Chapter4 Allowable Stresse

7/29/2019 Chapter4 Allowable Stresse

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4-Chapter

Allowable stresses


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contents

Introduction 2.6.1(p8) Compression element, Axial or

bending

Axial tension Allowable shear stress qall Axial compression

Bending stress

Allowable crippling stress in web qall

Combined stresses Back(home)
http://localhost/var/www/apps/conversion/tmp/scratch_3/chapter1-Introdution.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_3/chapter1-Introdution.ppt


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Introduction

The actual stresses in any part of steel

bridge must not exceed the elastic limit of

the material otherwise permanentdeformation would occur. All structural

calculations are approximate even if all

loads are carefully considered. In trussesneglect the secondary stresses due to the

rigidity of joints.


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The forces in members are determined under the

assumption that the connections are hinge and the

forces along the members are axial. Only the primarystresses can be calculated. In some cases the

secondary stresses may reach 3060 % of the

primary stresses. The analyses neglect also the

torsion in the main girders due to the deflections ofthe X-girders. The unequal distribution of stresses

over the cross section due to bolts holes hasnt taken

into consideration


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The allowable stresses (maximum stresses used in the

calculation) must therefore be lower than the elastic limit.

The more accurate calculations of steel bridge and the

better shop work, the higher allowable stresses may betaken. Also, in the calculation if all possible forces are

taken into account the allowable stresses can be taken

higher than in case that only D.L., L.L, and Impact are

considered.


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The permissible stresses for standard grade

structural steel determined according to the grade of

steel. Structural sections shall be classified,depending on dw/tw for web and c/tf for flanges

under compression, axial bending, to compact,

noncompact, and slender sections as shown Fig(4-1)

Figure-4.1


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Fy and Fu (t/cm2) depend on the thickness

t(1.4-p2).

Grade of

steel

t40mm 100mm t >400mm

Fy

Fu

Fy

Fu

ST37

2.40

3.60

2.15

3.40

ST44

2.80

4.40

2.55

4.10

ST52

3.60

5.20

3.35

4.90


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2.2.1(p6) Primary + additional stresses (wind load

or earthquake loads, lateral shock, etc.)

2.2.3(p7) Additional stresses

Additional stresses (allowable) = Primary

stress 1.20

2.3(p7) Secondary stresses in truss members

1. Chord member's depth > 1/10 of their length.

Diagonal member's depth > 1/15 of their length.

2. Truss with sub-panel.

Reduce 20 % of the allowable stress

back


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2.6.1(p8) Compression element, Axial or

bending

yF

Factorand

Selender

NoncompactCompact

f

f

w

w

t

C

t

d

Factor depends on:

1. Support of element ((One side (unstiffened

element) or two sides (stiffened element))

and shape of the cross section, I, C, , L, etc.

2. Load on element [(N) or (M) or (M+N)]

(p9,10,11-Table 2.1.a,b&c)


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2.6.2(p13) Axial tension

yyy

y FFFmmtmm

FmmtF get,1.4clauserom10040

4058.0Ft

Hence for,

25ST/10.2F

44ST/60.1F37ST/40.1F

40

2

t

2

t

2

t

cmt

cmtcmt

mmt

25ST/00.2F

44ST/50.1F37ST/30.1F

10040

2

t

2

t

2

t

cmt

cmtcmt

mmtmm

back


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2.6.3(p13) Allowable shear stress

qall

yall Fget1.4,clauserom1004040

35.0q FFmmtmm

FmmtF

y

y

y

Hence for,

25ST/26.1q

44ST/98.0q

37ST/84.0q

40

2all

2all

2all

cmt

cmt

cmt

mmt

25ST/17.1q

44ST/89.0q

37ST/75.0q

10040

2

all

2all

2all

cmt

cmt

cmt

mmtmm


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2.6.3.1(p13) Effective web area

Rolled section = Total height twBuilt up section = Web height tw2.6.3.2(p14) Shear buckling of web

yw

w

F

105

t

d

dd1

Stiffened web

2q34.54K1

2q

434.5K1

d1

d


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Unstiffened web = Kq = 5.34

If 80.0,F

K45

t

dq

y

q

w

w

no web buckling occur qp = 0.35 Fy

If, F

K

45t

d

y

q

w

w

Check web buckling

yqbq

yqbq

ybq

q

yw

w

q

F35.0

90.0

q20.1

F35.0625.050.1q20.180.0

F35.0q80.0

K

F

57

td

(no web buckling occur)

back


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2.6.4(p15) Axial compression

r

lk

1.4F40

40

10

)75.058.0(58.0F y

2

4cfromget

mmt

mmtFF

yy

2c 000065.040.1F 2c 000055.030.1F

2c 000085.060.1F 2c 000075.050.1F

2c 000135.01.2F 2c 000125.00.2F

Gradeof steel

Fc (t/cm2)

ST37

ST44

ST52

t 40 mm 40 < t < 100 mm

Fc (t/cm2)


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- For compact and Non-compact

sections use full area(Table2.1-p9-11).

