The stress strain curve of concrete is assumed as lingar from zero at the neutral axis to a maximum value at the extreme fiber
Numbers determined by dividing ultimate stress by a factor of safety are used for concrete with a factor of safety of 3, and for steel with a different factor of safety, 1.78. This factor of safety accounts for any uncertainties in estimation of working loads and variation in material properties.
In working stress method, the structural members are designed for working loads such het weeshbat the stresses developed are with int the allowable stresses, Hence, the failure criterionde is the stress. The drawbacks of this method are
•Shess strain curve for concrete is assumed as linear, which is not true.
•Factor of safety doesnt predict the true margin of safety
•The effect of creep and shrinkage of concrete is ignored.
•This method gives uneconomical sections
In spite of above defects, the working stress method has the advantage of its emplicity, both in concept as well as in application.
This method has been deleted in IS 456-2000, but the concept of this method retained for checking the serviceability states of deflections and cracking. Hence, the knowedge of this method is essential and IS 456-2000 gives it in the appendix PRINCIPLES OF WORKING STRESS METHOD
As explained earlier, working stress method is based on elastic theory assuming reinforced concrete as elastic material. Working stress method assumes that both steel and concrete act together and are perfectly elastic at all stages. It assumes strain compatibility, in which the strain in the reinforcing steel is assumed to be equal to that in the adjoining concrete to which it is bonded. Consequently the stress in steel is linearly related to the stresses in adjoining concrete by a constant factor, called the modular ratio (defined as the ratio of modulus of elasticity of steel to that of concrete). The working stress method is therefore also known as modular ratio method. ASSUMPTIONS
1. At any cross section, plane sections before bending remain plain after bending.
2. All tensile stresses are taken up by reinforcement and none by concrete, except as otherwise specifically permitted.
3. The stress strain relationship of steel and concrete under working loads is a straight line.
4. The modular ratio m has the value 280/3σcbc where σ= permissible compressive stress due to bending in concrete in N/mm².
PERMISSIBLE STRESSES
Permissible stress for steel and concrete
MODULAR RATIO (m)
It is the ratio of modulus of elasticity of steel to the modulus of elasticity of concrete. m = Es/Ec
As per IS: 456-2000, modular ratio is given by 280/3σcbc where σ= permissible compressive stress due to bending in concrete in N/mm².
