Behaviour and Design of Light gauge Cold Formed Steel Flexural Members (Comparison of Channel and Built up Channel Section)

A Jayaraman1 V Senthilkumar2 S Athibaranan3

1 Assistant Professor, Department of Civil Engineering Bannari Amman Institute of Technology, Sathamangalam-638401, India.

2 Assistant Professor (Sr. G), Department of Civil Engineering Bannari Amman Institute of Technology, Sathamangalam-638401, India.

3 Assistant Professor, Department of Civil Engineering Bannari Amman Institute of Technology, Sathamangalam-638401, India

Abstract

Cold formed steel members are extensively used in the building construction industry,

especially in residential, commercial and industrial buildings. This paper presents a study

on behaviour and economical of cold formed steel (CFS) built up channel section and

channel section by same cross sectional area. This study involves in examination of

theoretical and numerical investigations of specimens in series. Overall two specimens

were designed and comparison of all the internal force, and hence, to evaluate the co-

existing moments and shear forces at the critical cross-section with same configuration

area by keeping all other parameters constant. The theoretical data are calculated using

Indian Standard code IS 801-1975 and the section properties of the specimens are

obtained using IS 811-1975. The specimens are designed under uniformly distributed

loading with simply supported condition. The theoretical results are verified using

ANSYS V11 software. The research project aims to provide which section is economical,

high bending strength, more load carrying capacity and high flexural strength. The

studies reveal that the theoretical investigations channel section have high bending

strength, high load caring capacity, minimum deflection and minimum local buckling&

distortional buckling compare to the built up channel section by same cross sectional

area.

Key words: Cold formed steel, built up channel section, ANSYS, bending strength,

deflection

I.INTRODUCTION

Light gauge steel sections are also known as cold formed steel sections. These sections

are made from thin sheets of uniform thickness without the applications of heat. The

thickness of the sheet used is generally between 1mm and 8mm. These types of sections

are extensively used in the building industry, as purlins girts, light struts roof sheeting,

and floor decking. These sections become economical for light loads and to form useful

surfaces such as roof covering, wall panels. Load carrying capacity should decreases

with increase in Length and Width to thickness (W/t) ratio. Due to minimum thickness of

cold rolled steel, considering the Local, torsional & distortional buckling characteristics

for its behaviour study most of the failures occurs at 1/3 distance for 1, 1.2mm elements

& at centre for 1.6, 2mm elements. The experimental investigation 2mm thick cold

formed steel “Long column with Web Stiffened” is preferable for “C Section”(1) . Both

their experimental and numerical investigation gives the good understanding about their

buckling classes and failure modes that are possible. Using of CUFSM software was

more useful in predicting the section properties of these specimens. Modal of the

specimens analyzed in ANSYS V11 gives an idea that of their failure modes.

Experimental results show that the failure of the section occurs mainly due to the

buckling of flange plates and distortional buckling. (2). These sections are manufactured

primarily by two processes. Cold rolling is used to produce more number of sections

having longer length whereas press breaking is used to produce a small number of

sections having shorter length. As the thickness of the light gauge section increases the

variation in increase of joint strength reduces for various thicknesses of Stiffener/packing

plates. For 1.2mm thick channel section it is observed that all failures are due to rupture

with 3 bolts connection, and also for 1.5mm thick channel section up to 3mm thick

Stiffener/Packing plate failure are due to rupture and for 4mm thick Stiffener/packing

plate the failure is due to vertical shear failure along the line of vertical connection. With

use of 5 mm thick Stiffener/packing plates the failure is due to block shear failure (3).

