Concept explainers
6-47* to 6-50* 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. If the life is not infinite, estimate the number of cycles. The force F is applied as a repeated load. The material is AISI 1018 CD steel. The fillet radius at the wall is 0.1 in, with theoretical stress concentrations of 1.5 for bending. 1.2 for axial, and 2.1 for torsion.
Problem Number | Original Problem, Page Number |
6-48* | 3-81, 154 |
3-81* Repeat Prob. 3-80 with Fx = 0, Fy = 175 lbf, and Fz = 100 lbf.
3-80* The cantilevered bar in the figure is made from a ductile material and is statically loaded with Fy = 200 lbf and Fx = Fz = 0. Analyze the stress situation in rod AB by obtaining the following information.
- (a) Determine the precise location of the critical stress element.
- (b) Sketch the critical stress element and determine magnitudes and directions for all stresses acting on it. (Transverse shear may only be neglected if you can justify this decision.)
- (c) For the critical stress dement, determine the principal stresses and the maximum shear stress.
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)
- An aluminum bar has length L = 6 ft and diameter d = 1.375 in. The stress-strain curse for the aluminum is shown in Fig. 1.34. The initial straight, line part of the curve has a slope (modulus of elasticity) of 10.6 × 106 psi. The bar is loaded by tensile forces P = 44.6 k and then unloaded. (a) That is the permanent set of the bar? (b) If the bar is reloaded. what is the proportional limit? hint: Use the concepts illustrated in Figs. l.39b and 1.40.arrow_forwardSolve the preceding problem if the thickness of the steel plate is. t = 12 mm. the gage readings are x = 530 × 10-6 (elongation) and y = -210 -× l0-6 (shortening), the modulus is E = 200 GPa, and Poisson’s ratio is v = 0.30.arrow_forwardSolve 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_forward
- -11 A rubber cube R of a side L = 3 in. and cross- sectional area A = 9 in2 is compressed inside a steel cube S by a force F = 5 lb that applies uniformly distributed pressure to the rubber. Assume E 0.3ksi and,, = 0.45. (a) Calculate the lateral pressure between the rubber and steel (disregard friction between the rubber and the steel, and assume that the steel block is rigid when compared to the rubber). (b) Calculate the change in volume of the rubber.arrow_forwardThe strength-to-weight ratio of a structural material is defined as its load-carrying capacity divided by its weight. For materials in tension, use a characteristic tensile stress obtained from a stress-strain curve as a measure of strength. For instance, either the yield stress or the ultimate stress could be used, depending upon the particular application. Thus, the strength-to-weight ratio RS/Wfor a material in tension is defined as Rs/w= in which a is the characteristic stress and 7 is the weight density. Note that the ratio has units of length. Using the ultimate stress Uas the strength parameter, calculate the strength-to-weight ratio (in units of meters) for each of the following materials: aluminum alloy 606I-T6, Douglas fir (in bending}, nylon. structural steel ASTM-A57.2, and a titanium alloy. Obtain the material properties from Tables [-1 and 1-3 of Appendix I. When a range of values is given in a table, use the average value.arrow_forwardRequired information The cold-drawn AISI 1040 steel bar shown in the figure is subjected to an axial load that fluctuates from 8 kN to 30 kN. Use the Modified Goodman criterion and estimate the fatigue factor of safety based on achieving infinite life and the yielding factor of safety. 25 mm 10mm -6-mm D. What is the number of cycles to failure for this part? The number of cycles is 120000arrow_forward
- This problem illustrates that the factor of safety for a machine element depends on the particular point selected for analysis. Here you are to compute factors of safety, based upon the distortion-energy theory, for stress elements at A and B of the member shown in the figure. This bar is made of AISI 1006 cold-drawn steel and is loaded by the forces F = 0.55 kN, P = 8.0 kN, and T = 30 N m = 280 MPa 100 mm A B d=20 mmarrow_forwardThe 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 cold-drawn AISI 1040 Q&T at 205 ◦C steel bar shown in the figure is subjected to a completely reversed axial load fluctuating between 28 kN in compression to 28 kN in tension. Estimate the fatigue factor of safety based on achieving infinite life, and the yielding factor of safety for the following cases. If infinite life is not predicted, estimate the number of cycles to failure.a) for the part given in Fig 2(a) and b) for the part given in Fig. 2 (b) using the same dimensions (W=25mm, r=3mm, the thickness of 10 mm)arrow_forward
- Required information This problem illustrates that the factor of safety for a machine element depends on the particular point selected for analysis. Here you are to compute factors of safety, based upon the distortion-energy theory, for stress elements at A and B of the member shown in the figure. This bar is made of AISI 1006 cold-drawn steel and is loaded by the forces F= 0.55 kN, P= 4 kN, and T=25 N-m. Given: Sy= 280 MPa. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. B 15-mm D. -100 mm What is the value of the axial stress at point A? The value of the axial stress at point A is MPa.arrow_forwardA solid square rod is cantilevered at one end. The rod is 0.6 m long and supports a completely reversing transverse load at the other end of ±2 kN. The material is AISI 1080 hot-rolled steel. If the rod must support this load for 10* cycles with a design factor of 1.5, what dimension should the square cross section have? Neglect any stress concentrations at the support end.arrow_forwardThe plate of the figure is subjected to a bending moment with irregular cycles, which are repeated. In the graphic one of this cycles is represented in terms of stress which appears in each section whose height is h. The piece is made of ductile steel. Determine the number of repetitions of the sequence which the piece can resist before the failure takes place due to fatigue considering a reliability of 95 %. Data: Sult = 1.000 MPa Syp 3D800 Mра thickness e = 4 mm H = 10 cm h = 5 cm r=1 cm ka = 0,72 kp = 0,95 S(MPa) M 400 h 300 200 100 W -100 -200arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning