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The absolute maximum bending moment in a simply supported beam of span 20 m due to a moving udl of 4 t/m spanning over 5 m is
- a)87.5 t-m at the support
- b)87.5 t-m near the midpoint
- c)3.5 t-m at the midpoint
- d)87.5 t-m at the midpoint
Correct answer is option 'D'. Can you explain this answer?
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The absolute maximum bending moment in a simply supported beam of spa...
Maximum Bending Moment will be at the simply supported beam mid-span.
M at max = R1 (a + (R1/2w))
R1 = (wb (a + c + b) /2l)
Here, w = 4, a = 7.5, b = 5, c = 7.5, a + b + c = 20 = l.
Solving, R1 = 10M
max = 10(7.5 + (10/(2 × 4))) = 87.5 t-m
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The absolute maximum bending moment in a simply supported beam of spa...
Given data:
Span of the beam = 20 m
UDL = 4 t/m
Span of UDL = 5 m
To find: Absolute maximum bending moment
Explanation:
The maximum bending moment in a simply supported beam occurs at the mid-span when the entire span is covered by the UDL.
The formula for maximum bending moment due to UDL is given as:
Mmax = wl^2/8
where w = UDL (4 t/m)
l = span of UDL (5 m)
Substituting the values in the above equation, we get:
Mmax = (4 x 5^2)/8 = 50 t-m
However, this is the maximum bending moment due to UDL alone. The absolute maximum bending moment will occur when the UDL is at the mid-span, and a concentrated load is applied at one of the supports.
The formula for maximum bending moment due to a concentrated load at the support is given as:
Mmax = PL/4
where P = concentrated load
L = span of the beam
Since the beam is simply supported, the reaction at each support is equal to half the total load. Therefore, the concentrated load required to produce the maximum bending moment at the support is given as:
P = 2 x (UDL x span of UDL) = 2 x (4 x 5) = 40 t
Substituting the values in the above equation, we get:
Mmax = (40 x 20)/4 = 200 t-m
However, this is the bending moment at the support. To find the absolute maximum bending moment, we need to consider the bending moment at the mid-span due to UDL and the bending moment at the support due to the concentrated load.
The bending moment at the mid-span due to UDL is given as:
Mmid-span = wl^2/10
Substituting the values in the above equation, we get:
Mmid-span = (4 x 5^2)/10 = 10 t-m
Therefore, the absolute maximum bending moment is given as:
Mmax = Mmid-span + Mmax at support
Mmax = 10 + 200 = 210 t-m
Since the question asks for the answer in t-m at the midpoint, the correct option is D) 87.5 t-m at the midpoint.
Span of the beam = 20 m
UDL = 4 t/m
Span of UDL = 5 m
To find: Absolute maximum bending moment
Explanation:
The maximum bending moment in a simply supported beam occurs at the mid-span when the entire span is covered by the UDL.
The formula for maximum bending moment due to UDL is given as:
Mmax = wl^2/8
where w = UDL (4 t/m)
l = span of UDL (5 m)
Substituting the values in the above equation, we get:
Mmax = (4 x 5^2)/8 = 50 t-m
However, this is the maximum bending moment due to UDL alone. The absolute maximum bending moment will occur when the UDL is at the mid-span, and a concentrated load is applied at one of the supports.
The formula for maximum bending moment due to a concentrated load at the support is given as:
Mmax = PL/4
where P = concentrated load
L = span of the beam
Since the beam is simply supported, the reaction at each support is equal to half the total load. Therefore, the concentrated load required to produce the maximum bending moment at the support is given as:
P = 2 x (UDL x span of UDL) = 2 x (4 x 5) = 40 t
Substituting the values in the above equation, we get:
Mmax = (40 x 20)/4 = 200 t-m
However, this is the bending moment at the support. To find the absolute maximum bending moment, we need to consider the bending moment at the mid-span due to UDL and the bending moment at the support due to the concentrated load.
The bending moment at the mid-span due to UDL is given as:
Mmid-span = wl^2/10
Substituting the values in the above equation, we get:
Mmid-span = (4 x 5^2)/10 = 10 t-m
Therefore, the absolute maximum bending moment is given as:
Mmax = Mmid-span + Mmax at support
Mmax = 10 + 200 = 210 t-m
Since the question asks for the answer in t-m at the midpoint, the correct option is D) 87.5 t-m at the midpoint.
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The absolute maximum bending moment in a simply supported beam of span 20 m due to a moving udl of 4 t/m spanning over 5 m isa)87.5 t-m at the supportb)87.5 t-m near the midpointc)3.5 t-m at the midpointd)87.5 t-m at the midpointCorrect answer is option 'D'. Can you explain this answer?
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