and T in the figure) of the parallel chord Pratt and the Warren occur at mid-span in the

top and bottom chords and at the ends of span in web members. When the top chords

are cambered, the maximum compressive forces shift away from the mid-span a litter

bit but overall force pattern remains similar. For the arched-top and gable Pratt trusses,

the situation seems quit different from the above three cases. The force distributes

evenly over the top and bottom chords o f the arched-top Pratt, and there is no force in

the web members at all. For the gable, the critical forces of the top and bottom chords

occur at the ends of the truss span and the force in the web bars, being uneven in length,

distributes more evenly than those of parallel-chord and cambered-chord trusses.

e pro duc ed with perm ission of the copyright owner. Further reproduction prohibited without permission.



w r D L i L L ( s h o w n in f i g . J - 1 )

1-2936-

234J ------------------------J

L2 5 6 V '~4461-

'-256P

w i D L

Tw / DL 4 LL

-2466-

90C 246V __

r

" *1 __

Eg N Tto a c“ T __ _ J---

i—m -----------------------

L26 6V ~- — -4241-^--. - - -236P

Symmetric Lotdiog Asymmetric Lading

Figure 3-5 Interna l Axial Force Diagrams of 200 ft Span Trusses(Continuous line Compre ssion; Dashed line: tensi on. Drown in Scole. Unit: Kip.)



For the asymmetric loading situation, force patterns of all cases look similar to

those o f the symmetric loading situation. However, the critical forces occur at the live

load side, but are less than those in the symmetric loading situations. Except that, some

small compressive and tensile forces occur in the web members o f arched-chord trusses.

So. the selection o f the web members of arched-chord trusses should be based on the

asymmetric loading situation, while all others should be based on the symmetric loading

situation.

In consideration o f uneven distribution o f force in truss chords and limitation of

the length cf steel elements being able to be transported (less than 60 feet), design of top

and bottom chords are done for every other panel (50 feet per piece) except for the 100-

ft span cases. For simplicity, however, truss web members are designed as vertical or

compressive bars and diagonal or tensile bars in accordance with their critical

compressive and tensile forces.




5.1. Design of Steel Compressive Members

By assuming all trusses are braced at their panel joints, all compressive members

are designed for their own lengths.

Theoretically, design o f a compressive bar is a trial and error process, since the

allowable stress is a function of L/r . with L being the full length o f the member and r

being that for the weak axis, which cannot be known until the member is chosen.

However, the selection can be easily done by using available Column Design tables in

the AISC Manual, in which allowable compression loads have been predetermined for

specific lengths of various elements.

Example: Select a structural Tee o f A36 steel from AISC for a top chord o f the 200ft-

span parallel Pratt with C = 293 kips (Figure 3-5).

Solution:

From the data in table, we can make following reasonable choices:

a) WT12 x 81— KL = 26 ft . allowable Cxv = 342.298 kips:

b) WT13.5 x 80.5 — KL = 26 ft. allowable Cxv = 367 309 kips;

c) WT15 x 86.5— KL = 26 ft . allowable Cxy = 387/324 kips.

The lightest section— WT13.5 x 80.5— is the best choice.

26




5.2. Design of Steel Tensile Members

Assuming the cross section of member is not reduced, the stress permitted for

design is simply:

F, = 0.6Fy = 0.6 x 36 = 21.6 Icsi fo r A36 steel.

T A cross area A for a tension force T isA = — and the maximum allowable L r

F,

240. so rmm = L/240

Based on these two considerations, some possible choices from AISC Manual

can be made.

Example : Select a structural Tee o f A36 steel from AISC for a bottom chord of the

200ft-span parallel Pratt with T - 274 kips (Figure 3-5).

Solution:

, T 274.000 A = — = ----------- = 12.69 in

F, 21.600

L 25 x 12 _ J mtn — I ^ IH

240 240

From the data in table, following possible choices can be made:

a) WT7 x 45 — A = 13.2 in'. rxv = 1.66'3.70 in:

b) WT8 x 44.5— A = 13.1 in'. rxv = 2.2~ 2.49 in:

c) WT9-X. 43 — A = 12. ~ in'. rxv = 2.55/2.63 in:

d) WT10.5 x 46.5— A = 13. ~ in'. rxv = 3.25 1.84 in:

e) WT12 x 47 — A = 13.8 in2. rxv = 3.67/1.98 in:




f) WT13.5 x 47 — A = 13.8 in2, rxy = 4.16/2.12 in;

g) WT15 x 49.5 — A = 14.3 in2, rxy = 4.71/2.10 in.

The lightest section—WT9 x 43--is the best choice.

All trusses are designed to have lightest possible weight and designs are

recorded in Appendix A.

5.3. Comparison of Truss Self-Weight and Deflection

Total weight (in pounds per square foot) of all trusses shown in Figure 3-2 are

plotted in Chart 3-2. It is obvious that the self-weights o f trusses increase unlinearly

after a 250-ft span and the weight differences among trusses of different configurations/

types increase as trusses span longer. The biggest differences are 0.56psf. 1,29psf.

1.75psf. 1.93psf and 3.83psf for 100-ft to 300-ft span groups respectively. They are. in

other words. 26.4%. 34.4%. 32.1%. 26.3% and 36.3% increases based on each group's

lightest cases.

The arched-chord Pratt has the lightest self-weight among all truss

configurations/types at all spans except 200-ft span. The irregular situation at 200-ft

span, where the Warren weighs least, seems to be caused by the limitation of steel

sections and the roughness of design. And actually, the Warren, being the second

lightest truss type, weighs very close to the arched-chord Pratt at all spans. The

28

p rod uced with perm ission o f the copyright owner. Further reproduction prohibited without permissio n.



o 'SeV

X &

t ^ u s s c S

at ' s

\ 6



cambered-chord Pratt weighs alm ost the same as the Warren and less than the parallel

Pratt at the shorter spans o f 100-ft and 150-ft and the longer span of 300-ft: but at the

mid spans o f 200-ft and 250-ft. it weighs more than the parallel one. which could be

also caused by the roughness of the design. The gable has highest weight at all spans

except at 10 0 - f t .

Chart 3-3 compares the self-weight o f every truss with its original self-weight

assumption. The arched-chord Pratt, having the lowest self-weight, is 1.466psf lower

than the assumptions on average; the Warren, the second lightest truss type, is 1.378psf

lower: being the third and fourth, the cambered-chord and the parallel-chord Pratt

trusses are 0.99psf and 0.732psf lower than the assumptions respectively; the heaviest

truss type, the gable one. having higher self-weight than the assumptions o f 5psf .7psf.

9psf and 13psf from 150-ft through 300-ft spans, has slightly higher self-weight

(0.282psf) than the assumptions on average.

While the self-weights o f both top/bottom chords and web members increase

constantly for all truss types along with the increase of their spans, we observe that the

proportion of the web member weight increases and eventually exceeds that of chords

for some cases at longer spans (Chart 3-4). The average percentages o f web member

weight are 45.36%. 42.5%. 47.37%. 32.08% and 42.44% for the five groups

respectively. According to truss span, the average percentages o f web members are

33.37%. 36.78%. 42.98%. 45.93% and 52.2% from 100-ft to 300-ft span.




