Beam Bending & Stress: Solve 2 Cantilever Problem

[paddy-boy66]

I'm stuck on a beam bending problem I have. I have 2 cantilever beams one one top of the other applying a force. I need to know find the stress on the left hand beam and the deflection. I have the formulas (using Roark's formulas of stress and strain) but there's nothing about two cantilevers interacting with each other. Can anybody tell me how I go about this? Thanks
Paddy
see attached doc for pic

 

[radou]

If they touch one another after the load F is applied, then you can somehow use the fact that their vertical displacements in that point are equal.

 

[ravenprp]

There are a few steps you can follow to solve this beam bending problem with two cantilever beams.

1. Draw a free body diagram for each beam, showing all the external forces acting on them (including the applied force and any reactions at the fixed end).

2. Apply the equilibrium equations (sum of forces and moments) to each beam separately to find the reactions at the fixed end.

3. Use the reactions calculated in step 2 to determine the internal bending moment and shear force diagrams for each beam.

4. Apply the bending and shear stress formulas from Roark's formulas to find the stress at any point along the beams. Keep in mind that the stress will change as you move along the beams due to the varying bending and shear forces.

5. To determine the deflection, you will need to use the deflection formula for each beam, taking into account the interactions between the two beams. This will require you to consider the combined stiffness of the beams and how they affect each other's deflection.

Overall, solving this problem may require some trial and error and iteration to find the correct deflection and stress values for both beams. It may also be helpful to consult with a professor or tutor for guidance on how to approach this specific problem. Good luck!