Question

7 of 15 6-of-9 Problem 4 (35 Points) The rod has a diameter of 40 mm. It is subjected to the force and moment system shown. (a) (15 points) Determine the stress components that act at point B. Show the results on a volume element below located at this point. (b) (10 points) Assume that the stress components at point A are given by Ox = -37 MPa, y = 0 MPa, Try = - 8 MPa. Draw a Mohr's circle based on these stress components on the provided Mohr's circle diagram (shown next page), and label taxis and all the important points and angles found in parts (C). (c) (10 points) Determine the principal stresses and their directions 0, at point A from Mohr's circle. Note: You may use the stress transformation equations to check your work, but only the Mohr's circle analysis will be graded. 100 mm 300 mm 1500 N 100 Nm 800 N 7- of - 9 Problem 4 (continued)

Answer 1

Stress in x- axis due to 15oon force = 1.19 MPa 1500 4x40² Since the point B lies on y-axis, the strees due to bending force soon, will be zero along y- axis. = M2, where zao at point B. shear stress in gaz plane due to torque 100 Nm, Tyz = I.R= 100x103 40 100 7/32 x 40 x 20 7.96 MPa Gyro Eyz7.96 Caso 24-0 -7.96 02 -01_ 21°220 K Ž

6) on = -37 MPa oyao, Zny = -8 MPa Zny=8 I center of Mohr's circle, co -37 to ż =18.5 Radius of Mohr's Circle, R = √(18.5² + 82 = 20.15 Principle stresses, Gi - C-R = -18.5–20:15 - 38.65 MPa 02 = CAR = -18.5+ 20.15 = 1.65 MPa Directions, 20- tan' (195) – 23.38° ce coo p angle to other .. 0 = 11.69° and A l-Q+45°

Thank you.