neural network modeling for rotational capacity of … · benjamin w. schafer (2005) [6]. the...

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International Journal of Civil Engineering and Technology (IJCIET)

Volume 8, Issue 12, December 2017, pp. 362–372, Article ID: IJCIET_08_12_043

Available online at http://http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=8&IType=12

ISSN Print: 0976-6308 and ISSN Online: 0976-6316

© IAEME Publication Scopus Indexed

NEURAL NETWORK MODELING FOR

ROTATIONAL CAPACITY OF COLD-FORMED

PURLIN STEEL SECTIONS

Dr. Ahmed Ajel Ali

Department of Structures and Water Resources, Faculty of Engineering,

Kufa University, Najaf, Iraq

ABSTRACT

The possibility of consuming artificial neural networks (ANN) using Matlab

software to calculate the rotational capacity of steel cold-formed C- and Z-section

purlins. Rotational capacity is a significant phenomenon as in the situation of steel

purlins which are extensively used in roofing wide-ranging buildings. The complex

conducts of such members make the conventional design approaches not satisfactory

from a reliability standpoint.

The main aim of this paper was to give a quick and precise technique for

estimating local buckling capacity of C-and Z-section purlin. Good agreement was

attained concerning (ANN) technics outcomes and data from literature.

Trained neural network develops easy to-utilize method for calculating yielding

and ultimate moment's capacity of C-and Z-section. Broad parametric investigations

were additionally performed and introduced graphically to analyse the impact of

geometric and mechanical properties on rotational capacity. It was found that the

proposed (ANN) based technics is practical in predicting both the yield and buckling

rotational strength of cold-formed purlin steel sections.

Key words: Rotational capacity, Purlin, cold-formed steel, Neural Networks,

Analytical methods.

Cite this Article: Dr. Ahmed Ajel Ali, Neural Network Modeling for Rotational

Capacity of Cold-Formed Purlin Steel Sections. International Journal of Civil

Engineering and Technology, 8(12), 2017, pp. 362-372.

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=12

1. INTRODUCTION

There are fundamentally two sorts of basic steel members in construction development: cold-

formed and hot-rolled members. The common hot-rolled shape members are molded at lifted

temperatures whereas the cold-formed members are molded at normal temperatures. Members

of cold-formed sections were shapes regularly fabricated from steel plate, sheet metal or strip

material. The assembling procedure includes framing the material by either press-braking or

cold move shaping toward accomplish fancied form.

Neural Network Modeling for Rotational Capacity of Cold-Formed Purlin Steel Sections


For cold-formed members, the width-to-thickness ratios of distinct elements are frequently

large. These thin elements could buckle locally at a stress level lower than the yield stress of

the material when they are subject to compression in flexural bending. Therefore, for the

design of such thin-walled sections, for example, Z-and C-purlins which may experience

flexural-torsional clasping due to their low torsional solidness, if not appropriately braced,

local buckling and post buckling strength have regularly been the actual design

contemplations. From the steel designers view point the cold-formed steel members are most

preferable to use mainly on non-load bearing partition, curved walls, etc. due to its flexural

strength and good appearance. Nonetheless, this adaptability, depend on design guidelines

that dealt with cold-formed steel , creates the determination of the best economical section for

a specific request troublesome, together in optimization terms, and as far practical design.

Choosing the best section needs various emphases including investigation of a few

conceivable profiles and aspect ratios. This procedure turns out to be restrictively costly

because of the measure of time essential on behalf of meeting to a most favorable scheme.

The paper discovers the opportunity of utilizing artificial neural network to solve some of

these design issues.

2. NEURAL NETWORK MODELLING BACKGROUND

The method that organic sensory schemes (ex. the human minds) used as a design handling

for data is the main principal of the Artificial Neural Network (ANN).

The ANNs, like any organic brain learn by practice (data collection and expert), such as,

ordering information, acknowledgment design or even remembering by using learning

process. The data preparing is the major part of this pattern and it is the unique assembly of

the framework. It is made of extensive correlated processing elements (neurones) that are

solving problems. Learning in the frameworks depends on the relations and variations that

happen among the neurones.

