Concept explainers
Generalize Prob. 3-62 for a solid shaft of diameter d replaced with a hollow shaft of the same material with an outside diameter d, and an inside diameter that is a fraction of the outside diameter, x × d, where x is any value between zero and one. Obtain expressions for percentage reduction in torque transmission and percentage reduction in weight in terms of only x. Notice that the length and diameter of the shaft, and the material, are not needed for this comparison. Plot both results on the same axis for the range 0 < x < 1. From the plot, what is the approximate value of x to obtain the greatest difference between the percent decrease in weight and the percent decrease in torque?
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
- 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).arrow_forwardCompare the angle of twist 1 for a thin-walled circular tube (see figure) calculated from the approximate theory for thin-walled bars with the angle of twist 2 calculated from the exact theory of torsion for circular bars, Express the ratio 12terms of the non-dimensional ratio ß = r/t. Calculate the ratio of angles of twist for ß = 5, 10, and 20. What conclusion about the accuracy of the approximate theory do you draw from these results?arrow_forwardA motor driving a solid circular steel shaft with diameter d = 1.5 in, transmits 50 hp to a gear at B, The allowable shear stress in the steel is 6000 psi. Calculate the required speed of rotation (number of revolutions per minute) so that the shear stress in the shaft does not exceed the allowable limit.arrow_forward
- A tubular shaft being designed for use on a construction site must transmit 120 kW at 1,75 Hz, The inside diameter of the shaft is to be one-half of the outside diameter. If the allowable shear stress in the shaft is 45 MPa, what is the minimum required outside diameter d?arrow_forwardWhat is the maximum power that can be delivered by a hollow propeller shaft (outside diameter 50 mm, inside diameter 40 mm, and shear modulus of elasticity 80 GPa) turning at 600 rpm if the allowable shear stress is 100 MPa and the allowable rate of twist is 3.0°/m?arrow_forwardRepeat Problem 3.3-1, but now use a circular tube with outer diameter d0= 2.5 in. and inner diameter di= 1.5 in.arrow_forward
- Mechanical design A shaft with the following data: 1- The pulley (A) is 1000 mm in diameter and weight 300N. 2- The gear (B) pitch diameter is 600mm and weight -250N. 3- The pulley is keyed to the shaft at 400mm to the left of left hand bearing. 4-the distance between bearing C and B is 1250 mm. 5- The power is 20 kW at 750 rpm. 6- Tension ratio T1 / T2-2.5 7- The shaft d.livers power to a gear placed horizontally in front, the pressure angel of gear is 20. 8- The allowable shear stress is 70N / mm, kt-2 and km- 1.5. Determine: the diameter of shaftarrow_forward3. A motor is connected by a belt to pulley B. T, is the tight-side tensile force equal to 1800 N. The shaft spins at a constant speed, 650 rpm. The power delivered by the motor is 12.6 kW. On pulley A, connected to the load, the slack side of the belt has a tension equal to th of the tight side. b T T, B d shaft Dimensions are as follows: da 200 тm 300 тт | 250 тm |180 тm | 250 тm 26 тm dB dahaft a We analyzed a problem similar to this on Test 01 using static failure theories. Is this strictly correct? Because the shaft is spinning, would not a material particle see a time-varying reversal of the the bending stress as in the R.R. rotating beam test? Would a particle see a reversal of the torsional shear stress? Assume Sut = 370 MPa and Sy = 300 MPa. Ignore Marin factors. Ignore stress concentrations. Ignore direct shear stress (that due to V). Find the safety factors with respect to fatigue and yielding. Be guided by section 6-14 on combined loading.arrow_forwardAs seen in the figure, a construction machine is rotated by a drive mechanism consisting of belt-pulley and spur gear mechanisms. Engine power P = 5.5 kW ; engine shaft speednm = 1500 rpm ; drive pulley diameter Dt = 16 cm ; diameter of the opposite pulley Dk = 55 cm ; number of pinion teeth z1 = 21 ; number of teeth of the counter gearz2 = 60 ; pulley mechanism efficiency ηk = 0.95 ; Since the efficiency of the gear mechanism is ηd = 0.97: a) Find the output shaft speed nç and the torque Mç on this shaft.b) The force on the taut arm of the belt S1 = 450 N;coefficient of friction μ = 0.3 ; If the winding angle α = 160⁰, is the frictionally transmitted moment Ms sufficient to compensate for the Mg moment on the input shaft? Calculate.arrow_forward
- For the gear mechanism in the figure: P1 = 4 kW, η1 = 1000 rpm, z1 = 18, z2 = 36, z3 = 54, z4 = 108, z1 is the driving gear. Total efficiency values for each stage; Since η12 = η34 = 0.96; Find the output torque and speed of gear z4.arrow_forwardShaft 2 Engine D2 Flywheel Shaft 1 Propeller Refer to the figure which shows a ship's propeller, drive train, engine, and flywheel. The diameter ratio of the gears is D1/D2=2/3. The inertias in kg-m2 of gear 1 and gear 2 are 100 and 500, respectively. The flywheel, engine, and propeller inertias are 104, 103, and 2500, respectively. The torsional stiffness of shaft 1 is 5×106 N-m/rad, and that of shaft 2 is 106 N-m/rad. Because the flywheel inertia is so much larger than the other inertias, a simpler model of the shaft vibrations can be obtained by assuming the flywheel does not rotate. In addition, because the shafts between the engine, gears and propeller are short, we will assume that they are very stiff compared to shaft 2. However, there are losses in the gear system which are represened by a damper with a damping coefficient of 300 Ns/rad. If we also disregard the shaft inertias, the resulting model consists of two inertias, one obtained by lumping the engine and gear inertias,…arrow_forwardThe problem is stated below. However, change the position of torque to point C from point D. What is the effect of variation of torque placement in shaft CB?arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningPrinciples of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning