General Instructions Solve this assignment on engineering paper. Follow the instructions accurately for full credit. Choose an appropriate scale for drawing each Mohr’s Circle. Use the axis orientations shown in class . Use a new set of axes for each circle. Instruction for Problems 1-6 (60 points) Each element shown below describes the stresses applied on an element, resulting from the load and geometry calculations. For each element:
a) Draw the Mohr’s Circle. Label the axes, and the stresses on the x-face and y-face. (3) b) Label the origin of the plane as 0, and the center of the circle as C. Compute the stress described by length OC. Put a dimension on the circle to show this stress value. (1) c) Compute the radius of the circle using Pythagoras’ theorem. Show your calculations. (1)
d) Find the principal stresses (a1, 02) and the maximum shear stress (rte) from the geometry of the circle, instead of using the equations. Do not estimate by “eyeballing” the circle on the grid. Instead, use geometric calculations, as shown in class. (2) e) The maximum normal stress is % higher than the larger of the two normal stresses applied on the element. (1) f) The maximum shear stress is % higher than the shear stress applied on the element. (1) g) By how much angle must you rotate the given element in the CW direction in order to arrive at the orientation experiencing the principal stresses? (1)
100 M Pa 41—HOO M Pa Problem 1 1C0 M Pa 40 PAPE. ‘ n Pa 200 M Pa Problem 3 Fin en 2 10OMPa 1:: ,r’a M Pa Make up your own problem involving both normal and shear stresses, where one set of normal stresses is tensile and the other compressive —unequal values. Problem 6 .0 200 M Pa Problem 4 Problem 5
