In reinforced concrete design using the Ultimate Strength Method, the nominal moment capacity M_n of a singly reinforced rectangular beam where a is the depth of the equivalent rectangular stress block is:

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Architecture Engineering QUESTION #2336

Question 1

In reinforced concrete design using the Ultimate Strength Method, the nominal moment capacity \(M_n\) of a singly reinforced rectangular beam where \(a\) is the depth of the equivalent rectangular stress block is:

\(M_n = A_s f_y \left(d - \dfrac{a}{3}\right)\)
\(M_n = A_s f_y \left(d - \dfrac{a}{2}\right)\)✔️
\(M_n = 0.85 f'_c \cdot b \cdot d^2\)
\(M_n = A_s f_y \cdot d\)

Correct Answer Explanation

The nominal moment capacity is \(M_n = A_s f_y \left(d - \dfrac{a}{2}\right)\), where the lever arm is taken from the centroid of tension steel to the centroid of the compression block at \(a/2\) from the top fiber. The stress block depth \(a = \dfrac{A_s f_y}{0.85 f'_c b}\) per ACI 318.

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