Singly Reinforced Concrete Beam

Analysis of Singly reinforced concrete beam

Concrete is weak in tension therefore steel is added in tension zone of the section to provide strength in tension. The figure given below shows a typical section of singly reinforced concrete beam with strain distribution and equivalent stress distribution (proposed by Whitney).

The actual stress distribution of concrete is parabolic. Whitney (1930) proposed an equivalent rectangular stress distribution, which is adopted by ACI - 318. This rectangular stress block has  made the calculations easy. It has an average stress of 0.85f_C^'  and the depth "a" equal to β₁  times neutral axis of section. The value of β₁  is taken as 0.85 for f_C^'  upto 4000  psi (30 MPa), and 0.05 less for each 1000 psi (7 MPa) of f_C^'   in excess of 4000 psi (30 MPa), but not less than 0.65.

The nominal moment strength is obtained by applying static equilibrium and compatibility of stress and strain. The design strength is calculated by dividing nominal strenght by strength reduction factor φ (phi).

With reference to the equivalent stress diagram as per Whitney,

 Force of tension due to tension rebar;

 T = (area tension rebar) * (stress of steel)

 T =  As fy   

 It is required that tension steel has yielded when failure takes place. This makes sure that the section is not controlled by concrete.

 Foce of compression (due to concrete);

 C_c = (average compressive stress) * (equivalent area of concrete)

 C_c = (0.85f_C' ) * (b a)    

  For equilibrium, the force of tension equals the force of compression.This gives the values of "a";

  a = (A_s f_y ) / (0.85f_C' b)

 The depth of neutral axis; x = a/β₁

 The nominal moment strength M_n of the section is calculated by taking the moment of compressive force about the centroid of tension steel area. 

 M_n = C_c (d - a/2)

 effective depth "d" is the distance from extreme compression fibre to the centroid of tension rebar.  Do you want to know what is doubly reinforced Concrete beam?

 To learn more about calculating the strength of reinforced concrete beam please visit solved Example 9-1 , Example 9-2, Example 9-3

You can also use our free online calculator for strength of Reinforced Concrete beam.