Tension-Controlled Section Check

Mediumstraintension-controlledsection-classification

At nominal strength, a reinforced concrete section has neutral-axis depth c = 150 mm and extreme tension-steel depth dt = 500 mm, both measured from the extreme compression face. Plane sections remain plane and the extreme concrete compressive strain is 0.003. Using the supplied ACI 318-14 rule (εt ≥ 0.005 is tension controlled), what is the tensile strain εt and the classification?

Aεt = 0.0070, tension controlled
Bεt = 0.0100, tension controlled
Cεt = 0.0021, not tension controlled
Dεt = 0.0009, not tension controlled

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Answer: A. εt = 0.0070, tension controlled

Equation: similar triangles in the strain diagram, εt/(dt − c) = εcu/c. Inputs: εcu = 0.003, c = 150 mm, dt − c = 350 mm. Substitution: εt = 0.003(350)/150 = 0.0070, which exceeds 0.005, so the section is tension controlled. Wrong: 0.0100 uses dt/c instead of (dt − c)/c; 0.0021 divides by dt instead of c; 0.0009 uses c/dt, which is inverted. Strain is dimensionless so the mm cancel.

ε_{t}

= ε_{c u} \frac{d _{t} - c}{c}

= 0.003 \cdot \frac{500 - 150}{150}

= 0.0070

\geq 0.005

\Rightarrow

tension controlled

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Tension-Controlled Section Check

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