006 Elastic And Plastic Bending Moment

In the other Video, we derived the relationship between the strain and curvature of a beam under bending moment. Also, in the former Video, we derived from calculating Elastic and Plastic load for a rigid bar supported by several deformable bars.

In this example, we will learn how the elastic axial stress in a beam is determined and the axial stress due to bending distribution. Moreover, the elastic section modulus is introduced. The fully plastic behavior of a cross-section is reviewed with two examples. In the end, a symmetrical I-Beam is studied in terms of elastic bending moment, plastic bending moment, and partial bending moment calculation. The descriptions of the questions in the Video are as follows:

1. Determine a rectangle beam’s elastic and plastic section modulus, b as width and height.
2. If 𝑏=120𝑚𝑚 and ℎ=200𝑚𝑚 determine the elastic and plastic bending moment.
3. If the bending moment applied to the cross-section is 250𝑘𝑁.𝑚, what is the plastic depth of the rectangular section?
4. Determine the elastic and plastic section modulus for the given I-Beam section.
5. For the I-Beam, determine the elastic and plastic moment.
6. Determine the required bending moment so that only flanges become plastic.
7. If the applied bending moment is 180𝑘𝑁.𝑚, what is the plastic depth of the cross-section?

Assume the material is elastic and perfectly plastic with a yield stress of 250𝑀𝑃𝑎.

Link to the description and detailed solution notes: Downoad