Plastic Section Modulus for Rectangular Section

Plastic section modulus is used to calculate the bending capacity of a cross-section of a structural member. In the case of a rectangular section, the plastic section modulus is given by:

Zp = bd2/4

where b is the width of the section and d is the depth of the section.

Explanation of the Formula

To understand the formula for plastic section modulus of a rectangular section, let's consider a beam that is subject to bending. When a beam is subjected to bending, the top and bottom fibers of the beam are in compression and tension, respectively. At some point, the stress in the extreme fibers reaches the yield strength of the material, and plastic deformation begins to occur.

The plastic section modulus is a measure of the ability of a cross-section to resist plastic deformation. It is defined as the ratio of the moment of inertia of the cross-section to the distance from the extreme fiber to the neutral axis. For a rectangular section, the distance from the extreme fiber to the neutral axis is equal to half the depth of the section, i.e., d/2.

The moment of inertia of a rectangular section is given by:

I = bd3/12

Substituting this expression into the formula for plastic section modulus gives:

Zp = I/(d/2) = bd3/12/(d/2) = bd2/4

Therefore, the plastic section modulus for a rectangular section of width b and depth d is given by:

Zp = bd2/4

Conclusion

The plastic section modulus for a rectangular section is an important parameter in the design of structural members. The formula for plastic section modulus of a rectangular section is derived based on the moment of inertia of the section and the distance from the extreme fiber to the neutral axis. The plastic section modulus is a measure of the ability of a cross-section to resist plastic deformation and is used to calculate the bending capacity of a structural member.