GATE CE 2016 Set 2 — Question 46
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Structural Engineering → Stress, Strain & Beams → Flexural Stresses
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Question
A 450 mm long plain concrete prism is subjected to the concentrated vertical loads as shown in the figure. Cross section of the prism is given as 150 mm 150 mm. Considering linear stress distribution across the cross-section, the modulus of rupture (expressed in MPa) is ________
Correct answer
2.9 to 3.1
Solution
1.Identify the loading condition:
The prism is subjected to symmetric four-point bending. The distance of each load from the nearest support is mm. The total span is mm. Since , this is a standard third-point loading test.2.Calculate the maximum bending moment ():
The maximum bending moment occurs in the central zone between the two loads:Nm.
3.Calculate the modulus of rupture ():
The modulus of rupture is the extreme fiber stress at failure, calculated using the flexure formula:Given mm = 0.15 m and mm = 0.15 m:
Pa = 3.0 MPa.
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