1 6

14

12

(0Q. 10

.2* 8

is= 6 o

CO

Chart 3-3 Comparison of Truss Weights with Assumptions

—O — T op /B ot . — X — W eb • T ot al - A ssu m p ti o n

coQ.

coQ.

o

I

0mCM

1

oIf )

e<0a

oIf )CM

ECO

O

oIf )

oIf )CM

Oif )

X>CO

O

oIf )CM

oTruss Type - Span

16

^ 14

a 12tT 10

8

6

4

2

0

Chart 3-4 Comparison of Top/Bottom Chordswith Web Members

I T o p /B o t . O W e b

a

1. . i

a>co

ca

CO 100%

8 0 %

60 %

o ©o oCM CM

CO COQ . 5

.Oa5ofl■S 40%

Oa

20%

0%

□ W e bTop /Bo t

Truss Type - Span

e prod uced with permission of the copyright owner. Further reproduction prohibited without permission.



Assuming the allowable deflection of truss with both dead and live roof loads

being L/240, which means 5 inches, 7.5 inches. 10 inches, 12.5 inches and 15 inches for

100-ft to 300-ft span respectively, the design results and compute r analyses show that all

trusses have far less deflections than the allowables (Chart 3-5). The average deflections

of 100-ft to 300-ft span trusses are 1.91 inches, 2.75 inches, 3.70 inches. 4.84 inches and

5.92 inches respectively. They are 38.2%. 36.67%. 37.00%, 38.72% and 39.47% of their

allowables.

Chart 3-5 Truss Deflection

Arc-300 — ------- ----- ---

W a r-3 00 i i ^ m m ' - - - •

Arc-250

W a r -2 5 0

etoQ.

CO

^ A r c- 20 0

aK W a r -2 0 0

Arc-150

W a r -1 5 0

Arc-100

W a r -1 0 0

0

□ A l l o w a b l e■ Def l ec ti on

6 8 10 12 14 16

Deflection (in.)

pr odu ced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.



It is interesting to notice that, while the gable Pratt has the highest self-weight at

almost all spans, it has the smallest deflection at all spans~an average of 32.71% of

allowable deflection amount—among all truss types. The second to the fifth are the

cambered Pratt—36.04%. the arched Pratt—38.56%. the Warren— 40.19% and the

parallel Pratt— 42.61%.

It needs to be pointed out that, in reality, the flat roof system shall be

investigated to assure adequate strength and stability under ponding conditions, which is

out o f the scope o f this study.

5.4. Conclusions

Trusses seem to be very economic structure types at a span less than 250 feet:

after this point, their self-weight increases non-linearly.

Truss configuration has an increasing impact on weight as the truss span

increases. The parabolic-arched-top shape, which follows a beam's moment curve, is

the most effective configuration by distributing internal forces/stresses even in its top

and bottom chords and dramatically reducing those in its web members. The cambered-

chord Pratt, surprisingly, does not show superiority over the paralle 1-chord Pratt at some

spans. Between the two parallel-chord ones, the Warren has more even internal

forces/stresses distribution and lighter self-weight than the Pratt over all spans. The

gable has reasonable self-weight only at small spans: so it seems not a good choice for

longer spans.

pro duc ed with perm ission o f the copyright owner. Further reproduction prohibited without permissio n.



The deflection o f a planar truss seems not to be a big concern except ponding

needs to be considered.

6. Com paring TS Construction with the WT&DL

Structural tube is used in this series of design o f chosen cases (100-ft. 200-ft and

300-ft span) in order to compare with the construction o f WT&DL. Loading conditions

and design methods are basically the same as the study before. However, there are two

points which need to be noticed: 1) the structural tube is o f A46 steel instead of A36: 2)

the selections o f member sections must have comparable dimensions in order to be

constructed and transfer load efficiently (Figure 2-7b).

pro du ced with perm ission of the copyright owner . Further reproduction prohibited without perm ission.



6.1. Design of TS Trusses

Example'. Select a structural tube of A46 steel from AISC for the 200ft-span arched-top

Pratt.

Solution: Referring to Figure 3-5. we design

1) top chords fo r C = 255 kips, L = 27ft.

From the data in table, possible square tube sections from the smallest are:

a) TS9x 9 x9 /16 (61.83)— KL = 27ft. allowable C = 279 kips:

b) TS10 x 10 x 1/2 (62.46) — KL = 27 ft. allowable C = 318 kips:

b) TS12 x 12 x 3/8 (58.10))— KL = 27ft. allowable C = 341 kips.

2) bottom chords fo r T = 234 kips, L = 25 ft.

. T 234.000 . . . . , L 25x12 soA = — = ------------= 8.48 in . rmm =------= ----------- = 1.23 in.

F, 27.600 240 240

From the data in table, following choices can be made in accordance with the top chord

choices.

a) TS9x 5 x 3/8 (32.58)— A = 9.58 in2. i\ = 2.0/ in:

TS9 x 6 x 5/16 (29.72)—A = 8.73 in2. ry = 2.43 in:

TS9 x 7 x 5/16 (31.84)—.-! = 9.36 in2. ry = 2.80 in:

TS9x 9x 5/16 (36.10 )— A =10.60 in2, r = 5.55 in

b) TS10 x 5 x 5/16 (29. ~2)—A =8.73 in'. rv = 2.07 in:

TS10 x 6 x 5/16 (31.84)— A =9.36 in'. rv = 2.46 in:

TSIOx 8 x 1/4 (29.23) — A = 8.59 in'. rv = 3.24 in:

TS10 x 10x 5/16 (40.35)— A = 11.90 in', r = 3.93 in:




c) TS12 X 6x3/8 (42.79)— A = 12.60 in2, ry = 2.48 in;

TS12 x 8 x 3/8 (47.90) — A = 14.10 in2, r , = 3.26 in;

TS12 x 12x 3/8 (58.10)— A = 17.10 in2, r = 4.72 in.

3) Vertical web bars fo r critical C = 4 kips, L = 23 ft.

From the data in table, following choices can be made in accordance with the top and

bottom chord choices.

a) TS9 x 5 x 5/16 (27.59) — KL = 23 ft, allowable C = 66 kips:

TS9 x 6 x 5/16 (29.72)— KL = 23 ft, allowable C = 101 kips:

TS9 x 7x 1/4 (25.82)— KL = 23 ft, allowable C = 113 kips:


b) TSIOx 5 x 5/16 (29.72) — KL = 23ft. allowable C = 74 kips;

TS 10x 6 x 5/16.(31.84)— KL = 23ft, allowable C = 111 kips :

TSIO x 8 x 1/4 (29.23)— KL = 23 ft, allowable C = 147 kips:

TS10 x 10x 5/16 (40.35) — KL = 23 ft. allowable C = 234 kips.

b) TS 12x 6 x 3 /8 (42.79)— KL = 24ft, allowable C = 139 kips:

TSIOx 8 x 3/8 (47.90) — KL = 24ft. allowable C = 233 kips :

TS12x 12 x 3/8 (58.10) — KL = 23 ft. allowable C = 367 kips.

4) Diagonal web bars fo r critical C= 10 kips, L = 34 ft.

