Which of the following correctly represents the ultimate tensile force (Tu ) in the tensile reinforcement (As) of a singly reinforced beam at the ultimate limit state of flexure, considering the characteristic yield strength of steel (fy)?
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A.
Tu = 0.5 fy As
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B.
Tu = 0.87 fy As
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C.
Tu = 0.67 fy As
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D.
Tu = fy As
Correct Answer:
B. Tu = 0.87 fy As
Explanation:
The correct answer is Tu = 0.87 fy As.
In the ultimate limit state of flexure for a singly reinforced beam, the ultimate tensile force (Tu) is calculated based on the design yield strength of the steel reinforcement. According to standard design codes like IS 456, the characteristic yield strength (fy) is divided by a partial safety factor for material strength, which is 1.15. This results in a design strength of approximately 0.87fy (1 / 1.15 = 0.869). Therefore, the total tensile force, which is the product of the design stress and the area of the tensile steel (As), is expressed as Tu = 0.87 fy As. This force acts through the centroid of the reinforcement and must be balanced by the compressive force in the concrete to maintain equilibrium.
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