# Buckling of Slender Struts/Columns - Lab Report Explained

Updated: Feb 28

__What does Buckling mean?__

__What does Buckling mean?__

Buckling is one of the major causes of failures in structures and particularly in slender columns. Buckling is caused by the failure in compression due to the material strength and stiffness properties but also from instability and geometric failure.

**Buckling** is the *sudden* change in the shape of a structural component under loads such as the *bowing* of a column under compression or the *wrinkling* of a plate under shear. A member is said to have *buckled *when the structure suddenly changes shape.

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The transition between stable and unstable conditions happens at a value called " *critical buckling load "( Pcr )* which can be calculated using __Euler’s Formula. __

__Where:__

Pcr = Critical Buckling load

𝐸 = Elastic Modulus

𝐼 = least second moment of area (I=bd3/12)

Stated that 𝐸 and 𝐼 are material constants, the linear relationship between the length and critical load can be found.

__Stable, Unstable and Neutral Equilibrium__

__Stable, Unstable and Neutral Equilibrium__

__Stable Equilibrium ( 0 < P < Pcr )__

When an axial load is less than the critical load and the geometry of the strut is straight** 𝜃=0.**

__Unstable Equilibrium (P > Pcr )__

When an axial load is greater than the critical load. Nevertheless, the structure is still in equilibrium if the angle is kept to 0 degrees (𝜃 = 0). However, the strut is unstable and cannot maintain its stability therefore by the slightest disturbance, the strut will buckle and fail.

__Neutral Equilibrium (P = Pcr )__

When an axial load is equal to the critical load the strut is neither stable nor unstable, it is at the peak of stability and instability. That been said the structure can handle small angles without buckling.

__Different Support Reactions Effects__

__Different Support Reactions Effects__

The conditions of the support reactions influence the buckling of a material. As shown above, the effective length is at a maximum (2L) when there are no support reactions placed to the strut. Therefore, we can evaluate that the number of support reactions has a relationship to the buckling displacement of the strut.

Buckling due to compression can be observed by comparing it to the sin curve elongations. The strut tends to buckle in the centre of its length. By looking at the data collected in a laboratory test the theoretical buckling load is higher than the experimental and this is due to the material imperfection but also due to the different support reactions that can create different displacement of the strut (buckling).

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__A conclusion for your Lab Report__

__A conclusion for your Lab Report__

To conclude, the experiment showed the __linearity between load and length__. The data obtained indicate that the longer struts were experiencing a lower buckling load than the shorter struts. Both of them had the same material properties so due to the length of the strut the buckling values vary.

Linear elastic behaviour is shown of the material as the graph logP vs logL is plotted. The evaluation is that by decreasing length and increasing the cross-section of the strunt, critical buckling load is higher making the material to resist to buckling at higher loads applied. A linear relationship is shown on the graph