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Finding the width of a bar

  1. Oct 4, 2016 #1
    1. The problem statement, all variables and given/known data
    There are 4 axial forces that are applied to 25mm thick structural steel bar with 40mm diameter . If the maximum allowable tensile stress in the bar is 135MPa and the maximum allowable deformation (extension or contraction) of bar is 1.25mm , determine the minimum width , w of the bar , E = 200GPa


    2. Relevant equations


    3. The attempt at a solution

    i have divided the bar into 3 sections , namely AB , BC and also CD. For part AB, the force acting on it 90kN tensile force , for BC , the force acting on it is 50kN compressive force , for CD, the force acting is 220kN tensile force. )


    We know that δ(defomation ) = PL / AE , where P - force , L = length of bar , A = area

    so i let 1.25x10^-3 = ((90x10^3)(250x10^-3) - (50x10^3)(500x10^-3) + (220x10^3)(750x10^-3) / (25x10^-3 x w x 200x10^9) , so w = 26mm ,

    but the ans given is w = 65 mm , which part of my working is wrong ?
     

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    Last edited by a moderator: Oct 4, 2016
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  3. Oct 4, 2016 #2

    PhanthomJay

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    Deformation analysis looks good, but did you check this wording from the problem statement "... the maximum allowable tensile stress in the bar is 135MPa..."?
     
    Last edited by a moderator: Oct 4, 2016
  4. Oct 4, 2016 #3
    So how should I proceed?
     
  5. Oct 4, 2016 #4
    ok , when using force = 220kPa , i found that w = 65.2mm, but when i use P = 50kN , w = 14.8mm , when using P = 90kPa , my t = 24mm , why is it so ?

    if so , then it's maximum t , right ?
     
    Last edited: Oct 4, 2016
  6. Oct 4, 2016 #5

    PhanthomJay

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    yes, since the bar is uniform in dimensions, the higher number controls for stress.
     
  7. Oct 4, 2016 #6
    Just to double check, the 65.2mm is the maximum t, not minimum t, am I right?
     
  8. Oct 4, 2016 #7

    PhanthomJay

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    I may not have responded clearly. The 65 mm thickness is the minimum t required such that no point in the bar is stressed beyond the max allowed stress of 135 MPa. The stress in the left and mid sections will be less, as the right section with the higher load, and hence higher stress, controls the design.
     
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