Truss Angle Section

EFFECTS OF DIFFERENT TRUSS SHAPES TO THE DESIGN OF PLANE

TRUSS USING ANGLE SECTIONS

LAU WEI THENG

UNIVERSITI TEKNOLOGI MALAYSIA

UNIVERSITI TEKNOLOGI MALAYSIA PSZ 19:16 (Pind. 1/97)

BORANG PENGESAHAN STATUS TESIS

JUDUL : EFFECTS OF DIFFERENT TRUSS SHAPES TO THE DESIGN OF

PLANE TRUSS USING ANGLE SECTIONS

SESI PENGAJIAN : 2005/2006

Saya : LAU WEI THENG

(HURUF BESAR)

mengaku membenarkan tesis ini disimpan di Perpustakaan Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut :

1. Hakmilik tesis adalah dibawah nama penulis melainkan penulisan sebagai projek bersama dan

dibiayai oleh UTM, hakmiliknya adalah kepunyaan UTM. 2. Naskah salinan di dalam bentuk kertas atau mikro hanya boleh dibuat dengan kebenaran bertulis

daripada penulis. 3. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan pengajian

mereka. 4. Tesis hanya boleh diterbitkan dengan kebenaran penulis. Bayaran royalti adalah mengikut kadar

yang dipersetujui kelak. 5.*Saya membenarkan/tidak membenarkan Perpustakaan membuat salinan tesis ini sebagai bahan

pertukaran di antara institusi pengajian tinggi. 6. **Sila tandakan (9 )

SULIT (Mengandungi maklumat yang berdarjah keselamatan atau kepentinganMalaysia seperti yang termaktub di dalam AKTA RAHSIA RASMI 1972)

TERHAD (Mengandungi maklumat TERHAD yang telah ditentukan oleh organisasi/

badan di mana penyelidikan dijalankan)

TIDAK TERHAD

Disahkan oleh

____________________________________ _______________________________ (TANDATANGAN PENULIS) (TANDATANGAN PENYELIA) Alamat Tetap : 6, TAMAN TAIPING SELATAN, TN. HJ. YUSOF B. AHMAD JALAN KAMUNTING, (NAMA) 34000 TAIPNG, PERAK.

Tarikh : 27 APRIL 2006 Tarikh : 27 APRIL 2006

CATATAN : * Potong yang tidak berkenaan.

** Jika Tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/organisasi berkenaan dengan menyatakan sekali tempoh tesis ini perlu dikelaskan sebagai SULIT atau TERHAD.

I hereby declare that I have read this report and in my opinion

this report is sufficient in terms of scope and quality

for the award of the degree of Bachelor of Civil Engineering.

Signature : ....................................................

Name of Supervisor : HJ. YUSOF B. AHMAD

Date : 27 APRIL 2006

EFFECTS OF DIFFERENT TRUSS SHAPES

TO THE DESIGN OF PLANE TRUSS

USING ANGLE SECTIONS

By

LAU WEI THENG

A report submitted in partial fulfillment of the requirements for the

award of the degree of Bachelor of Civil Engineering

Faculty of Civil Engineering

Universiti Teknologi Malaysia

2006

KESAN PERBEZAAN BENTUK KEKUDA

DALAM REKABENTUK KEKUDA SATAH

DENGAN MENGGUNAKAN KERATAN SESIKU

Oleh

LAU WEI THENG

Laporan ini dikemukakan sebagai memenuhi syarat

penganugerahan Ijazah Sarjana Muda Kejuruteraan Awam

Fakulti Kejuruteraan Awam

Universiti Teknologi Malaysia

2006

ii

I declare that this thesis entitled Effects of Different Truss Shapes to the Design of

Plane Truss Using Angle Sections is the result of my own research except as cited

in the references. The thesis has not been accepted for any degree and is not

concurrently submitted in candidature of any other degree.

Signature : ....................................................

Name : LAU WEI THENG

Date : 27 APRIL 2006

iii

Specially dedicated to my family, friends and coursemates.

iv

ACKNOWLEDGEMENTS

First of all, I would like to thank my supervisor, Tn. Hj. Yusof B. Ahmad for

his generous advices and guidance throughout this study for almost a year. Thank

you very much for your support and kindness.

I would also like to express my appreciation to my previous and present

academic advisors, En. Abdul Rahim Abdul Hamid and En. Muhammad Nassir bin

Hanapi, for their kindness and always willing to help me throughout my study life in

UTM.

