[Structural Mechanics] Conceptual Questions - Mechanisms & Plastic Analysis

[MarleyDH]

Homework Statement

Determine the failure mechanism and plastic moment for the following structure, using either the upper bound or lower bound theorem for plastic analysis.

Picture

(There is a physical hinge in the middle of the structure)

Homework Equations

Internal Work = External Work

Euler-Bernoulli Beam Theory

The Attempt at a Solution

The structure is a mechanism from the word go. My question is the conceptual question; namely, why?

Solving the structure via equilibrium confirms the problem, but its the concept that I can not grasp.

Any help would be appreciated.

 

[KataKoniK]

Thank you for your question. From the given picture, it appears that the structure is a cantilever beam with a physical hinge in the middle. In order to determine the failure mechanism and plastic moment, we can use the upper bound or lower bound theorem for plastic analysis.

The upper bound theorem states that the plastic moment is equal to the external moment that can be applied to the structure without causing failure. This means that if we apply a moment greater than the plastic moment, the structure will fail. On the other hand, the lower bound theorem states that the plastic moment is equal to the internal moment that can be developed in the structure without causing failure. This means that if the internal moment in the structure is greater than the plastic moment, the structure will fail.

In this case, since the structure has a physical hinge in the middle, it can be assumed that the failure mechanism will occur at this hinge. This means that the plastic moment will be equal to the moment applied at the hinge. To determine the plastic moment, we can use Euler-Bernoulli beam theory, which states that the maximum moment in a cantilever beam occurs at the fixed end and is equal to 3/2 times the applied moment.

Therefore, the failure mechanism for this structure will be the physical hinge in the middle, and the plastic moment will be equal to 3/2 times the moment applied at the hinge. I hope this helps to clarify the concept for you. If you have any further questions, please don't hesitate to ask.