Various types of section may be manufactured using light gauge steel. They includes

angles, channel with and without lips, hat section lipped Z Section etc.. Cold Formed

steel product such as Z-purlin has been commonly used in metal building industry more

than 40 year in unites state due to their wide range of application, economy, ease of

fabrication and high strength-to-weight ratios. Z- Purlins are predominantly used in light

load and medium span situations such as roof systems (4). There are several failure modes

among which distortional buckling is one such failure mode that affects the strength of

the section. In order to assess the influence of distortional buckling, a parametric study

has been conducted by varying the lip depth, which is the influencing factor for

distortional buckling strength (5). Channels may be used as compression or flexural

members. Hat section and Z section are used as flexural members. Hollow rectangular

section used for variety of sections. Built up I section using Light gauge steel with lower

H/t aspect ratio behaves significantly showing elastic and plastic deformation both. With

increment in H/t aspect ratio this behaviour changes and shows failure in elastic zone (6).

Black bolts and high strength friction grip bolts may be used for the connection of the

light gauge sections. However, high strength friction grip bolts are most suitable for the

connection of light gauge sections. Advances in computational features and software

have brought the finite element method within reach of both academic research and

engineers in practice by means of general-purpose nonlinear finite element analysis

packages, with one of the most used nowadays being ANSYS. The program offers a wide

range of options regarding element types, material behaviour and numerical solution

controls, as well as graphic user interfaces (known as GUIs), auto-meshers, and

sophisticated postprocessors and graphics to speed the analyses. In this paper, the

structural system modelling is based on the use of this commercial software. Several

numerical modelling issues related to potential convergence problems, loading strategies

and computer efficiency. The accuracy and simplicity of the proposed model make it

suitable to predict and/or complement experimental investigations (7) .most of structural

elements are analysis by using STADD pro and ANSYS.

II. AIM OF THE STUDY

The main aim of the study provides which section is economical, high bending strength,

more load carrying capacity and high flexural strength by analysis of theoretical and

numerical investigation.

III .EXPERIMENTAL INVESTIGATION

3.1 Materials

3.1.1 Light gauge steel physical properties: The rolled steel sheet is used. The physical

properties of light gauge steel section given in Table 1.The properties taken from the

Indian Standard code IS 800-2007

Table 1. Physical properties light gauge steel section

Density of steel ( ᵨ ) 7850 kg / m3

Modulus of elasticity ,E 2 x 105 N / mm2

Poisson ratio 0.3

Modulus of rigidity , G 0.769 x 10 5 N / mm2

CO efficient of thermal expansion (α ) 12 x 10-6

3.1.2 Light gauge steel channel section properties: The rolled steel sheet is used. The

channel sectional properties of light gauge steel section (given in Table 2.The properties

taken from the Indian Standard code IS 811-2007

Table 2. Properties of (60 x 30 x 1.6) light gauge steel Channel section

Area 181 mm2

Elastic Section modulus 3370mm

plastic Section modulus 752mm

Moment of inertia of section xx direction (Ixx) 101 x 103 mm4

Moment of inertia of section yy direction (Iyy) 16.3 x 103 mm4

Radius of gyration (rx) 23.6 mm

Radius of gyration (ry) 9.49 mm

3.1.3 Light gauge steel built up channel section properties: The rolled steel sheet is

used. The built up channel sectional properties of light gauge steel section (given in Table

3) The properties taken from the Indian Standard code IS 811-2007

Table 3. Properties of light gauge steel built up Channel section

Area 170 mm2

Elastic Section modulus 22

plastic Section modulus

Moment of inertia of section xx direction (Ixx) 22.03 x 103 mm4

Moment of inertia of section yy direction (Iyy) 7.25 x 103 mm4

Radius of gyration (rx) 11.4mm

Radius of gyration (ry) 4.64 mm

3.2 Theoretical investigations of channel section ¿30 x60 x1.6) mm 3.2.1 Slenderness ratio (λ): The Slenderness ratio value is given in table 4

Slenderness ratio (λ) =Effectivelengt h

Radiousofgyration(rmin)

Table 4. Slenderness ratio

Effectivelength (mm) Slenderness ratio (λ)1000 105.262000 210.753000 316.12

4000 423.285000 529.410

The slenderness ratio for flexural member as per IS Code provide 300 mm for

compression flange of a beam against lateral torsional buckling ,so in this channel section

(30 x60 x1.6) mm using construction up to 3m only .

