The thin-walled hollow cylindrical member AB has a noncircular cross section of nonuniform thickness. Using the expression given in Eq. (3.50) of Sec. 3.10 and the expression for the strain- energy density given in Eq. (11.17), show that the angle of twist of member AB is
where ds is the length of a small element of the wall cross section and ɑ is the area enclosed by center line of the wall cross section.
Fig. P11.70
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Mechanics of Materials, 7th Edition
- 2mm The piece of plastic is originally rectangular. Suppose that a = 300mm and b = 420 mm 2mm 5mm TIC 300mm = a 1 Blac b 1 d A B 1 1 1 1 1 1 = 420mm 3mm 14mm 2mm У Determine the shear strain rxy at corner B if the plastic distorts as shown by the dashed lines.arrow_forwardQ.4) By using the strain rosette shown in figure below, we obtained the following normal strain data at a point on the surface of a machine part made of steel [E = 207 GPa, v= 0.29]: ε-770 μ, E = 520 µ, & = - 435 µ (a) Determine the strain components &, &, and %y at the point. (b) Determine the principal strains and the maximum in-plane shear strain at the point using Mohr's circle. (c) Draw a sketch showing the angle Op, the principal strain deformations, and the maximum in-plane shear strain distortions. (d) Determine the magnitude of the absolute maximum shear strain. b ' 60°| 60°arrow_forwardThe normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression vy/3E where y = 2.4 lb/in.³ is the specific weight of the material, y = 3.8 in. is the distance from the free (i.e., bottom) end of the bar, L = 19 in. is the length of the bar, and E= 24000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar. (c) the maximum normal strain in the bar. Part 1 Calculate the change in length of the bar due to its own weight. Answer: d = i x10-6 in.arrow_forward
- Rigid bar ABCD is supported by two bars as shown. There is no strain in the vertical bars before load P is applied. After load P is applied, the normal strain in bar (2) is measured as −3,300 μm/m. Use the dimensions L1 = 1,600 mm, L2 = 1,200 mm, a = 240 mm, b = 420 mm, and c = 180 mm. Determine (a) the normal strain in bar (1). (b) the normal strain in bar (1) if there is a 1 mm gap in the connection at pin C before the load is applied. (c) the normal strain in bar (1) if there is a 1 mm gap in the connection at pin B before the load is applied.arrow_forward5 decimal places Determine the total strain (mm/mm) of a 2.64-m bar with a diameter of 21 mm subjected to a tensile force of 71 kN at a temperature increase of 49 C°. Consider the α=27.3 µm/mC° and E = 122 GPa.arrow_forwardThe normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression yy/3E where y = 2.9 lb/in.³ is the specific weight of the material, y = 0.5 in. is the distance from the free (i.e., bottom) end of the bar, L = 5 in. is the length of the bar, and E = 25000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar. (c) the maximum normal strain in the bar. Part 1 * Your answer is incorrect. Calculate the change in length of the bar due to its own weight. Answer: d= i 2.416 eTextbook and Media x10-6 in.arrow_forward
- The normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression yy/3E where y = 3.0 lb/in.³ is the specific weight of the material, y = 6.3 in. is the distance from the free (i.e., bottom) end of the bar, L = 21 in. is the length of the bar, and E = 27000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar (c) the maximum normal strain in the bar. Answer: (a) d = i (b) avg (c) Emax i x10-6 in. με μεarrow_forwardThe normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression yy/3E wherey= 2.2 lb/in.³ is the specific weight of the material, y = 5.0 in. is the distance from the free (i.e., bottom) end of the bar, L = 25 in. is the length of the bar, and E = 23000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length of the bar (c) the maximum normal strain in the bar. Answer: (a) ō = i (b) Eave = i (c) Emax = i x10-in. με μεarrow_forwardA 45° strain rosette was placed on the surface of a critical point on an engineering part. The following were measured: Ea = 400 μ C ли 45° mm mm 45° ли Gauge a was aligned with the x-axis. a. Determine Ex, Ey, Yxy b. Using Mohr's Circle, find the principal strains and the maximum shear strain at that point, and find the orientation of the principal planes from the given x-y axes. y ли & = 450 μ ஆ b a mm X mm & c = 500 μ y+ ос mm mm eb 10₂ Xarrow_forward
- The normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression yy/3E where y = 2.0 lb/in.³ is the specific weight of the material, y = 2.8 in. is the distance from the free (i.e., bottom) end of the bar, L = 14 in. is the length of the bar, and E = 20000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar (c) the maximum normal strain in the bar. Answer: (a) 8- i (b) Eavg (c) Emax = i x10-6 in. με μεarrow_forwardThe normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression yy/3E where y=2.4 lb/in.³ is the specific weight of the material, y = 0.6 in. is the distance from the free (i.e., bottom) end of the bar, L = 6 in. is the length of the bar, and E=30000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar (c) the maximum normal strain in the bar. Answer: (a) 5 = 1 (b) Sa (c) Emax= i x10-6 in. με μεarrow_forwardThe normal strain in a suspended bar of material of varying cross section due to its own weight is given by the expression yy/3E where y = 2.4 lb/in.³ is the specific weight of the material, y = 1.8 in. is the distance from the free (i.e., bottom) end of the bar, L = 9 in. is the length of the bar, and E= 26000 ksi is a material constant. Determine, (a) the change in length of the bar due to its own weight. (b) the average normal strain over the length L of the bar. (c) the maximum normal strain in the bar. Calculate the change in length of the bar due to its own weight. Answer: x10-6 in.arrow_forward
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