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Load Calculation Safely Supported

  1. Jul 13, 2012 #1
    1. The problem statement, all variables and given/known data

    A mild steel column has a cross section of 100mm by 50mm. Assuming a safety factor of 6 calculate the load that it can safely support.


    2. Relevant equations

    Column material: mild steel
    Column cross section: 100mm x 50mm
    Safety factor: 6

    On the basis that the tensile strength of steel is equivalent to its compressive strength and that there is no compressive stress value provided in the tables of my study module. I have used the average tensile stress value which is provided in my study material.
    ∴ Tensile stress of mild structural steel: 430 to 510 N/mm2
    ∴ Average tensile stress of mild structural steel: 470N/mm2

    Is this correct?

    3. The attempt at a solution

    Area = 100mm x 50mm = 5,000mm2

    σ = 470N/mm2 x 0.167 = 78.49N/mm2

    ∴ Load = Aσ

    ∴Load = 5,000mm2 x 78.49N/mm2 = 392,450N

    Therefore the safe load that the column can support is 392,450N.

    Is this correct, any help on this would be much appreciated.

    Thanks
     
  2. jcsd
  3. Jul 13, 2012 #2

    PhanthomJay

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    That is the safe load if the column is in tension or if it is 'short' in compression. Long columns in compression are governed by buckling strength which requires knowledge of its length to solve. Safe buckling loads for long slender
    columns are independent of
    the material yield or ultimate stress
     
  4. Jul 17, 2012 #3
    Hi PhanthomJay,

    Thanks for your reply.

    Considering your advice, is it as simple as follows then:

    P = AσK

    Where:
    P is safe working load - ?
    A is sectional area - 100mm x 50mm = 5000mm2
    σ is ultimate strength of material (mild steel) - 480N/mm2
    K is fraction - 1/6 or 0.167

    Therefore:

    P = 5000 x 480 x 0.167 = 400,800N or 400.8kN

    Can you confirm this is correct or am I missing something?

    Thanks in advance
     
  5. Jul 17, 2012 #4

    PhanthomJay

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    This is the safe load if the column is in tension (usually columns are in compression). This is also the safe load if the column is in compression but ONLY IF it is relatively 'fat and short'. If it is a long column, Euler Buckling may apply, that is, the allowable compressive load is (0.167) pi^2 E I /(kL)^2, where k is determined from the support conditions.. But since you do not state the value of L, the problem can't be solved unless you assume that the column is short enough so that buckling is not a factor.
     
  6. Jul 17, 2012 #5
    Hi again PhanthomJay,

    the question is this:
    "A mild steel column has a cross section of 100mm by 50mm. Assuming a safety factor of 6 calculate the load that it can safely support."

    So with this in mind, the length is not stated. So assuming buckling is not required in the answer to this question have I correctly answered it? Or do I need to look at anything else?

    Thanks again
     
  7. Jul 17, 2012 #6

    PhanthomJay

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    If buckling is not a factor, your answer is correct.....short solid steel rectangular sections have the same maximum compressive stress values as the max tensile stress, which you are assuming to be 480 MPa. Please round off your answer to 400 kN.
     
  8. Jul 17, 2012 #7
    Thank you very much PhanthomJay, your help is much appreciated!!
     
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