CFS Subject to Bending

8/16/2019 CFS Subject to Bending

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ε ε !05/35/ ≤≤ t d t b#%!9

Class 4 “slender ” : Cross sections in which it is necessary to make

explicit allowance for the effect of local buckling.

ε ε !05/35/ >> t d t b#%#0

where,

b

" flange 'idth

d " 'eb depth

t " flange or 'eb thickness

ε 4

5%0

#15

y p

y p

" design strength%

2.2 Mat"#ial P#$"#ti"s

The properties of material of cold-formed steel should be taken in line 'ith sub

section 3%3 of the BS 5950 art 5" !99$ as follo's%

esign strength py, should be taken as Y s but not greater than 0%$2 U s, 'here"

Y s : minimum yield strength or in the case of the material does not show the

yielding clearly, either the 0.2 % proof stress or the stress at 0.5 % total

elongation;

U s : minimum ultimate tensile strength.

Y s may normally be taken as specified in the British Standard as indicated in ppendi(

B% s an alternative, for any cold-formed steel the material strength may be determined bytesting according to &hapter !0 of the code%

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The design strength may be increased as the effect of cold forming as mentioned in

sub section 3%2 of the standard%

6or the elastic properties the follo'ing value can be used as mentioned in &lause

3%3%# of the code"

- Modulus of elasticity E = 205 kN/mm2

- Shear modulus G = 79 kN/mm2

- Poisson’s ratio υ = 0.3

- Coefficient of linear thermal expansion α = 12 x 10-6 per °C

7ean'hile, for calculating of the section properties of materials up to 3%# mmthickness, usually it is enough to assume the material is concentrated at the mid-line of the

section and the round corners are replaced by the flat element intersections )&lause 3%5%! of

BS 5950 art 5" !99$+%

2.% Eff"ct f Lcal B&c'li!(

The effect of local buckling must be taken into account for determining the design

strength and thickness of the cold-formed steel members% This can be solved by using the

effective section properties calculated based on the 'idth of each element individually

)&lause 2 of BS 5950 art 5" !99$+%

The ma(imum 'idth to thickness ratio b/t of the plate for compressive elements is as

follo's )&lause 2%# of BS 5950 art 5" !99$+"

(a) Stiffened elements having one longitudinal edge connected to a flange or web

element, the other edge stiffened by:

- Simple lip 60

- Any other type of stiffener 90

- (b)Stiffened elements with both longitudinal edges connected other

stiffened element: 500

(c) Unstiffened compression elements 60

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8n addition, determination of effective 'idth of compression element is assigned as

follo's )&lause 2%3 of BS 5950 art 5" !99$+"

(i) For

!#3%0/


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The compressive stress,0 p

, in a stiffened element 'hich results from bending in its

plane, should not e(ceed the smaller one of the follo'ing values )&lause 5%#%#%# of BS 5950

art 5" !99$+"

y

s pY

t

D p

−=

#

!

0#$0

00!9%0!3%!

#%#2

or

y p p =0#%#5

'here,

p0 " compressive stress ) in /mm#+

py " design strength ) in /mm#+

D" overall 'eb depth ) in mm+

sY

" material yield strength )in /mm#+

t " 'eb thickness )in mm+

y p

" design strength )in /mm#+%

:here a 'eb element has an intermediate stiffener, the limiting compressive stress,

0 p

, may be used the smaller one of the follo'ing values )&lause 5%#%#%3 of BS 5950 art 5"

!99$+"

y

se pY

t

D p

−=

#

!

0#$0

00!9%0!3%!

#%#.

or

y p p =0#%#1

where,

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cc M M =;

#%33

)c+ for $ )#$0/Y s+!/# ≤ b/t ≤ !3 )#$0/Y s+

!/# ,

;

c M

may be obtained by linear interpolation

bet'een )1+ and )$+, i%e%"

+)

+/#$0)5

/+/#$0)!3

#

!

#

!

;

c p

s

scc M M

Y

t bY M M −

−+=

#%32

where,

b : width of the compression element;

t : compression element thickness;

sY

" yield strength

;

c M

" actual ma(imum moment capacity

p M

: fully plastic moment for the full section

S Y M s p %=, 'here S is the plastic modulus of the section

c M

: the moment capacity of the section determined in accordance with Clause

5.2.2 of the BS 5950 Part of the BS 5950 Part 5;

Z p M c %0=, where Z is the elastic modulus of the section.

