The radius of gyration for a column is defined as $r_g = sqrt{frac{I}{A}}$ where $I$ is the moment of inertia of the cross-section about the neutral axis and $A$ is the cross-sectional area. The slenderness ratio is defined as $L/r_g$ where $L$ is the effective length of the column. Consider a pin-pin I-beam column with Young's modulus $E$ and length $L$ subjected to a force $f$ as shown in the figure to the right. (3a) Find the critical buckling load $f_c$ in terms of $E, L, t$. (3b) Determine the radius of gyration $r_g$ and the slenderness ratio for the beam. (3c) Let the beam be made of steel with $L = 3m$. If the beam fails under a compressive stress of $sigma_0$, for what $t$ is the beam equally likely to fail under buckling as under axial stress, and what is the corresponding slenderness ratio? Answer: for structural steel, $t = 4.6cm$
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(2) We use the equation of elasticity to calculate the critical buckling load. (3) The critical buckling load is inversely proportional to the material's Young's modulus. In this case, the critical buckling load is given by: = E*L*t/g (4) Show more…
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