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Quick stress calculation with one force on an I-Beam

  1. Mar 30, 2015 #1
    1. The problem statement, all variables and given/known data
    Determine the state of stress at point A on the cross section of the beam at section a−a. TakeP = 33kN .

    2. Relevant equations
    σ = My/I

    3. The attempt at a solution
    Moment = Fd = 33000N(500mm) = 165000000
    Y = 90.71 (100-9.29, 9.29 being the Ybar of the little piece)
    I = 22926666.67 (used on Part B and was correct)
     

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  3. Mar 31, 2015 #2

    SteamKing

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    It's not clear what the "little piece" means. In any event, the I-beam has two axes of symmetry, so the location of its centroid can be found by inspection.

    The beam will have shear stress and bending stress created at section a-a. You should solve this beam to find the support reactions at the ends and use these reactions to create the shear force and bending moment diagrams. The value of the moment you have calculated is not the correct bending moment for this problem.

    For calculating the shear stress at point A, you should show your calculation of the first moment Q of the area of the beam above point A.

    Since this beam is 200 mm deep in total and point A is located 50 mm below the topmost fiber, y measured from the centroid of the beam can be found by simple subtraction.
     
  4. Mar 31, 2015 #3
    I'm just looking for the normal here. My big question is did I calculate Y right (the beam has a height of 200, so it's center is at 100, 100-9.29 where the "A" Ybar is is how I got 90.71. And moment I did . . . as shown up above . . .
     
  5. Mar 31, 2015 #4

    SteamKing

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    Are you looking only for the bending stress? The problem statement asks for the state of stress at point A.

    For σ = My / I, the y value is a simple measurement from the centroid of the beam to point A. It is not a y-bar.

    Since the centroid of the entire beam is located 100 mm below the top fiber, and point A is located 50 mm below the top fiber, y is just the difference between these two distances. It's not clear what 9.29 represents, but it's not what you need to calculate the bending stress of this beam.

    You should solve this beam to find the support reactions at the ends and use these reactions to create the shear force and bending moment diagrams. The value of the moment you have calculated is not the correct bending moment for this problem.
     
  6. Mar 31, 2015 #5
    Yeah, I already have the other stress.

    So I have to solve the moment diagram to find M, Y is just 50mm (where "A" is located), and then divide?
     
  7. Apr 1, 2015 #6

    SteamKing

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    Divide by I for the I-beam cross section to find σ, yes.
     
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