The use of neural schemes began from several decades. McCulloch-Pitts (1943) [1]

depicted paired limit neurons officially in 1940's. In 1958, Rosenblatt [2] promoted the

utilization of perceptron, a particular kind of neurons, such as exceptionally adaptable

instruments used for playing out an assortment of errands. The neural systems rise was

stopped afterward Minsky and Papert (1969) [3] distributed a book dealt with abilities of

perceptron's, so scientifically verified that it can't generally ensure in particular. That outcome

immediately summed up near every single neural system, while it really connected just to a

particular kind of perceptron's, prompting the being of neural systems neglected as a machine

learning technique.

In the last two decade there was a great improvement in computing hardware that

permitting us to train precise huge and compound networks in practical period. The neural

network has made an exciting comeback since many investigations become much more

active. An inclusive explanation of this kind of neural networks is afar the latitude of this

paper and can be found in numerous literatures e.g., [4- 5].

3. DATABASE INFORMATION

Data was selected carefully from the test information incorporated by Cheng Yu and

Benjamin W. Schafer (2005) [6]. The database containing of 50 cold-formed tested steel

purlins. The experimental local buckling results are given in Table 1 .The elastic buckling

moments was computed via the same researchers above numerically by using finite element

analysis.

Dr. Ahmed Ajel Ali


Table I compresses the parameters scope of the chosen experiments.

Figure 1 Descriptions of purlin measurements for C and Z-section [6]

Table 1 Input Parameters Range.

Parameter Range

Min. Max.

h,in 8 12.02

bc,in 1.79 3.52

dc,in 0.49 0.98

θc, deg 45.4 89.3

bt,in 1.96 3.54

dt,in 0.42 1.0

θt, deg 44.2 94.8

t,in 0.047 0.118

fy,ksi 32 68.8

Table 2 outlines the properties of the chosen database[6].

Table 2 Database Information's [6]

G. Specimen

t

(in.)

bt

(in.)

Dt

(in.)

Bc

(in.)

dc

(in.)

h

(in.)

Rhc

(in.)

rdt

(in.)

rdc

(in.)

rht

(in.)

Өc

(deg)

Өt

(deg)

Fy

(ksi)

Mtest

(kip-in)

My (kip-in)

