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The maximum positive bending moment in a fixed beam of span 8m and subjected to a central point load of 120 kN is (in kN-m)
- a)240
- b)120
- c)80
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The maximum positive bending moment in a fixed beam of span 8m and sub...
Bending moment at centre of the span
= (W×L)/4 ie (120 kn × 8 m )/4
= 240 kn-m.
Since the load acting in the middle of span. Hence the load will be equally distributed at both endsTherefore max bending moment in fixed beam
= 240 kn-m / 2= 120 kn-m .
Most Upvoted Answer
The maximum positive bending moment in a fixed beam of span 8m and sub...
Given data:
Span of the fixed beam = 8m
Central point load = 120kN
To find: Maximum positive bending moment in the beam
Solution:
1. Calculation of reaction forces:
As the beam is fixed, it can resist both vertical and horizontal forces. Hence, there will be three reaction forces at the supports: vertical reaction force (Rv) and two horizontal reaction forces (Rh) in opposite directions. By taking the moment about any point, we can calculate the reactions.
Taking moments about the left support:
∑M = 0
Rh × 8 = 120kN × 4
Rh = 60kN
Taking moments about the right support:
∑M = 0
Rv × 8 = 120kN × 4
Rv = 60kN
2. Calculation of bending moment:
As the load is at the center of the beam, the bending moment will be maximum at the center. The bending moment equation for a simply supported beam with a point load at the center is:
Mmax = WL/4
where W = load, L = span
Substituting the values,
Mmax = 120kN × 8m / 4
Mmax = 240kN-m
However, the beam is fixed, not simply supported. The bending moment equation for a fixed beam with a point load at the center is:
Mmax = WL/8
Substituting the values,
Mmax = 120kN × 8m / 8
Mmax = 120kN-m
Therefore, the maximum positive bending moment in the fixed beam is 120 kN-m.
Answer: Option (b) 120.
Span of the fixed beam = 8m
Central point load = 120kN
To find: Maximum positive bending moment in the beam
Solution:
1. Calculation of reaction forces:
As the beam is fixed, it can resist both vertical and horizontal forces. Hence, there will be three reaction forces at the supports: vertical reaction force (Rv) and two horizontal reaction forces (Rh) in opposite directions. By taking the moment about any point, we can calculate the reactions.
Taking moments about the left support:
∑M = 0
Rh × 8 = 120kN × 4
Rh = 60kN
Taking moments about the right support:
∑M = 0
Rv × 8 = 120kN × 4
Rv = 60kN
2. Calculation of bending moment:
As the load is at the center of the beam, the bending moment will be maximum at the center. The bending moment equation for a simply supported beam with a point load at the center is:
Mmax = WL/4
where W = load, L = span
Substituting the values,
Mmax = 120kN × 8m / 4
Mmax = 240kN-m
However, the beam is fixed, not simply supported. The bending moment equation for a fixed beam with a point load at the center is:
Mmax = WL/8
Substituting the values,
Mmax = 120kN × 8m / 8
Mmax = 120kN-m
Therefore, the maximum positive bending moment in the fixed beam is 120 kN-m.
Answer: Option (b) 120.
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The maximum positive bending moment in a fixed beam of span 8m and sub...
Bending moment at centre of the span = (W×L)/4 ie (120 kn × 8 m )/4 = 240 kn-m. Since the load acting in the middle of span. Hence the load will be equally distributed at both endsTherefore max bending moment in fixed beam = 240 kn-m / 2= 120 kn-m .
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