Whenever the value of actual shear stress exceeds the permissible shear stress of the concrete used, the shear reinforcement must be provided. The purpose of shear reinforcement is to prevent failure in shear, and to increase beam ductility and subsequently the likelihood of sudden failure will be reduced.

Permissible shear stress in concrete is a function of the percentage of steel reinforcement and the grade of concrete. Let's discuss this in detail.

Shear stress in concrete:
Shear stress is the stress that occurs when a force is applied parallel to the surface of the material. In reinforced concrete structures, shear stress occurs in the horizontal planes of the members, such as beams and slabs. The shear stress in concrete is resisted by the shear strength of the concrete.

Factors affecting permissible shear stress in concrete:
The permissible shear stress in concrete depends on various factors, such as:

1. Grade of concrete:
The strength of concrete is directly proportional to its grade. As the grade of concrete increases, the permissible shear stress also increases. This is because higher grade concrete has higher compressive strength, which results in higher shear strength.

2. Percentage of steel reinforcement:
The amount of steel reinforcement in a concrete member affects its shear strength. As the percentage of steel reinforcement increases, the shear strength of the member also increases. This is because the steel reinforcement provides additional strength to the member, which helps to resist the shear stress.

3. Grade of steel reinforcement:
The grade of steel reinforcement also affects the shear strength of the member. As the grade of steel reinforcement increases, its strength and stiffness also increase, which helps to resist the shear stress.

Permissible shear stress in concrete formula:
The permissible shear stress in concrete can be calculated using the following formula:

τ_c = k_c x (100ρ_w x √f'_c)

Where,
τ_c = Permissible shear stress in concrete
k_c = Coefficient of shear strength of concrete
ρ_w = Percentage of steel reinforcement
f'_c = Compressive strength of concrete

Conclusion:
In conclusion, the permissible shear stress in concrete is a function of the percentage of steel reinforcement and the grade of concrete. The higher the percentage of steel reinforcement and the grade of concrete, the higher the permissible shear stress. It is important to consider all these factors while designing reinforced concrete structures to ensure their safety and durability.