Working Stress Method (WSM) - Assumptions & Features

The working stress method (WSM) is the first theoretical method for structural design that evolved in the 1900s and was accepted by the national codes of practice for the design of reinforced concrete sections.

This article explains in detail the philosophy of the working stress method and the assumptions followed for the design of structures by the WSM method. 

Concept of Working Stress Method

The assumptions followed by the working stress method in the design of structures (steel and concrete) can be concluded by first understanding the design considerations followed in the WSM method.

In the WSM method, the structural member or materials are assumed to behave in a Linear elastic manner. Hence, this method is called the Linear Elastic Method. It is also used for steel and timber.

Permissible /Allowable Stress is Kept below Material Strength

As shown in the stress-strain graph, σy is the yield stress of the material or material strength.

While designing the structures in the WSM method, the permissible or allowable stress σallow will be taken less than material strength. For this, we divide the characteristic strength of the material by a factor of safety (FOS). The allowable stress or permissible stress is given by the formula:

Allowable Stress/Permissible Stress = Yield or Ultimate Strength/ Factor of Safety (FOS)

Yield Strength is used when the material is ductile or steel (fy or σy ). Ultimate Strength is used when the material is concrete (fck).

The FOS for concrete and steel is mentioned in IS:456-2000. For concrete it is 3 and for steel it is 1.78.

Example : If we consider a stress-strain curve of a steel, and fy = 500 N/mm2 which is the yield strength. Now, the permissible or allowable stress = yield strength / FOS = 500/1.78 = 280 MPa. For the design calculation, the stress value will be 280 MPa not 500 MPa.

Features of the Working Stress Method

Design the Members not to exceed the elastic range

When designing a beam, we initially calculate the expected loads on the structure. These estimated loads are used to design i.e. determine the cross-section of the beam. So we must design the beam dimensions in such a way that, under the action of estimated loads, the structure must no way go beyond the elastic range.

Strain Compatibility and Modular Ratio
R.C.C is a composite material with two different materials concrete and steel. We cannot directly apply the strength of materials, we need to apply the concept of strain compatibility. Strain compatibility is the property of having a perfect bond between the concrete and steel. That means the strain developed in steel and the surrounding concrete remains almost the same.

In addition, the stresses in steel are indirectly related to the stresses in surrounding concrete. This indirect relation between the concrete and steel is expressed in terms of modular ratio (m).

Modular Ratio (m) = stress in steel (fs)/stresses in concrete (fc) = Es/Ec

Modular ratio is the ratio of two moduli of elasticity. Hence, the WSM method is also called as Modular Ratio Method.

As mentioned above, the modular ratio is the ratio of the modulus of elasticity of steel to that of concrete. (i.e. Es/Ec) However, this value will vary for all the grades of concrete. Hence the below formula for modular ratio is taken for the calculation in reinforced concrete designs. Here, 𝛔cbc is the permissible compressive stress in concrete in bending.

m = 280/3𝛔cbc

Assumptions in Working Stress Method (WSM)

As we have dealt with the important concept of the WSM method, let's brief the assumptions related to WSM design philosophy. 

1. Plane Section before bending will remain plane after bending
2. All tensile stresses are taken by reinforcement and none by concrete
3. The steel and concrete behaves as a linear elastic material
4. The Stress-strain relationship of steel and concrete is a Straight line under working load
5. The bond between steel and concrete is perfect within the elastic limit of the steel
6. The stresses in steel and concrete are related by a factor known as “modular ratio

Drawbacks

1. The actual stress distribution of concrete is not described. Concrete is assumed as elastic, but it is not elastic. 
2. To accommodate the permissible stress, we increase the dimension of the structure so that it does not fail and does not go beyond elasticity. This would result in designing heavy and uneconomical design. 
3. The same factor of safety is used for different types of loads. 
4. The failure mode cannot be observed, so warning before failure cannot be studied. 
5. Any shrinkage or creep effects are not considered.

Read More On: Working Stress Method (WSM) and Limit State Method (LSM)