Bond (development) length: For a reinforcing bar of diameter d subjected to allowable tensile stress ft in concrete with allowable bond stress fb, what is the required development/bond length Lb?
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ALb = (d * ft) / (2 * fb)
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BLb = (d * ft) / (3 * fb)
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CLb = (d * ft) / (4 * fb)
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DLb = (4 * d * fb) / ft
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ELb = (d^2 * fb) / ft
Answer
Correct Answer: Lb = (d * ft) / (4 * fb)
Explanation
Introduction / Context:The bond length (development length) is the minimum embedment required so that the stress in a reinforcing bar can be safely transferred to surrounding concrete through bond. It is a fundamental detailing parameter in reinforced concrete design.
Given Data / Assumptions:
- Bar diameter = d.
- Allowable tensile stress in steel = ft.
- Allowable bond stress in concrete = fb.
- Straight bar in tension; standard bond conditions.
Concept / Approach:Equating the tensile force in steel to the bond resistance along the embedded length gives the basic formula. Tensile force = area * stress = (π d^2 / 4) * ft. Bond resistance = perimeter * length * bond stress = (π d) * Lb * fb. Solving for Lb yields the classical expression.
Step-by-Step Solution:Tension in steel: T = (π d^2 / 4) * ft.Bond capacity: R = (π d) * Lb * fb.Equate T = R and simplify: (π d^2 / 4) * ft = (π d) * Lb * fb.Cancel π d and solve: Lb = (d * ft) / (4 * fb).
Verification / Alternative check:The derived expression matches standard RC design texts for straight tension bars under allowable stress design assumptions.
Why Other Options Are Wrong:
- Forms with 2fb or 3fb in denominator mis-state the equilibrium constants.
- Inverse or squared-diameter forms do not come from basic force equilibrium of bar area vs. bond perimeter.
Common Pitfalls:Forgetting to multiply perimeter by length, or using area times bond stress; mixing design stress formats (working vs. ultimate) without adjusting fb values.
Final Answer:Lb = (d * ft) / (4 * fb)