L4 Analysis and design of Tee-Section 20s.pdf

8/10/2019 L4 Analysis and design of Tee-Section 20s.pdf

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Analysis and Design of Tee-Beam Sections

3bFlanged section effective flange width

As

Section Stress Block

0.567f

ck

Fst

Fcc

axisneutral

b

hf

b

w

f

s=0.8xx

z

s/2

d

Note that the slab and the beam rib are monolithic.

If the slab and the lower rectangular section are separated, then

0.45fcu

s=0.9x

neutral axis

back

To

slab thickness

effective flange

width

beam

width


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3bThe effective flange width bf for a T beam or L beam may

be taken as:

with i=1 or 2 for two sides of beam, and

and

2

,

1

f eff i w

i

b b b

, 0.2 0.1 0.2eff i i pi pib b l l

,eff i i

b b

Cl. 5.2.1.2(a)


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3bFlanged sections neutral axis within flange

As

Section Stress Block

0.567f

ck

Fst

Fcc

axisneutral

b

hf

b

w

f

s=0.8xx

z

s/2

d

0.45fcu

s=0.9x

neutral axis

To

Now it behaves like a

rectangular section of width

bf !!!

Fill with

brittle

material

with

zeromass

Fill with

brittle

material

with

zeromass

Cross-section under applied moment M,


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3bFlanged sections neutral axis within flange (Ex 4.5)

s

2

f f

cc st

, .d=420, b =800, h =150, A =1470 mm fy 460,fcu 30What i s t he moment of resi st ance of cross-secti on ?

F =F

0. 45 0.87

0. 87 460 147054. 5

0. 45 30 800/ 0.9 60. 5 150

0.5 i mpli es tensi on steel h

cu y s ff b s f A

s

x s

x d

as yi el ded.Also

The assumed stress block

arrangement is all right !

500

500

Given data

59.2

65.8

Assume

stress block

before concrete

crushes


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3b

cc

6

Theref ore t he st eel bar have yi el ded when provi di ngt he maxi mu mf orce.

z = d - s/ 2 = 420 - 54.5/ 2 = 393 mm

M = F

0. 45

0. 45 30 800 54. 5 393 10231 ;

M=T z 231

cu f

z

f b s z

k Nm or

k Nm

Ans.

Therefore the steel bars have

yielded when providing the

maximum tension force.

59.2/2 = 390.4 mm

59.2 x 390.4 x 10-6

249.6 kNm OR

249.6 kNm


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3bFlanged sections neutral axis below flange

How to find the steel area As

required for a given applied moment ?

- refer to the design procedure below.

Resisting Moment

Couples

Fst2

Fcw

z2

Fcf

z1

Fst1

+

To

Fst=As*0.87fy

Cross-section under applied moment M,


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3bDesign procedure

K

K

f

f

If N.A. lies within the flange depth, the assumption of a rectangular

beam is valid and the above calculations can be retained. Then,

Firstly assume a

rectangular beam

section bf

h.

Check x < slab thickness

where M is the design ultimate moment

0.45

d - zx

assumed to

consist ofbrittle

material only


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3b

Flange componentprovides ultimate

moment of

resistance Muf from

concrete section

Web componentprovides the rest of

the required moment

resistance (M-Muf)

Steel area As = Asf + Asw

3. If N.A. lies in the web, the assumption of a rectangular

beam is incorrect and the above calculation is not valid.The beam is designed as if consisting of two components.


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3b

Backfrom Muf=T x z

Fcf

z1

Fst1

Muf b or bf

It is a constant for a

given cross-sectionand fcu


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3b(provided by a rectangular section)

2factorKtheCheck

dbf

MMK,

wcu

uf

bw

K

(M - Muf)

Up to now, we have covered the design

of beam with tension steel only !!!


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3b

To

is neededK


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3b

As

Compression Asc

and tension Asassuming

d/x


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3b

Evolution of Concrete Compressive Block with Moment of Resistance

for Design Flange Beam Section - Iincreasing applied bending moment on section

x


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3bSteel arrangement of a continuous beam

Figure 7.17:Typical arrangement of bending reinforcement

2 H252 H20

2 H251 H202 H16

2 H20 1 H20 - 1 H25

4.5m 6.0m

B.M Envelope

A B C

1H20 2H25

In practice, there will be moment at the

end supports of a beam die to fixity at

supporting columns

Anti-crack steel will beprovided at top of section


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3bSteel curtailment - simplified rules for beams

0.08L 0.08L

L

0.1L 0.15L

L

c=0.15L

c=0.25L

c


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3b

Usual Size of bars for different components:-

8, 10, 16, 20, 25mm diameter - for slab

12, 16, 20, 25mm - for small beam (beam of

short span) 25, 32, 40mm - for large beam

20, 25, 32, 40mm - for column

25, 32, 40, 50mm - for foundation and pile 12, 16, 20, 25mm - for stirrup and link

back


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3b

To

Back


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3b

frictional (shear) force at theinterface

If the lower and upper

parts are separated

back

slip

slip

L4 Analysis and design of Tee-Section 20s.pdf

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