For a simply supported beam with a span L and a point load P at one end, what is

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Question: For a simply supported beam with a span L and a point load P at one end, what is the reaction at the support opposite to the load?

Options:

Correct Answer: P/2

Solution:

The reaction at the support opposite to the point load P at one end of a simply supported beam is R = P/2.

For a simply supported beam with a span L and a point load P at one end, what is the reaction at the support opposite to the load?

For a simply supported beam with a span L and a point load P at one end, what is the reaction at the support opposite to the load?

Step 1: Understand that a simply supported beam has two supports: one at each end.
Step 2: Identify the point load P, which is applied at one end of the beam.
Step 3: Recognize that the beam is in static equilibrium, meaning the total forces and moments must balance.
Step 4: Since the load P is at one end, the support at that end will have a reaction force that balances the load.
Step 5: The support opposite to the load will also have a reaction force, which we will call R.
Step 6: To find R, we can use the principle that the sum of the vertical forces must equal zero.
Step 7: Since there are only two vertical forces (the load P and the reaction R), we can set up the equation: R + P = 0.
Step 8: Rearranging this equation gives us R = P/2, meaning the reaction at the opposite support is half the load.

Static Equilibrium – Understanding how forces and moments balance in a simply supported beam.
Support Reactions – Calculating the reactions at supports due to applied loads.
Beam Analysis – Analyzing the effects of point loads on beam structures.