2./ Stailit* f Cl+-F#,"+ St""l S"cti!s S&"ct t B"!+i!(

The ne(t process of structural member design after determination of preliminary

section dimension is the stability check% 6or cold-formed steel sections subjected to bending

the stability should be checked in accordance 'ith &hapter 5 of BS 5950 art 5" !99$, 'hich

includes crushing, shear in 'eb, combined effect, lateral buckling, deflection, flange curling

and effect of torsion%

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The value of force and moment of the members may not e(ceed the section capacity

calculated using the suitable formulas and should satisfy the follo'ing provisions"

(a) Web crushing (Clause 5.3 and Table 7 of BS 5950 Part 5: 1998)

+

−=

t N

t DC C C k t P w %0!%0!%%$%3#0.0%%%%% !#23

#

#%35

where,

P ' " concentrated load resistance of a single 'eb

D " overall 'eb depth )in mm+


r " inside bend radius )in mm+

N " actual length of bearing )in mm+ determined in accordance 'ith &lause 5%3of

BS 5950 art 5" !99$

P ' " concentrated load resistance of a single 'eb )in /mm#+

c " distance from the end of the beam to the load or the reaction )in mm+

C 3, C 2, C !# are constants

k C 33%033%!3 −= #%3.

0%!+/!5%0!5%!)2 ≤−= t r C but not less than 0%5 #%31

#

!# +90/)3%01%0 θ +=C #%3$

k

4

##$/ y p

, 'here

y p

is the design strength )/mm#+

θ : angle (in degrees) between plane of web and plane of bearing surface, where

45°

≤≤ θ 90°.

(b) Shear in web (Clause 5.4 of BS 5950 Part 5: 1998)

Maximum shear stress (Clause 5.4.2 of BS 5950 Part 5: 1998)

yv p f 1%0≤#%39

Average shear stress (Clause 5.4.3 of BS 5950 Part 5: 1998)

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cr yav qor p f %.%0≤#%20

#%!000

= D

t qcr

/mm# #%2!

where,

y p

" design strength )in /mm#+


D

" 'eb depth )in mm+%

(c) Combined bending and web crushing (Clause 5.5.1 of BS 5950 Part 5: 1998)

5%!%!%! ≤

+

cw

w

M

M

P

F

#%2#

0%!≤w

w

P

F

#%23

0%!≤c M

M

#%22

where,

w F

" concentrated 'eb load or reaction

w P " 'eb concentrated load resistance

M " applied bending moment at the point of application of

w F

c M

" moment capacity%

(d) Combined bending and shear (Clause 5.5.2 of BS 5950 Part 5: 1998)

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!

##

≤

+

cv

v

M

M

P

F

#%25

where,

v F

" shear force

v P

" shear capacity or shear buckling resistance and is e


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where,

E

" effective length

yr

" radius of gyration of the section about = a(is

bC

" coefficient 'hich may be conservatively assumed to be unity, or can be

calculated using"

3%#3$%005%!15%! # ≤+−= β bC 2.50

where,

β

" is the ratio of the smaller end moment to the larger end moment M

in the

unbraced length of a beam%

β

is taken as positive in the case of single

curvature bending and negative in the case of double curvature bending )See

ppendi( +%

(f) Deflections (Clause 5.7 of BS 5950 Part 5: 1998)

- For M

orcr c M M ≤

The full cross section should be used in evaluating the second moment of area

and the deflection calculated using simple beam theory;

- Forccr M M M ≤<

Either M or ∆ is determined from a specified value of the other quantity usingthe equation:

cr c

cr

cr c

cr

M M

M M

∆−∆∆−∆

=−−

#%5!

where,

M " bending moment for a loading system

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∆" deflection for the given loading system

c M

" moment capacity

c∆" deflection corresponding to

c M

, calculated using the reduced cross section

cr M

" critical bending moment, given by"

ccr Z b

t K M %%%!#0000

#

=

2.52

K " buckling coefficient of the compression flange )See ppendi( &+

t " thickness of the compression flange

c Z

" bending compression modulus for the full cross section

b " flat 'idth of the compression flange

cr ∆" deflection of the beam corresponding to

cr M

calculated using the full cross

section%

g) Flange curling (Clause 5.8 of BS 5950 Part 5: 1998)

Du

yt E

! f u

t

! For a 0

0 >

##

2#

5

%%

%%##50 ≤=⇒〉

#%53

where

u " deflection of the centre of the flange to'ards the neutral a(is

a f

" average stress in the flange

!" flange 'idth for unstiffened or edge stiffened flanges, or half the overall

flange 'idth for stiffened flanges

E " modulus of elasticity

t " flange thickness

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Documents

CFS Subject to Bending