3.2.2 Bending Moment (BM) of channel section ¿30 x60 x1.6) mm

Maximum Bending Moment = 0.6 x fy x Zxx

M = 479.7 x 103 Nmm

fy = yield stress in cold form steel

Zxx = section modulus channel section

3.2.3 Load caring capacity (p) of channel section ¿30 x60 x1.6) mm

Bending Moment = W l2

8

Maximum Load (p) = 3.79 kN / m

3.2.4 Moment of resistance of channel section ¿30 x60 x1.6) mm

Moment of resistance (MR) = Fb x Zxx

Fb = 23

fy− f y2

5.4 x π2 x E xcb ( A)

Fb = 154.16N / mm2

Moment of resistance (MR) = 519 x 103Nmm

Fb = basic design stress

E = young’s modulus of steel

Cb = bending coefficient

3.2.5 Shear capacity of channel section ¿30 x60 x1.6) mm

Maximum shear = Wl2 = 1.89 kN / m

Maximum average shear stress = V

2bd = 10.42 N / mm2

3.2.6 Allowable stresses in web of beam

Shear stresses in webs – The maximum average shear stresses (Fv), on the gross area of a

flat web shall not exceed (0.4 x fy)

For ht <

1425√ fy

Fv = 396 √ fy

ht

= 181.2 N / mm2

ht

= 33.5

1425√ fy = 92.95

Fv = 181.2 N / mm2 > 10.42 N / mm2 Hence Safe in shear

3.2.7 Combined bending and shear stress in webs: fbw’ = 0.6 fy ⦋ y−tt

⦌ = 3140 N /

mm2

3.2.8 Bending and shear stress in webs: fbw = 3525000

( ht )2 = 133.6 N/mm².

3140 N/mm² ˃ 133.6 N/mm². Hence safe in bending stress

3.2.9 Check for deflection of channel section ¿30 x60 x1.6) mm

The actual deflection (Δ) and Permissible deflection is given in table 5.

Actual deflection (Δ) = 5W l4

384 EI

Permissible deflection =

span325

Table 5. Deflection

Effectivelength (mm) Actual Deflection ( Δ) (mm)

Permissible deflection (Δ) (mm)

1000 2.44 3.072000 3.92 6.153000 198.03 9.2304000 625.56 12.305000 1326.67 15.38

3.3 Theoretical investigations of built up channel section ¿30 x 60 x1.6) mm

3.3.1 Slenderness ratio (λ): The Slenderness ratio value is given in table 4

Slenderness ratio (λ) =Effectivelengt h

Radiousofgyration(rmin)

Table 6. Slenderness ratio

Effectivelength (mm) Slenderness ratio (λ)1000 153.842000 306.273000 459.414000 612.555000 765.69

The slenderness ratio for flexural member as per IS Code provide 300 mm for

compression flange of a beam against lateral torsional buckling ,so in this channel section

(30 x60 x1.6) mm using construction up to 2 m only .

3.3.2 Bending Moment (BM) of built up channel section ¿30 x 60 x1.6) mm

Maximum Bending Moment = 0.6 x fy x Zxx

M = 103.917 x 104 Nmm

3.3.3 Load caring capacity (p) of channel section ¿30 x 60 x1.6) mm

Bending Moment = W l2

8

Maximum Load (p) = 0.82 kN / m

3.3.4 Moment of resistance of channel section ¿30 x 60 x1.6) mm

Moment of resistance (MR) = Fb x Zxx

Fb = 23

fy− f y2

5.4 x π2 x E xcb ( A)

Fb = 154.16N / mm2

Moment of resistance (MR) = 113 x 103Nmm2

3.3.5 Shear capacity of channel section ¿30 x 60 x1.6) mm

Maximum shear = Wl2 = 0.41 kN / m

Maximum average shear stress = V

2bd = 0.142 N / mm2

3.3.6 Allowable stresses in web of beam

Shear stresses in webs – The maximum average shear stresses (Fv), on the gross area of a

flat web shall not exceed (0.4 x fy)

For ht <

1425√ fy

Fv = 396 √ fy

ht

= 181.2 N / mm2

ht

= 33.5

1425√ fy = 92.95

Fv = 181.2 N / mm2 > 0.142 N / mm2 Hence Safe in shear

3.3.7 Combined bending and shear stress in webs: fbw’ = 0.6 fy ⦋ y−tt

⦌ = 3140 N /

mm2

3.3.8 Bending and shear stress in webs: fbw = 3525000

( ht )2 = 133.6 N/mm².