From the data in table, following choices can be made in accordance with the top and

bottom chord choices.

a) TS9 x 5 x 5/16 (27.59) — KL = 34 ft. allowable C = 30 kips:

TS9 x 6 x 5/16 (29.72)— KL = 34 ft. allowable C = 46 kips:

36






b) TS 10 x 5 x 5/16 (29.72 )— KL = 34 ft, allowable C = 34 kips:

TS 10 x 6 x 5/16 (31.84)— KL = 34 ft , allowable C = 51 kips :

TSIO x 8 x 1/4 (29.23)— KL = 34ft, allowable C = 81 kips:

TSIOx 10x 5/16 (40.35)— KL = 34ft, allowable C = 162 kips.

c) TSI2 x 6 x 3/8 (42.79) — KL = 34 ft, allowable C = 69 kips:

TS 12 x 8 x 3/8 (47.90)— KL = 34 ft, allowable C = 134 kips :

TS 12 x 12 x 3/8 (58.10)— KL = 34 ft, allowable C = 289 kips.

Total weights o f TS9. TS10 and TS12 designs are 26,9901b, 28.1041b and 34.2071b

respectively. Since smaller section seems to achieve lighter truss weight, let us try TS8

sections, starting from a rectangle tube for the top chords.

1) Top chords:

TSIOx 8 x 5/8 (67.82)—KL = 27ft. allowable Cxv = 326/260 kips.

2) Bottom chords:

TS8 x 4 x 1/2 (35.24 )— A = 10.40 in : . ry = 1.54 in:

TS8 x 6 x 3/8 (32.58 )— A = 9.58 in " . i\ = 2.36 in:

TS8 x 8 x 5/16 (31.84)— A = 9.36 in 2 , r = 3.12 in:

TSIOx 8x 1/4 (29.23)—A = 8.59 in 2. ry = 3.24 in.

3) Vertical web bars:

TS 8x 4 x 1/4 (19.02)— KL = 24 ft , allowable C = 27 kips.

p roduc ed with perm ission o f the copyright owner. Further reproduction prohibited without perm ission.



4) Diagonal web bars:

T S 8 x 6 x 1/4 (22.42)—KL = 24ft, allowable C = 70 kips.

Total weight o f the TS8 truss is summed as 26.6151b. so it is the best choice.

By the same procedure, another 14 trusses are designed to have the lightest

possible weight and the designs are recorded in Appendix B.

6.2. Comparing with the WT&DL Construction

Chart 3-6 shows self-weights of all TS trusses. The weight differences between

trusses of different configurations/types increase, just like those o f the WT&DL trusses,

as trusses span longer, but they are not as dramatic as those of the WT&DL trusses. The

biggest differences are 0.29psf. 0.41psf. and 2.27psf for 100-ft to 300-ft span groups,

which are 13.74%. 8.45%. and 24.3% increases based on each group's lightest cases.

Except for the gable, the weight o f all other trusses increase almost linearly from 100-ft

to 300-ft span, which is different from the WT&DL trusses.

pro duc ed with perm ission o f the copyright own er. Further reproduction prohibited without permissio n.



Chart 3-6 Comparison of Self-Weights of

Tube Trusses @ Different Spans1 0

10

(0o(0(03

o>

£ £"5

CO

— P ara ll e l

-X— W a r r e n

C a m b e r e d

- © — A r c h ed

-X — G a b le

100 200

Truss Span (ft.)

3 0 0

rod uced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.



The arched-chord Pratt still weighs least among all truss types at all spans. The

cambered Pratt is the second lightest one this time. The Warren switches to the third

place. At 100-ft and 200-ft spans, the gable Pratt has lower weight than the parallel Pratt

and at 300-ft span , the gable weights most.

Chart 3-7 compares the self-weights o f TS trusses with those o f WT&DL

trusses. It shows obvious weight reduction at all cases. At 100-ft span, the truss weight

reduces 20.43% on average; at 200-ft span. 24.95%; at 300-ft span. 32.6%.

The truss weight distribution between its top/bottom chords and web members is

similar as that o f the WT&DL truss (Chart 3-8 and 3-4). The weights o f truss chords and

web members increases straightly for all truss types along truss span, and the proportion

of the web members increases as truss spans longer.

6.3. Conclusions

In concern o f the self-weight of truss, the tubular construction is more economic

than the WT&DL one. Reasons must be: 1) the TS sections have higher stress capacity:

2) tube sections have more even gyration radius between .v-.v and y-y axis, which makes

the use of material more efficient.

pro duc ed with permission of the copyright owner. Further reproduction prohibited without perm ission.



% o f C h o r d s & W e b B a r s

Chart 3-7 Comparison of TB Trusseswith WT&DL Trusses

16

14

^ 12

«a10 •

£8

12 6o

W 4

2

0

□ WT&DL IT B

o oin in

CM

CQ0 .

CQCL

O Oin wCM

| |

o oin in■»- CM

E £CO CO

O O

#o

iO

o

mCM

6<

o

m-OtoO

Truss Type - Span

Ma

o>

£

a>to

10

9

87

65

4

3

21

0

Chart 3-8 Comparison of Top/Bottom Chordswith Web Members

I T o p /B o t . □ W e b

8

100%

80 %

60%

40%

20%

0%I T o p / B o t. D W e b

.o o to o O ^

Truss Type - Span

pro duc ed with perm ission of the copyright owner. Further reproduction prohibited without permission.

G a b - 2 5 0



7. Com paring Combined Stresses with Axial Stresses for 200ft-Span

Cases

7.1. Design for Combined Stresses

Assuming that the dead and live loads of the roof are applied uniformly on the

top chords of the 200-ft span trusses directly, this study is trying to find out how loading

condition changes truss weight. Figure 3-6 shows a study schedule, in which the

concentrated load of P is that of the assumed dead weight o f truss only:

P = 7 x 25 x 30 = 5.25 Kips;

the distributed load of w generated by roof loads is calculated as

w = (12+20) x 30 = 0.96 Klf.

Computer analyses show that a moment of 75kip-ft occurs in all top chords and

axial forces in all members keep unchanged from the concentrated loading condition

(Chart 3-6 & 3-5). An asymmetric loading has also been checked for the arched-top

Pratt and internal forces in its web members are shown in the diagram by not showing

zero force o f the symmetric loading condition.

In investigating the combined actions of compression and bending, the following

formula must be satisfied.

f f — + — < 1.0

in which f a is the axial compression stress:

Fa is the allowable compression stress;

42

pro du ced with perm ission of the copyright owner. Further reproduction prohibited without permission.



P/ 2 P P P P P P P P/ 2

T f T f f ^ T T T T

p p p p p p p p

T T T TH'T ? ¥ ?

; j { i . J c f

/ 0 0 ' = B X 25

29JC j — m — tr-Ttr-

29JC

-zW-

gfflf wl2S6F--- --^■256fi

latenul Axiil Force 1 Moaeat Ditgrtm(Some os Fig.J-5. M = 75Kip-lI)

Figure 3-6 Trusses of Co mbined Stresses

4-04



f , is the actual bending stress;

Fb is the allowable bending stress.

