Stress Block Depth in a Concrete Beam
Mediumreinforced concretestress block
A singly reinforced concrete beam is 300 mm wide with 1,500 mm² of tension steel. With f′c = 28 MPa and fy = 420 MPa, the depth of the equivalent rectangular stress block a is most nearly:
- A88 mm
- B44 mm
- C75 mm
- D104 mm
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Answer: A. 88 mm
Equation: force balance C = T, with C = 0.85f′c·a·b and T = As·fy, so a = As fy /(0.85 f′c b). Values: As = 1,500 mm², fy = 420 MPa, f′c = 28 MPa, b = 300 mm. Step 1: T = 1,500 × 420 = 630,000 N. Step 2: 0.85 × 28 × 300 = 7,140 N/mm. Step 3: a = 630,000/7,140 = 88 mm. 75 mm leaves out 0.85; 104 mm is c = a/β₁ with β₁ = 0.85; 44 mm is a/2.
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