Prob. 4.4-13. For the generic torsion member, T = 600 N·m, G = 28 GPa, d, = 50 mm, and d 40 mm. Determine (a) the maximum shear strain, Ymax; and (b) the maximum ten- sile strain, EmaxT.
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- The specimen shown is made of Aluminum Alloy 6061-T6. If P = 0.7N, Q = 1.3 N, θ = tan -1(4/3), φ = tan-1 (12/5), h = 0.50 mm, w = 0.39 mm, and the thickness t = 0.5 mm. (a) Find the net force on the specimen. (b) Find the net moment about the origin of the given coordinate system. (c) Determine the normal stresses (σxx, σyy, σzz) and shear stresses (σxy, σyz, σxz) acting on the specimen.The dimensions are d1=2.15 m, d2=1 m, d3=1.3 m m, d4=330 mm and r=200 mm. The applied force has magnitude P=6 kN . Part A - Support Reactions and Internal Loading Determine the support reactions Cy and Cx and the internal normal force, shear force, and moment on the cross-section containing point A. Cy= , Cx= , N= , V= , M= part B What are the normal and shear stresses at point A? σA= , τA=The T-bracket is formed by welding together two cylindrical rods AB and CD. If the allowable shear stress is 80 MPa, what is the smallest allowable diameter of rod AB? Neglect the stress caused by the transverse shear force
- Show by integration that the strain energy of the tapered rod AB is U = 1/4 P^2L/EA min Now solve the problem again but add a torque at point B, which acts together with P as shown in the figure.A circular steel tube of length L = 1.0 m is loaded by torques T a) If the inner radius of the tube is r1 = 45 mm and the measured angle of twist betweenthe ends is 0.5°, what is the shear strain γ1 (in radians) at the inners surface? b) If the maximum allowable shear strain is 0.0004 rad and the angle of twist is to bekept at 0.45° by adjusting the torque T, what is the maximum permissible outer radius(r2)max?The solid shaft of radius c is subjected to a torque T at its ends. Show that the maximum shear strain in the shaft is gmax = Tc>JG. What is the shear strain on an element located at point A, c>2 from the center of the shaft? Sketch the shear strain distortion of this element.
- A 60˚ strain rosette measures the following strain at a point on the aluminum skin ofan airplane. ϵ0 = 160 ×10-6 m/m, ϵ60 = -220 ×10-6 m/m and ϵ120 = 360 ×10-6 m/m. Using E = 10 ×106 psi and v = 0.3, Determine the principle stresses and the maximum in-plane shear stress.To determine the state of stress in a solid rod using the principle of superposition. A solid rod has a diameter of e� = 55 mmmm and is subjected to the loading shown. Let a� = 200 mmmm , b� = 220 mmmm , c� = 350 mmmm , d� = 250 mmmm , and P� = 3.0 kNkN . Take point A to be at the top of the circular cross-section. As shown (Figure 2), a cut was made at A to determine the resultant internal loadings. Determine the moment about the x axis, Mx��. b) Part B - Moment about the z axis at A Part C - Stress due to the normal force To find the state of stress at A, the principle of superposition must be used. If the rod has a diameter of 55 mm , find the stress σA�� due to the normal force. Part D - Stress due to the bending moment about the x axis To find the state of stress at A, the principle of superposition must be used. If the rod has a diameter of 55 mm , find the stress σA�� due to the bending moment about the x axis.Define the terms shear stress and shear strain, illustrating your answer by means of a simple sketch. Two circular bars, one of brass and the other of steel, are to be loaded by a shear load of 30 KN. Determine the necessary diameter of the bars (a) in single shear, (b) in double shear, if the shear stress in the two materials must not exceed 50 MN/m² and 100 MN/m² respectively. Ans: [27.6, 19.5, 19.5, 13.8mm.]
- Forces of F1=15 kN in the z direction from the B point, F2=10 kN in the z direction from the C point and F3=10 kN in the y direction act on the arm in the figure. The lengths of the arm are also given as L1=0.15 m and L2=0.16 m. The radius r in the a-a section taken over the arm is r=0.2 m and it is desired to determine the stress state at point A. The shear modulus of the sleeve material is G=65 Gpa. According to this; WRITE YOUR RESULTS IN THE BOXES WITHOUT THE UNITS IN kPa. a) Find the shear stress due to the shear force at point A. Response b) Find the shear stress due to the torsional moment at point A. Response c) Find the total shear stress at point A. Response d) Find the normal stress due to the normal force at point A. Response e) Find the normal stress due to the bending moment at point A. Response f) Find the total normal stress at point A. ResponseThe strain at point A on a beam has components Px = 450(10-6), Py = 825(10-6), gxy = 275(10-6), Pz = 0. Determine (a) the principal strains at A, (b) the maximum shear strain in the x–y plane, and (c) the absolute maximumshear strain.A 60 ̊ strain rosette measures the following strain at a point on the aluminum skin of an airplane. ε0 = 160 ×10-6 m/m, ε60 = -220 ×10-6 m/m and ε120 = 360 ×10-6 m/m. Using E= 10 ×106 psi and v = 0.3, Determine the principle stresses and the maximum in-plane shear stress.