# Beam Deflection Using Work Methods

• stinlin
In summary, the problem at hand involves finding the deflection at the point of load application using the equation W = (P*delta)/2 = U = (M^2*dx)/2EI, which equates work and energy. However, this method may not be applicable for structures with multiple loads.
stinlin

## Homework Statement

Find deflection at point of load application.

See attached.

## The Attempt at a Solution

I know the equation to use, but I have NO idea how to apply it here. Also - can't use virtual work. The problem explicitly states real work. How on Earth do I begin this? ^.^

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Your attachments aren't available for viewing yet, but the general strategy here is to equate work (applied force times deflection at point of load) and energy (total strain energy in the beam). Does this help?

Mapes gave the correct idea.

Basicly in linear elastic materials

$$W = \frac{P \delta}{2} = U = \int_{0}^{L} \frac{M^{2}dx}{2EI}$$

Of course if you notice due to the nature of the strain energy being quadratic function of the loads instead of being linear, it does not allow us to find the displacements for 2 or more loads acting on the structure. This is because we will have multiple unknowns and just 1 equation (the one above).

Your case is solvable by this method.

## 1. What is beam deflection?

Beam deflection is the bending of a structural beam due to the application of external loads, such as weight or force. It is a measure of how much the beam deforms under these loads and is an important factor in determining the strength and stability of a structure.

## 2. What are work methods used for beam deflection analysis?

Work methods, also known as energy methods, are mathematical techniques used to analyze beam deflection. They involve calculating the work done by the external loads on the beam and comparing it to the work done by internal forces, such as bending and shear, to determine the deflection of the beam.

## 3. How accurate are work methods for predicting beam deflection?

Work methods are generally accurate for predicting beam deflection, especially for simple beam structures with evenly distributed loads. However, they may not be as accurate for more complex structures with varying loads and support conditions. It is important to use appropriate assumptions and equations for the specific beam being analyzed.

## 4. Can work methods be used for all types of beams?

Work methods can be used for most types of beams, including cantilever, simply supported, and overhanging beams. However, they may not be suitable for analyzing beams with complex geometries or non-uniform loading conditions. In these cases, other methods such as finite element analysis may be more appropriate.

## 5. What are some factors that can affect beam deflection according to work methods?

The factors that can affect beam deflection using work methods include the magnitude and distribution of external loads, the geometry and material properties of the beam, and the support conditions at each end of the beam. Additionally, any assumptions made during the analysis, such as neglecting shear deformation, can also affect the accuracy of the results.

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