Difficulty: Easy
Correct Answer: La = (φ * fs) / (4 * fbd)
Explanation:
Introduction:
Anchorage or development length ensures that reinforcing steel can safely develop the required stress by bonding with surrounding concrete. In compression, bond transfer is generally more favorable than in tension, but the fundamental relationship between steel stress, bar size, and design bond stress remains at the core of the calculation.
Given Data / Assumptions:
Concept / Approach:
The basic equilibrium is that the total bond force mobilized along the embedded perimeter over length La must equal the steel force to be developed. Idealizing uniform bond along the bar, this leads to a proportionality with bar circumference and development length. In common code formulations, this resolves to La = (φ * fs) / (4 * fbd) for straight bars (compression case uses the same form when fbd is the design value for compression).
Step-by-Step Solution:
Verification / Alternative check:
Codes may allow reduced La in compression by adopting higher fbd in compression than in tension; when fbd already represents the compressive bond design value, the expression above holds directly.
Why Other Options Are Wrong:
Options B, C, and E alter the denominator and would underestimate or overestimate anchorage. Option D ignores the 4 factor from derivation, giving an unconservative length.
Common Pitfalls:
Confusing characteristic bond stress with design bond stress; forgetting to adjust for hooks, confinement, or closely spaced bars; misapplying tension formula without considering compressive enhancement rules for fbd.
Final Answer:
La = (φ * fs) / (4 * fbd)
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