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If a beam simply supported at its two ends is loaded by a point load at the middle
of the span, the maximum bending moment is M. If the same load is equally distributed over the
beam span, then the maximum bending moment, neglecting the weight of beam will be
(a) M/2 (b) M () M/3 (d) M/4?
of the span, the maximum bending moment is M. If the same load is equally distributed over the
beam span, then the maximum bending moment, neglecting the weight of beam will be
(a) M/2 (b) M () M/3 (d) M/4?
Most Upvoted Answer
If a beam simply supported at its two ends is loaded by a point load a...
**Solution:**
To determine the maximum bending moment in a beam, we can use the equation:
**M = (wL^2)/8**
Where:
M = maximum bending moment
w = load applied to the beam
L = span of the beam
In the given scenario, we have a beam that is simply supported at its two ends and loaded by a point load at the middle of the span. Let's consider the load applied to the beam as P.
**Case 1: Point load at the middle of the span**
In this case, the load is concentrated at the middle of the beam. Therefore, we can consider the load as a point load P.
Using the bending moment equation, we can determine the maximum bending moment:
**M = (PL^2)/8**
**Case 2: Load equally distributed over the beam span**
In this case, the load is distributed equally over the entire span of the beam. Therefore, the load per unit length can be considered as P/L.
Using the bending moment equation, we can determine the maximum bending moment:
**M = ((P/L)L^2)/8**
= (PL)/8
Comparing the maximum bending moments in both cases:
**M (Case 1) = (PL^2)/8**
**M (Case 2) = (PL)/8**
We can see that the maximum bending moment in Case 2 is half of the maximum bending moment in Case 1. Therefore, the correct answer is (a) M/2.
**Conclusion:**
When a beam is simply supported at its two ends and loaded by a point load at the middle of the span, the maximum bending moment is given by M = (PL^2)/8. However, if the same load is equally distributed over the beam span, the maximum bending moment is half of the point load scenario, given by M = (PL)/8.
To determine the maximum bending moment in a beam, we can use the equation:
**M = (wL^2)/8**
Where:
M = maximum bending moment
w = load applied to the beam
L = span of the beam
In the given scenario, we have a beam that is simply supported at its two ends and loaded by a point load at the middle of the span. Let's consider the load applied to the beam as P.
**Case 1: Point load at the middle of the span**
In this case, the load is concentrated at the middle of the beam. Therefore, we can consider the load as a point load P.
Using the bending moment equation, we can determine the maximum bending moment:
**M = (PL^2)/8**
**Case 2: Load equally distributed over the beam span**
In this case, the load is distributed equally over the entire span of the beam. Therefore, the load per unit length can be considered as P/L.
Using the bending moment equation, we can determine the maximum bending moment:
**M = ((P/L)L^2)/8**
= (PL)/8
Comparing the maximum bending moments in both cases:
**M (Case 1) = (PL^2)/8**
**M (Case 2) = (PL)/8**
We can see that the maximum bending moment in Case 2 is half of the maximum bending moment in Case 1. Therefore, the correct answer is (a) M/2.
**Conclusion:**
When a beam is simply supported at its two ends and loaded by a point load at the middle of the span, the maximum bending moment is given by M = (PL^2)/8. However, if the same load is equally distributed over the beam span, the maximum bending moment is half of the point load scenario, given by M = (PL)/8.
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If a beam simply supported at its two ends is loaded by a point load at the middleof the span, the maximum bending moment is M. If the same load is equally distributed over thebeam span, then the maximum bending moment, neglecting the weight of beam will be (a) M/2 (b) M () M/3 (d) M/4?
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If a beam simply supported at its two ends is loaded by a point load at the middleof the span, the maximum bending moment is M. If the same load is equally distributed over thebeam span, then the maximum bending moment, neglecting the weight of beam will be (a) M/2 (b) M () M/3 (d) M/4? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If a beam simply supported at its two ends is loaded by a point load at the middleof the span, the maximum bending moment is M. If the same load is equally distributed over thebeam span, then the maximum bending moment, neglecting the weight of beam will be (a) M/2 (b) M () M/3 (d) M/4? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a beam simply supported at its two ends is loaded by a point load at the middleof the span, the maximum bending moment is M. If the same load is equally distributed over thebeam span, then the maximum bending moment, neglecting the weight of beam will be (a) M/2 (b) M () M/3 (d) M/4?.
If a beam simply supported at its two ends is loaded by a point load at the middleof the span, the maximum bending moment is M. If the same load is equally distributed over thebeam span, then the maximum bending moment, neglecting the weight of beam will be (a) M/2 (b) M () M/3 (d) M/4? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If a beam simply supported at its two ends is loaded by a point load at the middleof the span, the maximum bending moment is M. If the same load is equally distributed over thebeam span, then the maximum bending moment, neglecting the weight of beam will be (a) M/2 (b) M () M/3 (d) M/4? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a beam simply supported at its two ends is loaded by a point load at the middleof the span, the maximum bending moment is M. If the same load is equally distributed over thebeam span, then the maximum bending moment, neglecting the weight of beam will be (a) M/2 (b) M () M/3 (d) M/4?.
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