experimental and numerical study on cold-formed steel

EXPERIMENTAL AND NUMERICAL STUDY ON

COLD-FORMED STEEL BUILT-UP I BEAM WITH

DIFFERENT SPAN LENGTHS

BY

TY KHIEV

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

(ENGINEERING AND TECHNOLOGY)

SIRINDHORN INTERNATIONAL INSTITUTE OF TECHONOLOY

THAMMASAT UNIVERSITY

ACADEMIC YEAR 2017

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Abstract

EXPERIMENTAL AND NUMERICAL STUDY ON COLD-FORMED STEEL

BUILT-UP I BEAM WITH DIFFERENT SPAN LENGTHS

by

TY KHIEV

Bachelor of Civil Engineering, Institute of Technology of Cambodia, 2016

Master of Science (Engineering and Technology), Sirindhorn International Institute of

Technology, 2018

Investigation on the structural behavior of cold-formed steel beam has become

more interesting due to its wide utilization in constructional steel application. However,

singly-symmetric cold-formed steel section such as lipped channel section cannot carry

heavy load because of its weak torsional rigidity. Therefore, cold-formed steel built-up

I section has been one of alternatives to overcome this disadvantage. This study

intended to investigate the behavior of built-up I beams made of cold-formed steel back-

to-back C section under four-point bending test. There were four types of sections:

IC10019, IC15015, IC15019, IC15024 and two different span lengths Ls=1.9m,

Ls=3.8m. The cold-formed steel built-up I beams were assembled by bolts on flat webs

of two identical lipped channel sections with four different connection spacings L/2,

L/3, L/4, and L/6 where L is clear span length. The lateral bracing steel frame was

installed at each load-bearing plate for preventing the lateral displacement or twist of

specimen. The influences of web height, thickness, bolted connection spacing, and span

length were examined in this research. From experimental results, it was found that the

web height and thickness of cold-formed steel are the key factors to improve load

capacity of the cold-formed steel built-up I beam. In addition, the effect of connection

spacing on maximum loads in case of 3.8m span length is higher than that in case of

1.9m span length and the effects of span length for the section IC15019 are smaller than

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that for the section IC10019. Finite element program, Abaqus, is used to model the

cold-formed steel built-up I beam and numerical results are compared with

experimental results. The failure loads of all specimens obtained from experiment are

larger than those from finite element analysis. The failure mode of local or/and

distortional buckling is found in both results of experiment and finite element analysis.

Hence, finite element method can be used to safely predict the ultimate strength of cold-

formed steel built-up I beam.

Keywords: Cold-formed steel, Lipped channel section, Built-up I beam, Connection

spacing, Four-point bending test, Finite element analysis.

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Acknowledgements

First of all, I would like to express my special thanks of gratitude to my advisor,

Assoc. Prof. Dr. Taweep Chaisomphob, for his supervision and valuable time on my

master degree during two years.

I gratefully acknowledge the committee members, Assoc. Prof. Dr. Winyu

Rattanapitikon, and Col. Asst. Prof. Dr. Nuthaporn Nuttayasakul, who provide

advantageous comments on my thesis.

I would like to deeply thank to NS BlueScope (Thailand) Limited for providing

steel materials for doing this research

I am also grateful to AUN-SEED/Net and Sirindhorn International Institute of

Technology, Thammasat University for their scholarship.

I would like to express my profound gratitude to Col. Asst. Prof. Wasan

Patwichaichote and laboratory of Chulachomoklao Royal Military Academy (CRMA)

for providing facilities.

I would like to thank to Professor Eiki Yamaguchi who allows us to use software

Abaqus for modelling the cold-formed steel built-up I beam in this research.

Finally, I would like to be grateful to my mother, father, seniors, juniors, and

friend who always encourage me during my research.

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Table of Content

Chapter Title Page

Signature page i

Acknowledgements iv

Table of Content v

List of Tables viii

List of Figures ix

1 Introduction 1

1.1 General information on cold-formed steels 1

1.2 Statement of problem 3

1.2.1 Lateral and torsional stiffness 3

1.2.2 Lateral movement or rotation 4

1.3 Purpose of research 5

1.4 Scope of research 5

2 Literature Review 6

2.1 Previous researches on beams made of cold-formed steel 6

2.2 AISI specification 9

2.2.1 Lateral-torsional buckling 9

2.2.2 Local buckling 10

2.2.3 Distortional buckling 10

2.3 Eurocode 3 10

2.3.1 Local buckling and distortional buckling 11

2.3.2 Lateral-torsional buckling 11

3 Experimental Study 12

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3.1 Specimen properties 12

3.2 Material properties 13

3.3 Specimen’s connection 14

3.4 Lateral bracing steel frame 14

3.5 Test set-up 15

3.6 Test procedures 17

3.7 Experimental results and discussion 17

3.7.1 Influence of web height on maximum loads 18

3.7.2 Influence of thickness on maximum loads 20

3.7.3 Influence of span length on maximum loads 20

3.7.4 Load-deflection curves. 21

3.7.5 Load-lateral displacement curves 23

3.7.6 Load-strain curves 23

3.7.7 Failure modes of specimens 26

4 Numerical Study 35

4.1 Cold-formed steel built-up I beam modelling 35

4.2 Bolt connection modelling 36

4.3 Element selection 36

4.4 Material behavior 37

4.5 Contact condition 38

4.6 Boundary and loading condition 39

4.7 Element mesh 40

4.8 Analysis procedures 41

4.9 Comparison between FEM and experimental results 42

5 Conclusions 52

References 54

Appendices 56

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Appendix Specification calculation 57

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List of Tables

Tables Page

3.1 Section’s dimension 12

3.2 Experimental result of maximum loads and deflections 17

3.3 Experimental result (Failure mode of section IC10019) 27

3.4 Experimental result (Failure mode of sections IC15015, IC15019, IC15024) 27

4.1 Comparison of Experimental and FEM’s results 42

4.2 Comparison of Experimental and FEM’s results 42

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List of Figures

Figures Page

1.1 Types of structural members made of cold-formed steel 1

1.2 Cold roll-forming method 2

1.3 Types of sections made from cold-formed steel 2

1.4 Eccentrically loaded channel beam 4

1.5 Rotation of I beam in case without lateral bracing 4

2.1 Failure mode of lipped channel section 9

3.1 Dimension of built-up I section 13

3.2 Stress-strain curve of all thicknesses 13

3.3 Detail of specimen’s connection 14

3.4 Overall view of the experimental set-up 15

3.5 (a) Checking center of specimen, (b) Data logger 16

3.6 Hydraulic pump 17

3.7 . Influence of web height on increase of maximum loads 19

3.8 Influence of thickness on maximum loads 20

3.9 Influence of span length on maximum loads 21

3.10 Load-deflection curves of LVDT 1 and LVDT 2 of all specimens 22

3.11 Load-deflection curves of all connection spacing 23

3.12 (a) Load-lateral displacement curves, (b) Separation between the two webs 24

3.13 Load-strain curves of all specimens 25

3.14 Typical failure mode of specimens 28

3.15 Failure mode of specimen IC10019, Ls=1.9m 29






4.1 Cold-formed steel built-up I beam modelling of connection spacing L/6 for

section IC15019, Ls=1.9m 35

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4.2 Bolt connection modelling 36

4.3 Shell element 36

4.4 Solid element 37

4.5 Surface-to-surface contact (standard) 38

4.6 Tie constraint (surface-to-surface) 38

4.7 Boundary condition at each support 39

4.8 Boundary condition and displacement controlled at load-bearing plate 40

4.9 Detail of mesh size 40

4.10 Comparison of load-deflection curves between experiment and FEM for

Ls=1.9m (a) deflection 2, (b) deflection 1 45

4.11 Comparison of load-deflection curves between experiment and FEM for

Ls=3.8m (a) deflection 2, (b) deflection 1 46

4.12 Comparison of load-strain curves between experiment and FEM for Ls=1.9m

(a) strain 2 and strain 4 of C2, (b) strain 1 and strain 3 of C1 47

4.13 Comparison of load-strain curves between experiment and FEM for Ls=1.9m

(a) strain 2 and strain 4 of C2, (b) strain 1 and strain 3 of C1 48

4.14 Comparison of failure mode (LB+DB) between experiment and FEM 49



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Chapter 1

Introduction

1.1 General information on cold-formed steels

Currently, cold-formed steels have been commonly utilized in structural steel

constructions such as warehouses, factories, low-rise office building. Cold-formed steel

members can be used for secondary members such as purlin for supporting roof

sheeting, as girt for connecting wall sheeting and, sometimes, cold-formed steel can be

used for main members in building such as rafters, joist, beams, columns, and trusses

as shown in Figure 1.1. Moreover, columns and rafters are the members carry the heavy

loads. So, the built-up section is one of alternatives to overcome this problem.

Figure 1.1 Types of structural members made of cold-formed steel

Rafter

Column

Column

Rafter

Purlin

Girt

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Cold-formed steel sections are manufactured from press bake operation,

bending bake operation, and cold roll-forming which is the most widely used method.

In the cold roll-forming method, steel strip made from carbon steel is sent without the

heat application through a series of rolls which form the steel strip until wanted section

as shown in Figure 1.2.

Figure 1.2 Cold roll-forming method

There are many types of sections made of cold-formed steel such as C sections,

Z sections consisting of single or double lips and also internal stiffeners, built-up closed

sections, built-up open sections (see Figure 1.3). According to NS BlueScope

(Thailand) Limited, the height of sections is ranged from 100mm to 350mm and the

thickness of sections ranged from 1mm to 3mm.

Figure 1.3 Types of sections made from cold-formed steel

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Cold-formed steels provide interesting advantages. First of all, cold-formed

steels are easy to handle during construction and transportation because of its

lightweight. Secondly, it provides high strength-to-weight ratios if compared to many

building materials due to its high-strength as well as stiffness, wider spans and also

better material usage. Thirdly, fabricating the building component made of cold-formed

steels is high accuracy as a result of efficiency and ensures construction quality. Last,

the formworks are not needed in cold-formed steel building constructions.

However, cold-formed steel is a thin-walled material which is easy to have

imperfection. There are three types of imperfections such as mechanical imperfection,

material imperfection, and geometric imperfection. Mechanical imperfection is caused

by load eccentricities and support eccentricities. Material imperfection happens in

forming process that influences on yield strength and residual stress. Geometric

imperfection refers to sectional imperfection (shape of section) and global imperfection

(shape of member). As mentioned above, cold-formed steel members are so

complicated that the researches are necessary to be continuously conducted on them.