Designing such a member is a trial and error process. Following steps are set up

to do the work. 1) find the area (A) and section modules (S) required if the actions of

compression and bending occur separately; 2) find possible sections with higher values

of both A and S from the step one; 3) verify the combined effect of compression and

f f bending o f one section at one time: if the formula — + — < 1.0 is satisfied, the section

Fa FH

is OK: but if — + — « 1.0. the section mav be more than enough~a section with a F, Fhd n

slightly lower A and/or S’values needs to be checked following the same procedure: if

~ r + — > 1.0. the section is not adequate and a section of higher A and/or S values*. F'ha n

must be verified and used.

Exam ple: Select a structural tube of A46 steel for the top chord o f the 200-ft span

arched-top Pratt with C = 255 kips and M = 75 kip-ft (Figure 3-6).

Solution:

1) For Ur = 50. Fa = 22.66 ksi

required A - — = --------% 11.25 in. F 22.66

For noncompact section. Fb = 0.6Fy = 0.6 x 46 = 27.6 ksi

Required S = -

4 4

e prod uced with perm ission o f the copyright owner. Further reproduction prohibited without permission .



2) For a first try. let us double both of A and 5 values and look for steel sections with

A = 2 x 11.25 =22.50 in.2

S = 2x32.61 =65.22 in.3

From AISC. we find following possible sections:

a) TS14x 10 x 1/2—w = 76.07p l f A = 22.4 in.2, Sx = 86.9 in.3, rx = 5.22 in.

b) TS12 x 12 x1/2—w = 76 .07plf, A = 22.4 in.2. S = 80.9 in.3, r = 4.66 in.

c) TS14 x 14 x 1/2— vv = 89.68 plf, A = 26.4 in.2. S = 113 in 3, r = 5.48 in.

3) Verify a) TS14 x 10 x 1/2

f , = — = — * 11.38 ksi. A 22.4

L r = =s 62, therefore Fa = 20.94 ksi.

M 75x12 Jb = — = --------- ' 10.36 ksi.

S 86.9

, 10 190 _ub. t = -— = 20 < - t— =28 => compact section,

X2

therefore Fb = 0.66FV= 0.66 x 46 = 30.36 ksi.

f L + f L= + 10^6 ^ Q 54 ^ = <

F, Fh 20.94 30.36

So the section ofT S1 4x 10 x 1/2 is OK! From previous experience, the design

of smaller section (TS 10) is lighter than that of bigger one (TS12). The sections of

TS12 x 12 x 1/2 and TS14 x 14 x 1/2 need not to be checked. Furthermore, a section of

45

p rodu ced with permission of the copyright owner. Further reproduction prohibited without permission.



TS9 can not be found for the top chord, TS10 sections should be best choice. TS10 for

other members need to be picked.

Another four trusses are designed in the same way and designs are recorded in

Appendix C.

7.2. Comparing with the Joint Loading Cases and Conclusion

Chart 3-9 shows that the combined stress cases weigh more than the joint

loading cases. For the five trusses of different configurations, the increases are 18.14%.

10.04%. 28.77%. 16.22% and 19.09% respectively.

10

9

8

-r- 7to

B 6

® 5

55 4

CO 3

Chart 3-9 Comparison of Trusses Loaded Differently

□ A x i a l ■ C o m b i n e d

o o o o o oo o o o o o*■“ CM CO CM CO

CQ CQ CQ (0 CQ CQQ . 0 . CL

§ § 5

oo

E(0O

ooCM

ECQ

O

ooCO

ECQ

o

o o oo o o

CM CO

O o< <

oo

ACQ

o

ooCM

ACO

o

ooCO

.oCQ

o

Truss Type - Span

46

rodu ced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.



8. Com paring D ifferent H /L Ratios for 20 0-ft Span C ases

8.1. Ratios of 1/5,1 /8,1/10,1 /12 .5 and 1/15

The height-to-span ratio o f trusses is to be studied to see how it affects the self

weight of trusses. Ratios o f 1/5. 1/8, 1/10. 1/12.5 and 1/15 are assumed to 200-ft span

trusses. Figure 3-8 shows complete study schedules (big dots show the original cases in

previous study) and internal ax ial force diagrams reproduced from MultiFrame. It is not

surprising to see that the lower the truss, the larger the compressive and tensile forces in

top and bottom chords. While vertical bars change lengths, the magnitude of the

compressive force in them remains unchanged. However, from higher to lower trusses,

tensile force in diagonal bars becomes larger in order to have the same amount of

vertical component to resist the same amount of shear force o f the truss viewed as a

beam.

Structural tubes are used in this series of designs. Design procedure is the same

as that in the section 6 and designs are recorded in Appendix D.

rodu ced with permission of the copyright owner. Further reproduction prohibited without permission.



m

e

e prod uced with perm ission o f the copyright owner. Further reproduction prohibited without permissio n.



m

e

‘N\

\ \

4%

I

H

$

%V >

r ❖

/ >»

<❖

§

j#<

\

<

&

i

ia

.OP

^ 0. ► 0. •> Q. ►

O. ►

' , o z ' / /.91 - p t i

49

p rodu ced with p ermission of the copyright owner. Further reproduction prohibited without perm ission.

F i g u r e

3 - 7

- 2

W a r r e n

T r u s s

a t D i f f e r e n

t H / L

R a

t i o s



\ I 5}i

}

p-K

o

CU •»

Q> f *r

x .0* ' .S t , o t .5 /

\

'Z

I

>-r /

<*>n

*?

1£eCQ

50

e pro du ced with perm ission of the copyright owner. Further reproduction prohibited without permission .



H:L = l: 5 p

T T f

T P/2

H;L = l: 8

T T T

p/2 T T ft*

H:L * / : ,

..1 ft? f ? ' ! * T T /*/?

H : L = 1:1 2.5

7*

H: L = 1; I.

200' = 8 X 25'

i OL i LL (shown ol left)

--2MT --------------- L-fft H ----------------------- M - J

------

n !L - 2m ----------

L ------------------------- --------------------------J

-4&&

i !■285T --------------------------------------

Atff-

C S d rK E p n s t s s c n-439C-

i iJ ---------------------- - 4 m -

latemil Axitl Farce Dugnai (Some as Fig.j-5)

Figure 3-7-4 Arched-To p Pratt at Dif feren t H/L Ra tios



roduc ed with perm ission of the copyright owner. Further reproduction prohibited without permission.



8.2. Comparison and Conclusions

Self-weights o f the 15 trusses are plotted in Chart 3-10-1. It is c lear that the

parallel-chord Pratt and the Warren have the lightest weight at a height-to-span ratio o f

1/10; the cambered-chord Pratt has the lightest weight at 1/8; the arched-chord has the

same and lightest weight at 1/8 and 1/5; and the gable Pratt has the lightest weight at

1/5. In each truss configuration/ type group, the worst case could raise the truss weight

up to 36.83%. 47.65%. 73.97%, 36.49% and 103.90% of the lightest case. It seems that

the height-to-span ratio is a key fact to the self-weight of trusses.

Chart 3-10-2 and 3-10-3 show more details. We see that the self-weights of

chords go straight up as trusses get lower. However, the tricky part is the weight o f web

members. On one hand, in the higher truss, the vertical web bars are actually designed to

have reasonable slenderness ratios rather than resisting forces/stresses. On the other

hand, in the lower truss, the diagonal web bars need to be designed to resist much bigger

tensile forces. Combined result is that a medium height-to-span ratio around 1/10 seems

better.

p roduc ed with perm ission o f the copyright owner. Further reproduction prohibited without perm ission.



