# Beam/column sizing

If a load P is applied as shown to a fixed column-beam, pinned at the bottom, should the beam or column (or both) sizes be increased to resist the load?

Assuming your beam-column connections are fixed and column- support connections pinned and the length of the columns L and the length of the beam S and lateral load p:

The frame will deflect to the left a little and the two joints will rotate counterclockwise a bit.

Due to symmetry at equilibrium, the two columns have to support a moment of (1/2p)/L and an axial load of $$\frac{p*L}{S } \$$ which is the support reactions acting tensile in the right column and compressive in the left column.

The beam acts as a beam with an axial load of p/2 and moment of the end joints transferred by the columns of (1/2p)/L at each end.

• can you please explain how the math relates to sizing of the beam and column? – San Aug 27 at 1:58
• Sure. I will do it tomorrow. – kamran Aug 27 at 2:10

Yes, the three elements must be at least analyzed to determine if a size increment is required. The left column will be subjected to a bending action induced by P thus increasing the requirements on is stifness.

At the same time the beam element will be subjected to not proper bending but axial compression that might result in an unstable behaviour, the Euler load for the given links and beam should be evaluated. This is even more a problem as the right column will bend too causing also it to need resizing after load P is introduced.

• So...the columns need to get bigger but the beam can remain because it's only subjected to axial compression? I would have thought both the beam and columns need to be bigger b/c they are rigidly connected? – San Aug 27 at 17:47
• All the three elemens must be analyzed, can't say if they need to be bigger without any number, engineering comes with numbers, without numbers everyting may be good. In principle the columns are those that will likely need resizing as Euler load is often quite high and won't be a problem in most application meaning the beam won't need any resizing. – Alberto Brambilla Aug 27 at 21:07
• Yes, I understand the needs of number but I'm just trying to understand the basic concept/formula/logic. And whether type of connection will play a part as well. – San Aug 28 at 1:23