1.2 Statement of problem

1.2.1 Lateral and torsional stiffness

Among cold-formed steel sections, lipped channel section is one type of

sections which tends to easily buckle due to its thin-walled elements and it is generally

considered as slender section because the section cannot reach full yield strength.

Moreover, the shear center of lipped channel section does not coincide with the

centroid and often have load eccentricity to the shear center causing the section failed

by combination between torsion/twist and bending as shown in Figure 1.4. These are

the reasons that lipped channel section has low lateral and torsional stiffness. Therefore,

when cold-formed steel members such as rafter are under heavy load, the lipped channel

section cannot resist that load. So, the built-up I section is a method which can convert

the shear center coincides to the centroid which means that lateral and torsional stiffness

will be increase.

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Figure 1.4 Eccentrically loaded channel beam

1.2.2 Lateral movement or rotation

The built-up I beam is still open section member which is easy to twist even the

shear center coincides to the centroid. Hence, lateral bracing steel frame must be

applied at each load-bearing plate in order to reduce the unbraced length of beam for

preventing the horizontal movement or rotation of specimens as shown in Figure 1.5.

Figure 1.5 Rotation of I beam in case without lateral bracing

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1.3 Purpose of research

The purpose of this study is to observe the flexural structural behavior of cold-

formed steel built-up I beam under four-point bending test. The web height, thickness,

span length, and connection spacing are parameters selected in this study. Further, the

finite element analysis using Abaqus program is conducted in order to compare between

experimental and numerical results.

1.4 Scope of research

The experiments were conducted under four-point bending system with four

different sections, two different span lengths, and four different connection spacings.

The lateral bracing steel frame is provided at each load-bearing plate for all specimens.

The bolts are used to form built-up I beams. The heights of section are 102mm and

152mm. The thicknesses of section are 1.5mm, 1.9mm, and 2.4mm. There are four

types of connection spacing such as L/2, L/3, L/4, and L/6 where L represents for clear

span length (distance between second bolt connection of each beam’s end). The span

lengths of specimens are 1.9m and 3.8m.

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Chapter 2

Literature Review

This chapter cover on the previous studies on cold-formed steel behavior both

experiment and numerical simulation. Moreover, this literature review also mentions

about AISI specification and Eurocode 3 used for calculating the ultimate strength of

flexural member.

2.1 Previous researches on beams made of cold-formed steel

Experimental and numerical investigation on the structural behavior of four

types of cold-formed steel beams were studied by Laím et al. (2013). Among these

beams, the built-up I beam was mentioned to describe detailly the structural behavior.

It was formed by identical lipped channel section (C-section) as back-to-back C-section

with dimension of 250mm, 43mm, 15mm, and 2.5mm for web depth, flange width, lip,

and thickness respectively. The specimens were tested three times under four-point

bending test without lateral bracing at load-bearing plates and length of beam was 3.6m,

but the span length was only 3m due to span length of supports in the laboratory. The

results show that the failure load of built-up I beam increased 3.5 times if compared to

C-section. Furthermore, Abaqus program was used to model the built-up I beam. The

maximum loads of experiment are higher 4% than those of FEM. Additionally, the

height, thickness, and length was examined by FEM for investigating the strength-to-

weight ratio. According to numerical simulation results, strength-to-weight ratio of

built-up I beam is greater 80% than C-section beam. Eurocode 3 was used to estimate

the capacity of built-up I beam that all results from Eurocode are almost lower than

FEM. The failure modes occurred on built-up I beams were lateral-torsional buckling

and distortional buckling.

Kang et al. (2017) investigated on cold-formed steel C back-to-back beams both

experimental tests and numerical simulation without lateral bracing steel frame. The

cold-formed lipped channel sections were combined together by bolts on their webs as

built-up I section. The height of section are 102mm with thickness of 1.2mm, 1.5mm

and 152mm with thickness of 1.5mm while the length of beam is 4m. The connection

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spacing and thikness are the important parameters. The increase 25% of thickness

improves the capacity of built-up I beam in the range of 3% to 98% while the connection

spacing improve the capacity of beam from 3% to 41%. The finite element program,

Abaqus, was utilized for clarifying the experimental results with different percentage

of 30%. The failure mode was concluded by considering individually as C-section. The

lateral-torsional buckling was controlled on one C-section and distortional buckling

occurred on another C-section both experiment and numerical simulation.

Wang and Young (2016) studied both experiment and numerical validation

about the behavior of intermediate stiffened cold-formed steel built-up sections under

bending condition. The results obtained from three-point bending test were compared

with those obtained from four-point bending test. The ultimate moments obtained from

four-point bending test were lower than those obtained from three-point bending test

for built-up I section with lips while ultimate moments obtained from three-point

bending test were lower in case without lips. However, the deflections at mid-span of

three-point bending test always smaller than those of four-point bending test both built-

up I section with lips and without lips. It was found within 12% that experimental

results differ from numerical results modelled by program Abaqus and comparisons

were conducted only in case of four-point bending test. The local buckling and flexural

buckling happened on built-up I beam without lips while the distortional buckling and

flexural buckling occurred on built-up I beam with lips.

Faridmehr et al. (2015) investigated on stiffened cold-formed steel C section in

primarily shear condition and in pure bending condition separately. Screws were used

to combined two C sections as built-up I section and cover plate was applied between

the two concentrated loads for improving the ultimate moment of built-up I beam. The

cover plate increases the ultimate moment of built-up I beam within 82% in case of

pure bending condition and 73% in case of primarily shear condition. Abaqus was

chosen to elucidate the experimental results with different FEM-to-experiment ratios of

0.96 in case of pure bending condition and 1.06 in case of primarily shear condition.

The built-up I beam with cover plate was failed by local bucking while distortional

buckling happened on built-up I beam without cover plate.

The effect of hole on web of built-up I sections made of cold-formed steel C

sections under four-point bending test were studied by Wang and Young, (2015). All

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specimens were formed by screws and the circular holes were on webs located at

moment span in order to understand the reduced capacity of moment by focusing on

hole diameter-to-web depth ratio (dh/hw). This ratio decreases capacity of beam within

6% when it is in the range from 0.25 to 0.5; however, when ratio increases until 0.7,

maximum reduction of moment capacity is 16%. Local, distortional, flexural buckling,

and their interaction presented in these built-up I beams. The mean value of 0.98 is the

different ratio between experimental and FEA’s result conducted by Wang and Young

(2017).

The influence of geometric imperfection of cold-formed steel sigma-shape

sections on the ultimate moment was done by Gendy and Hanna (2017). ANSYS

software was used for modelling the specimens under four-point bending test. Four

beam slenderness ratios (L/ry=50, 75, 100, 125) corresponding to each five modes were

discussed in linear buckling analysis. Then, the first five elastic buckling modes

represented for initial imperfection of beam in nonlinear analysis. The result show that

local buckling gotten from linear buckling analysis represented well for the initial

imperfect shape of beam with slenderness ratio L/ry=50, 75, and 100 that influenced on

both moment capacity and failure shape of beam. On the other hand, lateral-torsional

buckling of linear buckling analysis played important role for affecting on moment

capacity of beam with slenderness ratios L/ry=125.

Bonada et al. (2012) indicated the methodologies for selecting the initial

imperfection of specimens. Three methodologies were suggested for providing the

imperfection shape of beam: utilization the first buckling mode, iteration on all mode

shapes, and the combination between finite element analysis and generalized beam

theory (GBT); then, the results of those were compared with experimental results.

Utilizing only first buckling mode makes FEA’s results differ by up to 15% from

experimental results with disagreeable failure modes. Significantly, the iterative

method finding an appropriate mode yields FEA’s results close to experiment in term

of failure loads and failure modes. Finally, the combination between FEA and GBT

lead to differ below 6%. Therefore, iterative method is powerful method for predicting

both failure loads and failure modes of thin-walled members.

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2.2 AISI specification

Direct strength method in AISI specification is a conservative method for

predicting confidently the flexural member strength (AISI, 2016). This method

considers on three main failure modes such as lateral-torsional, local, and distortional

buckling (see Figure 2.1).

Figure 2.1 Failure mode of lipped channel section

2.2.1 Lateral-torsional buckling

The ultimate strength of flexural member for failure mode of lateral-torsional

buckling, neM is calculated by following:

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Where y fy yM S F= is yield moment

b ocre ey t

f

C r AF

S= is critical elastic lateral-torsional buckling stress.

and

( )

2

2ey

y y y

E

K L /r

= ,

( )

2

22

1 wt

o t t

ECGJ

Ar K L

= +

2.2.2 Local buckling

The ultimate strength of flexural member for failure mode of local buckling,

nLM is calculated by following:

crL g crLM S f= is critical elastic local buckling moment.

2.2.3 Distortional buckling

The ultimate strength of flexural member, Mnd, for failure mode of distortional

buckling shall be calculated by following:

crd g crdM S f= is critical elastic distortional buckling moment.

2.3 Eurocode 3

Eurocode 3 is widely used for designing the strength of cold-formed steel

members such as beams. This code is considered on the effective width of each

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elements: web, flanges, and lips in order to define the available strength of members

for against to the local, distortional, and lateral-torsional buckling which multiply with

reduction factor.

2.3.1 Local buckling and distortional buckling

The ultimate strength of flexural member for failure mode of both local and

distortional buckling is calculated by following expression.

y eff ,x

c,Rd

M0

F WM =

This effective section modulus is resulted from effective widths of a part of web,

effective width of flange, and effective width of lip. The procedure for calculating the

effective section modulus has been described in (En, 2006).

