MECHANICAL DESIG AND MACHINE ELEMENTS ME 322A
Jing Zheng
Problem 6-3 (23.1%)
Statements: For the bicycle pedal-arm assembly in Figure P6-1 assume a rider-applied force that ranges from 0 to 1500 N at the pedal each cycle. Determine that fluctuating stresses in the 15-mm-diameter pedal arm. Find the fatigue safety factor if S ut
=500 Mpa.
Hints:
(a) (30%) From Problem 4-3, the maximum principal stresses in the pedal arm due to
F max
are at point A:
σ
1max
=793 Mpa;
σ
2max
=0 Mpa;
σ
3max
=-23 Mpa
If your answers on homework 4 do not agree, use these numbers, because these are correct!
Calculate the maximum and minimum von Mises stress. Then find out the alternating and mean components of the von Mises stress (6.1)
(b) (10%) Calculate the unmodified endurance limit (Page 324~326):
(c) (40%) Calculate the endurance limit modification factors for a non-rotating round beam. Remember these factors are C load
(Page 326), C size
(Page 326~327), C surface
(Page 327~330), C temperature
(Page 330~331), and C reliability
(Page 331).
(d) (10%) Calculate the modified endurance limit.
(e) (10%) Assuming a Case 3 load line, use equation (6.18e) (Page 360~3364)to determine the factor of safety.

MECHANICAL DESIG AND MACHINE ELEMENTS ME 322A
Jing Zheng
Problem 6-5 (15.4%)
Statements: For the data in row “a” assigned in Table P6-3, find the corrected endurance strength (or limit), create equations for the S-N line, and draw the S-N diagram.
Hints:
(a) (10%) Using equation 6.5, Page 324~326, calculate the uncorrected endurance limit.
(b) (50%) Calculate the endurance limit modification factors for a non-rotating round rod. Page (326~331)
(c) (10%) Calculate the modified endurance limit
(d) (10%) Use equation 6.9 (Page 333) to calculate the fatigue strength at N=10
3 cycles.
(e) (20%) Determine the constants a and b for the S-N curve equation in the HCF region from equations 6.10c and 6.10a. From Table 6-5, for N=10
6
, z=-3.000
Plot the S-N curve over the range from N=10
3
to N=10
8
.

MECHANICAL DESIG AND MACHINE ELEMENTS ME 322A
Jing Zheng
Problem 6-7 (23.1%)
Statements: Design the wrist pin of Problem 3-7 (p.127) for infinite life with a safety factor of 1.5 if the 2500 g acceleration is fully reversed and S ut
=130 ksi.
Hints:
(a) (30%) The piston and wrist pin along with the connecting rod assembly cut-away view is shown as the figure on the right. We can see that the wrist pin is under pure shear
(well, almost) stress. It is reasonable to assume that the pin is under direct shear stress only.
From the answer of the Problem 3-7, the total force on wrist pin is 12258 kN. Calculate the force on each shear plane in unit of lbf.
Calculate the shear stress at each shear plane.
Find the relationship of the factor of safety for fully reversed loading, Nd, with the outer diameter and inner diameter, and S e
.
(b) (10%) Calculate the unmodified endurance limit.
(c) (40%) Calculate the endurance limit modification factors for a non-rotating round rod. Page (326~331). Remember, one of the modification factor can NOT be calculated because the od and id are unknown. (right?) Then calculate the modified endurance limit.
(d) (20%) Since the outer diameter and inner diameter of the pin are not known yet, we have to guess the one of them in order to solve for another. In order to make life easier, let’s say we assume that the od = 0.375 in. Now, we have an equation that has N d
on one side, and an implicit expression of id on the other side. In order to solve for id , we can use a excel sheet and guess an initial id number, say, 0.2 in, to solve for id . After you find the accurate id , you may want to round it up to a common fraction, 5/32, 7/64, for example. Then, use this id to find out the realized factor of safety.

MECHANICAL DESIG AND MACHINE ELEMENTS ME 322A
Jing Zheng
Problem 6-41 (31%)
Statements: A 10-mm-ID steel tube carries liquid at 7 MPa. The pressure varies periodically from zero to maximum. The steel has S ut
=400 MPa. Determine the infinitelife fatigue safety factor for the wall if its thickness is: (a) 1mm. (b) 5mm.
Hints: The tubing is long, therefore the axial stress is zero.
(a) (20%) For t=1mm. This is a thick wall cylinder, calculate the maximum principal stresses by using the equations on Page 201 (4.47). Is there any applied shear stress in this case? What is the difference between principal stresses and the radial and tangential stresses you calculated by directly using equation 4.47a and 4.47b?
Calculate the minimum, maximum, alternating, and mean von Mises effective stress by using equation (5.7c), page 245.
(b) (40%) Calculate the unmodified endurance limit;
Calculate the endurance limit modification factors for axial loading, C load
, C size,
C surface, etc.
Calculate the modified endurance limit;
(c) (10%) Assuming a Case 3 load line, calculate the factor of safety from equation
(6.18e).
(d) (20%) For t=5mm, calculate the maximum principal stresses.
Calculate the minimum, maximum, alternating, and mean von Mises effective stress.
(e) (10%) Do you have to re-calculate the endurance limit?
Assuming a Case 3 load line, calculate the safety factor.

MECHANICAL DESIG AND MACHINE ELEMENTS ME 322A
Jing Zheng
Problem 6-58 (7.7%)
Statements: A steel, grooved shaft similar to that shown in Figure E-5 (Appendix E) is to be loaded in bending. Its dimensions are D=2.25 in, d=1.5 in, r=0.125 in. Determine the fatigue stress-concentration factor if the material S ut
=164 ksi.
Hints:
(a) (30%) The geometric stress-concentration factor is found from the equation in
Figure E-5.
(b) (10%) The Neuber constant is found by linear interpolation of the values in Table
6-6, page 340.
(c) (30%) Calculate the notch sensitivity by using equation 6.13, page 339.
(d) (30%) The fatigue stress-concentration factor can now be found from equation
6.11b, page 339.