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F.1.16 Buckling Modulus (EI)
Equal to E*I, where E = modulus of Elasticity, and I = area moment of inertia about the weakest axis.
Explanation
Buckling is "the sudden change in shape (deformation) of a structural component under load". In other words, buckling is what happens when a component or member bends because it is being put under more compressive force than it can handle, even though the bar does not completely break it is still considered failure because the structure can no longer support the weight it was intended to. A mathematician from the 18th century named Leonhard Euler (pronounced "Oiler") derived the Buckling Equation which produces the critical load that a component will begin buckling at.
Euler's formula has 3 components that affect when the material will buckle:
-The Young's Modulus of the material
-The Area Moment of Inertia
-The column length (in our case the length of a chassis tube)
Modulus of Elasticity (Young's Modulus)
Young’s modulus is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression, it is essentially a measure of stiffness. It tells us how much a material will deform under applied stress. It is found by plotting a stress vs strain graph and finding the slope of the elastic region of curve, it is the ratio between stress and strain. Young modulus is the number that helps you transform stresses to strains and vice versa but only within the elastic range of the material, it is within this range that the materiel will reform after being compressed or tensioned.
The higher the Young's Modulus the stiffer the material. The lower the Young's Modulus the more flexible the material.
Area Moment of Inertia
The area moment of inertia, also called the second moment of area, is a parameter that defines how much resistance a shape has to bending because of its geometry. This resistance to bending can be quantified by calculating the area moment of inertia of the cross-section. It is denoted using the letter I, has units of length to the fourth power, which is typically mm^4 or in^4.
The resistance to bending depends on how the material of the cross-section is distributed relative to the bending axis. Cross sections with more material located further from the bending axis have larger moments of inertia which means the stiffer the structure is going to be. This is why I-beams are so resistant to bending, much of their material located far from the bending axis
In our case, we will be calculating the area moment of inertia for chassis tubes. As a circular cross section is common and widely used, a formula to calculate the area moment of inertia has already been derived. For typical cross sections such as solid squares and rectangles, formulas to find the area of inertia can be found by doing a quick search on the internet.
If you would like to know more about different ways to find area moments of inertia, such as cases where the shape is arbitrary. You can visit this website to learn more, but for the purposes of FSAE it most likely wont be necessary.
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