2.3.2 Lateral-torsional buckling

The ultimate strength of flexural member for failure mode of lateral-torsional

buckling is calculated by following formula.

eff ,x yb

b,Rd LT

M1

W fM =

Where

( )LT

22

LTLT LT

1 =

+ −

, LT 1.0

( ) ( )2

LT LTLT LT0.5 1 0.2 = + − +

, c,Rd

LT

cr,LT

M

M =

LT 0.21 = (Recommended imperfection factor)

M1 1.0 =

( )

22

wx

cr,LT b t2 2

y cr w cr

EIEIM C GI

k L k L

= +

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Chapter 3

Experimental Study

3.1 Specimen properties

The specimens tested in this study are formed by two identical lipped channel

sections as C back-to-back section. There are four types of section presented in this

experiment: IC10019, IC15015, IC15019, and IC15024. The name of sections related

to configuration of cross-section, thickness and height. As an example of section

IC10019, the word IC refers to built-up I beam made from two identical lipped channel

sections as C back-to-back, the number 100 represents the approximate value of

section’s height, and 19 is the number of 1.9mm thickness. From these sections, it can

be seen that there are three types of thickness and two types of web height for

discussing in the experimental results. The section IC10019 and IC15019 consist of

two types of span lengths: Ls=1.9m and Ls=3.8m and other sections IC15015, IC15024

have only one type of span length, Ls=1.9m where Ls is span length of specimen. Table

3.1 shows information of dimension of all sections (see Figure 3.1) with different span

lengths, different connection spacings. The inner radius of all sections equals to 5mm.

Table 3.1 Section’s dimension

Specimen Web height

h (mm)

Thickness

t (mm)

Flange width

b (mm)

Lip

c (mm)

Connection

Spacing (mm)

L/2, L/3, L/4, L/6

IC10019

(Ls=1.9m) 102 1.9 51 14.5

900, 600,

450, 300

IC10019

(Ls=3.8m) 102 1.9 51 14.5

1800, 1200,

900, 600

IC15015

(Ls=1.9m) 152 1.5 64 15.5

900, 600,

450, 300

IC15019

(Ls=1.9m) 152 1.9 64 16.5

900, 600,

450, 300

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IC15019

(Ls=3.8m) 152 1.9 64 16.5

1800, 1200,

900, 600

IC15024

(Ls=1.9m) 152 2.4 64 18.5

900, 600,

450, 300

Figure 3.1 Dimension of built-up I section

3.2 Material properties

The coupon tests are necessary to conduct with different thickness for

determining the yield strength (Fy), ultimate strength (Fu), and Young’s modulus (E) of

steel. The thickness of 1.5mm, 1.9mm, 2.4mm provides yield strength (Fy) equals to

522 MPa, 510 MPa, 476MPa and ultimate strength (Fu) equals to 610 MPa, 546MPa,

497MPa respectively. Young’s modulus of steel is 208 MPa. Figure 3.2 illustrates the

stress-strain curves of all thickness obtained from coupon test results.

Figure 3.2 Stress-strain curve of all thicknesses

b b

c

t

C2 C1h

Strain

Ten

sile

str

ess

(MP

a)

Stress-strain curves

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

0

100

200

300

400

500

600

700

t=1.5mm

t=1.9mm

t=2.4mm

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3.3 Specimen’s connection

The bolt connection has been common fastener used in cold-formed steel built-

up beam (Lee et al., 2014). In this study, all specimens were made up by connecting

two identical lipped channel sections bolting on flat portion of webs making its

thickness become double. There were two bolts in one connection which one bolt was

at upper web and another bolt was at lower web. The vertical distance between the two

bolts is 40mm for section IC10019 (h=102mm) and 70mm for sections IC15015,

IC15019, and IC15024 (h=152mm). It can be seen that there is one bolt connection

located at 35mm from each beam’s end and another bolt connection was at 100mm,

200mm from beam’s end for span length of Ls=1.9m and Ls=3.8m respectively in order

to protect strongly from failing by chance at each support (see Figure 3.3). It was also

the started point for clear span length, L, to divide into four different connection

spacings for all specimens.

Figure 3.3 Detail of specimen’s connection

3.4 Lateral bracing steel frame

The failure mode of lateral-torsional buckling were found in cold-formed steel

built-up I beams because of low torsional rigidity as well as flexural rigidity about weak

axis (Kang, 2017). Consequently, the lateral bracing steel frame (see no.8 in Figure 3.4)

was proposed for reducing the unbraced length of specimen in this study. It was

installed at each load-bearing plate for preventing the twist, rotation, or bending about

weak axis of built-up I beam during testing. This lateral bracing steel frame was made

of hollow rectangular steel sections with dimension of 32mm×16mm which can protect

strongly the lateral displacement of specimens during testing without deformation. All

hollow rectangular steel sections are connected to each other by bolts and the holes can

40mm(h=102mm)70mm(h=152mm)

35mm

100mm (Ls=1.9m)

200mm (Ls=3.8m)

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be adjusted to the built-up I section’s dimension in order to set up easily the specimens.

Additionally, the big C-clamps were put at connections of lateral bracing steel frame

for protecting the slipperiness of frame by chance.

3.5 Test set-up

Figure 3.4 Overall view of the experimental set-up

As a consequence of constant bending moment between concentrated loads,

four-point bending system was used in this study. The specimen (no.1 in Figure 3.4)

was placed on simply support (no.2 and 3 in Figure 3.4) with dimension:

100mm×240mm, 200mm×400mm for span length of 1.9m and 3.8m respectively. Two

LVDT

Strain gauges

L=clear span length

Ls/3 Ls/3Ls/3

Ls=span length

Pinned Support Roller SupportLVDTs

Load-bearing plate

specimen

Load-transferring beamLoad cells

L/6L/6L/6L/6L/6L/6

Bolts

Lateral bracing

Angle steels

steel frames

Ref. code: 25605922040315TJU

16

strain gauges (no.4 in Figure 3.4) were stuck on top flanges and other two strain gauges

were at bottom flanges at mid-span of all specimens for measuring the deformation of

specimen. Checking center of specimen in longitudinal and transversal direction was

necessary to ensure that load was provided perfectly straight from hydraulic jack to

specimen (see Figure 3.15(a)) Two vertical LVDTs (no.5 in Figure 3.4) were put at

mid-span of specimen for measuring vertical deflections and one horizontal LVDT

(no.6 in Figure 3.4) was also put at mid-span for measuring horizontal displacement of

specimen. Support constraint steels (angle steels: no.7 in Figure 3.4) formed by bending

on steel plates of 5mm thickness were put at both pinned support and roller support.

The sizes of support constraint steels are 5mm×100mm, 5mm×200mm for span length

of 1.9m and 3.8m respectively and C-clamps were utilized to connect specimen with

supports and with support constraint steels. The lateral bracing steel frames (no.8 in

Figure 3.4) were erected at each load-bearing plate (no.9 in Figure 3.4). The dimension

of load-bearing plate is 100mm×200mm were placed at Ls/3 from center of each support

where Ls is span length. The load-transferring beam (no.10 in Figure 3.4) was necessary

to put on load-bearing plates for converting one-point load from hydraulic jack (no.11

in Figure 3.4) connected with 2D steel frame (no.12 in Figure 3.4) to two-point load on

specimen. The load cells (no.13 in Figure 3.4) was put between hydraulic jack and

load-transferring beam for recording continuously the data of loads. Finally, LVDTs,

the strain gauges, and the load cells were linked to data logger (see Figure 3.15(b)) for

converting into numerical data in computer during testing and specimen was also

labelled.

(a) (b)

Figure 3.5 (a) Checking center of specimen, (b) Data logger

Ref. code: 25605922040315TJU

17

3.6 Test procedures

After specimen as well as all transducers were prepared already, specimen was

loaded gradually by hydraulic pump (see Figure 3.6) under load control. Camera was

also set in order to examine structural behavior of specimen such as failure modes.

Specimen was under continuous slightly load until specimen reached its ultimate load.

Specimen was considered to be failed when load dropped noticeably, then, unloading

was conducted.

Figure 3.6 Hydraulic pump

3.7 Experimental results and discussion

The total specimens for testing in this study are 24 beams. Table 3.2 shows the

experimental results of maximum loads, vertical deflection of lipped channel section

C1 (v1), C2 (v2), and horizontal displacement (h) at mid-span for all specimens.

Table 3.2 Experimental result of maximum loads and deflections

Specimen Connection

spacing

Max. load

(kN)

v1

(mm)

v2

(mm)

h

(mm)

IC10019

(Ls=1.9m)

L/2 48.72 26.50 27.26 -

L/3 44.83 35.59 28.43 -

L/4 46.79 26.11 29.67 -

L/6 45.18 25.61 22.18 -

Ref. code: 25605922040315TJU

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IC10019

(Ls=3.8m)

L/2 22.97 85.61 84.15 -

L/3 22.91 87.09 87.39 -

L/4 22.17 78.07 80.21 -

L/6 20.70 73.45 75.20 -

IC15015

(Ls=1.9m)

L/2 47.48 14.02 14.59 0.29

L/3 47.53 14.58 14.37 4.12

L/4 47.09 13.86 13.66 0.45

L/6 47.25 13.82 14.41 0.33

IC15019

(Ls=1.9m)

L/2 71.83 20.75 20.87 0.10

L/3 70.70 18.27 17.95 3.38

L/4 71.64 19.18 18.94 0.21

L/6 72.83 17.96 18.60 0.03

IC15019

(Ls=3.8m)

L/2 35.29 45.11 46.64 -

L/3 38.39 53.14 55.40 -

L/4 38.21 51.04 52.84 -

L/6 37.63 48.35 49.98 -

IC15024

(Ls=1.9m)

L/2 97.50 19.32 20.38 0.95

L/3 98.32 22.20 22.43 3.68

L/4 101.82 21.79 21.98 0.43

L/6 104.32 23.57 23.12 0.54

3.7.1 Influence of web height on maximum loads

The web height is an important parameter for improving the capacity of bending

member. From Table 3.2, there are two different web heights of section IC10019 and

IC15019 consisting of the same thickness 1.9mm. According to Figure 3.7, the increase

of web height of section leads to an increase in the maximum load. In case of span

length Ls=1.9m, the maximum loads increase 47%, 58%, 53%, and 61% for connection

spacing L/2, L/3, L/4, and L/6 respectively when web height increases 57%. Similarly,

the maximum load increases 54%, 68%, 72%, and 82% for connection spacing L/2,

L/3, L/4, and L/6 respectively when web height increases 57% in case of span length

Ref. code: 25605922040315TJU

19

Ls=3.8m. According to these percentages, it can be noticed that when connection

spacing becomes smaller and span length gets longer, the web height is more influential

on the increase of ultimate loads.