1

8.5Z120,3 0.118 2.46 0.99 2.58 0.96 8.44 0.36 0.35 0.36 0.35 47.2 48.90 61.3 280 268

8.5Z120,2 0.118 2.46 1.00 2.59 0.96 8.47 0.36 0.34 0.36 0.34 47.8 48.90 60.1 280 264

8.5Z105,2 0.104 2.36 0.95 2.66 0.95 8.48 0.32 0.34 0.32 0.34 50.5 48.70 68.8 268 270

8.5Z105,1 0.105 2.36 0.91 2.69 0.97 8.42 0.31 0.34 0.31 0.34 50.7 48.70 66.8 268 264

8.5Z092,4 0.090 2.41 0.96 2.61 0.93 8.41 0.29 0.31 0.29 0.31 53.00 50.80 57.3 181 192

8.5Z092,2 0.088 2.40 0.95 2.61 0.92 8.43 0.28 0.31 0.28 0.31 51.80 50.40 57.0 181 189

8.5Z082,1 0.080 2.36 0.97 2.5 0.95 8.46 0.28 0.30 0.28 0.30 49.00 50.30 58.4 162 174

8.5Z082,2 0.080 2.40 0.95 2.51 0.95 8.45 0.28 0.30 0.28 0.30 47.90 52.40 58.1 162 174

8.5Z073,6 0.072 2.40 0.94 2.52 0.92 8.50 0.28 0.30 0.28 0.30 49.60 50.90 54.0 121 146

8.5Z073,5 0.072 2.40 0.94 2.52 0.92 8.50 0.28 0.30 0.28 0.30 49.60 50.90 55.6 121 152

8.5Z073,4 0.071 2.41 0.92 2.53 0.93 8.51 0.28 0.29 0.28 0.29 49.60 50.30 56.1 134 151

8.5Z073,3 0.072 2.38 0.96 2.53 0.91 8.50 0.28 0.30 0.28 0.30 50.10 51.00 55.6 134 150

8.5Z073,2 0.071 2.41 0.92 2.54 0.93 8.50 0.28 0.30 0.28 0.30 50.20 51.00 55.7 123 150

8.5Z073,1 0.072 2.41 0.95 2.5 0.92 8.49 0.28 0.30 0.28 0.30 48.40 51.20 54.8 123 147

8.5Z065,3 0.064 2.43 0.79 2.42 0.83 8.47 0.27 0.28 0.27 0.28 47.30 47.30 53.5 96 125

8.5Z065,1 0.064 2.43 0.84 2.44 0.76 8.47 0.28 0.27 0.28 0.27 47.40 47.10 53.1 96 123

8.5Z059,4 0.059 2.35 0.72 2.5 0.77 8.50 0.28 0.28 0.28 0.28 50.90 48.90 58.6 100 126

8.5Z059,3 0.059 2.22 0.69 2.44 0.78 8.50 0.28 0.28 0.28 0.28 50.20 50.40 58.5 100 125

8.5Z059,2 0.059 2.33 0.70 2.51 0.78 8.49 0.28 0.28 0.28 0.28 50.60 50.20 59.1 99 127

8.5Z059,1 0.059 2.33 0.71 2.51 0.78 8.50 0.28 0.28 0.28 0.28 51.20 49.40 58.9 99 127

2

8C097,2 0.098 2.08 0.52 2.12 0.57 8.04 0.30 0.30 0.28 0.28 85.60 85.70 59.9 172 166

8C097,3 0.094 2.08 0.54 2.09 0.56 8.03 0.30 0.29 0.28 0.28 84.00 88.20 59.6 172 157

8C068,5 0.075 2.04 0.53 2.03 0.52 8.03 0.28 0.24 0.25 0.24 83.20 87.00 48.6 104 102



G. Specimen

t

(in.)

bt

(in.)

Dt

(in.)

Bc

(in.)

dc

(in.)

h

(in.)

Rhc

(in.)

rdt

(in.)

rdc

(in.)

rht

(in.)

Өc

(deg)

Өt

(deg)

Fy

(ksi)

Mtest

(kip-in)

My (kip-in)

