# Strength and material Essay Example

Table of Content

## Objectives

1. To determine the critical buckling load.

2. To compare the theoretical and practical values of critical load.

## Introduction

Columns that resist axial loads are referred to as struts. They mostly fail by buckling when critical load is exceeded. The strut undergoes permanent deformation at the point of buckling thus reducing the stability of the strut and ultimate failure. Struts should therefore be designed for buckling especially when under critical use. Resistance of a strut to buckling is dependent on the diameter of strut, slenderness of strut and the material used.

The fixity of the ends also determine the resistance to buckling. The ends either be (a) fixed at both ends, (b) pinned at both ends, (c) fixed at one end and free at the other end or (d) fixed at one end and pinned at the other. The focus of the exercise however, was one that is pinned or hinged on both ends. The effective length Le is equal to the actual length L which shows that the deflection of the strut occurs with the entire length of the strut. Moments do not build up at the ends due to rotation by the hinges. Euler’s formula (1) was used to calculate critical load.

E is the rigidity modulus, I the moment of inertia and L the actual length of the strut.

## Materials & Equipment

The apparatus used included; force measurement device, specimen holders, deformation measurement device, load device and the specimen. The test device consists of the devices above interconnected together to form the test device. The height of the specimen can vary and the cross bars have been designed to be adjustable for this reason. A vertical arrangement was chosen for this exercise as shown in fig. 1 below.

Figure 1: Experiment Set-up

## Procedure

1. The test device was set up vertically, the force gauge placed perpendicularly.

2. The specimen was then inserted to the notches and clamped lightly. The specimen is 0.8m long with a cross section width of 12mm and a depth of 12mm. The elastic modulus of the specimen is 200GN/m² and pinned on both ends.

3. Cross bar fastened along the guide column and a small distance left between the two for measurement and observation of deformation.

4. Measuring gauge now placed at 90° to the buckling direction in the middle portion of the specimen where deformation will be maximum thus buckling

5. The specimen is loaded with force at intervals of 1000N initially after which the value reduces to 5N incrementally past 5000N.

## Result

The experiment yielded a critical load of 5.725kN. The table below is a summary of work plan for the buckling test experiment.

Table 1: Strut Experiment Work plan

 Task title Description 0-30 minutes Setting up of the apparatus The testing machine and all the components were fixed together and set ready for the experiment. Specimen dimensions verified and recorded 30-45 minutes Trial and demonstration test A trial test was carried out to demonstrate how the experiment is to be conducted and how to make proper observations 45-55minutes Clamping of specimen to machine This procedure was keenly carried out to ensure that the specimen is free to rotate at the ends so it can be a pinned support 55-100 minutes Loading incrementally The loads were imposed on the specimen to produce compression forces on the specimen. Loads were added in multiples of 1000N up to 5000N after which the force was added in multiples of 25N. 100-120 minutes Buckling observed and recorded At 5275N, the strut failed by buckling. The deformation and the load were recorded 120-140 minutes Dismantling of devices After the successful experiment the specimen was removed from the testing machines and machine cleaned.

## Discussion

Critical load is the load beyond which the strut will fail. The struts fail by buckling. The experimental critical load has been found to be 5275N which is less compared to the theoretical value of 5379N by 104 N. This is equivalent to an error of 1.95%. The specimen was a bit uneven thus not straight leading to some error. The error incurred was also in the level of bubble which on top level of test machine was not perfectly horizontal. There was observed misalignment of the load when being added incrementally on the strut resulting to error. Human error in recording data was another source of error in the strut experiment.

The environment of performing the experiment could be different from the one that the theoretical value was based on. For instance, higher temperature would result in expansion of specimen which could consequently result in the critical load changes. In addition, there could be human error, apparatus error or reading error. The deviation from the theoretical value is not as large and is within acceptable limits.

## Conclusion

The experiment was successful because all the objectives of the test were achieved. The experimental critical load was found to be 5275N and the difference from theoretical found to be acceptable.

## Reference

Schafer, B.W., 2002. Local, distortional, and Euler buckling of thin-walled columns. Journal of structural engineering, 128(3), pp.289-299.