Ratio of Permissible Shear Stress in LSM and WSM

The permissible shear stress is an important consideration in the design of structures. There are two methods of design, the Limit State Method (LSM) and the Working Stress Method (WSM), each with its own set of permissible shear stresses. The ratio of permissible shear stress in LSM and WSM is given by:

Ratio = Permissible Shear Stress in LSM / Permissible Shear Stress in WSM

The options given are:

a) 25 : 16
b) 5 : 4
c) 16 : 25
d) 4 : 5

The correct answer is option A, i.e., 25 : 16.

Explanation

The permissible shear stress in LSM is calculated based on the ultimate strength of the material, while in WSM, it is calculated based on the yield strength of the material. The formula for calculating the permissible shear stress in LSM is:

τp = 0.4 x fu / γm

where τp is the permissible shear stress, fu is the ultimate strength of the material, and γm is the partial safety factor for material strength.

The formula for calculating the permissible shear stress in WSM is:

τp = 0.4 x fy / γm

where τp is the permissible shear stress, fy is the yield strength of the material, and γm is the partial safety factor for material strength.

By substituting the values of fu and fy, we get:

Ratio = (0.4 x fu / γm) / (0.4 x fy / γm)
Ratio = fu / fy

For steel, the ultimate strength is approximately 1.25 times the yield strength. Hence, the ratio of permissible shear stress in LSM and WSM for steel is approximately 1.25.

Therefore, the ratio of permissible shear stress in LSM and WSM is 25 : 16.

Conclusion

The ratio of permissible shear stress in LSM and WSM is an important aspect of structural design. The correct answer to the given question is option A, i.e., 25 : 16. It is important for civil engineers to understand the difference between LSM and WSM and their respective permissible shear stresses to ensure safe and efficient design of structures.