1. (Book Problem) A round steel bar having S = 800 MPa is subjected to loads producing y calculated stresses o Axial = 70 MPa, τ = 200 MPa, σ, = 300 MPa and Torsion Bending τ = 170 MPa. ט a. Sketch Mohr's circle showing the relative locations of maximum normal stresses and maximum shear stresses. b. Determine the safety factor with respect to the initial yielding according to the max shear stress theory and to the distortion energy theory.

A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded in biaxial stress by normal stresses r and cry. (sec figure). A strain gage is bonded to the plate at an angle 4 = 350 If the stress o is 10,700 psi and the strain means used by the gageise = 390 X 106.whatisthcmax- imum in-plane shear stress (Tr, ),. and shear strain (>‘ ).? What is the maximum shear strain (y ) in the x-: plane? What is the maximum shear strain (y ).. in the y-r plane?

Solve the preceding problem if F =90 mm, F = 42 kN, and t = 40°MPa

Solve the preceding problem if the diameter is 480 mm, the pressure is 20 MPa, the yield stress in tension is 975 MPa, the yield stress in shear is 460 MPa, the factor of safety is 2,75, the modulus of elasticity is 210 GPa, Poissorfs ratio is 0.28, and the normal strain must not exceed 1190 x 10" . For part (b), assume that the tank thickness is 8 mm and the measured normal strain is 990 x 10~ .

-4. - An element in plane stress is subjected to stresses ??x= 105 MPa, ??y= 75 MPa, and sxy= 25 MPa (see the figure for Problem 7.3-1). Determine the principal stresses and show them on a sketch of a properly oriented element.

An element on the top surface of the fuel tanker in Problem 7.2-1 is in biaxial .is in the and is subjected to stresses a, = 6250 psi and a. = -1750 psi, as shown in the figure. Using Mohr s circle, determine the following: (a) The stresses acting on an element oriented at a counterclockwise angle ? = 550 from the x axis. (b) The maximum shear stresses and associated norm al stresses. Show all results on sketches of properly oriented elements.

(a) Solve part (a) of the preceding problem if the pressure is 8.5 psi, the diameter is 10 in., the wall thickness is 0,05 in., the modulus of elasticity is 200 psi, and Poisson's ratio is 0.48. (b) If the strain must be limited to 1.01, find the maximum acceptable inflation pressure

1. A machine frame is made of steel with a yield strength of Sy = 400 MPa. When loaded in a test fixture, the stresses were found to vary linearly with load. Two points A and B on the surface of the frame were found to be most critical. With a 4-kN test load, stresses at these points were as in the sketches below: d-100 MPa --100 MPa d-200 MPa d-150 MPa Use the template on the following page to answer these questions: (i) A scaled drawing of the failure locus for steel using the Distortion Energy (DE) theory is shown on next the page. Mark the axes labels and the yield strength values on the σ-σg axes. Then, draw the failure locus for the Maximum Shear Stress (MSS) superimposed on the given - plot to scale, represent the given stress states at points A and B on the plot, and draw the load lines corresponding to the two points. (ii) From the load lines drawn in part (i), graphically estimate the factors of safety and predict which of the two points will experience initial yielding first…

1. (Book Problem) A round steel bar having Sy = 800 MPa is subjected to loads producing calculated stresses Axial = 70 MPa, TTorsion = 200 MPa, Bending = 300 MPa and T = 170 MPa. a. Sketch Mohr's circle showing the relative locations of maximum normal stresses and maximum shear stresses. b. Determine the safety factor with respect to the initial yielding according to the max shear stress theory and to the distortion energy theory.

Consider the 2-D state of stress shown below. Using the provided scales graph the Mohr's Circle for the 2-D state of stress with “full" details II-Obtain the Principal Stresses, the Maximum Shear Stress, and complete the table below III- Draw the Planes of Principal and Maximum Shear Stresses in the space provided below Provide "full" details and Use 3 Sig. Fig. in this problem Oy = 15 Ksi Tcw > S y Ox =10 Ksi Тух 5 Ksi 10 5 -20 -15 -10 5 10 15 20 5 10 Tccw > S' O Avg. TMax. 01 02 Op1