- #1
Northbysouth
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- 2
Homework Statement
Two vertical forces are applied to a beam of the cross section shown. Determine the maximum tensile and compressive stresses in portion BC of the beam
I have attached an image of the question
Homework Equations
σ = P/A +/- My/Ix
Ix = Ix + Ad2 ---> parallel axis theorem
The Attempt at a Solution
I calculated the centroid to be:
x = 4.5 in
y = 3 in
I did this by dividing the shape into two rectangles, determining the centers of those rectangles from an arbitrarily assigned origin, O, which I assigned to be at the bottom left of the lower rectangle.
I then used the parallel axis theorem to calculate the Inertia, Ix
P = 0 because the sum of the forces is 0.
M is the greatest moment value, which I found to be 600 kip-in.
My confusion is how do I determine the y value? I believe that the greatest tensile and compressive stresses would be at the bottom and top of the bar respectively, but my notes indicate that the correct y-values are 3 in for the tensile stress and 5 in for the compressive stress. I had thought that the y values was from the centroid of the cross-section which makes me think it should be 3 in for the max compressive and tensile forces.
Can anyone clarify this for me?
I know the final answers are
8.82 ksi T
14.72 ksi C
