Loaded beam in compression? (buckles?)

aortucre

Hey guys, I know this is a simple question but I'm not really sure how to do it.

Let's say we have a beam supported by two pins at both extremes.
There is a central load on the beam, so it will deflect in the direction of the load.
But we also have an axial force compressing the beam.

My question is how do we calculate the beam's deflection? Do we have to add the deflection due to the transverse load and the deflection due to buckling?

Also, how would we find the maximum stress?

Thanks in advance for any help!

PhanthomJay

The beam will not buckle if the axial load is below its critical value for buckling. The max stress would be at mid point and at the outer compression fibers and be equal to the bending stress from the transverse load H (bending moment M = HL/4 and bending stress = Mc/I ) plus the compressive stress from the axial load P, (axial stress = P/A), plus the bending moment stress from the axial load P, P(d), where d is the deflection under the transverse load, plus second order stresses from the additional deflection. These latter 2 stresses can sometimes be ignored if P or d is small enough. Beam deflection would be the sum of the deflection due to the transverse load plus the additional deflection due to the eccentric moment caused by the axial load.