Figure 3.7 . Influence of web height on increase of maximum loads

(a) Ls=1.9m, (b) Ls=3.8m

Connection spacing

Max

imum

load

(k

N)

0

20

40

60

80

100

120

L/2 L/3 L/4 L/6

48.7244.83 46.79 45.18

71.83 70.7 71.64 72.83

Span length: Ls=1.9m

IC10019 IC15019

(a)

Connection spacing

Max

imu

mn

lo

ad (

kN

)

0

10

20

30

40

50

60

L/2 L/3 L/4 L/6

22.97 22.91 22.17 20.7

35.2938.39 38.21 37.63

Span length: Ls=3.8m

IC10019 IC15019

(b)

Ref. code: 25605922040315TJU

20

3.7.2 Influence of thickness on maximum loads

Another key factor for developing the capacity of beam is the thickness

of section. From Figure 3.8, changing the thickness from smaller to larger (1.5mm,

1.9mm, and 2.4mm) results in the increase of the load capacities of beam for all

connection spacing. When the thickness changes from 1.5mm to 1.9mm (27%), the

maximum load increases 51%, 49%, 52%, and 54% for connection spacing L/2, L/3,

L/4, and L/6 correspondingly. Moreover, when the thickness changes from 1.9mm to

2.4mm (26%), the maximum load increases 36%, 39%, 42%, and 43% for connection

spacing L/2, L/3, L/4, and L/6 respectively. Therefore, as the connection spacing is

smaller, the increase of maximum load due to change of thickness is higher.

Figure 3.8 Influence of thickness on maximum loads

3.7.3 Influence of span length on maximum loads

The influence of span length on maximum load for the different sections is

shown in Figure 3.9. There are two span lengths considered in this study: 1.9m and

3.8m. For section IC10019, the maximum load decreases 53%, 49%, 53%, 54% for

connection spacing L/2, L/3, L/4, and L/6 respectively when the span length changes

from 1.9m to 3.8m. For section IC15019, similarly, the maximum load decreases 51%,

46%, 47%, 48% for connection spacing L/2, L/3, L/4, and L/6 respectively when the

Connection spacing

Max

imu

m l

oad

(k

N)

0

20

40

60

80

100

120

140

160

L/2 L/3 L/4 L/6

t=1.5mm

t=1.9mm

t=2.4mm

Ref. code: 25605922040315TJU

21

span length changes from 1.9m to 3.8m. Hence, it can be found that the effects of span

length for the section IC15019 are smaller than that for the section IC10019.

Figure 3.9 Influence of span length on maximum loads

3.7.4 Load-deflection curves

Relations between load and two mid-span deflections are plotted for all

specimens in Figure 3.10. It is noticed that the defections of LVDT 1 (v1) and

deflections of LVDT 2 (v2) are matched from the beginning of loading up to the load

level close to the failure loads. At the failure load, however, the deflections of LVDT 1

and LVDT 2 differ slightly from each other except the specimen IC10019 of span length

1.9m with connection spacing L/3, L/4, L/6.

For the same span length, load-deflection curves for all specimens are plotted

as shown in Figure 3.11. For span length of 1.9m, the differences of maximum loads

for connection spacing L/3, L/4, L/6 compared with the case of L/2 are in the range

from 3.96% to 7.98%, from 0.11% to 0.48%, from 0.26% to 1.57%, and from 0.84% to

6.99% for sections IC10019, IC15015, IC15019, and IC15024, respectively. For span

length of 3.8m, similarly, the differences are from 0.26% to 9.88% and from 6.63% to

8.78% for section IC10019 and IC15019 respectively. The effect of connection spacing

on maximum loads in case of 3.8m span length is higher than that in case of 1.9m span

length.

Connection spacing

Max

imu

m l

oad

(k

N)

0

20

40

60

80

100

120

L/2 L/3 L/4 L/6

IC10019 Ls=1.9m

IC10019 Ls=3.8m

IC15019 Ls=1.9m

IC15019 Ls=3.8m

Ref. code: 25605922040315TJU

22

Figure 3.10 Load-deflection curves of LVDT 1 and LVDT 2 of all specimens

Deflection (mm)

Load

(kN

)

0 10 20 30 40 50

0

20

40

60

80

100

120Ls=1.9m L/2

IC10019

IC15015

IC15019

IC15024

v1

v2

v1

v2

v1

v2

v1

v2

Deflection (mm)

Load

(kN

)

0 10 20 30 40 50

0

20

40

60

80

100

120Ls=1.9m L/3

IC10019

IC15015

IC15019

IC15024

v1

v2

v1

v2

v1

v2

v1

v2

Deflection (mm)

Load

(kN

)

0 10 20 30 40 50

0

20

40

60

80

100

120Ls=1.9m L/4

IC10019

IC15015

IC15019

IC15024

v1

v2

v1

v2

v1

v2

v1

v2

Deflection (mm)

Load

(kN

)

0 10 20 30 40 50

0

20

40

60

80

100

120

IC10019

IC15015

IC15019

IC15024

Ls=1.9m L/6 v1

v2

v1

v2

v1

v2

v1

v2

Deflection (mm)

Lo

ad (

kN

)

0 20 40 60 80 100 120

0

10

20

30

40

50Ls=3.8m L/6

IC10019

IC15019

v1

v2

v1

v2

Deflection (mm)

Lo

ad (

kN

)

0 20 40 60 80 100 120

0

10

20

30

40

50Ls=3.8m L/3

IC10019

IC15019

v1

v2

v1

v2

Deflection (mm)

Lo

ad (

kN

)

0 20 40 60 80 100 120

0

10

20

30

40

50Ls=3.8m L/2

IC10019

IC15019

v1

v2

v1

v2

Deflection (mm)

Lo

ad (

kN

)

0 20 40 60 80 100 120

0

10

20

30

40

50Ls=3.8m L/4

IC10019

IC15019

v1

v2

v1

v2

Ref. code: 25605922040315TJU

23

Figure 3.11 Load-deflection curves of all connection spacing

3.7.5 Load-lateral displacement curves

Load-lateral displacement curves of IC15015, IC15019, IC15024 in case of

1.9m span length are shown in Figure 3.12(a). It was found that for all three sections,

the values of lateral displacement in case of connection spacing L/3 are higher than

those in case of connection spacing L/2, L/4, L/6. The reason might be that the web of

lipped channel section separates significantly from each other due to absence of bolt

connection spacing at mid-span as shown in Figure 3.12(b).

3.7.6 Load-strain curves

The relationship between loads and strains measured from the tests of 24 cold-

formed steel built-up I beam was illustrated in Figure 3.13. It is noted that there are four

different sections, IC10019, IC15015, IC15019, IC15024 in one graph for span length

Deflection (mm)

Lo

ad (

kN

)

0 10 20 30 40 50

0

20

40

60

80

100

120Ls=1.9m v1

IC10019

IC15015

IC15019

IC15024

L/2

L/3

L/4

L/6

Deflection (mm)

Lo

ad (

kN

)

0 10 20 30 40 50

0

20

40

60

80

100

120Ls=1.9m v2

IC10019

IC15015

IC15019

IC15024

L/2

L/3

L/4

L/6

Deflection (mm)

Lo

ad (

kN

)

0 20 40 60 80 100 120

0

10

20

30

40

50Ls=3.8m v1

IC10019

IC15019

L/2

L/3

L/4

L/6

Deflection (mm)

Lo

ad (

kN

)

0 20 40 60 80 100 120

0

10

20

30

40

50Ls=3.8m v2

IC10019

IC15019

L/2

L/3

L/4

L/6

Ref. code: 25605922040315TJU

24

Figure 3.12 (a) Load-lateral displacement curves, (b) Separation between the two webs

of 1.9m and for each connection spacing L/2, L/3, L/4, L/6 in the left part of Figure

3.13. Also, there are two different sections, IC10019, IC15019 in one graph for span

length of 3.8m and for each connection spacing L/2, L/3, L/4, L/6 in the right part of

Figure 3.13. In addition, each section consists of four different strains: two compressive

Separation between the two webs for

IC15015 in case of connection spacing L/3 Lateral displacement (mm)

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

10

20

30

40

50

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

10

20

30

40

50Load (kN)

IC15015

Ls=1.9m L/2

L/3

L/4

L/6

Lateral displacement (mm)

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

20

40

60

80

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

20

40

60

80Load (kN)

IC15019

Ls=1.9mL/2

L/3

L/4

L/6

Lateral displacement (mm)

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

30

60

90

120

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

30

60

90

120Load (kN)

IC15024

Ls=1.9mL/2

L/3

L/4

L/6

(a) (b)


IC15024 in case of connection spacing L/3


IC15019 in case of connection spacing L/3

Ref. code: 25605922040315TJU

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Figure 3.13 Load-strain curves of all specimens

-4000 -2000 0 2000 4000

30

60

90

-4000 -2000 0 2000 4000

30

60

90

Ls=1.9m L/3

IC10019IC10019

IC15015 IC15015

IC15019 IC15019

IC15024IC15024

Strain (10-6)

Load (kN)

-4000 -2000 0 2000 4000

30

60

90

-4000 -2000 0 2000 4000

30

60

90

IC10019IC10019

IC15015 IC15015

IC15019 IC15019

IC15024IC15024

Strain (10-6)

Load (kN)

Ls=1.9m L/2

-4000 -2000 0 2000 4000

30

60

90

-4000 -2000 0 2000 4000

30

60

90

Ls=1.9m L/6

IC10019IC10019

IC15015IC15015

IC15019IC15019

IC15024 IC15024

Load (kN)

Strain (10-6)

-4000 -2000 0 2000 4000

30

60

90

-4000 -2000 0 2000 4000

30

60

90

Ls=1.9m L/4

IC10019IC10019

IC15015IC15015

IC15019IC15019

IC15024IC15024

Load (kN)

Strain (10-6)

-4000 -2000 0 2000 4000

10

20

30

40

-4000 -2000 0 2000 4000

10

20

30

40

Ls=3.8m L/2

IC10019IC10019

IC15019IC15019

Strain (10-6)

Load (kN)

-4000 -2000 0 2000 4000

10

20

30

40

-4000 -2000 0 2000 4000

10

20

30

40

Ls=3.8m L/3

IC10019 IC10019

IC15019IC15019

Load (kN)

Strain (10-6)

-4000 -2000 0 2000 4000

10

20

30

40

-4000 -2000 0 2000 4000

10

20

30

40

Ls=3.8m L/4

IC10019IC10019

IC15019IC15019Load (kN)

Strain (10-6)

-4000 -2000 0 2000 4000

10

20

30

40

-4000 -2000 0 2000 4000

10

20

30

40

Ls=3.8m L/6

Load (kN)

Strain (10-6)

IC10019IC10019

IC15019IC15019

-4000 -2000 0 2000 4000

30

60

90

-4000 -2000 0 2000 4000

30

60

90

IC10019IC10019

IC15015 IC15015

IC15019 IC15019

IC15024IC15024

Strain (10-6)

Load (kN)

Ls=1.9m L/2Strain 1

Strain 2

Strain 3

Strain 4

Strain 1

Strain 2

Strain 3

Strain 4

Strain 1

Strain 2

Strain 3

Strain 4

Strain 1

Strain 2

Strain 3

Strain 4

12

34

C1 C2

Ref. code: 25605922040315TJU

26

strains (strain 1 and strain 2) at the top compression flanges at mid-span and two tensile

strains (strain 3 and strain 4) at the bottom tension flanges at mid-span. The dash lines

represent results of compressive strains and the solid lines represent results of tensile

strains. From Figure 3.13, it can be observed that the tensile strains of sections with

smaller thickness are lower than those with larger thickness. Furthermore, the tensile

strains of sections with smaller height are larger than those with higher height.

