In reinforced concrete beams, the total length of a cranked (bent-up) bar that rises through a vertical distance d at a 45° angle, for a beam of effective length L, is taken as which of the following?

Introduction / Context:
Bent-up (cranked) bars are used to control shear near supports and to anchor tension steel efficiently. Estimators need a practical rule to add the extra length contributed by two 45° bends that raise and then return the bar over an effective depth d.

Given Data / Assumptions:

• Effective horizontal length of the bar = L.
• Crank rises through vertical d at 45° (and returns similarly).
• Standard detailing approximations are acceptable for bar length calculations.

Concept / Approach:
The true inclined length to traverse depth d at 45° is d / sin 45° = d * √2 ≈ 1.414 d. However, as the horizontal projection already counts d (since tan 45° = 1), practical estimation uses an empirical addition of approximately 0.42 d per crank to account for the extra length beyond the horizontal projection, bend curvatures, and allowances.

Step-by-Step Solution:
1) Two cranks (up and down) occur: total extra allowance ≈ 2 * 0.42 d = 0.84 d.2) Bar length = horizontal L + crank allowances = L + 0.84 d.3) Hence, adopt L + 2 × 0.42 d per standard estimation practice.

Verification / Alternative check:
Comparing with exact geometric surplus (2 * (√2 − 1) d ≈ 0.828 d) shows the 0.84 d allowance is a close, conservative approximation including bend curvature.

Why Other Options Are Wrong:

• L + 0.42 d: Only accounts for one crank, not two.
• Negative adjustments (options C and D) contradict the added length due to bending.

Common Pitfalls:

• Forgetting to include both up and down crank allowances.
• Omitting extra length for hooks/anchorage where specified separately.

Final Answer:
L + 2 x 0.42 d.