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A simply supported beam 8000mm in span is subjected to u.d.l 3000N/m on the entire span.
Estimate the maximum deflection and slopes at supports. Assume EI = 2 × 105 kN-m2
- a)0.8 mm, 0.00032 rad
- b)0.9 mm, 0.00032 rad
- c)1.0 mm, 0.00032 rad
- d)1.1 mm, 0.00032 rad
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A simply supported beam 8000mm in span is subjected to u.d.l 3000N/m ...
W = 3 KN/m, L = 8 m, EI = 2 × 105 KN-m2
= 8 x 10-4 m = 0.8 mm
= 3.2 x 10-4 rad
= 0.00032 radFree Test
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Community Answer
A simply supported beam 8000mm in span is subjected to u.d.l 3000N/m ...
To find the maximum deflection and slopes at the supports of a simply supported beam subjected to a uniformly distributed load (UDL), we can use the formula for the deflection of a beam under UDL.
We are given the following information:
- Span of the beam (L) = 8000 mm
- UDL (w) = 3000 N/m
- EI (flexural rigidity) = 2 × 10^5 kN-m^2
Let's calculate the maximum deflection and slopes at the supports using the following steps:
1. Calculate the reaction forces at the supports:
The total load on the beam (W) can be calculated as:
W = w * L
W = 3000 N/m * 8000 mm = 24,000,000 N-mm
Since the beam is simply supported, the reaction forces at the supports will be half of the total load:
R1 = R2 = W/2 = 24,000,000 N-mm / 2 = 12,000,000 N-mm
2. Calculate the maximum deflection (δ_max):
The maximum deflection occurs at the center of the beam, where x = L/2.
The formula for the deflection of a simply supported beam under UDL is given by:
δ_max = (5 * w * L^4) / (384 * EI)
Substituting the given values:
δ_max = (5 * 3000 N/m * (8000 mm)^4) / (384 * 2 × 10^5 kN-m^2)
δ_max = 0.8 mm
3. Calculate the slopes at the supports (θ1 and θ2):
The slopes at the supports can be calculated using the formula:
θ1 = θ2 = (w * L^3) / (24 * EI)
Substituting the given values:
θ1 = θ2 = (3000 N/m * (8000 mm)^3) / (24 * 2 × 10^5 kN-m^2)
θ1 = θ2 = 0.00032 rad
Therefore, the correct answer is option 'A': 0.8 mm, 0.00032 rad.
We are given the following information:
- Span of the beam (L) = 8000 mm
- UDL (w) = 3000 N/m
- EI (flexural rigidity) = 2 × 10^5 kN-m^2
Let's calculate the maximum deflection and slopes at the supports using the following steps:
1. Calculate the reaction forces at the supports:
The total load on the beam (W) can be calculated as:
W = w * L
W = 3000 N/m * 8000 mm = 24,000,000 N-mm
Since the beam is simply supported, the reaction forces at the supports will be half of the total load:
R1 = R2 = W/2 = 24,000,000 N-mm / 2 = 12,000,000 N-mm
2. Calculate the maximum deflection (δ_max):
The maximum deflection occurs at the center of the beam, where x = L/2.
The formula for the deflection of a simply supported beam under UDL is given by:
δ_max = (5 * w * L^4) / (384 * EI)
Substituting the given values:
δ_max = (5 * 3000 N/m * (8000 mm)^4) / (384 * 2 × 10^5 kN-m^2)
δ_max = 0.8 mm
3. Calculate the slopes at the supports (θ1 and θ2):
The slopes at the supports can be calculated using the formula:
θ1 = θ2 = (w * L^3) / (24 * EI)
Substituting the given values:
θ1 = θ2 = (3000 N/m * (8000 mm)^3) / (24 * 2 × 10^5 kN-m^2)
θ1 = θ2 = 0.00032 rad
Therefore, the correct answer is option 'A': 0.8 mm, 0.00032 rad.
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A simply supported beam 8000mm in span is subjected to u.d.l 3000N/m on the entire span.Estimate the maximum deflection and slopes at supports. Assume EI = 2 × 105 kN-m2a)0.8 mm, 0.00032 radb)0.9 mm, 0.00032 radc)1.0 mm, 0.00032 radd)1.1 mm, 0.00032 radCorrect answer is option 'A'. 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 simply supported beam 8000mm in span is subjected to u.d.l 3000N/m on the entire span.Estimate the maximum deflection and slopes at supports. Assume EI = 2 × 105 kN-m2a)0.8 mm, 0.00032 radb)0.9 mm, 0.00032 radc)1.0 mm, 0.00032 radd)1.1 mm, 0.00032 radCorrect answer is option 'A'. 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 simply supported beam 8000mm in span is subjected to u.d.l 3000N/m on the entire span.Estimate the maximum deflection and slopes at supports. Assume EI = 2 × 105 kN-m2a)0.8 mm, 0.00032 radb)0.9 mm, 0.00032 radc)1.0 mm, 0.00032 radd)1.1 mm, 0.00032 radCorrect answer is option 'A'. Can you explain this answer?.
A simply supported beam 8000mm in span is subjected to u.d.l 3000N/m on the entire span.Estimate the maximum deflection and slopes at supports. Assume EI = 2 × 105 kN-m2a)0.8 mm, 0.00032 radb)0.9 mm, 0.00032 radc)1.0 mm, 0.00032 radd)1.1 mm, 0.00032 radCorrect answer is option 'A'. 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 simply supported beam 8000mm in span is subjected to u.d.l 3000N/m on the entire span.Estimate the maximum deflection and slopes at supports. Assume EI = 2 × 105 kN-m2a)0.8 mm, 0.00032 radb)0.9 mm, 0.00032 radc)1.0 mm, 0.00032 radd)1.1 mm, 0.00032 radCorrect answer is option 'A'. 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 simply supported beam 8000mm in span is subjected to u.d.l 3000N/m on the entire span.Estimate the maximum deflection and slopes at supports. Assume EI = 2 × 105 kN-m2a)0.8 mm, 0.00032 radb)0.9 mm, 0.00032 radc)1.0 mm, 0.00032 radd)1.1 mm, 0.00032 radCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A simply supported beam 8000mm in span is subjected to u.d.l 3000N/m on the entire span.Estimate the maximum deflection and slopes at supports. Assume EI = 2 × 105 kN-m2a)0.8 mm, 0.00032 radb)0.9 mm, 0.00032 radc)1.0 mm, 0.00032 radd)1.1 mm, 0.00032 radCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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