Shear cracking in reinforced concrete: An R.C.C. beam without shear (web) reinforcement typically develops diagonal cracks at the bottom inclined at approximately what angle to the horizontal?

Introduction / Context:

In reinforced concrete beams, shear failure is associated with diagonal tension cracking. Understanding the typical crack inclination helps diagnose distress and guides the need for shear reinforcement (stirrups) in design and detailing.

Given Data / Assumptions:

• Simply supported beam with flexure and shear near supports.
• No shear reinforcement provided (critical case).
• Normal-strength concrete; typical stress fields.

Concept / Approach:

Principal stress trajectories lead to diagonal tension cracks that form where the combination of shear and flexure produces maximum principal tensile stress. Empirically and from Mohr’s circle reasoning, initial diagonal cracks form at ~45° to the beam axis in members without web reinforcement.

Step-by-Step Solution:

Verification / Alternative check:

Design codes often assume 45° compression struts and provide stirrups oriented to intersect potential diagonal tension cracks near this angle.

Why Other Options Are Wrong:

• 25°, 35°: Too shallow; not representative of classic diagonal tension cracking.
• 55°, 60°: Too steep; uncommon for first diagonal tension cracks in beams without stirrups.

Common Pitfalls:

• Confusing the angle of compression struts in truss analogy with exact crack angles; ~45° is the standard educational approximation.

Final Answer:

45°