Deflection & cracking of RC structure(limit state method)
DEFLECTION AND CRACKING
PREPARED BY : PRATIK PATEL( L.D.C.E)
A structure member DEFLECTS when it carries load.
It should not adversely affect the appearance or efficiency or finishes of the
structure apart from the structural considerations.
The deflection of RC beam is associated with cracking of concrete.
Crack develop at the region where the tensile strength of concrete is
Cracking (Codal Provision)
As given in Is-456(2000) cl.35.3.2 pg. 67. The surface width of crack should not
exceed the following value.
Surface Widthe Crack ( Limiting Value )
To assure the crack width does not exceed the above values IS:456 Suggest Two methods.
BAR SPACING CONTROL: cl.26.3 IS:456
CRACK WIDTH CALCULATION: Specific attention is required to limit the designed crack width to
a particular value , calculation can be done by formula given in annex F of IS:456
Bar spacing control(cl.26.3.2)
The horizontal distance between two parallel main reinforcing bar should not
be less than
Diameter of the bar if diameter are equal
Diameter of the larger bar if diameter are unequal
5mm more than the nominal size of coarse aggregates
When there are more than one row of bar
• The bar should be vertically in line
• The min vertical distance between the bars shall be greater of
2. ⅔ of the nominal max size of aggregate
3. Max size of bars
Span/effective depth ratio
The vertical deflections limit is assumed to satisfy if the span/depth ratio are not grater than
a) Basic values up to spans of 10m
Span/effective depth ration
b) For spans above 10m the values in a) may be multiplied by 10/span in meters except for
cantilever(calculation should be made)
c) Depending on area and stress of tension & compression reinforcement the values in a) or
b) shall be multiplied by modification factor obtained as per fig 4 and fig 5 respectively
given in IS:456 pg.38 and pg.39.
d) For flanged beam the values of a) or b) modified as per fig 6 in IS:456 pg.39.
DEFLECTION IN SIMPLE BEAM
For slabs spanning in two directions the shorter
of two spans should be used for calculating the
span/effective depth ratio.
For 2 way slab span up to 3.5m with mild steel
reinforcement ,the span/effective depth ratio to
satisfy vertical deflection limits for loading class
up to 3KN/m2
Simply supported slab
For hysd bar of grade 415,the above values
should be multiplied by 0.8.
Depending on are and stress of tension & compression reinforcement the values in a) or b)
shall be multiplied by modification factor obtained as per fig 4 and fig 5 respectively given in
IS:456 pg.38 and pg.39.
For flanged beam the values
of a) or b) modified as per fig
6 in IS:456 pg.39.
TOTAL DEFLECTION ( annex C)
The total deflection shall be taken as the sum of the short-term deflection and
the long-term deflection.
1. Short term deflection: It is due to loading
2. Long term deflection: It is due to the effect of creep and shrinkage .It is rapid
at the initial period of loading and then slows w.r.t. time. Within 2-3 years the
long term deflections are largely completed.
For continuous beam
Deflection shall be calculated using the values of Ir , Igr and Mr modified by the following equation:
Xe = modified value of X
X1,X2 = values of X at the support
Xo= values of X at mid span
X= value of Ir ,Igr or Mr as appropriate
Simply supported members
Members continuous at one end
Fully continuous member