011 Structural Mechanism Part1 Determinate Beams

In this video, the definition of a determinate beam to become a mechanism is introduced. Three beams, two under point load and one under distributed load will be solved to determine the elastic and plastic loads.

Moreover, the length of the beam before becoming a mechanism will also be studied to determine the beam’s elastic and partially plastic length.

In the first two cases, the rectangular cross-section with a width of 60mm and height of 120mm made of an elastic perfectly plastic material with 𝑓𝑦 = 210𝑀𝑃𝑎 is assumed. For the third one, use only the 𝑀𝑒𝑙 and 𝑀𝑝𝑙 parametrically.

Dimensions are in mm unless otherwise specified.

For parts a) and b), determine the elastic and plastic load and then determine the length of the beam, which will be elastic when the load approaches the plastic load. In part c) determine the elastic and plastic load and determine which point will be plastic first.

1. A simple beam with the force P at its one-third distance from the left support.
2. A simple beam under distributed load q.
3. A two spans beam with a mechanical hinge in the middle of the right’s span, as shown below.

Link to the description and detailed solution notes: Download