What is the shear force at the support of a simply supported beam with a point load at the center?

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Q: What is the shear force at the support of a simply supported beam with a point load at the center?

Solution: The shear force (V) at the supports of a simply supported beam with a point load (P) at the center is V = P/2.

Steps: 6

Step 1: Understand the setup. You have a simply supported beam, which means it is supported at both ends and can freely rotate.
Step 2: Identify the point load. In this case, there is a point load (P) applied at the center of the beam.
Step 3: Recognize that the beam is in static equilibrium. This means that the total forces and moments acting on the beam must balance out.
Step 4: Since the load is at the center, it will create equal reactions at both supports. This is because the beam is symmetrical.
Step 5: Calculate the reaction forces at the supports. The total load (P) is shared equally between the two supports, so each support will have a reaction force of P/2.
Step 6: Conclude that the shear force (V) at each support is equal to the reaction force, which is V = P/2.