RCC : Limit state method of design

Limit State Method

IS 456 Standards for Beams and Slabs and Columns

Effective span

A. Simply supported beams and slabs (l_eff)

Here, l₀ = clear span

w = width of support

d = depth of beam or slab

B. For continuous beam

(i) If width of support < 1/12 of clear span

(ii) If width of support > 1/12 of clear span

(a) When one end fixed other end continuous or both end continuous.

l_eff = l₀

(b) When one end continuous and other end simply supported

C. Cantilever

(i)  

(ii)  

D. Frames

l_eff = Centre to centre distance

Control of deflection

(i) This is one of the most important check for limit state of serviceability.

(a) The final deflection due to all loads including the effect of temperature, creep and shrinkage and measured from as cast level of the support of floors, roofs and other horizontal members should not normally exceed span/250

(b) The deflection including the effect of temperature, creeps and shrinkage occurring after erection of partition and application of finishes should not normally exceed span/350 or 20 mm which ever is less.

(ii) The vertical deflection limit may generally be satisfied if

(a) Basic span to effective depth ratio for span upto 10m is

Types of Beams: 

For cantilever → 7

For simply supported → 20

For continuous → 26

(b) For span > 10 m effective depth 

Where 'A' is span to effective depth ratio for span upto 10m.

(c) Depending upon the tension reinforcement the value 'A' can be modify by multiplying a factor called modification factor (MF₁)

effective depth

where, 

(d) Depending upon area of compression reinforcement, value (A) can be further modified using a modification factor (MF₂)

effective depth = 

(e) For flanged beam : A reduction factor is used

(f) Deflection check for two way slab:

Slenderness limit

1. For simply supported or continuous beams
    where, l₀ = Clear span
   b = Width of the section
   and, d = Effective depth
2. For cantilever beam 
   1. Minimum tension reinforcement 
   2. Maximum tension reinforcement = 0.04 bD
   3. Maximum compression reinforcement = 0.04 bD
      where, D = overall depth of the section
   4. Where, D > 750 mm, side face reinforcement is provided and it is equal to 0.1% of gross cross-section area (b × D). It is provided equally on both face.
   5. Maximum spacing of side face reinforcement is 300 mm.
   6. Maximum size of reinforcement for slab/beam is 1/8 of total thickness of the member
   7. Nominal cover for different members
      Beams → 25 mm
      Slab → 20 to 30 mm
      Column → 40 mm
      Foundations → 50 mm
   8. Moment and shear coefficient for beams/slabs

One way slab

(i) Ly/Lx ratio is less than 2

 where, l_y = length of longer span

l_x = length of shorter span

(ii) Slab is supported only on two edges.

Design of One way slab

Two way slab

(i)  Ly/Lx ratio is more than 2

(ii) Slab is supported on all edges.

Design of two way slab

1. Grasoff Ranking method
   It is used for corners not held down position.
   It is purely simply supported case.

(i) 

(ii) Moment in x-direction 

Moment in y-direction 

(iii) Shear force

At shorter edge (V_X)

At longer edge (V_y)

1. Design of slab with corner held down position

(a) Pigeauds method: 

where, the values of  are read from table

(b) I.S. code method

The values of  read from table (page 91, IS : 456-2000)

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