Working Stress Method

Working Stress Method

in this method, it is assumed that concrete is elastic. The permissible stress for concrete and steel is not allowed to exceed the limit. Permissible stress is multiplied by the factor of safety to account for deviation in properties of materials. IS code recommends using the factor of safety 3,1.78 for concrete and steel, respectively.

Assumption

1- Section remains plane before bending and after bending

2- Bond between steel and concrete is perfect within elastic limit.

3- Concrete has no tensile strength.

4- Stress in Concrete varies linearly

 Drawbacks of working stress

1- Concrete is not elastic

2- Difficult to account for shrinkage and creep effects.

3- Stress are factored, not load, so uncertainty for the load is not accounted.

Value of modules ratio, (m)

As per IS 456

m = 280/(3 σ_cbc)

ANALYSIS OF A RCC BEAM FOR FLEXURE

Stress behaviour

There are three types of sections.

(i) Under reinforced section

• Actual depth of neutral axis (X_a) < critical depth (x_c)
• At the maximum bending moment that can be allowed.

1. stress in concrete ⇒ C_a < σ_cbc 
2. stress in steel ⇒ t_a = σ_st  

(ii) Over reinforced section

• Actual depth of neutral axis (X_a) >critical depth (x_c) 
• At moment of resistance 

1. stress in concrete ⇒ C_a = σ_cbc 
2. stress in steel ⇒ t_a < σ_st 

(iii) Balanced section

• Actual depth of neutral axis (X_a)=critical depth (x_c)
• At moment of resistance,

1. stress in concrete ⇒ C_a = σ_cbc 
2. stress in steel ⇒ t_a = σ_st  

Note : For balanced section.

         x_c = k.d 

       k= [mc/(t+mc)]

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