Moreover, the compressive strains of specimens for connection spacing L/2, L/4, L/6

are always higher than tensile strains at the maximum load.

3.7.7 Failure modes of specimens

Two types of failure modes i.e. local buckling (LB) and distortional buckling

(DB) are observed in the test as listed in Table 3.3 and Table 3.4. The failure mode of

cold-formed steel built-up I beam was shown in two tables for two C-sections: C1 and

C2. It can be seen that there are three positions where failure modes occurred. One

position is at the location of the load-bearing plate on the side of pinned support (Point

A), at location of load-bearing plate on the side of roller support (Point B), and at mid-

span or between mid-span and load-bearing plate. It is noticed that local or distortional

buckling happens separately for some specimens; however, there is a combination

between local and distortional buckling (LB+DB) for some specimens. It is worth to

note that in case of connection spacing of L/3, failure never happened at mid-span, but

each web of lipped channel section separates from each other due to absence of bolt

connection at mid-span.

The different types of failure modes are illustrated in Figure 3.14. Figure 3.14(a)

presents the failure mode of distortional buckling (DB) because the top flange rotates

upward about web-flange junction. Also, Figure 3.14(b) shows the failure mode of local

buckling (LB) due to only bending on top flanges by keeping similarly the level of the

fold line between flange-web junction and flange-lip junction. Again, Figure 3.14(c)

and Figure 3.14(d) illustrate the failure mode of local and distortional buckling

(LB+DB) happened only one side and both sides of C-section respectively because the

top flange rotates and bends simultaneously downward about web-flange junction.

On the other, the failure of bolt connection was not found in experiment.

Ref. code: 25605922040315TJU

27

Table 3.3 Experimental result (Failure mode of section IC10019)

Specimen Connection

spacing

Failure modes

Point A Between mid-span

and point A or B Point B

C2 C1 C2 C1 C2 C1

IC10019

(Ls=1.9m)

L/2 DB DB - - DB DB

L/3 LB+DB LB+DB - - LB+DB LB+DB

L/4 LB+DB - DB - - -


IC10019

(Ls=3.8m)

L/2 - - DB - - -


L/4 - - - DB - -

L/6 LB+DB - - DB - -

LB = Local buckling, DB = Distortional buckling

Table 3.4 Experimental result (Failure mode of sections IC15015, IC15019, IC15024)

Specimen Connection

spacing

Failure modes

Point A Mid-span Point B

C2 C1 C2 C1 C2 C1

IC15015

(Ls=1.9m)

L/2 LB+DB LB+DB - - - -

L/3 LB+DB LB+DB - - - -

L/4 LB+DB LB+DB - - - -

L/6 LB+DB LB+DB - - - -

IC15019

(Ls=1.9m)

L/2 - - LB LB LB+DB LB+DB

L/3 LB+DB LB+DB - - - -

L/4 LB+DB LB+DB LB LB LB+DB LB+DB

Ref. code: 25605922040315TJU

28

L/6 LB+DB LB+DB LB LB LB+DB LB+DB

IC15019

(Ls=3.8m)

L/2 - - - LB+DB - -


L/4 - - - LB+DB - -

L/6 - - - LB+DB - -

IC15024

(Ls=1.9m)

L/2 LB+DB LB+DB - - - -

L/3 LB+DB LB+DB - - - -

L/4 LB+DB LB+DB - - - -

L/6 LB+DB LB+DB - - - -

LB = Local buckling, DB = Distortional buckling

Figure 3.14 Failure modes of specimens

The failure modes of 1.9m span length specimens are shown from Figure 3.15-

Figure 3.18 and failure mode of 3.8m span length specimens are indicated from Figure

3.19- Figure 3.20.

(a) Distortional buckling (DB) (b) Local buckling (LB)

(c) LB+DB on one side of C-section (d) LB+DB on both sides of C-section

Ref. code: 25605922040315TJU

29

Figure 3.15 Failure mode of specimen IC10019, Ls=1.9m

(a) Connection spacing L/2

DB at both load-bearing plates

(b) Connection spacing L/3

LB+DB at both load-bearing plates

(c) Connection spacing L/4

LB+DB at load-bearing plate

and DB between mid-span and load-bearing plate

(d) Connection spacing L/6

LB+DB on at both load-bearing plates

Ref. code: 25605922040315TJU

30



LB+DB at one load-bearing plate







Ref. code: 25605922040315TJU

31



LB+DB at one load-bearing

plate and LB at mid-span




and LB at mid-span




and LB at mid-span

Ref. code: 25605922040315TJU

32










Ref. code: 25605922040315TJU

33


DB between mid-span and load-bearing plate








Ref. code: 25605922040315TJU

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LB+DB on C1 at mid-span








Ref. code: 25605922040315TJU

35

Chapter 4

Numerical Study

The finite element analysis is an unavoidable method for investigating the

behavior of cold-formed steel built-up I beam. The software Abaqus is a popular finite

element program used in research for modelling structure with material and geometric

nonlinear behavior (Schafer et al., 2010). The purpose of this numerical study is to

illustrate the experimental results. So, there are 24 modelled beams corresponding to

tested 24 beams in this numerical study.

4.1 Cold-formed steel built-up I beam modelling

The cold-formed steel built-up I beam is drawn in center lines as cross section;

then, it is extruded for obtaining the required length of 2m or 4m. The thickness of

section is provided when sections are inserted the properties. The distance between the

two center lines of each web is the thickness of section, and the half of thickness is the

distance between bottom surface of load-bearing plate and center line of top flanges

and is the distance between top surface of support plate and center line of bottom

flanges. Moreover, there are circular holes on webs of sections for location of bolts and

the number of holes is relies on the four types of connection spacing.

Figure 4.1 Cold-formed steel built-up I beam modelling in case of connection spacing

L/6 for section IC15019, Ls=1.9m

Lipped channel

Load-bearing plate

Support plate

Bolt connection

Support plate

(100mm×240mm×20mm for

Ls=1.9m)

(200mm×400mm×20mm for

Ref. code: 25605922040315TJU

36

4.2 Bolt connection modelling

The real 3D bolt connection was modelled in program, Abaqus, for connecting

two lipped channel sections on flat portion of section’s web in order to make the same

fabricated condition of specimens in experiment. The modelled bolt connection consists

of bolt, washer, and nut as shown in Figure 4.2. For bolt, there are two parts: part of

bolt’s head and part of round steel bar. In order to create bolt, first, both parts were

created separately in Module (part). Then, both created parts were brought into Module

(Assembly) for creating instance. Finally, bolt’s head and round steel bar were merged

as one new instance (bolt). The bolt’s diameter is 12mm and the inner hole of nuts and

washers is also 12mm. The thickness of bolt’s heads is 8mm, the thickness of nuts is

10mm, and 3mm is the thickness of washers. All these dimensions are matched to the

real bolts used in experiment.

Figure 4.2 Bolt connection modelling

4.3 Element selection

Element selection is very important in finite element method for modelling the

cold-formed steel member and other parts. There are two types of element used in this

numerical study, shell element (S4R: S=Conventional stress/displacement shell, 4 =

4-nodes, R = Reduced integration) and solid element (C3D8R: C = Continuum

Figure 4.3 Shell element

Bolt Nut Washer

Element

Structural body

being modelled

Finite element model

Ref. code: 25605922040315TJU

37

stress/displacement, 3D=3 dimensions, 8= hexahedral and 8 nodes, R=Reduced

integration) as shown Figure 4.3 and Figure 4.4. According to Kirchhoff theory, shell

element can be used when one dimension of shell, thickness, is significantly small if

compared to other small comparing to other dimensions in the shell surface. The

geometry of conventional shell element is defined as the reference surface for

discretizing the structural modelled body. The shell element includes both displacement

and rotational degree of freedom. This is so good reason that cold-formed steel built-

up I beam was modelled with shell element (S4R). On the other hand, the load-bearing

plate, support plate, and bolt connection are modelled with solid element (C3D8R) due

to their big thickness compared to two other dimensions.

Figure 4.4 Solid element

4.4 Material behavior

Cold-formed steel built-up I beam was modelled with material nonlinearity

defined by relationship between stress and strain from coupon test. There are two parts

of stress-strain curves, elastic part and plastic part. For elastic part, Young’s modulus

was taken to 208 GPa and Poisson’s ratio equal to 0.3. For plastic part, yield stress and

plastic strain data depending on types of thickness require to insert (see section 3.2).

On the other hand, the load-bearing plate, support plate, and bolt connection were

regarded as rigid material which works only in elastic range because there was no any

deformation on them during testing. Hence the value of Young’s modulus for this

material is set to be one thousand time of cold-formed steel.

Structural body

being modelled Finite element model

Element

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38

4.5 Contact condition

The contact condition is an unavoidable considerable point in finite element

method especially in case of built-up sections. The interaction between top flanges of

lipped channel section and bottom surface of load-bearing plates is used by surface-to-

surface contact and interaction between web and web of channel section were also

considered as surface-to-surface contact (Portioli et al., 2012). There are two types of

contact property, tangential behavior and normal behavior. Frictionless was chosen for

tangential behavior and hard contact was selected for normal behavior. In addition,

surface-to-surface contact has two surfaces to selected called slave surface and master

surface. Slave surface is provided to thin-walled member (lipped channel section

member) and master surface is applied to load-bearing plate (see Figure 4.5).

