# determining the stress of a beam

I have a question regarding a beam. I first consider a force applied to both ends of a rectangular beam which is perpendicular to its cross section with dimensions w (width) and h (height). The length of the beam (l) is parallel to the applied force (F).

If I wanted to find an expression for the stress, my guess would be:

$$\sigma = F/A = \frac{F}{wh}$$

But since the force is applied to both ends, should it say be, 2F? Not sure how to account for the fact that the force is being applied from both ends.

• The answer is $F/A$ not $2F/A$. – lemon Mar 28 '16 at 20:55
• Regarding your follow-up question below: how exactly is the force being applied along a direction other than the length of the column? – lemon Mar 28 '16 at 20:58
• @lemon Basically I am suppose to assume that the force is parallel to the [111] direction, and re-calculate stress and strain values. I think I might have to use moments, but I am not 100% sure. – Jackson Hart Mar 28 '16 at 21:17

## 1 Answer

If I got it right, you probably mean the stress on a column - not a beam - caused by an axial load $F$. In that case your guess $F/A$ about the stress is right, otherwise the column should be moving!

• Thanks! May I ask a follow-up question? What if the force were parallel to the [111] direction instead of parallel to the length? How could I calculate say stress and strain in that case? – Jackson Hart Mar 28 '16 at 20:45
• First of all I would like to point out that a beam can also be under clear stress lets say compression but its not usual in structures. Now if the applied force is perpendicular to the beam or post axis then we have combined shear stresses among with compression and tension due to moments. We can have clear shear stress though in special occasions. – user98038 Mar 28 '16 at 21:00
• @aK1974 I realize that moments would play a role, but how would I actually begin working this problem out? It does not seem trivial considering the [111] direction – Jackson Hart Mar 28 '16 at 21:16
• @Jackson Hart: You can find some useful information here:en.m.wikipedia.org/wiki/Bending – user98038 Mar 28 '16 at 21:24