How Do You Calculate Incremental Axial Stress in a Preloaded Elastic Beam?

[will4]

Seems that most of the textbooks are dealing with elastic beam calculations, where a beam is fixed from both ends and initially there is no axial stress or load applied.

My problem is different in a way that an elastic rectangular beam is fixed from both ends and it is under certain tensile load F (given). I know the bending deflection y in the center of the beam due to applied load in transverse direction (that load is not given).

The question is how to calculate an increment in axial stress by knowing the deflection y in the center of the beam that is generated by applying a load in transverse direction?

Given:
Dimension of the beam, L, h, w
Elastic modulus (both tensile and bending)
Initial axial load, F
Deflection in the center, y

Any help appreciated.

 

[256bits]

If I recall correctly;
a) For a beam not under a preload, the top is in compression and the bottom in tension, and the middle fiber has no axial stress, when the beam is loaded tranversally.
b) Now apply a compressive force to both ends so that the bottom fibers have no axial stress, and the whole beam is in compression.

What would be the load on the top fiber? Would it be the compressive stress in a) plus that added in part b) .

As a side note, concrete beams are often preloaded in compression so that no part of the beam beam will ever (never) be in tension under a transverse load.

Hope that gets you started.