Figure 4.5 Interaction of surface-to-surface contact (standard)

Figure 4.6 Tie contraint (surface-to-surface)

Contact between

load-bearing plate

and C-sections

Contact between

the two webs of

C-section

Contact between

bolt, nut, and

washer

Contact between

web of C-section

and washer

Contact between

washer and

nut/bolt’s head

Contact between

support plate and

C-sections

Ref. code: 25605922040315TJU

39

However, tie constraint (surface-to-surface) is applied to interaction between

bottom flanges of lipped channel section and top surfaces of support plate because these

surfaces was touched together in testing (see Figure 4.6).

For bolt connection, there are three parts for providing the interaction as tie

constraint (surface-to-surface). First, the square surface is drawn on web holes for the

interactive area with washer. Another interaction is between another surface of washer

and nut/bolt’s head. Last, the inner hole surfaces of nut and washer interact with the

round bars part of bolt (see Figure 4.6).

4.6 Boundary and loading condition

The boundary condition is provided to pinned support, roller support, top

flange’s lips at both supports, and top flange’s lips at each load-bearing plate while

loading condition is provided load-bearing plates. Pinned support and roller support

were drawn one center line on bottom surface of plate. The translation in X, Y, and Z

direction (U1, U2, U3 respectively) and the translation in X, Y direction were

constrained by center line as pinned support and roller support respectively. All top

flange’s lips at both supports were constrained in X direction by one horizontal center

line for protecting the twist of beam at support (see Figure 4.7).

Figure 4.7 Boundary condition at each support

Lateral constraint at both supports

Pinned Support Roller Support

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40

For lateral bracing steel frame was simplified as one vertical line on top lips

constrained in X direction at each load-bearing plate. Top surface of load-bearing plates

was drawn one center line in X, and Z direction. The controlled displacement was

applied in Y direction on center line in X and Z direction of load-bearing plate. In

addition, there were two constrained points in X, Z direction located at both ends of

center line in Z direction (see Figure 4.8).

Figure 4.8 Boundary condition and displacement controlled at load-bearing plate

4.7 Element mesh

Figure 4.9 Detail of mesh size

Load-bearing plate (5mm×5mm×5mm)

Support plate (5mm×5mm×5mm)

Bolt connection

(1mm×1mm×1mm)

Cold-formed steel sections

(5mm×5mm)

Constraint in X, Z direction

Displacement

controlled

Lateral bracing at load-bearing plate

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41

The mesh sizes of cold-formed steel sections were approximately 5mm×5mm.

The support plates and load-bearing plates were provided approximate mesh size of

5mm×5mm×5mm and 1mm×1mm×1mm was the mesh size of bolt connection. All

corners of sections were divided to three parts.

4.8 Analysis procedures

There are two procedures in this finite element analysis. First, linear buckling

analysis was performed; then, geometrically and materially nonlinear analysis with

imperfections (GMNIA) was conducted.

Generally, real beams are not perfectly straight and are related to geometric

imperfections. These imperfections may be the result of the manufacturing process,

shipping, and storage, etc. Geometric imperfection can be divide into global

imperfections and cross-sectional imperfections. Therefore, when finite element

analysis was performed, the initial imperfection shapes of cold-formed steel required

to consider because it is a main factor for reducing the capacity of member. However,

the real initial imperfection shapes are visually unknown. Hence, linear buckling

analysis which provides different elastic buckling modes (eigenmodes) with eigen

values is an efficient predicted method of initial imperfection shapes of cold-formed

steel. There are two types of eigenvalue extraction method, Lanczos and Subspace

method. Subspace method have been suggested from Abaqus’s Manual because the

specimen has connectors (bolt connection) and eigenvalue is less than 20 (Hibbitt et al.,

2010). Five elastic buckling modes were suggested and recommended value of

magnitude for each mode equal to value of thickness of cold-formed steel section

(Schafer and Peköz, 1998). These five elastic buckling modes provided five different

buckling mode shapes representing for five different initial imperfection shapes.

Therefore, all five different buckling modes are necessary to input in nonlinear analysis

for considering imperfection of specimen and the elastic buckling mode providing the

ultimate loads and failure modes close to experimental results is selected. One general

static step was used in the nonlinear analysis and specified dissipated energy fraction

of 0.0002 was input for automatic stabilization. Automatic increment was selected for

allowing nonlinear problems to be run confidently in Abaqus without extensive

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42

experience with the problem. Moreover, in order to take into account of geometric

nonlinearity, the function of NLGEOM was turn on in case of large displacement

analysis.

4.9 Comparison between FEM and experimental results

Table 4.1 and Table 4.2 show the summaries of comparison between

experimental and FEM’s results. It can be seen that the failure loads of cold-formed

steel built-up I beam obtained from experiment are generally larger than those obtained

from finite element method. Hence, finite element method can be then used for

Table 4.1 Comparison of Experimental and FEM’s results

Spec

imen

CS

Experimental results Finite element method results

Exper

imen

t-to

-FE

M

rati

os

PExp

(kN)

Failure modes

PFEM

(kN)

Failure modes

Point A

Between

mid-span

and A/B

Point B Point A

Between

mid-span

and A/B

Point B

C2 C1 C2 C1 C2 C1 C2 C1 C2 C1 C2 C1

IC10019

(Ls=

1.9

m)

L/2 48.72 DB DB - - DB DB 41.15 LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.18

L/3 44.83 LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 37.30

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.20

L/4 46.79 LB+

DB - DB - - - 43.86

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.07

L/6 45.18 LB+

DB

LB+

DB - -

LB+

DB DB 44.58

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.01

IC10019

(Ls=

3.8

m)

L/2 22.97 - - DB - - - 19.85 LB+

DB

LB+

DB - DB

LB+

DB

LB+

DB 1.16

L/3 22.91 LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 20.71

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.11

L/4 22.17 - - - DB - - 21.18 LB+

DB

LB+

DB DB -

LB+

DB

LB+

DB 1.05

L/6 20.70 LB+

DB - - DB - - 20.06

LB+

DB

LB+

DB DB -

LB+

DB

LB+

DB 1.03

CS = Connection spacing, LB = Local buckling, DB = Distortional buckling

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Table 4.2 Comparison of Experimental and FEM’s results S

pec

imen

CS

Experimental results Finite element method results

Exper

imen

t-to

-F

EM

rat

ios

PExp

(kN)

Failure modes PFEM

(kN)

Failure modes

Point A Mid-span Point B Point A Mid-span Point B

C2 C1 C2 C1 C2 C1 C2 C1 C2 C1 C2 C1

IC15015

(Ls=

1.9

m)

L/2 47.48 LB+

DB

LB+

DB - - - - 42.89

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.11

L/3 47.53 LB+

DB

LB+

DB - - - - 41.82

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.14

L/4 47.09 LB+

DB

LB+

DB - - - - 43.63

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.08

L/6 47.25 LB+

DB

LB+

DB - - - - 42.90

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.10

IC15019

(Ls=

1.9

m)

L/2 71.83 - - LB LB LB+

DB

LB+

DB 64.49

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.11

L/3 70.70 LB+

DB

LB+

DB - - - - 63.52

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.11

L/4 71.64 LB+

DB

LB+

DB LB LB

LB+

DB

LB+

DB 65.65

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.09

L/6 72.83 LB+

DB

LB+

DB LB LB

LB+

DB

LB+

DB 68.77

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.06

IC15019

(Ls=

3.8

m)

L/2 35.29 - - - LB+

DB - - 35.23

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.00

L/3 38.39 LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 35.75

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.07

L/4 38.21 - - - LB+

DB - - 36.25

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.05

L/6 37.63 - - - LB+

DB - - 36.76

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.02

IC15024

(Ls=

1.9

m)

L/2 97.50 LB+

DB

LB+

DB - - - - 89.88

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.08

L/3 98.32 LB+

DB

LB+

DB - - - - 93.80

LB+

DB

LB+

DB - -

LB+

DB

LB+

DB 1.05

L/4 101.8 LB+

DB LB+

DB - - - - 91.33

LB+

DB LB+

DB - -

LB+

DB LB+

DB 1.11

L/6 104.3 LB+

DB LB+

DB - - - - 97.19

LB+

DB LB+

DB - -

LB+

DB LB+

DB 1.07

CS = Connection spacing, LB = Local buckling, DB = Distortional buckling

Ref. code: 25605922040315TJU

44

predicting the ultimate loads of cold-formed steel built-up I beam in the conservative

or safe manner.

The failure modes of local or/and distortional buckling are found in both results

from the experiment and finite element method (FEM). However, it is noticed that the

failure modes from experiments do not match with those from FEM in term of locations

along beam. The reason of this difference might be due to imperfect shape of

specimens.

The comparisons of load-deflections curves between experiment and FEM in

case of 1.9m and 3.8m span length specimens are shown in Figure 4.10 and Figure 4.11

respectively. The solid lines represent results of experiment and dash lines represent

results of FEM. For span length of 1.9m, the slopes of load-deflections from FEM for

large sections are higher than those from experiment, but the slopes of load-deflections

for small section from FEM agreed with those from experiment for all connection

spacing. For span length of 3.8m, the slopes of load-deflections from FEM and

experiment results agreed well for all connection spacing.

Moreover, the comparison of load-strain curves of 1.9m and 3.8m span length

specimens between experiment and FEM are indicated by Figure 4.12 and Figure 4.13

respectively. Load-strain curves of section C1 (strain 1 and strain 3) and section C2

(strain 2 and strain 4) are plotted separately. It can be seen that the tension strains (strain

3 and strain 4) from experiment match with those from FEM for all cases. However,

the compression strains (strain 1 and strain 2) from experiment match with those from

FEM for some cases.

The comparison of failure mode between experiment and FEM is illustrated

from Figure 4.14-Figure 4.16. In case of this connection spacing L/3, the failure mode

of local and distortional buckling from experiment happened on specimens at only one

side of load-bearing plate for high sections of Ls=1.9m (see Figure 4.14(b), Figure

4.15(a) and (b)) while this failure mode occurred on specimens at both sides of load-

bearing plates for small sections of Ls=1.9m (Figure 4.14(a)), small and high section of

Ls=3.8m (see Figure 4.16). For FEM, the failure mode of local and distortional buckling

happened on all specimens at both sides of load-bearing plates.

