Question

Using working stress method for design of RC members, the factor of safety considered for concrete and steel respectively are

• A. 1.5 and 1.15
• B. 3.0 and 1.5
• C. 3.0 and 1.8
• D. 1.5 and 1.8

Hint:

Do not mix up the safety factors for WSM and LSM:
- Working Stress Method (WSM): F.O.S on material strength is high. Concrete $\approx$ 3.0, Steel $\approx$ 1.8.
- Limit State Method (LSM): Partial safety factors for materials are lower. Concrete = 1.5, Steel = 1.15.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the factors of safety applied to the characteristic strengths of concrete and steel in the Working Stress Method (WSM) of design.

Step 2: Detailed Explanation:
The Working Stress Method is an older design philosophy where the stresses in the materials under service loads are not allowed to exceed a certain proportion of their ultimate strength. This proportion is determined by the factor of safety.
Permissible Stress = $\frac{\text{Ultimate Strength}}{\text{Factor of Safety}}$
According to IS 456, the factors of safety used in WSM are:

• For Concrete (in bending compression): The factor of safety is approximately

3.0. For example, for M20 concrete with a characteristic cube strength ($f_{ck}$) of 20 N/mm$^2$, the permissible stress ($\sigma_{cbc}$) is 7 N/mm$^2$. (20 / 7 $\approx$ 2.86, rounded to 3).

• For Steel (in tension): The factor of safety is approximately

1.8 (more precisely, 1.78). For example, for Fe 415 steel with a yield strength ($f_y$) of 415 N/mm$^2$, the permissible stress ($\sigma_{st}$) is 230 N/mm$^2$. (415 / 230 $\approx$ 1.8).


It is important not to confuse these with the partial safety factors used in the Limit State Method (LSM). In LSM, the partial safety factors for material strength are 1.5 for concrete and 1.15 for steel.

Step 3: Final Answer:
In the working stress method, the factors of safety are 3.0 for concrete and approximately 1.8 for steel.