If the internal torque experienced by a hollow brass shaft (G = 39 GPa) at a section with diameter d = 100 mm with 3 mm thick walls is T = 12 kNm, which of the following is closest to the magnitude of the minimum shear strain developed on that section? Select one: O A. 0.0072 rad O B. 0.0137 rad O C. 0.0128 rad O D. 0.0067 rad
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- During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as follows: gage A, 520 × l0-6; gage B. 360 × l0-6; and gage C,-80 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.A thin-walled rectangular tube has uniform thickness t and dimensions a x b to the median line of the cross section (see figure). How does the shear stress in the tube vary with the ratio = a/b if the total length Lmof the median line of the cross section and the torque T remain constant? From your results, show that the shear stress is smallest when the tube is square (ß = 1).The normal strain in the 45n direction on the surface of a circular tube (sec figure) is 880 × 10 when the torque T = 750 lb-in. The tube is made of copper alloy with G = 6.2 × 106 psi and y = 0.35. If the outside diameter d2of the tube is 0.8 in., what is the inside diameter dt? If the allowable normal stress in the tube is 14 ksi, what is the maximum permissible inside diameter d?
- Solve the preceding problem if the cross- sectional dimensions are b = 1.5 in. and h = 5.0 in., the gage angle is ß = 750, the measured strains are = 209 × 10-6 and B = -110 × 10, and the material is a magnesium alloy with modulus E = 6.0 X 106 psi and Poisson’s ratio v = 0.35.Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN - m is applied at x = 0.5 m, and uniformly distributed torque intensity t1= 250 kN m/m is applied on pipe BC. Both pipes have the same inner diameter = 200 mm. Pipe AB has thickness tAB=15 mm, while pipe BC has thickness TBC= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa.A circular aluminum tube subjected to pure torsion by torques T(sec figure) has an outer radius r2equal to 1.5 times the inner radius r1. (a) If the maximum shear strain in the tube is measured as 400 × 10-6 rad, what is the shear strain y1at the inner surface? (b) If the maximum a1lo-abk rate of twist is 0.125 °/m and the maximum shear strain is to be kept at 400 × 10-6 rad by adjusting the torque T, that is the minimum required outer radius ( r2)Min?
- If the internal torque experienced by a hollow brass shaft (G = 39 GPa) at a section with diameter d = 100 mm with 3 mm thick walls is T = 12 kNm, which of the following is closest to %3D the magnitude of the minimum shear stress developed on that section? Select one: O A. 262 MPa O B. 501 MPa O C. 279 MPa O D. 533 MPaA 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?1. A circular shaft with a keyway can be approximated by the section shown in Fig. r=b Ay r r=2acose Figure 1: Circular shaft with a keyway. The keyway is represented by the boundary equation r = b and the shaft is represented by the boundary equation r = 2a cos 0. Show that using a Prandtl stress function of the form ²) (₁ (1-2a cos) X v = K (b² − ²) (1 – : will solve the problem of torsion on this shaft and find the constant K (assume an applied torque T). Compute the shear stress components Txz and Tyz. (Hint: start by converting the stress function to Cartesian coordinates).
- An aluminum tube with the cross section shown has a constant wall thickness of 2 mm. A torque T = 400 N·m is applied to the tube. Use G= 28 GPa What is the area of the tube? a. 957.08mm2 b. 968.09mm2 c. 966.08mm2 d. 977.08mm2 What is the total length of the median line? a. 0.1313m b. 0.1314m c. 0.1315m d. 0.1316m What will be the result shear flow of the object? a. 207,967.94 N/m b. 208,968.98 N/m c. 209,978.96 N/m d. 209,979.00 N/m The shearing stress value will be? a. 104.5 MPa b. 105.6 MPa c. 104.6 MPa d. 105.7 MPa The angle of twist result is? a. 14.68 Deg/m b. 12.66 Deg/m c. 14.68 Deg/m d. None of the above.A steel shaft with a length of 3.00 m. One meter of the steel is contained in a brass tube and firmly attached. The diameter d1 = 70 mm and the diameter d2 = 90 mm. Brass G = 39GPa and steel G = 77.20 GPa. Determine: The torque that can be applied if the deformation at one end is 10 degrees. Answer: T = 8.64 kN – m The torque that can be applied if the maximum shear stress in brass is 70MPa and in steel is 110MPa. Answer: T = 6.352 kN – m Recommendation: analyze by segments. The first segment is only brass, then the composite part between brass and steel, and the last part only steel. In the composite segment, use only one material. In this same segment, equalize the deformations.Let's consider a solid circular shaft subjected to the torque loads as shown Determine the minimum required diameter "D" if the shaft is made of a material having a yielding shear stress Ty = 100 MPa, for a factor of safety FS = 2. The polar moment of inertia of a solid circular cross-section is given by Jr.R¹/2. 300 mm B 600 mm 100 N.m 500 N.m 600 mm 400 N.m