A structural engineer is designing a tire swing for some new playground equipment. For the design to be successful, the material used for the swing beam must be capable of withstanding the internal loads generated by the swing and its occupant.

What is known:

The beam length L is 8 ft.

The tire is connected at the mid-span of the beam.

The design load, F, for the swing is 300 lb.

Question

Force Diagram

What are the internal loads present in the beam at a location just to the left of the swing when the design load is applied? Assume the beam to be a pinned-roller configuration.

Approach

Solve for the external reactions.

Cut the beam at the point of interest to reveal the internal loads as equivalent external loads.

Form a free-body diagram with the appropriate sign convention for the two pieces.

Solve for the internal loads on either diagram.

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