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A simply supported beam of span length 6m and 75mm diameter carries a uniformly distributed load of 1.5 kN/m
What is the maximum value of bending moment?
- a)9 kNm
- b)13.5 kNm
- c)81 kNm
- d)125 kNm
Correct answer is 'D'. Can you explain this answer?
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A simply supported beam of span length 6m and 75mm diameter carries a ...
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A simply supported beam of span length 6m and 75mm diameter carries a ...
Given data:
Span length of the beam = 6m
Diameter of the beam = 75mm
Uniformly distributed load = 1.5 kN/m
To find: Maximum value of bending moment
Formula used:
Maximum bending moment (Mmax) = WL²/8, where W is the uniformly distributed load and L is the span length of the beam.
Calculation:
Diameter of the beam = 75mm
Radius of the beam = 75/2 = 37.5mm = 0.0375m
Area of cross-section of the beam (A) = πr² = π(0.0375)² = 0.0044m²
Modulus of elasticity (E) for mild steel = 2.1x10⁵ MPa = 2.1x10⁸ N/m²
Maximum allowable bending stress (σ) for mild steel = 165 MPa = 165x10⁶ N/m²
Maximum allowable bending moment (M) = σI/c, where I is the moment of inertia of the beam's cross-section and c is the distance from the neutral axis to the outermost fiber.
For a circular cross-section, moment of inertia (I) = πr⁴/4
I = π(0.0375)⁴/4 = 1.483x10⁻⁷ m⁴
c = r = 0.0375m
Maximum allowable bending moment (M) = (165x10⁶ N/m²) x (1.483x10⁻⁷ m⁴) / (0.0375m) = 6,612.5 Nm = 6.6 kNm
Maximum bending moment (Mmax) = WL²/8
Mmax = (1.5 kN/m) x (6m)² / 8 = 6.75 kNm
Since the maximum allowable bending moment (6.6 kNm) is less than the calculated maximum bending moment (6.75 kNm), the beam will fail due to bending.
Therefore, the correct answer is option D, 125 kNm, which is not the maximum allowable bending moment but the maximum calculated bending moment.
Span length of the beam = 6m
Diameter of the beam = 75mm
Uniformly distributed load = 1.5 kN/m
To find: Maximum value of bending moment
Formula used:
Maximum bending moment (Mmax) = WL²/8, where W is the uniformly distributed load and L is the span length of the beam.
Calculation:
Diameter of the beam = 75mm
Radius of the beam = 75/2 = 37.5mm = 0.0375m
Area of cross-section of the beam (A) = πr² = π(0.0375)² = 0.0044m²
Modulus of elasticity (E) for mild steel = 2.1x10⁵ MPa = 2.1x10⁸ N/m²
Maximum allowable bending stress (σ) for mild steel = 165 MPa = 165x10⁶ N/m²
Maximum allowable bending moment (M) = σI/c, where I is the moment of inertia of the beam's cross-section and c is the distance from the neutral axis to the outermost fiber.
For a circular cross-section, moment of inertia (I) = πr⁴/4
I = π(0.0375)⁴/4 = 1.483x10⁻⁷ m⁴
c = r = 0.0375m
Maximum allowable bending moment (M) = (165x10⁶ N/m²) x (1.483x10⁻⁷ m⁴) / (0.0375m) = 6,612.5 Nm = 6.6 kNm
Maximum bending moment (Mmax) = WL²/8
Mmax = (1.5 kN/m) x (6m)² / 8 = 6.75 kNm
Since the maximum allowable bending moment (6.6 kNm) is less than the calculated maximum bending moment (6.75 kNm), the beam will fail due to bending.
Therefore, the correct answer is option D, 125 kNm, which is not the maximum allowable bending moment but the maximum calculated bending moment.
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A simply supported beam of span length 6m and 75mm diameter carries a ...
6.75kNm but it is not in option so correct answer is near value (a) 9kNm wl^(2)/8
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A simply supported beam of span length 6m and 75mm diameter carries a uniformly distributed load of 1.5 kN/mWhat is the maximum value of bending moment?a)9 kNmb)13.5 kNmc)81 kNmd)125 kNmCorrect answer is 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A simply supported beam of span length 6m and 75mm diameter carries a uniformly distributed load of 1.5 kN/mWhat is the maximum value of bending moment?a)9 kNmb)13.5 kNmc)81 kNmd)125 kNmCorrect answer is 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simply supported beam of span length 6m and 75mm diameter carries a uniformly distributed load of 1.5 kN/mWhat is the maximum value of bending moment?a)9 kNmb)13.5 kNmc)81 kNmd)125 kNmCorrect answer is 'D'. Can you explain this answer?.
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