Methods of Design

There are 3 methods to design a structural component.

1. Working Stress Method
2. Ultimate Load Method
3. Limit State Method 

Working Stress Method

This is a classical method used to design RCC structures. In this method, the material is assumed to behave elastically. The relationship between stress and load is linear and stresses within the material is not allowed to exceed the permissible stress.

               $\text{Permissible Stress}=\frac{\text{Strength of Material}}{\text{Factor of Safety}}$

        Permissible Stress in Tension steel: $0.55{{f}_{y}}={{\sigma }_{st}}$
        FOS for Steel = 1.8

        Permissible Stress in Concrete in bending: ${{\sigma }_{cbc}}=0.33{{f}_{ck}}$
        FOS for Concrete = 3

Assumptions in Working Stress Method

1. A section which is plane before bending remains plane after bending.
2. The bond between concrete and steel is perfect within the elastic limit of steel.
3. Tension is borne entirely by steel.
4. The Modulus of Elasticity of concrete is same for all stresses.
5. There are no initial stresses in steel when it is embedded in concrete.

Deficiencies in Working Stress Method

1. Due to the long-term effect of creep and shrinkage and stress concentration, it may not be possible to keep the stresses within permissible limit.
2. Actual margin of safety is not equal to the factor of safety used in WSM because the stress-strain curve is not linear up to collapse. 
3. WSM does not discriminate between different types of loads that act simultaneously.

Although WSM has deficiencies still it is used to design structures like Bridges, Water tanks, chimneys etc because of its simplified approach.

Ultimate Load Method

This method was introduced in the 1960s. In this method stress condition at the state of impending failure is analysed and non-linear stress-strain curve of steel and concrete are made use of.
A safety measure is introduced by an appropriate choice of load factor.

               $\text{Load Factor =}\frac{\text{Ultimate Load}}{\text{Working Load}}$

In this method distribution of stress resultants at ultimate load is taken as distribution at service load magnified by load factor. This is clearly an error because significant inelastic behaviour and redistribution of stress resultant take place as loading is increased from service loads to ultimate loads.

Limit State Method

There is uncertainty in loading, properties of material and dimensions of a member and to account for these uncertainties FOS and Load Factor was introduced in WSM and Ultimate load Method respectively. But there was no theoretical justification for use of FOS and load factors.

To overcome this, a reliability-based analysis was performed and factors of safety for both loading and material properties were established and these factors were called Partial factors of safety. Selection of partial factors of safety was done on the probabilistic basis.

This analysis was called Limit State Method. Limit state is a state in which the structure becomes unfit for use.

There are 2 types of Limit States:

1. Limit state of serviceability:  Satisfactory performance under service load. Such as discomfort caused by excessive deflection, crack width, vibration, leakage, loss of durability etc.
2. Limit state of collapse: Adequate margin of safety for normal overloads. These include limit state of strength, overturning, sliding, buckling, fatigue etc.

Assumptions in Limit State of Collapse

1. A section which is plane before bending remains plane after bending.
2. The maximum strain in concrete at the outermost compression fibre is taken as 0.0035 in bending.
3. The relationship between compressive stress distribution in concrete and strain in concrete may be assumed to be rectangular, trapezoidal, parabolic or any other shape which results in the prediction of strength in substantial agreement with the result of the test.
   
   
                                                  Source: IS 456
   
   
4. The Tensile strength of concrete is ignored.
5. Partial Factor of Safety of Steel is 1.15 and that for concrete is 1.5.
6. Maximum strain in Tension reinforcement in the section at failure shall not be less than
   
   

                  ${{\varepsilon }_{st}}=\frac{{{f}_{y}}}{1.15{{E}_{s}}}+0.002$
   Where,
                 ${{\varepsilon }_{st}}=$ Strain in Tension Steel
                 ${{f}_{y}}=$ Characterstic Strength of Steel
                 ${{E}_{s}}=$ Modulus of Elasticity of Steel

prev 1 2 3 4 5 6 next