Chart 3-10-1 Comparison of Self-Weights of

Trusses @ Different Height-to-Span Ratios

10

<0a« 6a>«M3

t 5O

at

5 4

"35to

- P a r

- X — W ar

—I C a m

-© — A rc

-X — G ab

“ " “ A ssu m .

1to5 1to8 1to1 0 1to12.5 1to15

Height-to-Span Ratio




aco 3

2

1

Chart 3-10-2 Comparison of Self-Weight of Trusses@ Different H/L Ratios

1 0

9

8

‘a 7 S.r e£® 5o

5 4

—O — T op/ B ot .

• T otal

—X— W eb

— A ss um pti on

V < v <

a cm•i oCQ

o- ti.(Qa

00oI

tnCM

0

1

00o mCM

E £ CO I

O EcoO

u<

mCM

2o<

Truss Type - H/L Ratio

i i CMr-

.o 2COOCO

O

(0

O)

I£a>co

10

9

8

7

6

5

4

3

2

1

0

Chart 3-10-3 Comparison of Self-Weight of Trusses@ Different H/L Ratios

□ W e b

■ T o p / B o t .

co in2 oi

1 5ra »-O Aa

O

Truss Type - H/L Ratio

R eprod uced with permission of the copyright owner. Further reproduction prohibited without permission.



9. Comparing Different Panel Sizes for 200-ft Span Cases

9.1. Panel Sizes of L/4, L/6, L/8, L/10 and L/12

The panel size of trusses is to be studied to see how it affects the self-weight of

trusses. Panels o f L/4. L/6, L/8, L/10 and L/12 are assumed for 200-ft span trusses.

Figure 3-8 shows complete study schedules (big dots show the original cases) and

internal axial force diagrams reproduced from MultiFrame. The critical compressive and

tensile forces in top and bottom chords remain unchanged in all cases while the lengths

of truss chords change. While the critical compressive forces in the vertical bars at the

ends o f a span remain unchanged, the critical tensile forces in the diagonal bars at the

ends of the span get smaller in shorter panel size cases. A different situation is that of

the Warren: the smaller the panel size, the smaller the compressive forces, but the larger

the tensile forces in web members.

Structural tubes are used in this series o f designs. The design procedure is the

same as that shown in the section 6 and designs are recorded in Appendix E.

p rodu ced with permission o f the copyright owner. Further reproduction prohibited without permission.



4 X SO"Fuel

2P/3 4P/3 2P/3

1 1 1 1 1 1 1

6 X 33'-4’ Ptnel

P /2 P P /2

iX 2f Ptael

2P/5 4P/5 2P/5

1 1 1 1 1 1 1 1 1 1 1

A D10 X 20" Ptael

P /3 2P /3 P /3

1 1 1 1 1 1 1 1 1 1 1 1 1

p w i i w w| 12 X If-T Ptael

L 20 0 ' '

-2936-

-2J6T'i

-249P J

-2936 ----- •------

1------ 260 f ------r

-2936-

-2936-

■— -284 P-

- 2 9 3 6 -

SSSSEOZBSSM"^ -'-'-2 84 3'-'~-r'

latenul Axitl Font Diigrtau(Some as fig.3-5 )

F i g u r e 3 -8-1 P a r a l l e l - C h o r d P r a t t o f D i f f e r e n t P a n e l S iz e s

Vi —J



4P/3 4P/3

1 1 1 1 1 1

P P

4P/5 4P/5

1 1 1 1 1 1 1 1 1 1

f j w w w w \

2P/3 2P/3

1 1 1 1 1 1 1 1 1 1 1 1

/ W T O M A A A A A

12 X W4T

_________ i 293C i __________

4 X SO*Fuel -iWF

/ \ / \ / \ / \ / \ / \6 X W r P t a t l ' 1— 293T — r

/ v w w v v x8X2fPioel X" "L- — ------------J" " J

w / W \ / V V A V /

--2934'-

20 0 ' | Internal Axitl Force Diignms(Some os Fig.3-5)

F i g u r e 3- 8* 2 W a r r e n T r u s s o f D i f f e r e n t P a n e l S i z e s

oc



4 X SO’Prnel

4P/3

P /2

6 X J3’-4mPtne!

P /2

f ^ ^ T \ 1 7 P P T ^ i8 X 2 f Ptoel

4P/5

- T

10X20'Ptx!

2P/J

200 '

-2491- J

1 1------ 2401------1 1

" I - --------------!44T ^ -- T -

456 — IT

- — -2441- — -

Intend Ad d Farce Ditgnat (Some os Fig.J-5)

F i g u r e 3- 8- 3 C a m b e r e d - T o p P r a t t o f D i f f e r e n t P a n e l S i ze s



4 XSV Fuel

2P/3 ?

6 X 33’-4’ Fuel

t X 2 f Pint!

AP/5

» »__!» f * T 2P/5

10X20'PtotI

2P/3

» j J r m - T L L i T P/i

12 X I f r Fuel

2 0 0 ' latcm tl Axial Force Ditgnms (Some os Pig.3-5)

Figure 3-8-4 Arched-Top Pratt of Diffe ren t Panel Sizes



61


F i g u r e

3 - 7 - 5

G a b

l e

P r a t t o f

D i f f e r e n

t

P a n e l

S i z e s



9.2. Comparison and Conclusions

Self-weights of the 15 trusses are shown in Chart 3-11-1. At the panels of 16.7-ft

to 33.3-ft. the weights of trusses are pretty close; but at the big panel of 50-ft. trusses

weigh a lot more. Specifically, the 50-ft panel trusses weigh 64.89%, 46.01%, 68.01%.

56.67% and 48.68% more than the best cases in five truss groups respectively. Except in

the 50-ft panel cases, the differences are jus t 9.33%. 3.05%. 10.66%. 10.77% and

8.99%.

Chart 3-11-2 and Chart 3-11-3 show more details. We see that the self-weights

of the chords go down steeply, just like the total weights of trusses, from 50-ft to 33.3-ft

panel, but go down very slowly from 33.3-ft to 16.7-ft panel. Since the smaller the panel

size, the more the number of vertical bars, but in larger panel cases, diagonal web bars

need to be designed to resist much larger tensile forces at longer length, web bars weigh

less at medium panel sizes. Overall result is that the Warren weighs least at L/8 panel

size of 25-ft and all others weigh least at L/10 panel size of 20-fit.

p roduc ed with permission of the copyright owner. Further reproduction prohibited without permission.



Chart 3-11-1 Comparison of Self-Weights of

Trusses with Different Panel Sizes

8

— — P ar

-X— W ar

I Cam

O Arc

■X— G ab

■“ " A s s u m p t i o n

Truss Type - Panel Size

rod uced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.



Chart 3-11 -2 Comparison of Self-Weight of Trusseswith Different Panel Sizes

(0O ; 5

3 *

12 3

'sV ) _ >S<-x-*'XXV>fJC'x >Sc-x-x

-T o p /B o t. —X— W e b -T otal -A s s u m p t i o n

tO oCO CM

X XCO oO T -

CO OCO CM

X X

§ 2

CO oCO CM

X XCO oo

CO

0.CQ0. I I

ECQ

oECD

o

CO oCO CM

X X

5 26 6< <

CO oCO CM

X XCO o© ^x> .oCD CD

O O


Chart 3-11 -3 Comparison of Self-Weight of Trusseswith Different Panel Sizes

CA

.5* 4

I3

0)CO

□ W e b

■ T o p /B o t .


ep rodu ced with perm ission of the copyright owner. Further reproduction prohibited without permission.