Ref. code: 25605922040315TJU

45

Figure 4.10 Comparison of load-deflection curves between experiment and FEM for

Ls=1.9m (a) deflection 2, (b) deflection 1

(a)

(b)

2 1

C2 C1

Ref. code: 25605922040315TJU

46

Figure 4.11 Comparison of load-deflection curves between experiment and FEM for

Ls=3.8m (a) deflection 2, (b) deflection 1

(a)

(b)

2 1

C2 C1

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47

Figure 4.12 Comparison of load-strain curves between experiment and FEM for

Ls=1.9m (a) strain 2 and strain 4 of C2, (b) strain 1 and strain 3 of C1

(a)

(b)

12

34

C1 C2

Ref. code: 25605922040315TJU

48

Figure 4.13 Comparison of load-strain curves between experiment and FEM for

Ls=1.9m (a) strain 2 and strain 4 of C2, (b) strain 1 and strain 3 of C1

(a)

(b)

12

34

C1 C2

Ref. code: 25605922040315TJU

49

Figure 4.14 Comparison of failure mode (LB+DB) between experiment and FEM

(a) Section IC10019, 1.9m span length, Connection spacing L/3

(b) Section IC15015, 1.9m span length, Connection spacing L/3


Experiment: LB+DB

FEM: LB+DB

Experiment: LB+DB

FEM: LB+DB

Experiment: LB+DB

FEM: LB+DB

Experiment: None

FEM: LB+DB

Ref. code: 25605922040315TJU

50


Experiment: None

FEM: LB+DB

Experiment: LB+DB

FEM: LB+DB


Experiment: LB+DB

FEM: LB+DB

Experiment: None

FEM: LB+DB


Ref. code: 25605922040315TJU

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Experiment: LB+DB

FEM: LB+DB Experiment: LB+DB

FEM: LB+DB

Experiment: LB+DB

FEM: LB+DB

Experiment: LB+DB

FEM: LB+DB

Ref. code: 25605922040315TJU

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Chapter 5

Conclusions

An experimental and numerical investigation on 24 cold-formed steel built-up

I beams consisting of four connection spacing L/2, L/3, L/4, L/6 with four types of

section IC10019, IC15015, IC15019, IC15024 and two types of span length Ls=1.9m,

Ls=3.8m was conducted carefully. Four-point bending test was used in this study and

the lateral bracing frames were installed for preventing the lateral movement or rotation

of specimens. Bolts were used to create the cold-formed steel built-up I beam

specimens. Moreover, nonlinear finite element analysis was performed by considering

geometric nonlinearity, material nonlinearity, and imperfection shapes of specimens.

The program “Abaqus” was adopted in the present analysis. Bolts were modelled in

finite element analysis. Five elastic buckling modes obtained from linear buckling

analysis was input for providing as initial imperfection shapes of specimen with scale

factor of thickness of steel plate in nonlinear analysis and the elastic buckling mode

offering the results close to experiment results was selected. The conclusion can be

drawn as follows:

1. The maximum load in case of 1.9m span length increases 47%, 58%, 53%,

61% for connection spacing L/2, L/3, L/4, L/6 respectively when the web

height increases 57% and maximum load in case of 3.8m span length increases

54%, 68%, 72%, 82% for connection spacing L/2, L/3, L/4, L/6 respectively

when the web height increases 57%. According to these percentages, when

connection spacing becomes smaller and span length gets longer, the web

height is more influential on the increase of maximum load.

2. When the thickness changes from 1.5mm to 1.9mm (27%), the maximum load

increases 51%, 49%, 52%, 54% for connection spacing L/2, L/3, L/4, L/6

respectively and when the thickness changes from 1.9mm to 2.4mm, the

maximum load increases 36%, 39%, 42%, 43% for connection spacing L/2,

L/3, L/4, L/6 respectively. Therefore, as the connection spacing is smaller, the

increase of maximum load due to change of thickness is higher.

Ref. code: 25605922040315TJU

53

3. For section IC10019, the maximum load decreases 53%, 49%, 53%, 54% for

connection spacing L/2, L/3, L/4, and L/6 respectively when the span length

changes from 1.9m to 3.8m. For section IC15019, similarly, the maximum

load decreases 51%, 46%, 47%, 48% for connection spacing L/2, L/3, L/4, and

L/6 respectively when the span length changes from 1.9m to 3.8m. Thus, the

effect of span length for the section IC15019 are smaller than that for the

section IC10019.

4. For span length of 1.9m, the differences of maximum loads for connection

spacing L/3, L/4, L/6 compared with the case of L/2 are in the range from

3.96% to 7.98%, from 0.11% to 0.48%, from 0.26% to 1.57%, and from 0.84%

to 6.99% for sections IC10019, IC15015, IC15019, and IC15024, respectively.

For span length of 3.8m, similarly, the differences are from 0.26% to 9.88%

and from 6.63% to 8.78% for section IC10019 and IC15019 respectively. The

effect of connection spacing on maximum loads in case of 3.8m span length is

higher than that in case of 1.9m span length.

5. The failure of bolt connection was not found in the experiment.

6. The failure loads of specimens obtained from experiment are higher than those

obtained from FEM. Hence, FEM can be used for predicting ultimate strength

of cold-formed built-up I beam in the conservative or safe manner.

7. The failure modes of local or/and distortional buckling were found in both

results from experiment and FEM, but the failure modes from experiments do

not matched with those from FEM in term of locations along beam. The reason

of this difference might be due to imperfect shape of specimens.

For the future research, cold-formed steel built-up I beam with large sections

(height >200mm) is recommended for more understanding the structural behavior.

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References

American Iron and Steel Institute Committee, CSA Group Technical Committee, and

CANACERO. (2016). North American Specification for Design of Cold-

Formed Steel Structural Members.Washington, DC: AISI.

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geometrical imperfection in nonlinear FE analysis of cold-formed steel rack

columns. Thin-Walled Structures, 51, 99–111.

EN1993-1.3 (2006). Design of steel structures. General rules. Supplementary rules

for cold-formed members and sheeting. UK: BSI.

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(2015). An experimental investigation of stiffened cold-formed C-channels

in pure bending and primarily shear conditions. Thin-Walled Structures, 96,

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13(2), 163–170.

Hibbitt, D., Karlsson, B., & Sorensen, P. (2010). ABAQUS 6.10 analysis user’s manual.

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To-Back Beams. Thesis (Master), Sirindhorn International Institute of

Technology, Thammasat University, Pathum Thani, Thailand.

Kang, K., Chaisomphob, T., Patwichaichote, W., & Yamaguchi, E. (2017, August).

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on cold-formed steel connections. The Scientific World Journal, 2014.

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Sections with Intermediate Stiffeners under Bending. I: Tests and Numerical

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Validation. ASCE Journal of Structural Engineering, 142(3).

Portioli, F., Lorenzo, G. Di, Landolfo, R., & Mazzolani, F. M. (2012). Contact Buckling

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Schafer, B., & Peköz, T. (1998). Computational modeling of cold-formed steel:

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Schafer, B. W., Li, Z., & Moen, C. D. (2010). Computational modeling of cold-formed

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Simulia.ABAQUS/CAE. Version 6.14-1, USA.

Wang, L., & Young, B. (2015). Beam tests of cold-formed steel built-up sections with

web perforations. Journal of Constructional Steel Research, 115, 18–33.

Wang, L., & Young, B. (2017). Design of cold-formed steel built-up sections with web

perforations subjected to bending. Thin-Walled Structures, 120, 458–469.

Ref. code: 25605922040315TJU

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Appendices

Ref. code: 25605922040315TJU

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Appendix

Specification calculation

The Directed Strength Method (DSM) of AISI specification and Eurocode 3

were used to calculate the ultimate strength of built-up I beams for comparing with

experimental results. Section IC15024 is an example of specification calculation for

both method.

1 Gross section properties of lipped channel section

According to AISI Manual Cold-Formed Steel Design (AISI, 2003), the gross

section properties of lipped channel section can be calculated.

Basic parameter

h 152mm=

b 64mm=

c 18.5mm=

t 2.4mm=

r 5mm=

6 4

xI 2.54 10 mm=

9 6

wI 1.97 10 mm=

3 4

tI 1.37 10 mm=

yF 476MPa=

E 208000MPa=

G 80000MPa=

sL 1.9m=

crL 780mm= unbraced length

bC 1.0= , yk 0.8= wk 1.0=

2 Direct Strength Method of AISI specification

Direct Strength Method in AISI specification can be conducted by using critical

elastic buckling stress from CFS software. Software CFS cannot provide critical elastic

Ref. code: 25605922040315TJU

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buckling stress for built-up section. Fortunately, the failure mode of lateral-torsional

buckling is not controlled in experiment due to present of lateral bracing steel frame.

Hence, the critical elastic local and distortional buckling stress of C-section were

requested from CFS software for calculating the ultimate strength of C-section; then,

cold-formed steel built-up I beam is obtained by multiplying 2 times of ultimate

strength of C-section.

Figure 1 Critical elastic local buckling stress of section C15024

2.1 Local buckling

From Figure 1, the critical elastic local buckling stress of C15024 can be

obtained.

crLf 1292.7MPa=

63x

g

2I 2 2.54 10S 33421mm

h 152

= = =

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59

6

crL g crLM S f 33421 1292.7 10 43.20kNm−= = =

Since 6

ne y fy y g yM M S F S F 33421 476 10 15.90kNm−= = = = =

neL

crL

M 15.900.61 0.776

M 43.20 = = =

So nL neM M 15.90kNm= =

2.2 Distortional buckling

From Figure 2, the critical elastic buckling distortional stress of C15024 can be

obtained.

crdf 741.93MPa=

63x

g

2I 2 2.54 10S 33421mm

h 152

= = =

Figure 2 Critical elastic distortional buckling stress of section C15024

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60

6

crd g crdM S f 33421 741.93 10 24.80kNm−= = =

Since 6

y fy y g yM S F S F 33421 476 10 15.90kNm−= = = =

y

d

crd

M 15.900.8 0.673

M 24.80 = = =

0.5 0.5

crd crdnd y

y y

0.5 0.5

nd

M MM 1 0.22 M

M M

24.80 24.80M 1 0.22 15.90 14.40kNm

15.90 15.90

= −

= − =

( ) ( )n,c nL ndM min M ,M min 15.90,14.40 14.40kNm= = = for C15024

n n,cM 2M 2 14.40 28.8kNm= = = for IC1524

nn

s

6M 6 28.8P 90.94kN

L 1.9

= = =

Hence, failure load of cold-formed steel built-up I beam of section IC15024 is 90.94kN.

