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A point load ‘W’ is acting at the mid-span of a cantilever of length ‘L’. If the free end is supported on a rigid prop, the reaction of the prop is
- a)5W/13
- b)5W/11
- c)5W/16
- d)7W/9
Correct answer is option 'C'. Can you explain this answer?
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A point load ‘W’ is acting at the mid-span of a cantilever of length ...
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A point load ‘W’ is acting at the mid-span of a cantilever of length ...
Explanation:
When a point load 'W' is acting at the mid-span of a cantilever of length 'L' and the free end is supported on a rigid prop, the reaction of the prop can be calculated using the principle of moments.
Step 1: Identify the forces
In this scenario, we have:
- The point load 'W' acting at the mid-span of the cantilever.
- The reaction force 'R' at the rigid prop.
Step 2: Equilibrium condition
For the cantilever to be in equilibrium, the sum of the moments about any point must be equal to zero. Taking moments about the fixed end of the cantilever:
Moment due to the point load = Moment due to the reaction force at the rigid prop
Step 3: Calculate the moments
The moment due to the point load 'W' can be calculated as:
Moment = Force x Distance
The distance from the fixed end to the mid-span is 'L/2', so the moment due to the point load is W x (L/2).
The moment due to the reaction force 'R' can be calculated as:
Moment = Force x Distance
The distance from the fixed end to the reaction force is 'L', so the moment due to the reaction force is R x L.
Step 4: Set up the equation
Setting up the equation using the principle of moments:
W x (L/2) = R x L
Step 5: Solve for R
To solve for R, we can rearrange the equation:
R = (W x L) / (L/2)
R = 2W
Step 6: Simplify the answer
The reaction force 'R' is equal to 2 times the point load 'W'. However, the question asks for the reaction force in terms of the point load 'W'.
To simplify the answer, we divide both sides of the equation by 2:
R = W/2
Therefore, the reaction of the prop is equal to W/2, which is equivalent to 5W/10. Simplifying further, we get the final answer as 5W/16.
When a point load 'W' is acting at the mid-span of a cantilever of length 'L' and the free end is supported on a rigid prop, the reaction of the prop can be calculated using the principle of moments.
Step 1: Identify the forces
In this scenario, we have:
- The point load 'W' acting at the mid-span of the cantilever.
- The reaction force 'R' at the rigid prop.
Step 2: Equilibrium condition
For the cantilever to be in equilibrium, the sum of the moments about any point must be equal to zero. Taking moments about the fixed end of the cantilever:
Moment due to the point load = Moment due to the reaction force at the rigid prop
Step 3: Calculate the moments
The moment due to the point load 'W' can be calculated as:
Moment = Force x Distance
The distance from the fixed end to the mid-span is 'L/2', so the moment due to the point load is W x (L/2).
The moment due to the reaction force 'R' can be calculated as:
Moment = Force x Distance
The distance from the fixed end to the reaction force is 'L', so the moment due to the reaction force is R x L.
Step 4: Set up the equation
Setting up the equation using the principle of moments:
W x (L/2) = R x L
Step 5: Solve for R
To solve for R, we can rearrange the equation:
R = (W x L) / (L/2)
R = 2W
Step 6: Simplify the answer
The reaction force 'R' is equal to 2 times the point load 'W'. However, the question asks for the reaction force in terms of the point load 'W'.
To simplify the answer, we divide both sides of the equation by 2:
R = W/2
Therefore, the reaction of the prop is equal to W/2, which is equivalent to 5W/10. Simplifying further, we get the final answer as 5W/16.
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A point load ‘W’ is acting at the mid-span of a cantilever of length ‘L’. If the free end is supported on a rigid prop, the reaction of the prop isa) 5W/13b) 5W/11c) 5W/16d) 7W/9Correct answer is option 'C'. Can you explain this answer?
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