Next, I would also like to acknowledge my coursemates. They are so kind

and always willing to share their experience and knowledge with me.

Last but not least, to my family and my beloved friends for supporting and

encouraging me throughout my study.

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ABSTRACT

The purpose of this project is to study the effects of different truss shapes in

the design of plane truss by using angle section. The need of this study arises where

sometimes it is difficult or taking much time to choose an effective and economical

truss shape during the design period. In investigating the effectiveness of various

truss shapes, a total of 48 truss shapes with simply pinned supports are chosen. The

design loads are distributed to the joints so that there is no moment to be resisted by

the members. A total of five set trusses with same 48 shapes were analysed and

designed with the aid of STAADPro 2004. The analysis of all sets of trusses enables

comparisons to be made among the various spans, heights and height over span ratios

of trusses. Optimal trusses from each set of trusses are to be compared to determine

whether the effective shapes are the same for different spans and heights. The

selfweights obtained from the STAADPro are in the unit of kN and can be then

converted into masses in kg which are used in calculating the costs of materials since

the rates are in RM per unit kg. This study shows that there is no certainty in

determining the most effective shapes neither with same span, height nor height over

span ratio. The most effective truss shape is actually specific for every truss span

and height. However, close results might be obtained where it does help to provide a

good guideline in choosing a truss that does not waste much material. Thus, this

method to determine the effective trusses is acceptable and can be furthered for

future researches.

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ABSTRAK

Tujuan projek ini adalah untuk mengkaji kesan perbezaan bentuk kekuda

dalam rekabentuk kekuda satah dengan menggunakan keratan sesiku. Keperluan

kajian ini adalah disebabkan kadang kala banyak masa yang diperlukan dalam

menentukan bentuk kekuda yang berkesan dan ekonomi dalam fasa rekabentuk.

Dalam mengkaji keberkesanan pelbagai bentuk kekuda, sejumlah 48 jenis bentuk

dengan sokong mudah pin telah dipilih. Beban rekabentuk telah diagihkan ke atas

nod supaya tiada momen yang perlu ditanggung oleh anggota-anggota kekuda.

Sejumlah lima set kekuda dengan 48 bentuk kekuda yang sama dianalisis dan

direkabentuk dengan menggunakan STAADPro 2004. Analisis kesemua kekuda

tersebut membolehkan perbandingan dapat dibuat antara beberapa jenis rentang,

ketinggian and nisbah rentang kepada ketinggian kekuda. Kekuda yang optimum

daripada setiap set kekuda dibandingkan untuk memastikan sama ada bentuk yang

paling berkesan adalah yang sama untuk rentang dan ketinggian yang berbeza.

Beban diri yang diperoleh daripada STAADPro adalah dalam unit kN dan boleh

ditukarkan ke jisim dalam unit kg yang kemudian boleh digunakan untuk mengira

kos bahan memandangkan kadar harga adalah dalam unit RM per kg. Kajian ini

menunjukkan tiada kepastian dalam menentukan bentuk kekuda yang paling

berkesan sama ada dengan rentang, ketinggian atau nisbah rentang kepada ketinggian

yang sama. Bentuk yang paling berkesan sebenarnya adalah spesifik unutk setiap

rentang dan ketinggian yang berlainan. Walau bagaimanapun, bentuk kekuda yang

berkesan boleh jadi agak hampir di mana ia dapat membantu untuk memberikan

panduan dalam pemilihan bentuk yang sesuai yang tidak banyak membazirkan. Oleh

itu, cara kajian ini untuk menentukan bentuk kekuda yang berkesan adalah

munasabah dan boleh diteruskan untuk kajian-kajian pada masa akan datang.

