This is the traditional method of design, used not only for reinforced concrete but also for structural steel and timber. This method of designed was evolved around the year 1900. This method was accepted by many national codes. India’s code IS:456-1953 was based on this method. It was revised in 1957, 1964, 1978, 2000 and reaffirmed in 2005 and its tenth reprint was in 2007. This method is based on linear elastic theory.
This method ensures adequate safety by suitably restricting the stresses in the materials induced by expected working loads on the structure.
In this method it is assumed that the concrete and steel are elastic. At the worst combinations of working loads, the stresses in materials are not exceeded beyond permissible values. The permissible stresses are found out by using a suitable factor of safety to the material strength, e.g. for concrete in compression due to bending, a factor of safety equals to 3.0 is considered on 28 days. Characteristics strength and factor of safety equals to 1.8 is considered on the yield strength for mild steel reinforcement in tension due to bending.
Working stress method does not considered the mode of failure of the structure that whether it is ductile or brittle. Also the reserve strength of the material beyond yield point is not considered in this method of design.
Reinforced concrete is a composite material. The WSM assumes the strain compatibility, whereby the strain reinforcing steel is assumed to be equal to that in the adjoining concrete to which it is bonded. Consequently the stress in concrete by a constant factor, called the modular ratio, defined as the ratio of modulus of elasticity of steel to that of concrete. The WSM therefore also known as modular ratio method.
modular ratio, m = Es/Ec = 280/σcbc
Advantages of WSM:
- It is simple, both in concept as well as in application.
- It is reasonably reliable.
- It is essential to have a knowledge of WSM, since it forms a part of LSM. IS:456-2000 has incorporated LSM and WSM. But the concept of WSM is retained for checking serviceability states of deflection and cracking.
- The design usually results in large sections of structural members as compared to LSM. Due to this, structure design by WSM gives better serviceability performance, i.e. less deflection, less crack width, etc.
Dis-advantages of WSM:
- It gives larger section of structural members, thus it is uneconomical.
- It assumes that, stress and strain relationship is constant for concrete, which is not true.
- WSM does not consider the mode of failure of the structure (brittle or ductile).
- Because of creep and non-linear stress-strain relationship, concrete does not have definite modulus of elasticity.
- The modular ratio design results in larger percentage of compression steel than that given by the limit state design, thus its lead to uneconomic design.
- WSM fails to discriminate between different types of loads that act simultaneously but have different uncertainties.
