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A beam of rectangular cross-section is 100 mm wide and 200 mm deep. If the section is subjected to a shear force of 20 kN, the maximum shear stress is
  • a)
    1 N/mm2
  • b)
    1.125 N/mm2
  • c)
    1.33 N/mm2
  • d)
    1.5 N/mm2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A beam of rectangular cross-section is 100 mm wide and 200 mm deep. If...
The maximum shear stress in a rectangular beam occurs at NA and is given by,



∴ 

= 1.5 N/mm2  

Hence option (D)  is correct

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Most Upvoted Answer
A beam of rectangular cross-section is 100 mm wide and 200 mm deep. If...
Given data:
Width of the beam, b = 100 mm
Depth of the beam, d = 200 mm
Shear force, F = 20 kN = 20000 N

Formula used:
Shear stress = Shear force / Area of cross-section

Calculation:
Area of cross-section = b x d
= 100 mm x 200 mm
= 20000 mm²
= 20 cm²
= 0.002 m²

Shear stress = Shear force / Area of cross-section
= 20000 N / 0.002 m²
= 10,000,000 N/m²
= 10 MPa
= 10 N/mm²

Since the maximum shear stress is asked, we need to use the formula for maximum shear stress in a rectangular cross-section which is given by:
Maximum shear stress = 3/2 * (Shear force / Area of cross-section)

Maximum shear stress = 3/2 * (20000 N / 0.002 m²)
= 3/2 * 10,000,000 N/m²
= 15,000,000 N/m²
= 15 MPa
= 15 N/mm²

Therefore, the maximum shear stress is 1.5 N/mm², which is option D.
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A beam of rectangular cross-section is 100 mm wide and 200 mm deep. If the section is subjected to a shear force of 20 kN, the maximum shear stress isa)1 N/mm2b)1.125 N/mm2c)1.33 N/mm2d)1.5 N/mm2Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A beam of rectangular cross-section is 100 mm wide and 200 mm deep. If the section is subjected to a shear force of 20 kN, the maximum shear stress isa)1 N/mm2b)1.125 N/mm2c)1.33 N/mm2d)1.5 N/mm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam of rectangular cross-section is 100 mm wide and 200 mm deep. If the section is subjected to a shear force of 20 kN, the maximum shear stress isa)1 N/mm2b)1.125 N/mm2c)1.33 N/mm2d)1.5 N/mm2Correct answer is option 'D'. Can you explain this answer?.
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