Limit State Method | RCC & Prestressed Concrete - Civil Engineering (CE) PDF Download

IS 456 Standards for Beams and Slabs and Columns

Effective span

1. Simply supported beams and slabs (l_eff)
   Here, l₀ = clear span
   w = width of the support
   d = depth of beam or slab
2. For continuous beam
   (i) If the width of support < 1/12 of clear span
   
   (ii) If the width of support > 1/12 of clear span
   (a) When one end fixed other end continuous or both end continuous.(b) When one end continuous and the other end simply supported
3. Cantilever
   
4. Framesl_eff = Centre to centre distance

Control of deflection

1. This is one of the most important checks to limit the state of serviceability.
   (i) The final deflection due to all loads including the effect of temperature, creep and shrinkage and measured from the as-cast level of the support of floors, roofs and other horizontal members should not normally exceed span/250.
   (ii) The deflection including the effect of temperature, creeps and shrinkage occurring after the erection of partition and application of finishes should not normally exceed span/350 or 20 mm whichever is less.
2. The vertical deflection limit may generally be satisfied if
   (i) Basic span to effective depth ratio for span upto 10m is
   Types of Beams: span/effective depth
   For cantilever → 7
   For simply supported → 20
   For continuous → 26
   (ii) For span > 10 m effective depth = (span)²/10 x 2
   Where 'A' is span to effective depth ratio for span upto 10m.
   (iii) Depending upon the tension reinforcement the value 'A' can be modified by multiplying a factor called modification factor (MF₁)
   effective depth = span/A x MF₁
   where,  
   (iv) Depending upon the area of compression reinforcement, value (A) can be further modified using a modification factor (MF₂)
   effective depth = span / A x MF₁ x MF₂
   (v) For flanged beam: A reduction factor is used
   (vi) Deflection check for two way slab:

Slenderness limit

1. For simply supported or continuous beams
    where, l₀ = Clearspan
   b = Width of the section
   and, d = Effective depth
2. For cantilever beam
    
   (i) Minimum tension reinforcement =
   (ii) Maximum tension reinforcement = 0.04 bD
   (iii) Maximum compression reinforcement = 0.04 bD where, D = overall depth of the section
   (iv) 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 faces.
   (v) Maximum spacing of side face reinforcement is 300 mm.
   (vi) Maximum size of reinforcement for slab/beam is 1/8 of the total thickness of the member.
   (vii) Nominal cover for different membersBeams → 25 mm
   Slab → 20 to 30 mm
   Column → 40 mm
   Foundations → 50 mm
   (viii) Moment and shear coefficient for beams/slabs

One way slab

(i) l_y / l_x > 2 where l_y = length of a 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) l_y / l_x ≤ 2
(ii) Slab is supported on all edges.

Design of two way slab

Grasoff Ranking method
It is used for corners not held down position.
It is a 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)

Design of slab with corner held down the position

1. Pigeauds method: 
   
   where the values of r_x and r_y are read from the table
2. I.S. code method:
   M_x = α_xwl²_y, M_y = α_ywl_x²
   The values of α_x and α_y read from the table (page 91, IS : 456-2000)