Beam & Col Formulae

8/3/2019 Beam & Col Formulae

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13920,456

7.3.2,26.5.3.2

(b)(1)(2)

The parallel legs of rectangular hoop shall be spaced not more than300 mm centre to centre. If the length of any side of the hoop

exceeds 300 mm, a crosstie shall be provided (Fig.7B).Alternatively, a pair of overlapping hoops may be provided within

the column (see Fig.7C). The hooks shall engage peripheral

longitudinal bars.

b) Arrangement of transverse reinforcement:

1) If the longitudinal bars are not spaced more than 75 mm oneither side, transverse reinforcement need only to go round corner

and alternate bars for the purpose of providing effective lateralsupports (see Fig.8).

2) If the longitudinal bars spaced at distance of not exceeding 48

times the diameter of the tie are effectively tied in two directions by open ties (seeFig.9).

13920 93 7.4.8 The area of cross section, Ash, of the bar forming rectangular hoop, to be used as special confining reinforcement shall not be

less than

0.18 1 g ck

sh

y k

A f A S h

f A

13920 93 7.4.6 The spacing of hoops used as special confining reinforcement shall

not exceed 1/4 of minimum member of minimum member dimension but need not be less than 75 mm or more than 100 mm.

13920 93 7.4.1 Special confining reinforcement shall be provided over a length

‘l o’ from each joint face, towards mid span, and on either side of any section, where flexural yielding may occur under the effect of

earthquake forces (see Fig. 9). The length ‘l o’ shall not be lessthan (a) larger lateral dimension of the member at the section

where yielding occurs, (b)1/6 of clear span of the member, and (c)450 mm.

13920

,456

7.3.3,

26.5.3.2(c) (1)

The spacing of hoops shall not exceed half the least lateral

dimension of the column, except where special confiningreinforcement is provided, as per 7.4.

c)Pitch and diameter of lateral ties:

1) Pitch-The pitch of transverse reinforcement shall be not morethan the least of the following distances;



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i) The least lateral dimension of the compression members;ii) Sixteen times the smallest diameter of the longitudinal

reinforcement bar to be tied; and

iii) 300 mm.

4.4 FORMULAE TO CHECK IS CLAUSES

Formulae used in case of Beams

1. Area of reinforcement at bottom

Ast or Asc

Considered as tension reinforcement, when tension at bottom.

2. Area of reinforcement at top

Ast or Asc

Considered as tension reinforcement, when tension at top. Otherwise, compression

3. Exposure condition

Used to check the cover as per Table 16 & Table 16 A of IS 456

4. Fire resistance


5. Minimum tension reinforcement

ck

y

0.24 f b d

f

fck =

fy =

b =

d =

IS 13920-1993. Clause 6.2.1 (b)





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Divided equally on two faces

11. Spacing of side face reinforcement

Minimum (b, 300)

IS 456-2000. Clause 26.5.1.3

12. Check for Deep beams

Span

Dshall be more than 2.0 (for simply supported beams) and 2.5 (for continuous

beams)

IS 456-2000. Clause 29.1

13. Clear distance between supports for lateral stability

2250bMinimum 60b ,

d

IS 456-2000. Clause 23.3

14. Minimum spacing between bars

Maximum (Maximum size of bar, size of aggregate + 5 mm)

IS 456-2000. Clause 23.3.2 (a)

15. Maximum spacing between bars in tension

It shall never exceed 300 mm

IS 456-2000. Clause 23.3.3

Moment of Resistance

16. Limiting moment of resistance

Mu,lim = MOR index × f ck × b × d2

Table C, Page 10, SP – 16

17. Limiting area of tension reinforcement



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At,lim =ck

y

f Reinf index bd

f

Table C, Page 10, SP – 16

18. MOR for under-reinforced section

st y

y st

ck

A f 0.87 f A d 1

bd f

IS 456-2000, Annexure G

Section is under-reinforced when, Ast < At,lim

19. MOR for over-reinforced section

Ast2 = Ast - At,lim

fsc depends on d’/d

Asc =y st2

sc

0.87 f A

A

Mu2 = f sc Asc (d – d’)

Total MOR = Mu,lim + Mu2

Section is under-reinforced when, Ast > At,lim

Shear Capacity

20. Shear strength of concrete

c =ck 0.85 0.8f ( 1 5 1)

6

where, ck

t

0.8f 6.89p

and stt 100A p

bd

SP-16, Para 4.1, Page 175

21. Shear capacity of concrete



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c bd

22. Shear capacity of steel

y sv

v

0.87 f A d

s

IS 456-2000. Clause 40.4 (a)

23. Total shear capacity

Shear capacity of (steel + concrete)

Check for deflection

24. Basic value of span to effective depth ratio

IS 456-2000. Clause 23.2.1

25. Multiplication factor for span > 10 m

F110

span

26. Multiplication factor for tension reinforcement

F2

s 10s

1

bd0.225 0.00322f 0.625log 100A

where f s = 0.58 f y

SP-24, Page 55

27. Multiplication factor for compression reinforcement

F3 c

c

1.6 p

p 0.275

where pc = percentage of compression reinforcement

SP-24, Page 55

28. Permissible value of span to effective depth ratio

Basic value × F1 × F2 × F3



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Formulae used in case of Columns

Checking Codal Provisions

1 Exposure condition


2. Fire resistance


3. Min Dimension

150 mm / 200 mm (for span more than 5 m)

IS 456-2000. Clause 21.2

IS 13920-1993. Clause 7.1.2

4. Ratio of B/D

B

Dshall be more than 0.4

IS 13920-1993. Clause 7.1.3

5. Unsupported length

60 × Minimum (B, D)

IS 456-2000. Clause 25.3.1

6. Min longitudinal reinforcement

0.8BD

100

IS 456-2000. Clause 26.5.3.1 (a)

7. Max longitudinal reinforcement

4BD

100

IS 456-2000. Clause 26.5.3.1 (a)



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8. Max spacing of longitudinal reinforcement

300 mm

IS 456-2000. Clause 26.5.3.1 (g)

9. Dia of confining reinforcement

gck sh

y k

Af A 0.18 Sh 1.0

f A

IS 13920-1993. Clause 7.4.8

10. Max spacing of confining reinforcement

Lesser of 100 mm andMin(B,D)

4

It need not be lesser than 75 mm

IS 13920-1993. Clause 7.4.6

11. Max spacing of transverse reinforcement in the middle

Minimum of [16 × Dia of longitudinal reinforcement], 300 mm,Min (B, D)

2

IS 456-2000. Clause 26.5.3.2 (c)

IS 13920-1993. Clause 7.4.6

Analysis of Column for Axial Bending

12. Minimum Eccentricity

Maximum of L B

500 30 , 20 mm

IS 456-2000. Clause 25.4

13. Permitted eccentricity

0.05 × B

IS 456-2000. Clause 39.3



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14. Moment due to eccentricity

Factored load × Minimum eccentricity

Applicable only when minimum eccentricity exceeds permitted eccentricity

15. Design Moments

Maximum of initial factored moment and moment due to eccentricity

16. Slenderness ratio

L

B

17. Additional moments

2

uP B L2000 B

IS 456-2000. Clause 39.7.1

18. Modification factor

uz u

uz b

P Pk

P P

Maximum value of k is 1

IS 456-2000. Clause 39.7.1

19. Total design moments

Design moments + (k × Additional moments)

20. Interaction ratio

uy uz

uy1 uz1

M MM M

This value should not exceed 1

IS 456-2000. Clause 39.6

Documents

Beam & Col Formulae