# Can the Plastic Moment be smaller than Elastic Moment?

• CallumTheMan
In summary, the conversation discusses the calculation of maximum moments for a beam and compares the increase between elastic and plastic moments. The beam is an I beam with specific dimensions and the homework equations are given. The attempt at a solution includes the calculation of section moduli and distances, with two errors found in the calculation of the elastic section modulus and the distance of the centroid for the plastic section modulus. The locations of the elastic and plastic neutral axes and the moment of inertia are correct.
CallumTheMan

## Homework Statement

Stress = 320 MPa
Max Elastic Moment = Stress*Z
Max Plastic Moment = Stress*S
Solve the maximum moments and compare the % increase

Beam is an I beam with dimensions: (b and d)
Top Flange = 25*10
web = 10*180
Bottom Flange = 200*8

see above

## The Attempt at a Solution

Ybar elastic = 63.3mm
Ybay plas = 30.5mm

Ix=1.687*10^7

Zx = 266501.107
S = 191868.75

S is lower than Zx and this makes the plastic M smaller than M elastic. How is that possible?

S= (25*10*162.5)+(10*157.5*67.5)+(22.5*10*11.25)+(200*8*26.5) this is the only value I had to manually generate without computer aid so there must be an error here?
Can't seem to find out what's going wrong.

CallumTheMan said:

## Homework Statement

Stress = 320 MPa
Max Elastic Moment = Stress*Z
Max Plastic Moment = Stress*S
Solve the maximum moments and compare the % increase

Beam is an I beam with dimensions: (b and d)
Top Flange = 25*10
web = 10*180
Bottom Flange = 200*8

see above

## The Attempt at a Solution

Ybar elastic = 63.3mm
Ybay plas = 30.5mm

Ix=1.687*10^7

Zx = 266501.107
S = 191868.75

S is lower than Zx and this makes the plastic M smaller than M elastic. How is that possible?

S= (25*10*162.5)+(10*157.5*67.5)+(22.5*10*11.25)+(200*8*26.5) this is the only value I had to manually generate without computer aid so there must be an error here?
Can't seem to find out what's going wrong.
You've actually got two errors here.

1. In the elastic regime, there are two section moduli for this beam, and you have calculated the greater SM of the two. Since this section is not symmetric about a horizontal axis, can you figure out the other SM for this beam?
2. In the calculation of the plastic SM, check the distance of the centroid of the upper web piece located above the plastic NA. I think there is a mistake here.
3. The location of the elastic NA, the plastic NA, and the MOI all check out.

## 1. Can the Plastic Moment be smaller than Elastic Moment?

The simple answer is yes, it is possible for the plastic moment to be smaller than the elastic moment. This occurs when the material being tested has not reached its yield point and therefore has not begun to exhibit plastic behavior.

## 2. What is the difference between Plastic Moment and Elastic Moment?

The plastic moment is the point at which a material undergoes irreversible deformation, while the elastic moment is the point at which the material begins to deform elastically. In other words, the plastic moment is the maximum amount of deformation a material can sustain before breaking, while the elastic moment is the point at which the material starts to change shape but can return to its original form when the load is removed.

## 3. Is it possible for the Plastic Moment to be greater than Elastic Moment?

Yes, it is possible for the plastic moment to be greater than the elastic moment. This occurs when a material is loaded beyond its elastic limit and begins to exhibit plastic behavior. In this case, the plastic moment will be greater than the elastic moment as the material can sustain more deformation before breaking.

## 4. What factors can affect the difference between Plastic Moment and Elastic Moment?

The difference between the plastic moment and elastic moment can depend on various factors such as the type of material, its physical properties, and the load being applied. For example, a material with high ductility will have a larger difference between the two moments compared to a more brittle material.

## 5. How is the Plastic Moment determined in a material?

The plastic moment in a material can be determined through experimentation and analysis. This involves subjecting the material to increasing loads until it reaches its yield point and exhibits plastic behavior. The maximum load and corresponding deformation at this point can be used to calculate the plastic moment of the material.