IV. Conclusions and Recommendations

In summary of the previous studies, following conclusions can be drawn:

• Truss configurations have an increasing impact on the weight of the truss as

a truss span increases. The parabolic-arched top chord is the best configuration.

The gable is good only at short spans. The Warren and the cambered-chord Pratt

are usually better than the parallel-chord Pratt.

• A structural tube truss is more economic than WT&DL truss considering the

weight o f the truss alone.

• Direct chord loading could increase truss self-weight about 20% and should

be avoided.

• The height to span ratio plays an important role in reducing truss self-weight.

The study shows that the average ratio of 1/10 is the best ratio. For the parallel-

chord Pratt and the Warren, extremely high ratios should be first avoided: for the

gable, the cambered-top and the arched-top Pratt, extremely low ratios should be

avoided.

• For trusses of the H/L ratio of 1/10. L/10 is also the best panel size for all

Pratt trusses (web bar— 45°); however. L/8 is the best for the Warren (web bar—

50°). Larger panels over L/6 seem very uneconomical because of truss self

weight.

With truss weight alone, the final cost of a truss has not been determined yet.

Joint construction cost, which makes up another part of the total cost, needs to be

65

p rod uce d with perm ission of the copyright owner. Further reproduction prohibited without permission.



investigated and the investigation can only be done case by case because the labor cost

is mainly depended on other considerations such as the overall scale of a project, the

availability of skilled labor and etc. There is. actually, no straight forward answer to the

economics of the truss structure according to Professor Dimitry Vergun. who practices

in the field for over 40 years.

However, for a given truss with its span predominantly determined by

architectural concerns, its height-to-span ratio is the most important factor for material

efficiency according to this series study. Bearing this in mind at preliminary design

stage, architects will significantly contribute to architectural and structural synergy.

p rodu ced with perm ission o f the copyright owner. Further reproduction prohibited without permission.



Appendix A:

Design of WT&DL Trusses of 100-ft, 150-ft, 200-ft, 250-ft, 300-ft Spans

68-72

Appendix B:

Design of Tube Trusses of 100-ft, 200-ft, 300-ft Spans

73-75

Appendix C:

Design of 200-ft Span Trusses for Combined Stresses

76

Appendix D:

Design o f 200-ft Span Trusses at Different H/L Ratios

77-81

Appendix E:

Design o f 200-ft Span Trusses of Different Panel Sizes

82-86




Appendices

Appendix A: Design of WT&DL Trusses

WT7XJ0.5

DL3X3X5/16—^ r ^ r ^ r ^ L A S \ / \ / \ ~-DL4X4X5/l6

__________ WT5X19.5 _________ __

WT7X30.5

DL3X3X3/16 ~ A / \ / \ / \ / \ / \ / \ A - DL5 X5X5/I6

WT7X21.5

WT7X26.5

DL4X4X1/4 — f r s j x l ' x l \ [ / ' | y i / V > - t t W ? / <

__________ WT6X17.5 _________

WT7XJ0.5

DL3 .5X3.5XI/4 - -DL2 .5X 2.5 XJ /I6

WT7X17

WT7XJ0.5

DL4X4X1/4 -DL4X4X1/4

WT7X19

Figure A’l 100-ft Span

68

prod uced with permission of the copyright owner. Further reproduction prohibited without permission .



Appendices

WT10.SX50.5 WT 12X58.5 WT10.5X50.5

0L5X5X3/8-

WT7X19 WT9X30 WT7X19

— DL6X6X3/8

WT10.5X50.5 WT12X58.5 WT10.5X50.5

DL3.5X3.5X1/4~ -DL6X6X5/8

DL6X8XJ/8-

DL6X6X3/8 —

WT7X26.5 \ WT8X33.5 WT7X26.5

WT9X43 WTI0.5X50.5 WT9X43

WT8X20 WT9X27.5 WT8X20

WT 10.5X55.5

-DL5X5X5/16

— DL3.5X3.5X1/4

WT7X26.5

WT 12X58.5 WT10.5X50.5 WT12X58.5

DL8X8X1/2 — ------ ----- 0L5X5X3/8

WT9X27.5 WT9X38 WT9X27.5

F igu re A-2 150-ft Span

69




Appendices

WT10.5X6 1 . WT15.5X 80 .5 WT 10.5 X61

1 1

016X6X5, QHM6. 5 / p ^

WT7X21.5 WT9X45 WT7X21.5

WT10.5X61 WT15.5X80.5 , WT10.5X61

WT6X29 WT10.5X46.5 WT6X29

WT10.5X61 WT12X65.5 WT10.5X61

NWT9X25 WT8X58.5 WT9X25

WT15.5X75

^ ^ D M K 8 K 1 / 2

WT7X57

WTI5.5X80.5 WT 12X75 WT15.5X80.5

A iWT7X41 WT9X58 WT7X41

Fig ure A-3 200-ft Span

70

pro du ced with perm ission of the copyright owner. Further reproduction prohibited without permission.



Appendices

WT!2X 65 .5 WT!5X95.5 WT15X95.5 WTI5X95.5 WT12X65.5

WT13.5X5J WT! 0.5X22WT10.5X22 WT!3.5X51 WT15X58

WT12X65.5 WT15X9 5.5 WT15X95 .5 WT15X95.5 WT12X65.5

WT9X32.5 WT13.5X57 I WT10.5X61 ■ WT13.5X57 \ WT9X32.5

WT12X73 WT 15X86.5 WT13.5X80.5 . WT15X86.5 WT12X73

WT6X26.5 WT9X48.5 WTJ0.5X50.5 WT9X48.5 WT6X26.5

WT 13.5X89

DL9X8X1/2 6X3/J.

WT9X48.5

WT15X95.5 WT15X95.5 WTI2X73 WT15X95.5 WT15X95.5

X9 XJ /2

WT 10.5X55.5 WT10.5X55.5

Figure A-4 250-f t Span

71

e pro duc ed with permissio n of the copyright owner. Further reproduction prohibited without perm ission.



Appendices

WT13.5 X8 0.5 WT15X105.5 WT 16.5 X1 20 .5 WT 15X 105 .5 WT 13.5 X80 .5

WT8X25 WT 10.5X61 WT18X80 WT10.5X61 WT8X25

WT13.5X80.5 , WT15X105.5 , WT16.5X120.5 , WT15X105.5 WT13.5X80.5

/ y k \ / \ / \ / \ h N w \ A AWT10.5X36.5 WT18X67.5 WT18X80 WT18X67.5 WT10.5X36.5

WT13.5X80.5 WT15X105.5 WT15X105.5 WT 15X105.5 WT 13.5X80.5

WT9X30 WT10.5X61 WT18X67.5 WT10.5X61 WT9X30

WT16.5X120.5

8X1A

WT 18X130 WT 16.5X120.5 WT15X95.5 WT16.5X120.5 WT18X130

lilt X.

