For bar bending schedules in reinforced concrete, the internal bend radius when forming a standard hook should not be less than what multiple of the bar diameter?

Introduction / Context:
Minimum bend radii are specified to avoid cracking of concrete and bar damage during bending. Hooks provide anchorage in tension zones, and an adequate internal radius limits strain hardening and micro-cracking of the bar.

Given Data / Assumptions:

• Conventional reinforcing steel bending for standard hooks.
• General guideline for minimum internal bend radius.
• No special high-strength bar exception is invoked.

Concept / Approach:
Practical detailing rules cap the sharpness of bends by specifying a minimum internal radius as a multiple of bar diameter d. A commonly adopted minimum for standard hooks in mild steel is about 2d, ensuring the bar is bent without excessive damage and providing reliable anchorage.

Step-by-Step Solution:
Identify minimum internal bend radius requirement for hooks.Adopt the common detailing guideline: r(min) ≈ 2d for standard hooks in typical bars.Select the corresponding option.

Verification / Alternative check:
Detailing manuals provide bend diameter or radius limits; the 2d internal radius (equivalently bend diameter 4d) is a widely used baseline for plain bars. (Some codes specify larger radii for deformed/high-strength bars.)

Why Other Options Are Wrong:

• 3d, 4d, 5d: More conservative than the common baseline and may be required for certain bar grades, but not the typical minimum for standard hooks cited in many exam contexts.
• None of these: Incorrect because a standard minimum exists.

Common Pitfalls:
Confusing internal radius with bend diameter; using too small a radius causing bar distress; not checking code-specific exceptions for high-strength deformed bars or seismic hooks.

Final Answer:
twice the diameter