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.
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 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
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
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
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