- For slender sections use effectivearea(Tables 2.3&2.4-p23&24).

- For one angle reduce Fc

by 40

%(p15).

back


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2.6.5(p16) Bending stress

1- For compact sections and the laterally

unsupported length (Lu )of the compression flange islimited by:

(Lu is the smaller of)

- Box sections

Or

fy

u bF

L 84

y

fu

F

b

M

ML

2

184137

I-shape sections

y

fu

F

bL

20 b

y

f

u CFd

bL 1380

Or


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Cb From Table2.2

- Then

Fb = 0.64 Fy (Mx ) Boxand I-shapes Clause 2.6.5.1

Fb = 0.72 Fy (My) I-shapes Clause 2.6.5.2

Fb = 0.64 Fy (My) Box shapes Clause 2.6.5.3

1- 1- For Non-compact sections:

Fb = 0.58 Fy (Mx & My) Box shapes Clause 2.6.5.4

2- 2- For slender (Box and I-shapes) and Non-compact (I-

shapes) sections:

-


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Tension Clause 2.6.5.5

Fbt = 0.58 Fy

- Compression Clause 2.6.5.5

1- Lu Lall

Fbc = 0.58 Fy

2- Lu > Lall

i( Shallow thick flanged section Luxtf/ bfxd >10 (P18))

For any value of

(eq 2.23)

ii - ( Deep thin flanged section Luxtf/ bfxd


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t

u

y

b

r

L

F

C84

(eq2.24)yltb FF 58.02

y

b

t

u

y

b

F

C

r

L

F

C18884

(eq 2.25)yyb

yTultb FFC

FrLF 58.0

10176.1

)/(64.0 5

2

2

y

b

t

u

F

C

r

L188

(eq2.26)ybTu

ltb FCrL

F 58.0)/(

1200022

(eq2.27)yltbltbltb FFFF 58.02

221


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- II - For Channels( p21) Fltb;

(eq2.29)

)(58.0/

800xyb

fultb MFC

AdLF

III - For slender sections use effective width (be)

and the stress for non-compact(p21).

- Effective width be for slender sections(Table

2.3& 2.4p23&24);

1

2

f

f

)2.3(11112.0116

5.022 TableK

For any value of get from tables 2.3, and 2.4 for

stiffened and unstiffened elements respectively.

K


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Calculate K

Ftb y

44

/ (plate slenderness)

0.105.015.0 2 Calculate

bbe =


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bfu

ltb CAdL

F

/

8001

t

u

y

b

r

L

F

C84 yltb FF 58.02

y

b

t

u

y

b

F

C

r

L

F

C18884

y

b

yTultb F

C

FrLF

5

2

210176.1

)/(64.0

y

b

t

uFC

rL 188 b

Tu

ltb CrL

F 22 )/(

12000

22

21 ltbltbltb FFF yltb FF 58.0

Summary Table for Lateral Torsional Buckling

(Lu > Lall)

For all

back


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2.6.6 (p22)Allowable crippling stress in web qall

yycrp Fget1.4,clauseromFmm40t

mm40tF75.0F

In tension members we get smaller cross

sections by using high tensile stresses St. 52.

While in compression members we get smallersection if l/i is less than 100 but if l/i is more than

100 we get same section for all kinds of steel.

2.6.7 Combined stressesIn a continuous beam we have a state of

combined shear and bendingback


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pcpt ffqff

F

22,1

22

This stress may be greater than the bending stress

in the outside fibers.

The modern theory of equivalent structure is givenby;

pte fqfF 10.13 22


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2.6.7.1- Axial Compression And Bending

0.121 bcy

bcy

bcx

bcx

c

ca

F

f

F

f

F

f

1.015.0 21 c

ca

F

fWhen

EY

ca

my

EX

ca

mx

F

f

C

F

f

C

1

,

1

21

2EY2

7500F,

7500

EXF

Cmx , Cmy from code


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2.6.7.2- Axial Tension And Bending

0.1bty

bty

btx

btx

t

ta

Ff

Ff

Ff

Chapter4 Allowable Stresse

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