8C068,4 0.077 2.04 0.54 2.05 0.52 8.01 0.27 0.27 0.26 0.24 84.00 87.60 53.1 104 114

8C068,2 0.075 2.04 0.53 2.04 0.52 8.02 0.28 0.26 0.25 0.24 83.40 87.60 51.7 98 109

8C068,1 0.075 2.05 0.53 2.03 0.53 8.03 0.30 0.26 0.26 0.25 83.10 88.10 51.4 98 108

8C054,1 0.055 2.07 0.50 2.04 0.52 8.00 0.22 0.23 0.23 0.23 88.90 84.70 40 56 62

8C054,8 0.054 1.96 0.48 2.02 0.58 8.08 0.22 0.23 0.20 0.22 88.10 82.30 40.3 56 63

8C043,5 0.049 1.98 0.53 2.02 0.53 8.04 0.18 0.20 0.20 0.21 88.80 87.30 44.9 51 64

8C043,6 0.049 2.00 0.46 2.01 0.53 8.06 0.19 0.20 0.20 0.22 88.90 87.00 45.0 51 63

8C043,3 0.047 2.01 0.53 2.02 0.54 8.04 0.19 0.19 0.19 0.19 89.30 87.50 46.0 48 63

8C043,1 0.047 1.98 0.54 2.02 0.54 8.03 0.19 0.19 0.19 0.29 89.00 85.80 45.7 48 62

3

12C068,9 0.065 2.00 0.55 1.92 0.53 12.002 0.28 0.28 0.27 0.30 82.00 85.30 35.1 104 113

12C068,5 0.065 2.06 0.53 1.79 0.55 12.00 0.27 0.27 0.27 0.22 85.90 94.80 35.0 104 110

12C068,3 0.0671

1.99 0.56 1.96 0.59 11.97 0.26 0.27 0.27 0.27 82.50 77.40 56.6 137 190

12C068,4 0.067 2.00 0.52 2.01 0.52 12.02 0.26 0.27 0.27 0.26 80.60 83.30 57.3 137 192

10C068,2 0.057 1.98 0.52 1.93 0.50 10.08 0.27 0.25 0.25 0.27 83.20 83.30 33.6 70 73

10C068,1 0.057 1.97 0.54 2.04 0.55 10.03 0.27 0.25 0.26 0.28 80.70 81.90 34.2 70 76

6C054,2 0.061 2.00 0.52 2.00 0.56 6.04 0.21 0.25 0.24 0.26 85.70 90.00 36.1 45 42

6C054,1 0.061 2.05 0.52 2.01 0.56 6.03 0.22 0.24 0.25 0.25 86.50 90.50 37.0 45 43

4C054,1 0.055 2.02 0.55 1.99 0.55 3.95 0.24 0.24 0.24 0.23 79.20 77.40 45.0 28 27

4C054,2 0.056 1.96 0.55 1.95 0.50 3.96 0.22 0.25 0.27 0.25 74.20 74.80 44.7 28 27

3.62C054,1 0.055 2.00 0.42 1.97 0.49 3.65 0.23 0.25 0.26 0.26 77.10 88.10 32.8 20 17

3.62C054,2 0.055 1.97 0.44 1.99 0.51 3.67 0.24 0.26 0.25 0.26 79.80 79.80 32.0 20 17

4

11.5Z092,1 0.102 3.51 0.96 3.33 0.96 11.41 0.25 0.27 0.27 0.27 50.10 49.50 61.0 352 414

11.5Z092,2 0.103 3.54 0.89 3.33 0.98 11.34 0.28 0.28 0.27 0.28 48.30 48.10 60.4 352 409

11.5Z082-2 0.083 3.45 0.87 3.50 0.88 11.45 0.31 0.35 0.31 0.35 50.30 52.20 61.5 274 345

11.5Z082,1 0.083 3.43 0.88 3.49 0.9 11.47 0.32 0.35 0.32 0.35 50.60 51.00 60.4 274 341

11.5Z073,2 0.070 3.35 0.83 3.51 0.87 11.39 0.27 0.28 0.28 0.27 46.00 44.80 65.4 194 311

11.5Z073,1 0.069 3.40 0.90 3.52 0.95 11.35 0.27 0.07 0.11 0.27 45.40 44.20 66.8 194 315

4. NEURAL NETWORK DESIGN AND TRAINING

The utilization of the ANN models, first of all, the whole data was irregularly separated into

training and testing groups. When accessible data have been separated to subgroups, the

scaling process to the input and output variables was achieved by scaling them over the

vicinity of 0.0 and 1.0 [7], to take out their measurement and to guarantee that all factors get

equivalent consideration amid preparing.[8]

Ten of the selected data was used as monitoring group for the training process progress,

all training of the network [9] comprised of one pass over the entire 50 training data groups.

[9] In building the neural network model, the network topology is developed by

identifying the number of hidden layers and the number of neurons in each. Network learns

by contrasting its yield for each pattern and an objective chose output for that pattern, after

that the way toward learning the mistake and stimulating a mistake function in reverse

through the neural network was finished.

The pattern of the network consisted of thirteen input values and two outputs; the

justification for that was to consider the criticalness of geometry and materials data on the

cold-formed member's strength in bending.

The used network has two hidden layers with fifteen nodes each, and with two nodes

giving yielding and failure moment capacity of section in the output layer.

Figure (3) was demonstrated the minimum error that dispensed by neural network form as

shown in figure (2). The settled topology and featured are presented in Table 3 .

Dr. Ahmed Ajel Ali


Figure 2 Neural Network Architecture

Table 3 Network used Topology

Number of epochs required

for training 5000

Performance function in

terms of MSE 0.01

Architecture 13-15-15-2

Learning Algorithm Learn gdm

Activation Function Logsig- Logsig- purelin

Training algorithm used Back probation algorithm

5. RESULTS AND DISCUSSION

Results of the artificial neural network prediction and the investigational data are outlined in

figure 3 for the picking training and testing data.

The predicted ANN results precision due to rotational capacity of cold-formed steel

members in bending presented in Figures (7-10) to the designated investigational groups (1,

2, 3, 4), the comparison indicates that the results from the ANN model and the data from the

experimental results are in good agreements.

Figure 11 shows the rotational cold-formed strength in bending for different cross

sections.

Figure 3 Training outputs regression



6. VERIFICATIONS

The experimental records afford an adjustment opportunity for the ANN modeling and hers

numerous conventions. ANN models similarly offer a complementary implement to explore

the cold formed steel members buckling mechanism through numerous outlines. In this paper,

the customary ANN demonstrating stood substantiated by the data-base described in section 4

consequently a selected specimens (excluding similar specimens) from the four group of the

data-base was utilized to show validation of the established ANN graphically.

