5 in the shaft is fixed to the wall on the left end

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Unformatted text preview: D F B T3 1.5 in B Figure P5.4 C D 25 in 40 i n E F 30 in 5.5 A circular shaft of radius r and length Δx has two rigid discs attached at each end, as shown in Figure P5.5. If the rigid discs are rotated as shown, determine the shear strain γ at point A in terms of r, Δx, and Δφ, assuming that line AB remains straight, where Δφ = φ 2 – φ 1 . 1 2 Figure P5.5 x 5.6 A hollow circular shaft made from hard rubber has an outer diameter of 4 in and an inner diameter of 1.5 in. The shaft is fixed to the wall on the left end and the rigid disc on the right hand is twisted, as shown in Figure P5.6. The shear strain at point A, which is on the outside surface, was found to be 4000 μrad. Determine the shear strain at point C, which is on the inside surface, and the angle of rotation. Assume that lines AB and CD remain straight during deformation. Figure P5.6 36 in 5.7 The magnitude of shear strains in the segments of the stepped shaft in Figure P5.7 was found to be γAB = 3000 μrad, γCD = 2500 μrad, and γEF = 6000 μrad. The radius of section AB is 150 mm, of section CD 70 mm, and of section EF 60 mm.Determine the angle by which each of the rigid discs was rotated. 1 2 Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm Figure P5.7 2m 1.8 m 3 1 .2 m 5.8 Figure P5.8 shows the cross section of a hollow aluminum (G= 26 GPa) shaft. The shear strain γxθ in polar coordinates at the section is γ x θ = – 0.06 ρ , where ρ is in meters. Determine the equivalent internal torque acting at the cross-section. Use di= 30 mm and do = 50 mm. ρ θ x di Figure P5.8 do January, 2010 M. Vable Mechanics of Materials: Torsion of Shafts 5 213 5.9 Figure P5.8 shows the cross section of a hollow aluminum (G = 26 GPa) shaft. The shear strain γxθ in polar coordinates at the section is γ x θ = 0.05 ρ , where ρ is in meters. Determine the equivalent internal torque acting at the cross-section. Use di= 40 mm and do = 120 mm. 5.10 A hollow brass shaft (GB = 6500 ksi) and a solid steel shaft (GS = 13,000 ksi) are securely fastened to form a composite shaft, as shown in Figure P5.10.The shear strain in polar coordinates at the section is γ x θ = 0.001 ρ , where ρ is in inches. Determine the equivalent internal torque acting at the cross section. Use dB = 4 in. and dS = 2 in. θ ρ x Steel Brass dS dB Figure P5.10 5.11 A hollow brass shaft (GB = 6500 ksi) and a solid steel shaft (GS = 13,000 ksi) are securely fastened to form a composite shaft, as shown in Figure P5.10.The shear strain in polar coordinates at the section is γ x θ = – 0.0005 ρ , where ρ is in inches. Determine the equivalent internal torque acting at the cross section. Use dB = 6 in. and dS = 4 in. 5.12 A hollow brass shaft (GB = 6500 ksi) and a solid steel shaft (GS = 13,000 ksi) are securely fastened to form a composite shaft, as shown in Figure P5.10.The shear strain in polar coordinates at the section is γ x θ = 0.002 ρ , where ρ is in inches. Determine the equivalent internal torque acting at the cross section. Use dB = 3 in. and dS = 1 in. A hollow titanium shaft (GTi = 36 GPa) and a hollow aluminum shaft (GAl = 26 GPa) are securely fastened to form a composite shaft shown in Figure P5.13. The shear strain in polar coordinates at the section is γ x θ = 0.04 ρ , where ρ is in meters. Determine the equivalent internal torque acting at the cross section. Use di = 50 mm, dAl = 90 mm, and dTi = 100 mm. 5.13 Titanium Aluminum θ ρ x di d Al Figure P5.13 d Ti Stretch Yourself Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm 5.14 A circular shaft made from elastic - perfectly plastic material has a torsional shear stress distribution across the cross section shown in Figure P5.14. Determine the equivalent internal torque. τxθ 24 ksi ρ Figure P5.14 0.3 in. 0.3 in. A solid circular shaft of 3-in. diameter has a shear strain at a section in polar coordinates of γxθ = 2ρ (10-3), where ρ is the radial coordinate measured in inches. The shaft is made from an elastic–perfectly plastic material, which has a yield stress τyield = 18 ksi and a shear modulus G = 12,000 ksi. Determine the equivalent internal torque. (See Problem 3.144). 5.15 January, 2010 M. Vable Mechanics of Materials: Torsion of Shafts 5 214 A solid circular shaft of 3-in. diameter has a shear strain at a section in polar coordinates of γxθ = 2ρ (10-3), where ρ is the radial coordinate measured in inches.The shaft is made form a bilinear material as shown in Figure 3.40. The material has a yield stress τyield = 18 ksi and shear moduli G1 = 12,000 ksi and G2 = 4800 ksi. Determine the equivalent internal torque.(See Problem 3.145). 5.16 A solid circular shaft of 3-in. diameter has a shear strain at a section in polar coordinates of γxθ = 2ρ (10-3), where ρ is the radial coordinate measured in inches.The shaft material has a stress–strain relationship given by τ = 243γ 0 .4 ksi. Determine the equivalent internal torque. (See Problem 3.146). 5.17 A solid circular shaft of 3-in diameter has a shear strain at a section in polar coordinates of γxθ = 2ρ (10-3), where ρ is...
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