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TABLE OF CONTENTS CHAPTER TITLE PAGE

DECLARATION ii DEDICATION iii ACKNOWLEDGEMENTS iv ABSTRACT v ABSTRAK vi TABLE OF CONTENTS vii LIST OF TABLES x LIST OF FIGURES xii LIST OF SYMBOLS xiii

LIST OF APPENDICES xv

1 INTRODUCTION

1.1 Introduction 1

1.2 Problem Statement 2

1.3 Objectives of Research 4

1.4 Scope of Research 5

1.5 Importance of Research 6

2 LITERATURE REVIEW

2.1 Trusses 7

2.1.1 Triangulation, Joints and Member Forces of

Trusses 7

2.1.2 Stability and Statically Determinacy of Trusses 8

2.1.3 Methods of Analysis 9

2.1.4 Classification of Plane Trusses 10

2.1.5 Limit State Design 10

2.2 Structural Optimization 11

2.2.1 Level of Optimization 12

viii

2.2.2 Minimum Weight Frameworks 13

2.2.3 Depth of Trusses in Optimization 14

2.2.4 Cost Function 15

2.3 Previous Researchers in Trusses Optimization 16

2.4 Single Steel Angle 20

2.5 Background of STAADPro 20

2.6 Hypothesis 22

3 METHODOLOGY

3.1 48 Candidate Truss Shapes 25

3.2 Assumptions Used in the Research 29

3.3 Loading 30

3.4 Modeling of Trusses 46

3.5 Analysis of Trusses 47

3.6 Design of Trusses 48

3.7 Costs of Construction 49

4 RESULTS AND DISCUSSIONS

4.1 Selfweights of Trusses Obtained from Analysis 50

4.2 Summary of Lightest Truss for Each Group 71

4.3 Comparison of Truss Types among Different Spans

and Depths 73

4.4 Discussions on Selfweights for Each Group of Trusses 82

4.4.1 Comparison within Group 1 82





4.5 Proposed Effective Truss Shapes to be Used Practically 90

4.6 The Effects of Span, Depth and Depth over Span Ratio 92

5 CONCLUSIONS AND RECOMMENDATIONS

5.1 Conclusions 94

5.2 Recommendations 95

ix

REFERENCES 97

APPENDICES 99-133

x

LIST OF TABLES TABLE NO. TITLE PAGE

3.1 Load calculation for trusses with constant slope 33

3.2 Load calculation for trusses with various slopes 36

3.3 Load calculation for trusses with slope and horizontal top chords 39

3.4 Load calculation for trusses with horizontal top chords 42

3.5 Load calculation for nonsymmetrical trusses 43

4.1 Results for trusses with span = 10m and depth = 2m

(optimum weights) 51


(practical weights) 53

4.3 Results for trusses with span = 15m and depth = 1.5m


4.4 Results for trusses with span = 15m and depth = 1.5m














xi

4.11 Summary for truss shapes with lightest mass for each group 71

4.12 Comparison among different spans (10m, 15m and 20m) which

shows the arrangement of truss types according to selfweight

from low to high for each group 74

4.13 Comparison among different truss depths (1.5m, 2m and 3m, all

with span=15m) which shows the arrangement of truss types

according to selfweight from low to high for each group 76

4.14 Comparison between same depth/span ratio (1:5) which shows

the arrangement of truss types according to selfweight from low

to high for each group 78

4.15 Comparison between same depth/span ratio (1:10) which shows

the arrangement of truss types according to selfweight from low

to high for each group 80

4.16 Percentage difference between optimal weight and practical

weight for Group 1 83









4.21 Proposed effective trusses in practical usage 90

xii

LIST OF FIGURES FIGURE NO. TITLE PAGE

2.1 DOF for different types of structures 22

3.1 Trusses with constant slope 26

3.2 Trusses with various slopes 27

3.3 Trusses with slope and horizontal top chords 27

3.4 Trusses with horizontal top chords 28

3.5 Nonsymmetrical trusses 28

3.6 Typical layout of trusses with labels 31

3.7 Point loads acting on nodes or joints 32

xiii

LIST OF SYMBOLS Ai - area of the cross section

CDm - unit cost of the decking material per square foot

CDe - unit decking erection cost per square foot.

CJe - unit cost of joist erection expressed in cost per ton

CJf - unit cost of joist fabrication expressed in cost per ton

CTe - unit cost of truss erection expressed in cost per ton

CTf - unit cost of truss fabrication expressed in cost per ton

DL - dead load

[F] - applied loads matrix

Fx - total force at direction - x

Fy - total force at direction - y

Gk - total dead load in kN

[K] - stiffness of members

LL - live load

li - length of the ith bar

NJ - number of joints in the truss

NM - number of members

NR - number of support restraints

P - total point load in kN

Pi - value of the axial stress

Pu - maximum axial stress for the material of the bar

Py - design strength of steel

[P] - vector of internal forces

Qk - total imposed load in kN

[Q] - matrix of displacement of joints

SFD - square feet of decking

[S] - flexibility matrix

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TC - sum of the cost of the decking material, web joist and the trusses

