calculating bending stress

[ketanco]

Please see the simple drawing I attached. A 2 in diameter shaft is in Tension. The Tensile force is 10,000 lbf. The force line of action is 3" away from centerline of the shaft. The question asks the stress at point A.

So I know that we have two stresses at A, one is the tensile stress and one is the compressive stress due to bending.

I am confused about where to take the moment with respect to. And also when we calculate the bending stress, in the formula stress= M y / I I am confused about how to take the y. In the solution they took y as -3 inch. i dont understand where is this with respect to

And the answer is 3180 Tensile stress due to axial stress and the 38200 compressive stress due to bending. how did they calculate the compressive bending stress to that value.

 

[MA_PE]

no drawing attached.

 

[ketanco]

strange. i saw it as attached. anyway... let me describe

it is very simple

just a 2" diamater shaft and a 10000 lbf tensile force applied to the shaft, but not from its centerline, but 3" away from centerline, parallel to centerline. thats it. Point A is located at the face of the beam, in the opposite side of the tensile force, so it would be in compression

 

[captaincaution]

As you have used variables, y in this case should be 1 in, the distance from the centroid to the point you're calculating stress.

the 3 inches you are saying is y is being used to calculate the moment on the shaft about the centroid.

Take a look at your process again, and see if you get the correct result. I was able to get the results you stated.

 

[engrstructural11]

Late response, but there was a question in the sample ncees structural breadth that was similar in nature in which I disagree with the solution. When you resolve your moment into the shaft, the moment arm is the distance from the force to the neutral axis of the shaft. You then take P/A +/- Mc/I, c being from the neutral axis of the shaft to the point of interest (d/2 most likely).

In the NCEES solution, it was done incorrectly.