Can the Plastic Moment be smaller than Elastic Moment?

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SUMMARY

The discussion centers on the comparison between the maximum elastic moment and the maximum plastic moment for an I-beam subjected to a stress of 320 MPa. The calculated values indicate that the plastic moment (S = 191868.75) is smaller than the elastic moment (Zx = 266501.107), which raises questions about the accuracy of the calculations. Key errors identified include the calculation of the section modulus for the non-symmetric beam and the centroid distance for the plastic neutral axis. These discrepancies lead to the conclusion that the plastic moment can indeed be smaller than the elastic moment under specific conditions.

PREREQUISITES
  • Understanding of beam mechanics and section properties
  • Familiarity with stress-strain relationships in materials
  • Knowledge of calculating section moduli (S and Z) for I-beams
  • Ability to determine the location of the neutral axis in non-symmetric sections
NEXT STEPS
  • Review the calculation methods for section moduli in non-symmetric I-beams
  • Learn about the implications of the neutral axis location on moment capacity
  • Study the differences between elastic and plastic behavior in structural materials
  • Explore advanced beam analysis techniques, including software tools for structural analysis
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in beam design and analysis will benefit from this discussion, particularly those focusing on moment capacity and structural integrity of I-beams.

CallumTheMan
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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

Homework Equations


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.
 
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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

Homework Equations


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.