A circular bar of radius r = 1 cm is placed horizontally between two vertical su

Question

A circular bar of radius r = 1 cm is placed horizontally between two vertical supports that are separated by distance L = (1.1x10^0) m. The bar is made of silicon nitride in manufactured form, without any intentional scratches or cracks or other stress concentrators. Estimate the largest possible force (in N) that can be applied before the bar breaks. Assume the maximum flexural strength reported for this material. If it is possible I could have some insight, as it is I have nothing. Thank you for any help!

Explanation / Answer

For simply supported beam with point load at midway, we have Deflection x = FL^3/(48EI) where E is Elastic Modulus and I is second area of moment about the centroid. For circular bar, I = 3.14/64*d^4 = 3.14/64*(2*1)^4 = 0.785 cm^4 = 0.785*10^-8 m^4 4*10^-3 = 180*1^3/(48*E*0.785*10^-8) E = 119.4 GPa

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