WT12X73 WT10.5X6I WT9X48.5 WT10.5X61 WT12X73

Figu re A-5 300 -ft Span

72




Appendices

Appendix B: Design of Tube Trusses

_________ TS6X6X5/J6 _________

TS6XJXJ/16— f K S \ T \ i \ l / l / i / \ S h -TS6X4XJ/16

__________ TS6X4X1/4 __________ _

TS6X6X5/16

!S6X3X3/l6~ / \ / \ J \ J \ / \ / \ / \ / \ r - TS6X5XJ/16

_______ TS6XJX5/16 _______ _

_______ TS6X6X1/4 _______

TS6X3X3/16 — \ l X l X \ / \ / \ s S \— 156X3X3/16

TS6X3X1/4----

_______ 156X6X5/16 _______ _

156X3X3/16 - -156X3X3/16

__ _______ 1S6X5X3/16 ______

1S6X6X5/16

156X3X3/16 -1S6X4X3/16

' __________ 1S6X6X3/16 _________ J

Figu re B-l 100-ft Sp an

73

rodu ced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.



Appendices

T S 9 X 9 X 1 / 2 __________ TS9X9X9/16 _________ TS9X9X1/2

TS9X7X1/4 159X6X3/8 TS9X7X1/4

TS9X9X1/2 , T59X9X9/16 , TS9X9X1/2 ,

T S 9 X 7 X 1 / 4 ___________ TS9X9X5/16 _______________ TS9X7X1/4

T S 8 X 8 X 9 / 1 6 ___________ TS10X8X9/16 ______________ TS8X8X9/16

1S8X4X1/4 _______________ TS8X8X5/16 _________ TS8X4X1/4

TS10X8X5/8

TS10X8X1/4

TS9X9X9/16 ___________ T59X9X1/2 _______________ TS9X9X9/16

'7X//4

159X7X1/4 TS9X7X5/I6

Figure B-2 200-f t Span

74

pro duc ed with permissio n of the copyright owner. Further reproduction prohibited without permission .



Appendices

T S1 4 X1 0 X 3/ 8 1 5 1 4 X 1 0 X 5 / 8 __________ TS14X10X5/8 ____________ TS14X10X5/8 TS14X10X3/8

TS10X8X9/16 TS 10X8X1/4 TS10X10X3/8 TS10X10XJ/8 TS 10X8X1/4

TS 14X 10X3 /8 TS14X10X5/8 . TS14X10X5/8 , TS14X10X5/8 TS14X10X3/8

TS10X10X1/2TS 10X8X 1/4 TS 10X6X9/16 TS 10X6 X9/16 TS10X8X1/4

TS14X10X3/8 TS14X10X1/2 _____________ TS14X10X1/2 _____________ TS14X10X1/2 TS14X10X3/8

TS1DX8X /h

TS 10X8 X1/4 TS I OX 10X3 /8 TS 10X6X 9/16 TS10X10X3/8 TS10X8X1/4

TS 14X10 X5/8

fSIL X8 X1 /4

TS10X5X9/16

TS 12X12X5 /8 __ TS12X12X5/ 8 i _____________ TS12X12X1/2 _____________ TS 12X12X5/8 < 75/2X12X5/8

TS 12X1 2X3/8 TS12X8X3/8 TS1 2X8 X3/8 TS 12X12X3/8

Fig ure B-3 300-ft Span

pro duc ed with perm ission o f the copyright own er. Further reproduction prohibited without permissio n.



Appendices

Appendix C: Design of 200-ft Span Trusses for Combined Stresses

TS14X10X1/2 ______________ TS14X10X1/2 _________ TS14X10X1/2

TS W 8 X / 4 T ^d xa y i/ ’

TS10X8X1/4 TS10X5XJ/8 TS 10X8X1/4

TS14X10X1/2 , TS14X10X1/2 TS14X10X1/2

/ \ / s% ^ \/\/\/V /V /\TS10X8X1/4 ■ TS 10X8X5/16 ' TS 10X8X1/4

TS 14X10X1/2 TS14X10X1/2 TS14X10X1/2

NTS10X8X1/4 TS 10X6X5/16 TS 10X8X1/4

TS14X10X1/2

^ f ^ J S m 8 K l / 4

TS 10X8X1/4

TS14X10X1/2 TS14X10X1/2 TS14X10X1/2 .

n

TS 10X6X5/16 ' TS 10X8X1/4 i TS 10X6X5/16

F igure C

76

pro duc ed with permission of the copyright owner. Further reproduction prohibited without permission.



Appendices

Appendix D: Design of 200-ft Span Trusses at Different H/L Ratios

TS 10X8X1/4 , __________ TSWX10X5/16 _____________ TS10X8X1/4

TS10X8X

TS 10X8X1/4 TS10X8XJ/4 TS 10X8X1/4

T S 8 X 8 X 1 / 2 ____________ TS8X8X5/8 ________________ TS8X8X1/2

T S 8 X 4 X 1 / 4 ____________ TS8X4X3/8 ___________ ; TS8X4X1/4

See Figure B -2

TS10X10X1/2 _____________ TS10X10X9/16 TS10X10X1/2

TS 1 0 X 8 X 1 / 4 __________ TS10X8XJ/8 _________ TS 10X8X1/4

TS10X10X1/2 ____________ TS14X10X5/8 ______________ TSIOXlOXI/2^

TS 10X 8X1 /4 ____________ TS10X6X9/16 ________ TS10X8X1/4

Fi gure D- l Pa ra l l e l C ho rd P ra tt

77




Appendices

TS 10X8X 1/4 . TS10X 10X5/16 TS 10X8X 1/4

TS 10X8X1/4 TS10X8X1/4 TS 10X8X1/4

TS8X8X1/2 TS8X8X5/8 TS8X8X1/2

TS8X4X1/4 TS8X8X5/16 _________ TS8X4X1/4

/wwvw\ See Figure B- 2

TSI0XI0XJ/2 _________ TS 10X10 X9/16 TS10X10X1/2

TS 10X8X1/4 ____ TS1GX5X1/2 _________ TS10X8X1/4

TSI0XI0XJ/2 < TS14X10X5/8 < TSlOXlOXl/2^

TS 10X5X3 /8 __________ TS 10X6X 9/16 TS10X 5XJ/8

F igu re D -2 W ar ren

pro duc ed with perm ission o f the copyright own er. Further reproduction prohibited without permiss ion.



Appendices

TS8X8X 5/16 TS8X8X3/8 TS8X8X5/16

TS8X4X1/4 TS8X4XI/4 : TS8X4X1/4

See Figure 8 -2

TS9X9X9/I6 TS9X9X5/8 TS9X9X9/16

\r S 9 X S X 5 Y 1 6 FX7X1Z


TS10XWX5/8 TS10X10X5/8 JS1 0X10X5/8

XjsmshjA^K

TS 10X6X3/8 TSTSI0X5X9/I6 _____________ TS 10X6X3/8

TS 12X1 2X5 /8 TS 12X12X5/8 TS 12X12X5/8

r ~ ~ - ^ l l S T ? X 6 X J / 2 '

TS 12X6X 1/2 TS12X6X5/8 TS12X6X1/2

Figure D-3 Cambered-Top Pra t t

79

pro duc ed with perm ission o f the copyright owner. Further reproduction prohibited without perm ission.



