We have a steel shaft that rotates at 3 Hz shown in the figure. The shaft is divided into two segments; AB and BC. Segment Ab is a solid shaft that has a diameter derived from the equation x² + y² = 625 expressed in millimeters. For segment BC, we have a solid section with dimensions derived from the equation 25x² + 36y²-22500 = 0 expressed in millimeters. Find the maximum shear stress and the angle of rotation of point C relative to point A. Use G = 83 GPa 55 kNccw 30 kNccw B 85 kN 2 C A 6 m 3 m

We have a steel shaft that rotates at 3 Hz shown in the figure. The shaft is divided into two segments; AB and BC. Segment Ab is a solid shaft that has a diameter derived from the equation x² + y² = 625 expressed in millimeters. For segment BC, we have a solid section with dimensions derived from the equation 25x² + 36y²-22500 = 0 expressed in millimeters. Find the maximum shear stress and the angle of rotation of point C relative to point A. Use G = 83 GPa 55 kNccw 30 kNccw B 85 kN 2 C A 6 m 3 m

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.7.12P

See similar textbooks

Similar questions

A stepped shaft ABC consisting of two solid, circular segments is subjected to uniformly distributed torque t1acting aver segment 1 and concentrated torque t2applied at C, as shown in the figure. Segment 1 of the shaft has a diameter of d1= 57 mm and length of L1= 0.75 m; segment 2 has a diameter d2— 44 mm and length L2= 0.5 m. Torque intensity /,"= 3100 N . m/m and T2= 1100 N. m. (a) Find reaction torque TAat support A. (b) Find the internal torque T(x) at two locations: .x = L1/2 and at .x = L1+ L2/2. Show these internal torques on properly drawn free-body diagrams.
A stepped shaft ABC consisting of two solid, circular segments is subjected to torques T}and T2acting in opposite directions, as shown in the figure. The larger segment of the shaft has a diameter of dv- 2.25 in. and a length Lt= 30 in.; the smaller segment has a diameter d2— 1.75 in. and a length L, = 20 in. The torques are T, = 21,000 lb-in. and fz=10.000 lb-in. (a) Find reaction torque TAat support A. (b) Find the internal torque T(x) at two locations: x = L1/2 and x = L1+ L2/2. Show these internal torques on properly drawn free-body diagrams (FBDs).
Derive the following formula for the distancee from the centerline of the wall to the shearcenter S for the C-section of constant thicknessshown in the figure: e = [3bh2(b+2a)-8ba3] / [h2(h+6b)+4a2(2a-3h)] Also, check the formula for the special cases of achannel section (a = 0) and a slit rectangular tube(a =h/2).
A circular shaft of the dimensions shown in the following figure is subjected to three torques : T1 = 28 k-in, T2 = -8 k-in and T3 = 10 k-in. (a) What is the angle of twist of the right end due to the applied torque? (b) Plot the angle of twist diagram along the shaft. Let, G= 12×106 psi.
A solid shaft in a rolling mill transmits 30kW at 100 rpm. Find the diameter in mm of the shaft so as not to exceed a shearing stress of 80 MPa and an angle of twist of more than 10 degrees in a length of 8 meters. G = 83 GPa
A Solid shaft transmits 600 N.m torque. If the maximum shear stress induced in the shaft is 50 N/mm2, the minimum diameter of the shaft is
A solid shaft 100 mm diameter transmits 100.6 horsepower with a maximum allowable shear stress 25 MN/m ^2 . What is the spced of rotation of the shaft in (r.p.m)? (b) If the solid shaft is replaced by the hollow shafl transmitting 100 kW at the same rotation speed of the solid shaft. The hollow shaft has a mean torque =5/6 of maximum torque with the angle of twist 0.35° per meter length of the shafl and G= 80 GN/m^2 Determine the dimensions ofr the hollow shaft if the internal diameter of the shaft is to be 80 % of the external diameter.
A steel shaft with a diameter 1.85 inches and length 4.25 feet transmits 75 HP from an electric motor to a compressor. The allowable shear stress is 7500 psi and the allowable angle of twist is 2.1 Degress. G= 12x10^6Deterrmine the following: (No Scientific Notation answers) a. Determine the polar moment of inertia (in in^4) of the steel shaft: b. Determine the required torque (in lb-in) as limited by stress: c. Determine the required torque (in lb-in) as limited by the angle of twist: d. Determine the minimum allowable speed of rotation (in rpm):
A bar (AC) is effected by a torque (T) at the free end by (2T) in the opposite direction at the other end, as shown in the following figure. Find the total angle of distortion of the bar (AC) shown in the following figure if the shear stress (Ts = 700 N/cm?) and modulus of rigidity (G = 0.84* 106 N/cm?).
A motor drives a shaft at 12 Hz and delivers 20 kW of power as shown in Fig.4. (a) If the shaft has a diameter of 30 mm, what is the maximum shear stress τmax in the shaft? (b) If the maximum allowable shear stress is 40 MPa, what is the minimum permissible diameter dmin of the shaft? A solid circular bar of diameter d = 50 mm is twisted in a testing machine until the applied torque reaches the value T = 500 Nm as shown in Fig.4. At this value of torque, a strain gage oriented at 45 ° to the axis of the bar gives a reading ε =339 ×10-6 . What is the shear modulus G of the material?
Falcon company Nizwa is conducting a campus interview to you. You are asked to design the propeller shaft with the following specification. (i) Power transmission =60 kW,(ii) Shaft speed = 160 rpm,(iii)The angle of twist / m length = 1.1º(iv)Maximum twisting moment is 30% greater than its mean. (v) Take Modulus of rigidity as 105 Gpa. (i) Mean torque of the shaft (unit in Nm) = (ii)Maximum torque of shaft (unit in Nm) = (iii) The diameter of the shaft (unit in mm) = iv) Maximum shear stress in the shaft (Unit in MPa) is
Q4. A shaft of solid circular cross section consisting of two segments is shown in the first part of the figure. The left-hand segment has diameter 80 mm and length 1.2 m; the right-hand segment has diameter 60 mm and length 0.9 m. Shown in the second part of the figure is a hollow shaft made of the same material and having the same length. The thickness t of the hollow shaft is d/10, where d is the outer diameter. Both shafts are subjected to the same torque. If the hollow shaft is to have the same torsional stiffnesses the solid shaft, what should be its outer diameter d?