005 Introduction To Elastic and Plastic Bending Moment Calculation

This video teaches us how to determine the elastic and plastic load for a rigid element connected to deformable bars. The example is an introduction to understanding how to determine the elastic and plastic bending moment of an Euler-Bernoulli cross-section. The example description is as follows: A rigid horizontal element with a length of 6a is supported by a hinge at its mid-span. A couple of P forces are expected to be applied at both ends of the rigid component. With the interval of a from both ends, the element is supported by 6 rods. Rods are made from an elastic, perfectly plastic material. The yield limit of the material is 250MPa, and the elasticity modulus is 200GPa. The rods are with a diameter of 25mm with a length of 500mm. Assume the material is homogenous and has similar behavior in tension and compression. Also, we can ignore the effect of buckling in this example.

1. Derive the compatibility equations.
2. Determine the minimum required force P that the first bar(s) would yield.
3. Determine the load P when the next bar(s) would yield.
4. Determine the load P when the entire system becomes plastic (When the structure becomes a mechanism.)
5. Sketch the Force P and its node displacement graph.

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