A singly reinforced rectangular concrete beam has width b = 300 mm, effective depth d = 500 mm and tension steel As = 1,500 mm². Material strengths are f′c = 28 MPa and fy = 420 MPa. Assuming the steel yields, the nominal flexural strength Mn is most nearly:

Flexural Strength of a Concrete Beam

Mediumreinforced concreteflexurestress block

A singly reinforced rectangular concrete beam has width

b

= 300

mm, effective depth

d

= 500

mm and tension steel

A_{s}

= 1500

^{2} .

Material strengths are

f_{c}^{'}

= 28

MPa and

f_{y}

= 420

MPa. Assuming the steel yields, the nominal flexural strength

M_{n}

is most nearly:

A161 kN·m
B259 kN·m
C287 kN·m
D315 kN·m

Show solution

Answer: C. 287 kN·m

Force equilibrium sets the depth of the Whitney stress block: a = A_s f_y/(0.85 f′_c b) = (1,500 × 420)/(0.85 × 28 × 300) = 630,000/7,140 = 88.2 mm. The internal lever arm runs from the steel to the centre of the block, d − a/2 = 500 − 44.1 = 455.9 mm, so M_n = A_s f_y (d − a/2) = 630,000 × 455.9 = 287 × 10⁶ N·mm = 287 kN·m. Using the full depth d gives 315 kN·m and overstates the arm; subtracting the whole block depth a instead of a/2 gives 259 kN·m; 161 kN·m comes from putting b where d belongs. The design strength would be φM_n = 0.9 × 287 = 258 kN·m for a tension-controlled section.

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Flexural Strength of a Concrete Beam

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