Finding the stress of a rigid beam

[ethan118]

The question is simple.

i want to find the stress of a rectangular beam freely supported at both ends. A load F is acting in the middle.

I know that stress = moment / inertia

also inertia = (b h ^3 ) / 12

 

[Dr.D]

I think you have your equation wrong. I think what you want is
sigma = M*c/I
so, figure out M, c, and I and go to it.

 

[ethan118]

can you explain please how to proceed with that. i have been struggling for days

 

[ethan118]

i know that both sides there are 2 vertical forces acting upwards F/2

 

[mathmate]

You'd have to find out the maximum moment which is at the middle, by multiplying either reaction by the half-span (distance from end to middle).

As Dr. D said, the maximum (bending) stress is My/I.
M has already been determined above, you'd need to determine for the beam cross section
y = distance between the neutral axis and the distance at which stress is required (usually top or bottom edge)
I = second moment of area.

You only have to do a little google search to find out how these quantities are calculated, if you missed your class and do not have a textbook on Strength of Materials.

 

[ethan118]

if the length is L and the load is at the middle.

The moment, M is L/2 x F /2 ?

is y also L/2 ?

 

[Dr.D]

Look at what mathmate said about y. The neutral axis is a horizontal line (for a horizontal beam). Do you want the bending stress at a point L/2 above the neutral axis, which in this case is the midplane?

 

[srvs]

The maximum moment and hence highest stress is indeed situated at x = L/2, however the flexure formula above is used to calculate the stress distribution within a certain cross-section, as such the y is a coordinate within this cross-section. It has nothing to do with the dimensions of the beam itself. The distribution will look like this:

http://en.wikivisual.com/images/3/3a/Internal_Forces_and_Stresses_from_Bending.png

If your goal is to calculate the maximum stresses then the above equation may be used whereby y is the largest distance from the neutral axis (as already stated), and would in this case be h/2.