The essential attention in studying was the web slenderness (h/t) that achieved by

changing the section thickness t, while stock h, b, d unceasing or fluctuating h whereas

stocking b, d and t constant for both the selected Cee and Zee sections.

Figure 5 Data-base and predicted

moment gradient ratios vs. h/t ratios for

Cee Section from group 2.


moment gradient ratios vs. h/t ratios

for Zee Section from group 1.



for Zee Section from group 4.



for Cee Section from group 3.

Dr. Ahmed Ajel Ali


Moment gradient influence on local buckling of Cold-formed shape was so significant,

relatively since this topic has not been considered in details. Auxiliary, as moment gradient

could substantially effect of CFS buckling ability. Therefore in this paper all the results are

presented with respect to moment gradient.

Figures 4-7 offered a comparison between the ANN model results and the data-base

results for the selected specimens from (1, 2, 3, and 4) test group.

The assessment between the numerical NN model and the data-base results includes the

moment gradient vs. the web height slenderness ration. From figures, it is shown that the

developed NN model can give a close prediction to the elastic and buckling moment

resistance for the CFS section for both Cee and Zee sections.

7. PARAMETRIC STUDY

The moment capacity cold-formed steel members in bending depend mainly on the

mechanical properties of the materials and the geometry of section.

Efficacious neural network verification model, allowance to revision the utilization of more

prominent assortment of cold-formed sections (not tested tentatively) conceivable. The data

acquired from both the data-base and the prolonged neural techniques was helpful for

investigating the local buckling capacity on a board range of cold-formed steel C- and Z-

section beams.

The main concern in studying was the ratios of web slenderness (h/t) and flange

slenderness (b/t) to provide systematic variation in sections, which was achieved by variation

t and h while holding b constant.

Also by varying the steel yield strength while holding section geometry constant also

studied to accomplish materials strength effect.

However, in experimental work the commercially available sections were limited, while

shapes up to thickness of 1/2 and even 3/4 in. can be found, cold-formed steel construction is

usually restricted to thickness ranging from 30 gage (0.012 in.) to 4 (0.224 in.), the manner

wherein the (h/t) diversity might be completed was limited by the of cross sections

availability.

Figure 9 Predicted moment gradient ratio,

M/My vs. web slenderness ratios (h/t)

ratio for Cee Section from group 2.

Figure 8 Predicted moment gradient

ratio, M/My vs. web slenderness ratios

(h/t) ratios for Zee Section from group 1.



Fig.8 and 9 shows the relationship between critical moment gradient, M/My, and web

slenderness ratio (h/t) for increasing height for C-section and Z-section. The moment gradient

is non-dimensional with respect to elastic moment capacity, My. the study accomplished

through the adoption of specimen (8C097-2) from group 2 and specimen (8.5Z120-3) from

group 1, with a web height change within the limits (6 - 12 in) and section thickness change

within the (0.06 – 0.11 in ) , it can be noticed that by increasing section web depth there was

affordability increasing in buckling moment gradient for both Cee and Zee sections, in other

word it is clear that the buckling moment capacity is proportional to the section depth and has

the most significant effect on the buckling moment capacity of the section. The buckling

moment gradient significantly increased for both C and Z-section beyond the ratio of 0.7.

From figure 9, It was also can be seen that there is a change in behavior from stocky

(M/My ) to slender for section with (h=6 & 8 in) to be slender with the increase of Z-

section web height. The thicker specimens have high local buckling moment capacity then the

member strength controlled by lateral-torsional capacity.

In figure (10,11) presented the relationship between the buckling to the yielding moments

with the flange slenderness ratio (b/t), it was also don by adopting the same sections

properties and also by changing the web height of the members cross section for both of the

chosen Cee and Zee section.

The parametric conducted that results have shown a reduction in moment gradient

capacity exists with increase in the web slenderness ratio, the slenderness influence on

gradient was of little effect beyond the slenderness ratio about (35) regardless of member

height of the section. It is hypothesized that increased flange and web deformations decrease

moment capacity.


ratio, M/My vs. flange slenderness

ratios (b/t) ratios for Zee Section from

group 1.


ratio, M/My vs. flange slenderness

ratios (b/t) ratios for Cee Section from

group 2.

Dr. Ahmed Ajel Ali


Figure 12 Variation yield strength on moment gradient, M/My, for C purlin section with h=6 in.

