# Beam Bending & Stress: Solve 2 Cantilever Problem

In summary, Paddy is seeking help with finding the stress and deflection on a cantilever beam problem involving two beams stacked on top of each other. They have the necessary formulas for stress and strain, but are unsure how to approach the problem since there is no information on how the beams interact with each other. Paddy is asking for assistance in determining how to use the fact that the vertical displacements of the beams are equal when they touch after the load is applied.
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
see attached doc for pic

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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.

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!

## 1. What is beam bending and stress?

Beam bending refers to the deformation of a beam when a load is applied to it, causing it to bend. Stress refers to the internal force or pressure that is created within the beam as a result of the load, which can cause the beam to bend or break.

## 2. How is beam bending and stress calculated?

Beam bending and stress can be calculated using various equations, such as the Euler-Bernoulli beam equation or the Timoshenko beam equation. These equations take into account factors such as the beam's material properties, dimensions, and applied loads.

## 3. What is a cantilever beam?

A cantilever beam is a type of beam that is supported at only one end, while the other end is free to move. This creates a fixed support and a free end, allowing the beam to bend when a load is applied.

## 4. How do you solve a cantilever beam problem?

To solve a cantilever beam problem, you first need to determine the properties of the beam, such as its material, dimensions, and applied load. Then, you can use the appropriate beam bending and stress equations to calculate the deflection, bending moment, and stress at various points along the beam.

## 5. What are some real-world applications of beam bending and stress?

Beam bending and stress calculations are used in various engineering fields, such as civil, mechanical, and aerospace engineering. Some real-world applications include designing bridges, buildings, and aircraft structures, as well as analyzing the performance of machine components, such as beams and shafts.

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