Nominal shear stress in an R.C.C. beam: The maximum nominal shear stress in the concrete web for design is commonly evaluated as which of the following expressions, where Vu is the design shear force, b is the breadth (web width), and d is the effective depth?

Introduction / Context:
Shear design in reinforced concrete beams starts by computing the nominal shear stress in the concrete web. This value is compared with permissible concrete shear stress and shear capacity of stirrups to ensure adequate resistance against diagonal tension cracking and web shear failure.

Given Data / Assumptions:

• Vu = factored (design) shear force at the section under consideration.
• b = breadth of web (for flanged beams, the web width).
• d = effective depth to tension steel.
• Nominal shear stress symbol τv used for checks against τc and limits.

Concept / Approach:
Nominal shear stress is the shear force per unit area of the web resisting shear, approximated by b * d. This assumes the shear is primarily carried by the concrete web around the centroidal region and provides a consistent basis for code checks and stirrup design.

Step-by-Step Solution:
Compute Vu at the section (factored).Compute resisting area ≈ b * d.Evaluate τv = Vu / (b * d).Compare τv with code-permitted concrete shear stress; design stirrups if τv exceeds concrete capacity.

Verification / Alternative check:
This simple rectangular-block model aligns with standard code procedures, serving as the basis for minimum shear reinforcement and detailed stirrup design.

Why Other Options Are Wrong:

• Vu/(bb) or Vu/(dd): use incorrect resisting areas.
• 2Vu/(bd): applies an unjustified factor, over-estimating stress.

Common Pitfalls:
Using flange width instead of web width for T/L beams; forgetting to use factored shear; neglecting the effect of axial force or prestress on shear checks.

Final Answer:
τv = Vu / (b * d)