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 coexisting 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
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ
Slenderness ratio (λ) = 𝑅𝑎𝑑𝑖𝑜𝑢𝑠𝑜𝑓𝑔𝑦𝑟𝑎𝑡𝑖𝑜𝑛 (𝑟𝑚𝑖𝑛)
Table 4. Slenderness ratio
Effectivelength (mm)
1000
2000
3000
4000
5000
Slenderness ratio (λ)
105.26
210.75
316.12
423.28
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
W𝑙2
Bending Moment =
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
fy2
2
Fb = 3 𝑓𝑦 −
5.4 𝑥 π2 𝑥 𝐸 𝑥 𝑐𝑏
(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 =
𝑊𝑙
2
= 1.89 kN / m
𝑉
Maximum average shear stress = 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
Fv =
ℎ
𝑡
<
1425
√𝑓𝑦
396 √𝑓𝑦
ℎ
𝑡
= 181.2 N / mm2
h
t
1425
√𝑓𝑦
= 33.5
= 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’ = 0.6𝑓𝑦⦋
3.2.8 Bending and shear stress in webs: fbw =
3525000
ℎ
𝑡
( )2
y−t
𝑡
⦌ = 3140 N / mm2
= 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.
5𝑊l4
Actual deflection (Δ) = 384 𝐸𝐼
Permissible deflection =
𝑠𝑝𝑎𝑛
325
Table 5. Deflection
Effectivelength (mm)
1000
2000
3000
4000
5000
Actual Deflection ( Δ)
(mm)
2.44
3.92
198.03
625.56
1326.67
Permissible
deflection (Δ) (mm)
3.07
6.15
9.230
12.30
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
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ
Slenderness ratio (λ) = 𝑅𝑎𝑑𝑖𝑜𝑢𝑠𝑜𝑓𝑔𝑦𝑟𝑎𝑡𝑖𝑜𝑛 (𝑟𝑚𝑖𝑛)
Table 6. Slenderness ratio
Slenderness ratio (λ)
153.84
306.27
459.41
612.55
765.69
Effectivelength (mm)
1000
2000
3000
4000
5000
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 =
W𝑙2
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
fy2
2
Fb = 3 𝑓𝑦 −
5.4 𝑥 π2 𝑥 𝐸 𝑥 𝑐𝑏
(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 =
𝑊𝑙
2
= 0.41 kN / m
𝑉
Maximum average shear stress = 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
ℎ
𝑡
<
1425
√𝑓𝑦
Fv =
h
t
1425
√𝑓𝑦
396 √𝑓𝑦
ℎ
𝑡
= 181.2 N / mm2
= 33.5
= 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’ = 0.6𝑓𝑦⦋
3.3.8 Bending and shear stress in webs: fbw =
3525000
ℎ
𝑡
( )2
y−t
𝑡
⦌ = 3140 N / mm2
= 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.
5𝑊l4
Actual deflection (Δ) = 384 𝐸𝐼
Permissible deflection =
𝑠𝑝𝑎𝑛
325
Table 7. Deflection
Effectivelength (mm)
1000
2000
3000
4000
5000
Actual Deflection ( Δ)
(mm)
2.42
39.2
196.03
621.56
1322.67
Permissible
deflection (Δ) (mm)
3.07
6.15
9.230
12.30
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
comparison of channel and built up channel
section
3790
Channel section
Built up channel section
3140 3140
1039
820
519
479
113
Bending
moment
(knm)
Load carring
capacity (N)
10.42 0.142
Moment
resistance
capacity
(knm)
182.4 182.4
average shear allowable
stress
stress in web
(N/mm2)
of beam
2.44 2.46
actual
bending stress
deflection
in web
(mm) /m
(N/mm2)
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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