Figure 13 Variation yield strength effect on moment gradient, M/My, for C purlin section with h=8 in.

The Z-section cold formed steel beams have less variation in material properties in the

gathered experimental data, the steel yield stress are between (60 to 70 ksi). On in actuality,

the C-section have extraordinarily differing material properties, whereas steel yield stress

recorded from (20 to 66.8 ksi), so it is adopted to study the effect of materials property on the

buckling moment capacity of the cold formed steel purlin.

For the C-section section (8C097-2) from group 1, four levels of steel yield stress was

used (30, 40, 50, 60 psi) hence these values are compatible with most of that produced

industry standard sections. The study showed the relationship between the proportion of

buckling moment gradient to the web slenderness ratio and to the flange slenderness (b/t)

respectively with a web height change within the limits (6 - 12 in).

From Figs 12 to 15 it is clear that the steel yield strength has almost a constant effect on

the predicted buckling moment capacity of C-section that the four cases are approximately

parallel to each other, higher yield strength steel also increase the potential yielding moment

capacity of the section, also the same trend for the both web slenderness ratio and to the

flange slenderness was observed due to the yield strength change.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

40 60 80 100 120 140

M/M

y

h/t

Fy=60 ksi

Fy= 50 ksi

Fy= 40 ksi

Fy=30 ksi

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

20 25 30 35 40 45

M/M

y

b/t

Fy=60 ksi

Fy= 50 ksi

Fy= 40 ksi

Fy=30 ksi

0

0.2

0.4

0.6

0.8

1

1.2

1.4

60 110 160 210

M/M

y

h/t

Fy=60 ksi

Fy= 50 ksi

Fy= 40 ksi

Fy=30 ksi

0

0.2

0.4

0.6

0.8

1

1.2

20 25 30 35 40 45

M/M

y

b/t

Fy=60 ksi

Fy= 50 ksi

Fy= 40 ksi

Fy=30 ksi




8. CONCLUSIONS

The developed ANN model was tested and verified then extended to estimate rotational

capacity for the cold-formed sections with a wide geometric range for C- and Z-sections. The

ANN model also was used to yield a parametric study to illustrate the effect of steel yield

strength and the slenderness ratio of web and flange for C- and Z-sections.

The main conclusion to be drawn from the techniques used can be summarizing below:

1- Study the usage of ANN to calculate rotational moment capacity of cold-formed purlin

sections. The correlation, R, obtained using ANN models was about 0.99 in the calibration

and confirmation groups. Results from the ANN model results match well with the existing

structural information and investigational data.


2- The existing design methods for cold-formed steel sections are excessively difficult, a

substantial extent of this difficulty is owing to the requirement to compute elastic buckling

capacity by hand or with so complicated numerical methods. In this research, design methods

0

0.2

0.4

0.6

0.8

1

1.2

1.4

60 110 160 210

M/M

y

h/t

Fy=60 ksi

Fy= 50 ksi

Fy= 40 ksi

Fy=30 ksi

0

0.2

0.4

0.6

0.8

1

1.2

1.4

20 25 30 35 40 45

M/M

y

b/t

Fy=60 ksi

Fy= 50 ksi

Fy= 40 ksi

Fy=30 ksi

0

0.2

0.4

0.6

0.8

1

1.2

80 130 180 230

M/M

y

h/t

Fy=60 ksi

Fy= 50 ksi

Fy= 40 ksi

Fy=30 ksi

0

0.2

0.4

0.6

0.8

1

1.2

20 25 30 35 40 45

M/M

y

b/t

Fy=60 ksi

Fy= 50 ksi

Fy= 40 ksi

Fy=30 ksi

Dr. Ahmed Ajel Ali


may be accomplished numerically with great consistency and simplicity by using the

developed ANN model.

3- The buckling moment capacity for the CFS section was increased by increasing section

web depth and there was affordability increasing in buckling moment gradient for both Cee

and Zee section, in other word it is clear that the buckling moment capacity is proportional to

the section depth and has the most significant effect on the buckling moment capacity of the

section.

4- The steel yield strength has almost a constant effect on the predicted buckling moment

capacity of CFS C-section, higher yield strength steel also increase the potential yielding

moment capacity of the section, also the same trend for the both web slenderness ratio and to

the flange slenderness was observed due to the yield strength change.

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