TCD - cost of roof decking

TCT - cost of fabrication and erection of the steel truss system

TCWJ - cost of fabrication and erection of open web joist

V - total volumes for compression members c V - total volumes for tension members t w - weight for a truss

WT - total weight of the trusses expressed in tons

WWJ - total weight of web joist expressed in tons

- tension stress t c - compression stress

- specific weight of the material i

xv

LIST OF APPENDICES APPENDIX TITLE PAGE

A/1 Load Calculation for Trusses with 10m Span

and 2m Depth 99


and 1.5m Depth 104


and 2m Depth 109


and 3m Depth 114


and 2m Depth 119

B/1 Example of Truss Modeling in STAADPro 124

B/2 Example of Beam End Force Analysis from STAADPro 125

B/2 Example of Section Detail Design from STAADPro 130

B/3 Example of Design Summary from STAADPro 131

B/4 Example of Reaction Calculated from STAADPro 133

CHAPTER 1

INTRODUCTION 1.1 Introduction

A truss (or braced framework) is composed of members (or bars) connected

together at joints (or nodes). The members of a truss are usually straight but not an

essential. All the joints are considered to be pinned although some or all the joints

may be fixed rather than pinned. Generally, the design of truss system includes

selecting member sizes, joint locations and the number of members.

A truss acts like a deep beam. A beam becomes stronger and stiffer when it

is deeper. But when the span is long and just carries a light load, it may waste a lot

of material just carrying itself. This is because the bending moment capacity is most

efficiently governed by the depth of section. If only a single section is used, a large

portion of the web actually is unused. Besides, a single big section will be very

costly and also infeasible in erection and fabrication. Whereas a truss is useful when

there is plenty of depth and relatively light loading. It can look very complicated, but

it can be the simpler case in calculation when compared to a beam especially when

all the joints are considered pinned.

Before steel became an economically useful material, trusses were made of

wood or iron. Nowadays, trusses are almost always made of steel, though some

concrete trusses exist, and some small examples do use timber. The members used

in steel truss system are normally angles, double angles, C-channels, double C-

channels, square hollow section (SHS), circle hollow section (CHS), cold-formed

steel and so on.

2

The truss structures are required to be designed in such a way that they have

enough strength and rigidity to satisfy the strength and serviceability limitation. It is

not difficult to conceive that there are quite a number of structures with different

shapes which meet the requirement. But among them it is the most economical one

that interests the structural engineer the most. Until the advent of structural

optimization, the usual path to follow in the solution of this problem was to make use

of the experience and intuition of the designer.

The subject of optimization is a lively topic in almost every discipline. The

unprecedented developments in computational capabilities in the last 40 years have

fostered impressive developments in design optimization schemes in all discipline of

engineering, so as in structural engineering. The development of structural

optimization algorithms has helped engineers to a great extent in finding the most

suitable structural shape for a particular loading system. There has been quite a large

number of research works which the shape of the structure was treated as a design

variable.

1.2 Problem Statement

The design of trusses has to be carried out according to two important

requirements. Firstly, the best geometrically layout of bars and nodes has to be

determined, and secondly, the most adequate cross sections need to be calculated. In

general, the structural shape depends on the engineers criteria and its design depends

partly on economical, aesthetical, construction techniques and environmental aspects.

Moreover, the dimensions of the bars depend on failure and functional criteria. The

design requires determining member forces and comparing stresses and deflections

with allowable values. Whereas the stability of a truss structure depends on its

overall shape, number of members, arrangement of members and the support

condition. In spite of an engineer can design following his own criteria, there must

exist an optimum shape and a cross section distribution that bears the external loads.

In this work the optimization problem arises from the combination of the shape and

3

the parameter problems. The combination of design variables should safely support

the design load and selfweight for least cost.

The optimization, unlike analysis, is a multivalued problem. Generally, most

optimization problems do not have a unique solution, so as the truss optimization.

