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Homework Help: Elasto-plastic steel, axial loading

  1. Mar 20, 2010 #1
    in the following question, i am dealing with steel which is assumed to be have elasto-plactic behaviour,- its stress strain graph will be linear to the yield stress with a slope of "E" and then linear with a slope of zero.
    Capture.JPG

    i calculated and drew the P(delta) graphs for the 2 steel types and added them to get the displacement of point "c"

    untitled.jpg

    knowing that P=1080KN and looking for the maximum displacement of C, i went to the 3rd graph and said

    (1080-950)/(x-2.5)=(1140-950)/(3.5-2.5)

    ==> x=3.1842
    ===> x=0.31842mm

    which is correct,

    now looking for the permanent deflection of "c" i know that at x=0.31842mm mild steel will have plastic deformations but high strenght steel will not yet, so i went to the 1st graph and said
    (475)/(2.5)=(475)/(3.1842-x)
    ==> x=0.6842
    ===> x=0.06842mm

    but the correct answer is 0.0382mm which is half of the answer i got
    what am i doing wrong??

    then for the second part i need to find the maximum stress in each of the steel portions,
    for the mild steel i reached the plastic region- the maximum strenght, so as far as i can see the maximum stress felt in the mild steel is the stress corresponding to the 0.31842 displacement
    250MPA,
    which according to the question is the right answer

    for tyhe high strength steel i think the maximum stress wil be at the maximum deflection, but since this is before the yield stress,
    665/3.5=x/3.1842
    x=605KN
    x/A=318MPa

    but the correct answer is 818Mpa

    now i know p=1080KN
    P/A=568Mpa

    and using my answers 250+318=568MPa
    and using the correct answers 250-818=-568MPa

    so i know that i am in the right direction but dont know what to do,
    also how is it that the stress they found in the high strength steel is more than the yield stress?
     
  2. jcsd
  3. Mar 20, 2010 #2
    Can you explain the change of gradient in the graph for point C? Which parts are elastic, and which plastic?
     
  4. Mar 21, 2010 #3
    its not a stress strain curve- its a force displacement curve,
    the first part is totally elastic, the second part elastic(one steel is plastic one elastic) and the 3rd is totally plastic.
     
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