75 lb Consider the crank shown. It is made of 6061 aluminum alloy. The rider pushes straight down on the pedal with one foot, resulting in 75 lb load on the pedal. Treat the crank like a beam that is cantilevered at Point B. The y-axis is up and down. The x-axis is along the neutral axis of the crank. The z-axis is in and out of the page. Part 1: Perform hand calculations. B AO 3 in 4 in. T0.4 in. 0.4 in. 0.2 in. 0.3 in. 1. Draw a free-body diagram of only the crank. Don't include the chain, or the chainring that the crank is attached to. 2. Hand-draw a shear diagram, V(x), a bending moment diagram, M(x), and the elastic curve, v(x), for the crank. 3. How far down will the end of the crank be displaced due to the applied load? The crank is essentially a cantilever. Use the beam deflection equations at the back of your Mechanics of Solids book to calculate v at the end. 4. Compute the values of , , and TX at Point C. 5. Compute the first and second principal stresses at Point C, along with the angle of the principal plane. 6. Use my MATLAB simulation script to generate Mohr's circle for this state of stress. Double check to see if you're getting the same answers for the principal stresses and the angle of the principal plane. Paste in an image for when the element is positioned horizontally. Also paste in an image for when the element is rotated to the principle plane. 7. Compute the factor of safety at Point C. Use the ratio of the aluminum's yield stress to the von Mises stress, '. ' (0x-01) + (01-02) + (02-0x) + 3(1 y + 1}z + 12x) 2 2 2 The values of z and Tyz and Tzx are all zero at this surface, resulting in o' = - 8. Are you going to tell your boss that the crank is strong enough to sell (and not get a lawsuit)?