The usual procedure is to establish a set of necessary and sufficient conditions for an

optimum and then construct an algorithm that systematically leads to a solution that

satisfies such conditions. If more than one solution satisfy such conditions, the

question arises as to what is the optimum of all such optima. To meet the satisfied

design requirements sometimes it takes the designers much time. The design

engineers may have to do trial and error or sometimes have to redesign the truss

systems to meet the clients objective, which may cost a lot of undesirable waste of

time. The design costs of a project are time-dependent. Therefore the important

thing is to reduce the design time for any project.

With the development of the digital computer, matrix methods of structural

analysis have been programmed to solve complex structures reliably and with a

minimum of effort or preparation on the part of the engineer, and these have become

almost universally accepted in practice. However, there is no value in using

computers in the production of inefficient, over-expensive design. As mentioned in

above paragraph, extra valuable time is wasted. Therefore a computer should be

used to maximum effect in producing design information corresponding to

economical and efficient structures, in this case, the truss structures.

Besides, it is known that nowadays cost is not only directly related to the

quantity of material, but to other local factors such as the cost of labour or building

difficulties. However the weight as an objective function has been considered useful

because its significant effect to overall costs.

There are quite a lot of truss shapes which are commonly used in the

construction industry, such as Pratt, Warren, Howe and so on. It becomes an

important task for a design engineer to decide which the best is in term of minimum

weight cost among the large quantity of different shapes of trusses. Most

engineering software can help us design the optimum sections of truss members, but

4

as engineers we have to first decide the preliminary overall truss shape to use before

using the software for section design purpose.

1.3 Objectives of Research

The main objective of this research is to determine the effect of different truss

shapes to the optimized design of plane truss by using angle sections with the aid of

STAADPro 2004. Minimum weight is chosen as the objective function. The

research should be able to achieve the following objectives:

(a) To determine the most effective truss shapes in term of weight among the

48 candidate fixed geometry of shapes, in the design of trusses using steel

angle section for certain spans and heights to save the time of design by

avoiding the efforts of trial and error.

(b) To compare the costs of materials (by using weights) of the different truss

shapes normally used in the construction industry.

(c) To determine whether under which conditions the same optimum shape of

truss can be applied considering the different spans, heights and height

over span ratios of trusses.

(d) To determine whether the method of choosing the optimal truss shapes is

suitable to be applied to other similar studies.

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1.4 Scope of Research

The scope of research is the analysis and design on 48 candidate types of

general truss system with different truss shapes which can be generally grouped into

five. The research is carried out by using all plane (2-D) trusses supported at both

ends of span with pins and all the trusses are to bear the concentration load at joints

only. The software of STAADPro 2004 is used to run the structural analysis and

design using Code BS5950 2000. It helps to determine the optimum sections for all

48 trusses.

Span of trusses is limited between 10 to 20 meter and the height over span

ratio is limited between 1:10 and 1:5 which are generally used for normal load cases.

Whereas the height of truss used is between 1.5m and 3m. The spacing between

trusses is fixed at 5 meter. The loading used are dead load and imposed load whereas

wind load is not considered.

The shapes become the main interest of the study, rather than others like

span, spacing, height, slope, detailed arrangement of members of trusses etc. The

study should be able to provide a useful guideline to the design engineers to produce

a nearly optimal design. However, under certain conditions, designers may not able

to adopt fully the optimal geometry in this study such as the slope of top chords

especially when it becomes a constraint due to architectural design. This is because

this study is carried out for 48 fixed shapes with the assumption that no adjustment

on the shapes should be made.

The expected output of this research is the various weights of steel in

different shapes of structures. The members designed must be sufficient under

various axial stresses with adequate factor of safety. Truss shapes with minimum

weights from each group are determined then.

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1.5 Importance of Research

This research can help to determine whether this method of optimization is

suitable and can be applied to the studies for other types of sections, shapes, spans,

heights, materials etc. so that further researches can be carried out for practical

application purposes in the future. The study of optimisation is considered easy to

understand where involves the application of STAADPro and comparison among the

general used truss shapes.

It is also considered as a response to the previous research in truss

optimization especially the research done by Weniyarti bt. Yurnis (2005), a graduate

from UTM in her 2004/2005 thesis paper which the method used is about the same

but using different member sections [1]. Besides, some modifications and

improvements are made on it so that the research will be more applicable and reliable

for practical purposes.

Design time might directly affect the cost of project. This research should be

able to help the structural engineers to produce safe and economic design without

many trials, where the time and material costs are always the two main

considerations of all construction projects.

Documents

Truss Angle Section