Appendices

TS 10X8 X1/2

TS8X4X1/4

See Figure B -2

TS10X10X1/2

TS10X8X5/16

TS10X10X5/8

TS10X5X1/2

______________ TS12X12X1/2 __________________________ _

_______________ TS _12X6X1/2 ___________________________

Figure D-4 A rched-T op Pratt

80




Appendices

TS 14X1 0X5/8

See Figure B -2

TS10X10X9/16 TSI4X10X5/8

TS10X6X9/16 TS10X8X5/16 TS10X6X9/16

TS 12X12X5/8 TS 12X12X1/2 TS 12X12X 5/8

TS12X6X5/8 TS 12X8X5/8 TS12X6X5/8

TS 16X12X5/8 TS 12X12X5/8 TS 16X12X 5/8

TS16X12X1/2 TS 12X12X5/8 TS16X12X1/2

TS 16X16X5/8 TS16X16X1/2 TS 16X16X5 /8

TS 16X16X1/2 TS 16X8X1/2

i

1516X16X1/2

Figure D-5 Gable Pra t t

rodu ced with permission of the copyright owner. Further reproduction prohibited without permission.



Appendices

Appendix E: Design of 200-ft Span Trusses of Different Panel Sizes

TS12X12X5/8 TS 16X12X5/8 TS 12X12X5/8

TS1J/£X3/8— ~

TS 12X8X3/8 TS12X8XJ/8 TS 12X8X3 /8

TS10X10X5/16 , TS10X10X9/I6 TS14X10X1/2 TS10X10X9/16 , TS10X10X5/16

SIC (8X1.

TS 10X8X1/4 ITS 10X8X1/4 m TS10X5X3/8 _ \TS10X8Xl/4. TS 10X8X1/4

See Figure B -2

TS8X8 X1/2 TS 10X8X1/2 TS8X8X1/2

T S 8 X 4 X 5 / I 6 ________ TS8X4X1/2 TS8X4X5/16

T S 8 X 8 X 3 / 8 ___________ TS8X8X9/16 _______________ TS8X8X3/8

I 4.


Fig ure E-I Para l lel -Chord P ra t t

82

e prod uced with permission of the copyright owner. Further reproduction prohibited without permission.



Appendices

. TS12X12X5/8 . TS16X12X5/8 TS12X12X5/8

* TS 1 2X8X3/ 8 __________ TS12X8X3/8 _________ i TS 12X8 X3/8

TS10XWX 5/16 TSW XW X9/!61S,4XWX,/'2TSW XWX9/16 TSI0X10X5/16

! ;

TS 10X8X1/4' TS 10X8X1/4 TS 10X8X5/16 TS 1 0 X 8 X 1 /4 'JS 1 0X 8x f/4

M A / \ / W V \See Figure B -2

TS8X8X1/2 t | TS 10X8X1/2 _ _ TS8X8XI/2

M A A A A A A ^ ATS8X4X3/8 > TS 10X8X5/16 TS8X4 X3/8

TS8X8X3/8 _ _ TS8X8X9/I6 l TS8X8X3/8 _

/WVVXAAA/V^ATS8X8X1/ 4 _______ TS10X8X5/16 _________ : < TS8X8X1/4

Figu re E-2 W arren

83




Appendices

TS12X12X5/8 TS12X12X5/8 TS 12X12X5/8

TS13X8XJ/8

TS 12X8X3/8 TS12X8X3/8 TS12X8X3/8

TS! OX 10X 3/8 TS10X10X1/2 TS10X10X1/2 TS10X10X1/2 , TS10X10X3/8

S10X8X4/4 TS1M8XL

TS10X8X 1/4 TS10X8XJ/4 TS10X5X5/16 TS10X8X1/4 ' TS10X8X1/4

See Figure B- 2

TS8X8X1/41 TS8X8X1/2 < TS8X8X1/2 JS8X 8X1/2 JS8 X8 X1/4

- TS8X6K1/ E8X6X1Y4>

TS8X4XJ/4i TS8X8X1/4 TS8X8X5/16 JS 8X 8X I/4 TS8X4X1/4



Figure E-3 Cambered-Top Pra t t

8 4

p rod uced with perm ission o f the copyright owner. Further reproduction prohibited without permission .



Appendices

TS14X14X1/2

1x10X3/8

TS14X10XJ/8

TS 10X10X5/8

TS 10X8X1/4

See Figure B -2

TS8X8X9/16

TS8X8X5/16

TS9X7X9/16

TS7X7X3/8

Figure E-4 Arched-Top Pra t t

85

ro du ced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.



Appendices

TS14X14X1/2

7X3/1 7X3/8

: TS14X10X3/8 \ : TS14X10X3/8

TS14XJ0X1 /2 TS14X10XJ/8 , TS74X10X1/2

TS 10X6 X5/18 TSI0X8 XI/4' TS10X10X5/16 TS 10X8X1/4 I TS70X6X5(16

See Figure B- 2

TS8X8X5/8 [ TS8X8X9/16 TS8X8X3/8 TS8X8X9/16 TS8X8X5/8

'1X1/4 TSV

TS8X6X3/8 TS8X8X1/4 : TS8X6Xl/4_ <TS8X8X1/4 TS8X6X3/8

TS8X8X9/16 ____ TS8X8X1/2 ______________ TS8X8X9/16

TS8X4X1/ ? TS8X8X1/4 i TS8X4X1/2

F i g u r e E -5 G a b l e P r a t t

86

pro duc ed with permissio n of the copyright owner. Further reproduction prohibited without permissio n.



Reference

Reference

AISC. Manual o f Steel Construction/Ninth Edition.

Ambrose. James. Building Structures. John Wiley & Sons. Inc., 1993.

Ambrose, James. Design of Building Trusses. John Wiley & Sons, Inc., 1994

Griffin. C. W., and R. L. Fricklas. The Manual o f Low-Slope Roof Systems. McGraw-

Hill. 1996 & 1982.

Holgate. Alan. The Art in Structural Design. Clarendon Press, Oxford. 1986

MacDonald. Angus J. Structure and Architecture. Butterworth-Heinemann Ltd, 1994.

Mann. Thorbjoem. Building Economics for Architects. Van Nostrand Reinhold. NewYork. 1992.

Melaragno. Michele. Simplified Truss Design. Van Nostrand Reinhold Company.

Parker. Harry, and James Ambrose. Simplified Design o f Steel Structures. John Wiley& Sons. Inc.. 1990.

Parker. Harry, and James Ambrose. Simplified Engineering for Architects and Builders.

John Wiley & Sons. Inc.. 1994.

Salvadori. Mario and Robert Heller. Structure in Architecture. Prentice-Hall. Inc..

Englewood Cliffs. New Jersey. 1986.

Schueller. Wolfgang. The Design o f Building Structures. Prentice Hall. Inc.. 1995.

Torroja. Eduardo. Translated by J.J. Polivka and Milos Polivaka. Philosophy of

Structure . University of California Press. 1962.

pro duc ed with permissio n of the copyright owner. Further reproduction prohibited without perm ission.



w

IMAGE EVALUATION TEST TARGET (Q A -3 )

<

£

150mm

steel roof truss optimization

Documents