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A beam 40mm wide, 80mm deep, is freely supported over a span of 2m. A weight of 50 N is dropped on to the middle of the beam from a height of 40mm. Calculate the maximum instantaneous stress and deflection. E=200 GPa.
- a)34.14 N/mm2 and 2.42 mm
- b)24.14 N/mm2 and 2.42 mm
- c)24.14 N/mm2 and 1.42 mm
- d)34.14 N/mm2 and 1.42 mm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A beam 40mm wide, 80mm deep, is freely supported over a span of 2m. A ...
Let W be equivalent static load that will produce same deflection as dynamic load applied from a height of 40 mm. Strain energy in beam due to dropping of 50 N load = 50 (40 + δ)
Strain energy in the beam due to load W applied gradually = ½ Wδ
50(40 + δ) = ½ Wδ (1)
Substituting in (1)
Substituting in (1)
Most Upvoted Answer
A beam 40mm wide, 80mm deep, is freely supported over a span of 2m. A ...
Given:
- Width of the beam (b) = 40 mm
- Depth of the beam (d) = 80 mm
- Span of the beam (L) = 2 m
- Weight dropped on the beam (W) = 50 N
- Height from which the weight is dropped (h) = 40 mm
- Modulus of elasticity (E) = 200 GPa
To find:
- Maximum instantaneous stress (σ_max)
- Deflection (δ)
Calculation:
1. Moment of inertia (I) of the beam can be calculated using the formula:
I = (b * d^3) / 12
Substituting the given values:
I = (40 * 80^3) / 12
I = 1706667 mm^4
2. Maximum bending moment (M_max) can be calculated using the formula:
M_max = (W * L) / 4
Substituting the given values:
M_max = (50 * 2000) / 4
M_max = 25000 Nmm
3. Maximum stress (σ_max) can be calculated using the formula:
σ_max = (M_max * d) / (2 * I)
Substituting the values of M_max and I:
σ_max = (25000 * 80) / (2 * 1706667)
σ_max = 34.14 N/mm^2
4. Deflection (δ) at the center of the beam can be calculated using the formula:
δ = (W * L^3) / (48 * E * I)
Substituting the given values:
δ = (50 * 2000^3) / (48 * 200000 * 1706667)
δ = 1.42 mm
Answer:
The maximum instantaneous stress is 34.14 N/mm^2 and the deflection is 1.42 mm. Therefore, the correct answer is option 'D'.
- Width of the beam (b) = 40 mm
- Depth of the beam (d) = 80 mm
- Span of the beam (L) = 2 m
- Weight dropped on the beam (W) = 50 N
- Height from which the weight is dropped (h) = 40 mm
- Modulus of elasticity (E) = 200 GPa
To find:
- Maximum instantaneous stress (σ_max)
- Deflection (δ)
Calculation:
1. Moment of inertia (I) of the beam can be calculated using the formula:
I = (b * d^3) / 12
Substituting the given values:
I = (40 * 80^3) / 12
I = 1706667 mm^4
2. Maximum bending moment (M_max) can be calculated using the formula:
M_max = (W * L) / 4
Substituting the given values:
M_max = (50 * 2000) / 4
M_max = 25000 Nmm
3. Maximum stress (σ_max) can be calculated using the formula:
σ_max = (M_max * d) / (2 * I)
Substituting the values of M_max and I:
σ_max = (25000 * 80) / (2 * 1706667)
σ_max = 34.14 N/mm^2
4. Deflection (δ) at the center of the beam can be calculated using the formula:
δ = (W * L^3) / (48 * E * I)
Substituting the given values:
δ = (50 * 2000^3) / (48 * 200000 * 1706667)
δ = 1.42 mm
Answer:
The maximum instantaneous stress is 34.14 N/mm^2 and the deflection is 1.42 mm. Therefore, the correct answer is option 'D'.
