Concept explainers
6-37* to 6-46* For the problem specified in the table, build upon the results of the original problem to determine the minimum factor of safety for fatigue based on infinite life, using the modified Goodman criterion. The shaft rotates at a constant speed, has a constant diameter, and is made from cold-drawn AISI 1018 steel.
Problem Number | Original Problem, Page Number |
6-45* | 3–77, 153 |
3-77 A torque T = 100 N · m is applied to the shaft EFG, which is running at constant speed and contains gear F. Gear F transmits torque to shaft ABCD through gear C, which drives the chain sprocket at B, transmitting a force P as shown. Sprocket B, gear C, and gear F have pitch diameters of a = 150, b = 250, and c = 125 mm, respectively. The contact force between the gears is transmitted through the pressure angle ϕ = 20°. Assuming no frictional losses and considering the bearings at A, D, E, and G to be simple supports, locate the point on shaft ABCD that contains the maximum tensile bending and maximum torsional shear stresses. Combine these stresses and determine the maximum principal normal and shear stresses in the shaft.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
- Three round, copper alloy bars having the same length L but different shapes are shown, in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over one-fifteenth of its length. Elsewhere, the second and third bars have a diameter Id. All three bars are subjected to the same axial load P. Use the following numerical data: P = 1400 kN, L = 5m,d= 80 mm, E= 110 GPa. and v = 0.33. (a) Find the change in length of each bar. (b) Find the change in volume of each bar.arrow_forwardA crank arm consists of a solid segment of length bxand diameter rf, a segment of length bltand a segment of length byas shown in the figure. Two loads P act as shown: one parallel to — vand another parallel to —y. Each load P equals 1.2 kN. The crankshaft dimensions are A] = 75 mm, fr> = 125 mm, and b3= 35 mm. The diameter of the upper shaft isd = 22 mm, (a) Determine the maximum tensile, compressive, and shear stresses at point A, which is located on the surface of the shaft at the z axis. (b) Determine the maximum tensile, compressive, and shear stresses at point B, which is located on the surface of the shaft at the y axisarrow_forwardA 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_forward
- Solve the preceding problem for the following data:P = 160 kN,JV = 200 tN,L = 2 m,b = 95 mm, h = 300 mm, and d = 200 mmarrow_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_forwardA magnesium-alloy wire of diameter d = 4mm and length L rotates inside a flexible tube in order to open or close a switch from a remote location (see figure). A torque Tis applied manually (either clockwise or counterclockwise) at end 5, thus twisting the wire inside the tube. At the other end A, the rotation of the wire operates a handle that opens or closes the switch. A torque T0 = 0.2 N · m is required to operate the switch. The torsional stiffness of the tube, combined with friction between the tube and the wire, induces a distributed torque of constant intensity t = 0.04N m/m (torque per unit distance) acting along the entire length of the wire. (a) If the allowable shear stress in the wire is T allow = 30 MPa, what is the longest permissible length Lmaxof the wire?arrow_forward
- The figure shows a shaft mounted in bearings at A and D and having pulleys at B and C. The forces shown acting on the pulley surfaces represent the belt tensions. The shaft is to be made of AISI 1035 CD steel. The shaft is rotating at speed of 1000 rpm. Find the minimum factor of safety for fatigue based on infinite life. If the life is not infinite, estimate the number of cycles. Be sure to check for yielding. Take shaft diameter to be 1.5 inches.arrow_forwardThe rotating shaft shown in the figure is machined from AISI 1020 CD steel. It is subjected to a force of F = 6 kN. Find the minimum factor of safety for fatigue based on infinite life. If the life is not infinite, estimate the number of cycles. Be sure to check for yielding. The diameter of the bar is 35 mm and the radius of the step down in the shaft is 3 mm. All dimensions listed below are in mm. 25 D. 20 - 20 -35 D. 180 -3 R. 500- F 280- -175- -50 D. -25 D. -20 20arrow_forward7-5 A rotating step shaft is loaded as shown, where the forces FA and F3 are constant at 600 lbf and 300 lbf. respectively, and the torque T alternates from 0 to 1800 lbf - in. The shaft is to be considered simply supported at points O and C, and is made of AISI 1045 CD steel with a fully corrected endurance limit of S₂ = 40 kpsi. Let Kf = 2.1 and K = 1.7. For a design factor of 2.5 determine the minimal acceptable diameter of section BC using the (a) DE-Gerber criterion. (b) DE-Goodman criterion. n 6 in FA = 600 lbf 6 in FB = 300 lbf 6 in T, n Page 413arrow_forward
- 2. The rotating shaft shown in the figure is machined from AISI 1020 CD steel. It is subjected to a force of F= 5.7 kN. Find the minimum factor of safety for fatigue based on infinite life. If the life is not infinite, estimate the number of cycles. Be sure to check for yielding. 25 D.- 20- -20 -35 D. -180- -500- -3 R. 280- (units in mm) -175- -50 D. -25 D. -20 -20arrow_forwardQ-3 A 25-mm-diameter solid round bar has a groove 2.5-mm deep with a 2.5-mm radius machined into it. The bar is made of AISI 1050 CD steel and is subjected to a purely reversing torque of 250 N-m. For the S-N curve of this material, let f = 0.9. (a) Estimate the number of cycles to failure. (b) If the bar is also placed in an environment with a temperature of 400°C, estimate the number of cycles to failure.arrow_forwardCarbon Steel L=100mm dsmall= 20mm moment of inertia ratio between stepped cross-sectional area = 1:2 F=2500 N at A and a fillet radius at the step of 2mm -loading cycles that the design can withstand before fatigue failure - calculate cycles using goodman line and max stress from static analysis. -determine the effect of the 2mm fillet ratio on the fatigue analyisis. constant force at Aarrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning