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Can the Plastic Moment be smaller than Elastic Moment?

  1. May 20, 2015 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations
    see above

    3. 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 whats going wrong.
     
  2. jcsd
  3. May 20, 2015 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    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.
     
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