3 Eurocode 3

Eurocode 3 (En, 2006) can provide ultimate strength of flexural member by

using effective width method. Local and distortional buckling strength were calculated

simultaneously considering in effective section modulus about strong axis. This is the

process of calculation in Eurocode 3.

Checking of geometrical proportions

b 6426.67 60 OK

t 2.4= = →

c 18.57.71 50 OK

t 2.4= = →

h 15263.33 500 OK

t 2.4= = →

c 18.50.20 0.29 0.60 OK

b 64 = = →

Ref. code: 25605922040315TJU

61

Dimension of middle line section

ph h t 152 2.4 149.60mm= − = − =

pb b t 64 2.4 61.60mm= − = − =

p

t 2.4c c 18.5 17.30mm

2 2= − = − =

Calculation of gross section properties

p

c

h 149.6z 74.80mm

2 2= = =

t p cz h z 149.6 74.8 74.80mm= − = − =

Effective width of compression flange (Internal compression element)

Figure. 3 Effective width of internal compression element

From Figure. 3, stress ratio: 1.0 = (Uniform compression)

k 4 = (internal compression element)

y

235 2350.70

F 476 = = =

Ref. code: 25605922040315TJU

62

Relative slenderness

p

p,b

b / t 61.6 / 2.40.64

28.4 k 28.4 0.70 4

= = =

and 0.5 0.085 0.055 0.673+ − =

So p 0.673 1.0 →=

Effective width

eff pb b 1.0 61.60 61.60mm= = =

e1 effb 0.5b 0.5 61.60 30.80mm= = =

e2 effb 0.5b 0.5 61.60 30.80mm= = =

Figure. 4 Detail of effective width

Effective width of lip (Outstand compression element

Buckling factor:

p

p

c 17.300.28 0.35 k 0.5

b 61.60= → =

Relative slenderness

p

p,c

c / t 17.30 / 2.40.51

28.4 k 28.4 0.70 0.5

= = =

p,c 0.748 1.0 →=

Effective width

eff pc c 1.0 17.30 17.30mm= = =

Ref. code: 25605922040315TJU

63

Effective area of edge stiffener (one part of flange and lip)

( ) ( ) 2

s e2 effA t b c 2.4 30.80 17.30 115.44mm= + = + =

( ) ( )

2 2

e21 p

e2 eff

1

b t / 2 30.80 2.4 / 2b b 61.60

b c t 30.80 17.30 2.4

b 51.74mm

= − = −

+ +

=

2b 0= (Flange 2 in tension)

fk 0= (Flange 2 in tension)

( )

( )

3

2 321 p 1 1 2 p f

3

2 32

2

Et 1K

b h b 0.5b b h k4 1

208000 2.4 1K

51.74 149.60 51.74 04 1 0.3

K 1.47N / mm

=+ +−

=

+ + −

=

Effective moment of inertia of edge stiffener

( )

( )

3 3 2

e2 eff effs e2

e2 eff

22

4eff effeff

e2 eff

b t c t cI b t

12 12 2 b c

c cc t 3060.30mm

2 2 b c

= + + +

+

+ − =

+

s

cr,s

s

2 KEI 2 1.47 208000 3060.30529MPa

A 115.44

= = =

Reduction factor for the edge stiffener

y

d

cr,s

F 4760.95

529 = = =

Since d d d0.65 1.38 1.47 0.723 → = −

d 1.47 0.723 0.95 0.78315 = − =

Since d 1.0→ iteration need to be conducted

1st iteration

y

com,Ed1 d

M0

F0.78315 476 373MPa = = =

Ref. code: 25605922040315TJU

64

com,Ed1

p,b,red p,b

y M0

3730.64 0.57 0.673 1.0

F / 476

= = = → =

eff pb b 1.0 61.60 61.60mm= = =

e1 effb 0.5b 0.5 61.60 30.80mm= = =

e2 effb 0.5b 0.5 61.60 30.80mm= = =

com,Ed1

p,c,red p,c

y M0

3730.51 0.45 0.748 1.0

F / 476

= = = → =

eff pc c 1.0 17.30 17.30mm= = =

d1 d 0.78315→ = =

Final value of effective properties for flange and lip

e1 effb 0.5b 0.5 61.60 30.80mm= = =

e2 effb 0.5b 0.5 61.60 30.80mm= = =

eff pc c 1.0 17.30 17.30mm= = =

red dt .t 0.78315 2.4 1.88mm= = =

Effective width of web

( )

2 2p p eff d

p p p p

c

p p p e1 e2 eff d

c h cc h b h

2 2 2h 77.30mm

c b h b b c

− + + +

= =+ + + + +

p c

c

h h0.94

h

− = − = −

Since 20 1 k 7.81 6.29 9.78 22.25 − → = − + =

Ref. code: 25605922040315TJU

65

p

p,h

h / t0.66 0.5 0.085 0.055 0.87

28.4 k

1.0

= = + − =

→ =

eff ch h 77.30mm= =

( )

e1 eff

e2 eff

1 e1

2 p c e2

h 0.4h 0.4 77.30 30.92mm

h 0.6h 0.6 77.30 46.38mm

h h 30.92mm.

h h h h 118.68mm

= = =

= = =

= =

= − − =

( ) 2

eff p p 1 2 e1 e2 eff dA 2t c b h h b b c 1425.72mm = + + + + + + =

22

p eff d2 1p p p p 2 p

c,effeff

c ch ht c h b h h h

2 2 2 2y

A

2

− + + − + +

=

c,effy 77.30mm= from center line of top flange

t,eff p c,effy h y 72.30m= − =

Ref. code: 25605922040315TJU

66

Effective moment of inertia

( )3 3 3 3

1 2 p d eff 4

1

t h h c cI 342066.81mm

12

+ + += =

( )3 3

p e1 e2 d 4

2

t b b bI 123.56mm

12

+ + = =

2

p 4

3 p t,eff

cI c t y 168188.62mm

2

= − =

2 4

4 p t,effI b ty 772712.41mm= =

2

425 2 t,eff

hI h t y 47815.26mm

2

= − =

2

416 1 c,eff

hI h t y 283831.61mm

2

= − =

2 4

7 e1 c,effI b ty 441741.63mm= =

( ) 2 4

8 e2 d c,effI b t y 346454.21mm= =

( )2

4eff9 eff d c,eff

cI c t y 153486.18mm

2

= − =

( ) 4

eff ,x 1 2 3 4 5 6 7 8 9I 2 I I I I I I I I I 5112840.58mm= + + + + + + + + =

Elastic section modulus of effective section

eff ,x 3

eff ,x,c

c,eff

eff ,x 3

eff ,x,t

t ,eff

IW 66139.22mm

y

IW 70721.15mm

y

= =

= =

( ) 3

eff ,x eff ,x,c eff ,x,tW min W , W 66139.22mm= =

3.1 Local and distortional buckling

y 6

c,Rd eff ,x

M0

F 476M W 66139.22 10 31.48kNm

1.0

−= = =

3.2 Lateral-torsional buckling

y

b,Rd LT eff ,x

M1

FM W=

where LT is reduction factor for lateral-torsional buckling

Ref. code: 25605922040315TJU

67

( )

22

wxcr,LT b t 22

y cr w cr

EIEIM C GI 538.46kNm

k L k L

= + =

eff ,x y

LT LT

cr,LT

W F0.24 0.40 1.0

M = = → =

y

b,Rd LT eff ,x

M1

F 476M W 1.0 66139.22 31.48kNm

1.0→ = = =

( )n c,Rd b,RdM min M , M 31.48kNm= =

nn

s

6M 6 31.48P 99.42kN

L 1.9

= = =

Hence, failure load of cold-formed steel built-up I beam of section IC15024 is 99.42kN.

4 Comparison between experimental and specification’s results

The comparison between experimental and specification’s results is shown in

Table 1. The experiment-to-EC3 ratios shows that the maximum loads of small sections

from experiment are greater than those from Eurocode 3; however, maximum loads of

big sections from experiment are lower than those from Eurocode 3 except connection

spacing L/4, L/6 of section IC15024. According to experiment-to-DSM ratios, the

maximum loads of small sections from experiment are higher than those from Direct

Strength Method. However, the maximum loads of big sections from experiment are

lower than those from Direct Strength Method when the thickness becomes smaller.

Moreover, the ultimate strength of cold-formed steel built-up I beams from Eurocode 3

are higher than those from Direct Strength Method.

Table 1 Comparison between experimental and specification’s results

Specimen Connection

spacing

Maximum Load (kN) PExp/PEC3 PExp/PDSM

Experiment EC3 DSM

IC10019

(Ls=1.9m)

L/2 48.72

42.46 38.65

1.15 1.26

L/3 44.83 1.06 1.16

L/4 46.79 1.10 1.21

L/6 45.18 1.06 1.17

Ref. code: 25605922040315TJU

68

IC10019

(Ls=3.8m)

L/2 22.97

19.38 19.33

1.19 1.19

L/3 22.91 1.18 1.19

L/4 22.17 1.14 1.15

L/6 20.70 1.07 1.07

IC15015

(Ls=1.9m)

L/2 47.48

53.83 47.96

0.88 0.99

L/3 47.53 0.88 0.99

L/4 47.09 0.87 0.98

L/6 47.25 0.88 0.99

IC15019

(Ls=1.9m)

L/2 71.83

78.46 75.86

0.92 0.95

L/3 70.70 0.90 0.93

L/4 71.64 0.91 0.94

L/6 72.83 0.93 0.96

IC15019

(Ls=3.8m)

L/2 35.29

39.23 37.93

0.90 0.93

L/3 38.39 0.98 1.01

L/4 38.21 0.97 1.01

L/6 37.63 0.96 0.99

IC15024

(Ls=1.9m)

L/2 97.50

99.42 90.94

0.98 1.07

L/3 98.32 0.99 1.08

L/4 101.82 1.02 1.12

L/6 104.32 1.05 1.15

EC3 = Eurocode 3, DSM = Direct Strength Method

Ref. code: 25605922040315TJU

experimental and numerical study on cold-formed steel

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