Table of Contents

## Scope

In this experiment of Simply Supported Beam, cantilever beam, and Fixed ended beam, the recording of the deflection in the beam is done by changing the weight and comparing the measurement with the theoretical expressions. The experiment is divided into 2 major cases in which different types of beams and their deflections are demonstrated. The practical result obtained from the experiment is then compared with the theoretical results. The deflections formulae for each beam is also provided.

## Significance

Theoretical deflection can be distinguished from the measured deflections values due to the simplified set of assumptions made in the theory. Comparing theoretical values with measured values gives an idea of the deviations and hence we derive a correspondence & relationship between them. Which can be used in many civil engineering apparatuses.

## Apparatus

This experiment use the following items. In most of the cases there is a complete set of apparatus available at the Mechanics of Solids lab which includes: Sample Model of the beam, Weights, Deflection gauges, and weight hangers.

## Procedure

The procedure of this experiment is quite easy. Make sure your apparatus is ready and smooth. For the sake of checking take out the beam model (preferable made of steel or other metal) and place it on the table. It should be kept horizontally and firmly.

- It should be kept horizontal and tight.
- Also record beam length and cross section dimensions.
- Set the deflection gauge to where the deflection should be measured. Zero the dial indicator readings of the deflection gauge before applying the load to the bar.
- Weight Now apply the load with the help of a weight hanger. Also record the weight of the load.
- Now record the deflection of that point. When recording each inflation, all the small dials of the gauge should be read first because it shows the number of complete rotations of the dial rotated, one full rotation is equal to 1 mm, then the main dial of the gauge should be read. Each section of the main dial is equal to 0.01 mm.
- Also, record the deflection at any point on the beam. Also record the location of that point and the position and value of the new load.

## CASE # 1

##### Cantilever beam

One of the end is fixed at one end and the other is independent. Note the deflection by the dial gauge at the unsupported length and at least twice at the specified point between different loads.

## Observations and Calculations

- The Beam Moment of inertia about the centroid = I = bh
^{3}/12 - Deflection of the point with theoretical expression.
- Where b(breadth dimension) = __________ , h(height dimension) = _________ , L (Length dimension) = _______

## CASE # 2

- End fixed at one end and another center roller and load.
- Note the deflection by the dial gauge at any two specified points between different loads to measure the load and support at least twice.

## Observations and Calculations

Where x = Distance from fixed support to the point of interest. The point of interest is basically the point on beam where we apply the load.

v = Distance from roller support to the point of interest. The End of RELATION BETWEEN DEFLECTIONS AND APPLIED LOADS for more experiments and civil engineering related content please visit our blog page.

## Conclusion

So we observed the following data from experimental and theoretical calculations. The data is assigned in the table to make a clear difference between experimental and theoretical deflections. Hence proved that there are variations between observed data and calculated data. This is due to the fact that we use a set of assumptions to make our calculations simple and easy to understand. Due to these assumptions and hypothesis, the experimental data deviate from the theoretical.