3140 N/mm² > 133.6 N/mm². Hence safe in bending stress

3.3.9 Check for deflection of channel section ¿30 x60 x1.6) mm

The actual deflection (Δ) and Permissible deflection is given in table 7.

Actual deflection (Δ) = 5W l4

384 EI

Permissible deflection =

span325

Table 7. Deflection

Effectivelength (mm) Actual Deflection ( Δ) (mm)

Permissible deflection (Δ) (mm)

1000 2.42 3.072000 39.2 6.153000 196.03 9.2304000 621.56 12.305000 1322.67 15.38

IV EXPERIMENTAL PROCEDURE

Overall two specimens were designed and comparison of all the internal force, and hence,

to evaluate the co-existing moments and shear forces at the critical cross-section with

same configuration area by keeping all other parameters constant. The theoretical data are

calculated using Indian Standard code IS 801-1975 recommended. The theoretical results

of the channel section the bending moment, load caring capacity and moment resistance

is 46 % , 21% and 21.7% higher than the built up channel section. Allowable stress in

web of the beam, actual deflection and bending stress in web is same in both the section.

The average shear stress is maximum in built up channel section compare than the

channel section. The numerical investigations (using ANSYS) the bending moment,

torsional moment, deformation and shear stress is 22.68 % ,51.30 % 25.52 % and 13.13%

maximum in channel section in compare than the built channel section. The numerical

result software analysis is given figure 2,3,4,5,6,7,8 and figure 9. The comparison of

theoretical design value is given in figure 1.

Theoretical investigations of channel and built up channel section ¿30 x 60 x1.6)mm

479

3790

519

10.42182.4

2.44

3140

1 2 3 4 5 6 7

1039820

1130.142

182.42.46

3140

comparison of channel and built up channel section

Channel section Series4

Figure .1 comparison of theoretical design value channel and built up section

4.1 Numerical investigations (ANSYS) of channel section ¿30 x60 x1.6) mm

Figure .2 Bending Moment (BM) of channel section ¿30 x60 x1.6) mm

Figure .3 Torsion Moment (BM) of channel section ¿30 x60 x1.6) mm

Figure .4 Total deformation of channel section ¿30 x60 x1.6) mm

Figure .5 Total sheer force of channel section ¿30 x60 x1.6) mm

4.2 Numerical investigations (ANSYS) of built up channel section ¿30 x 60 x1.6) mm

Figure .6 Bending Moment (BM) of built up channel section ¿30 x 60 x1.6) mm

Figure .7 Torsion Moment (BM) of built up channel section ¿30 x 60 x1.6) mm

Figure .8 Total deformation of channel section ¿30 x60 x1.6) mm

Figure .9 Total sheer force of channel section ¿30 x60 x1.6) mm

CONCLUSIONS

The final results the theoretical and investigations of channel section have high bending

strength, high load caring capacity, minimum deflection and minimum local buckling &

distortional buckling compare to the built up channel section by same cross sectional

area. The numerical investigation of channel section is the maximum bending moment,

torsional moment and deformation is higher than the built up channel section by same

cross sectional area. But theoretical investigations are accuracy result. Channel section is

the high moment of resistance , high load caring capacity and The slenderness ratio for

flexural member as per IS Code provide 300 mm for compression flange of a beam

against lateral torsional buckling ,so in this channel section (30 x60 x1.6) mm using

construction up to 3m. Therefore channel section is most suitable and economical

compare than the built up channel section.

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