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A beam 40mm wide, 80mm deep, is freely supported over a span of 2m. A weight of 50 N is dropped on to the middle of the beam from a height of 40mm. Calculate the maximum instantaneous stress and deflection. E=200 GPa.a)34.14 N/mm2and 2.42 mmb)24.14 N/mm2and 2.42 mmc)24.14 N/mm2and 1.42 mmd)34.14 N/mm2and 1.42 mmCorrect 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 40mm wide, 80mm deep, is freely supported over a span of 2m. A weight of 50 N is dropped on to the middle of the beam from a height of 40mm. Calculate the maximum instantaneous stress and deflection. E=200 GPa.a)34.14 N/mm2and 2.42 mmb)24.14 N/mm2and 2.42 mmc)24.14 N/mm2and 1.42 mmd)34.14 N/mm2and 1.42 mmCorrect 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 40mm wide, 80mm deep, is freely supported over a span of 2m. A weight of 50 N is dropped on to the middle of the beam from a height of 40mm. Calculate the maximum instantaneous stress and deflection. E=200 GPa.a)34.14 N/mm2and 2.42 mmb)24.14 N/mm2and 2.42 mmc)24.14 N/mm2and 1.42 mmd)34.14 N/mm2and 1.42 mmCorrect answer is option 'D'. Can you explain this answer?.
A beam 40mm wide, 80mm deep, is freely supported over a span of 2m. A weight of 50 N is dropped on to the middle of the beam from a height of 40mm. Calculate the maximum instantaneous stress and deflection. E=200 GPa.a)34.14 N/mm2and 2.42 mmb)24.14 N/mm2and 2.42 mmc)24.14 N/mm2and 1.42 mmd)34.14 N/mm2and 1.42 mmCorrect 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 40mm wide, 80mm deep, is freely supported over a span of 2m. A weight of 50 N is dropped on to the middle of the beam from a height of 40mm. Calculate the maximum instantaneous stress and deflection. E=200 GPa.a)34.14 N/mm2and 2.42 mmb)24.14 N/mm2and 2.42 mmc)24.14 N/mm2and 1.42 mmd)34.14 N/mm2and 1.42 mmCorrect 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 40mm wide, 80mm deep, is freely supported over a span of 2m. A weight of 50 N is dropped on to the middle of the beam from a height of 40mm. Calculate the maximum instantaneous stress and deflection. E=200 GPa.a)34.14 N/mm2and 2.42 mmb)24.14 N/mm2and 2.42 mmc)24.14 N/mm2and 1.42 mmd)34.14 N/mm2and 1.42 mmCorrect answer is option 'D'. Can you explain this answer?.
Solutions for A beam 40mm wide, 80mm deep, is freely supported over a span of 2m. A weight of 50 N is dropped on to the middle of the beam from a height of 40mm. Calculate the maximum instantaneous stress and deflection. E=200 GPa.a)34.14 N/mm2and 2.42 mmb)24.14 N/mm2and 2.42 mmc)24.14 N/mm2and 1.42 mmd)34.14 N/mm2and 1.42 mmCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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A beam 40mm wide, 80mm deep, is freely supported over a span of 2m. A weight of 50 N is dropped on to the middle of the beam from a height of 40mm. Calculate the maximum instantaneous stress and deflection. E=200 GPa.a)34.14 N/mm2and 2.42 mmb)24.14 N/mm2and 2.42 mmc)24.14 N/mm2and 1.42 mmd)34.14 N/mm2and 1.42 mmCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A beam 40mm wide, 80mm deep, is freely supported over a span of 2m. A weight of 50 N is dropped on to the middle of the beam from a height of 40mm. Calculate the maximum instantaneous stress and deflection. E=200 GPa.a)34.14 N/mm2and 2.42 mmb)24.14 N/mm2and 2.42 mmc)24.14 N/mm2and 1.42 mmd)34.14 N/mm2and 1.42 mmCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A beam 40mm wide, 80mm deep, is freely supported over a span of 2m. A weight of 50 N is dropped on to the middle of the beam from a height of 40mm. Calculate the maximum instantaneous stress and deflection. E=200 GPa.a)34.14 N/mm2and 2.42 mmb)24.14 N/mm2and 2.42 mmc)24.14 N/mm2and 1.42 mmd)34.14 N/mm2and 1.42 mmCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A beam 40mm wide, 80mm deep, is freely supported over a span of 2m. A weight of 50 N is dropped on to the middle of the beam from a height of 40mm. Calculate the maximum instantaneous stress and deflection. E=200 GPa.a)34.14 N/mm2and 2.42 mmb)24.14 N/mm2and 2.42 mmc)24.14 N/mm2and 1.42 mmd)34.14 N/mm2and 1.42 mmCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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