# Strut Test to Determine Euler’s Buckling Load of Strut

Strut test is used to determine the Euler’s buckling load of the strut. Struts are long, slender columns that fail by buckling some time before the yield stress in compression is reached.

The Euler’s buckling load is a critical load value that forces the strut to bend suddenly to one side and buckle before achieving the acceptable compressive strain. At the point of failure, the actual compressive stress at the point of failure can be less than the ultimate compressive strength.

The buckling occurs due to imperfections in the straightness of the strut, the applied load is not along the axis of the strut, and one part of the material may yield in compression more readily than others owing to some lack of uniformity in the material properties throughout the strut.

Strut testing apparatus, which is designed to carry out tests on struts of various lengths, with ends either hinged or fixed, is employed to determine the Euler’s buckling load of a strut.

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**Theory and Principle**

In the case of very long columns, the failure happens mainly due to bending. The Euler’s relations give the crippling load for long columns for various end condition:

Where:

E: Modulus of Elasticity of the material (2.1 x 10^{5}N/mm^{2})

I: Moment of Inertia of the cross Section of the strut (mm^{4})

L: Effective length of the strut which is equal to total length of the strut (L) when both ends are hinged, 0.5L when the ends are fixed, L/(2)^0.5 when one end fixed and other end hinged, and 2L when one end fixed and the other end is free.

**Equipment**

- Strut Testing Apparatus
- Venire Caliper Scale

## Strut Test Procedure

- Clean the strut with sandpaper.
- Adjust the rope slide to suit the length of the strut and place the strut between the top and bottom adapter.
- For tests with hinged end, two balls are provided which should be tightened properly to ensure end fixity.
- Move the side sliding block so that the micrometer strut is approximately against the midpoint of the length of the strut and clamp it firmly.
- Now adjust the micrometer Sliding holder, so that the micrometer comes exactly at the midpoint of the strut.
- Place the weight hanger over the top socket such that the loading is purely axial.
- Put the switch `on’ so that whenever the micrometer touches the strut the indicator lamp glows.
- Carefully rotating the strut with fingers through one revolution, the maximum and minimum readings of the micrometer are noted. The purpose of this is to determine the direction of curvature of the strut and also to get the amount of initial curvature.
- The strut has to be placed such that the initial curvature is away from the micrometer side. First, determine the initial reading of the micrometer with the initial curvature away from the micrometer.
- Then add weights (in step of l kg) load on both sides of the hanger so that the strut bends in the direction away from the micrometer and note the reading.
- The difference between the two readings gives the actual deflection due to the weights now added. Do not rotate the strut while adding loads since the strut has to be kept such that the curvature is pointing the same direction always.

## Graphs

Plot a graph of load (P) versus the total deflection of the strut when a particular load is applied (Delta).

## Calculation

Use Euler’s formula for the computation of the buckling load of a strut. The equation is provided above which is equation 1.

## Results

1. By Eulers formula = ___________N

2. Experimental Values= _________N

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