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Calculating direct stress safety factor

  1. Jul 6, 2011 #1
    Hello Everyone,
    Below is a self assesment question I found in a study guide related direct and shear stress, it is in 2 parts. The guide only gives the answers. I managed part 1 but for part 2 my answer differs from the given safety factor solution of 7 mine is 12.5. In my attempt below i have tried to give a description of the approach I used.

    I would appreciate if someone could point out the error in my approach.

    Thanks in advance
    gpsza

    1. The problem statement, all variables and given/known data

    We have 2 steel rods connected using a clevis joint.
    Part 1. Determine maximum allowed force using given shear stress safety factor
    Part 2. Based on answer of part 1 determine the safety factor for the rods

    variables:
    pin diameter = 8 mm
    ultimate shear stress of pin material = 80 Mpa or Alternatively 80 N/(mm*mm)
    shear stress Safety Factor = 2

    rod material yield stress = 160 Mpa or Alternatively 160 N/(mm*mm)
    rod diameter = 20 mm


    2. Relevant equations

    Part 1:
    (working shear stress)=(Maximum Shear Stress)/(Safety Factor)
    Force = (shear stress)*(2*(Cross sectional area of pin))
    (Circle Area)=(pi*diameter*diameter)/4

    Part 2:
    (direct stress)=Force/Area
    (safety factor)=(Stress at Failure)/(Maximum Working Stress)

    3. The attempt at a solution

    Part 1:
    Calculate working stress:
    (working shear stress) = 80/2 = 40 Mpa or Alternatively 40 N/(mm*mm)

    Calculate force keeping in mind the need to double the area of the pin:
    Area = (pi*8*8)/4 = 50.2654824574 (mm*mm)
    2*Area = 100.5309649149 (mm*mm)
    Force = 40 * 100.5309649149 = 4021.2385965949 = 4.02 kN

    Part 2:
    Approach: use force calculated in part 1 to calculate the direct stress the rods would experience, use the direct stress and given yield stress to calculate the safety factor
    Area = (pi*20*20)/4 = 314.159265359 (mm*mm)
    (direct stress) = 4021.2385965949 / 314.159265359 = 12.8 Mpa
    (safety factor)=(Stress at Failure)/(Maximum Working Stress)
    (safety factor)= 160/12.8 = 12.5
     
  2. jcsd
  3. Jul 7, 2011 #2

    nvn

    User Avatar
    Science Advisor
    Homework Helper

    gpsza: Your answer currently looks correct, I think.

    By the way, the unit symbol for megapascal is spelled MPa, not Mpa. Only write MPa; do not write its derivation (N/mm^2) each time. Also, for exponentiation, write 8^2 or mm^3, not 8*8 nor mm*mm*mm. Also, usually do not list more than four to six decimal places for numerical values.
     
  4. Jul 8, 2011 #3
    Thank you nvn for your reponse to the question and the additional help it is really appreciated.

    gpsza
     
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