Jing Zheng
Problem 13-3 (13.3%)
Statements: Find the torsional yield and ultimate shear strength of an 0.105-in-dia, unset A230 wire to be used in a helical compression spring.
Hints:
(a) (10%) ASTM A230 is not listed in Table 13-4, but it is shown in Figure 13-3. At the wire diameter given, it has a tensile strength that is approximately the same as that for A229. From Table 13-4, find the A and b for A229
(b) (30%) Using equation 13.3, calculate the Tensile strength Sut.
(c) (30%) From Table 13-6, find the factor for maximum torsional yield strength, Sys. Calculate the yield strength, Sys.
(d) (30%) Using equation 13.4, calculate the ultimate shear strength, Sus.
Problem 13-6 (13.3%)
Statements: What are the spring rate and spring index of a squared and ground compression spring with d=1 mm. D=10 mm. And 12 total coils?
Hints: The spring wire is steel so that G=80.8 Gpa.
(a) (20%) From Figure 13-9, find the number of active coils, Na.
(b) (40%) Using equation 13.7, find the spring rate, k.
(c) (40%) Using equation 13.5, find the spring index, C.
Problem 13-7 (13.3%)
Statements: Find the natural frequency of the spring in Problem 13-6
Hints:
(100%) Calculate the natural frequency by using equation 13.11c. The spring wire is steel so that G=80.8 GPa and g=0.28 lbf·in-3, or 76005 N·m-3.
Problem 13-21 (20%)
Statements: Design a helical compression spring for a static load of 400 N at a deflection of 45 mm with a safety factor of 2.5. Use C=8. Specify all parameters necessary to manufacture the spring. State all assumptions.
Hints: Assume we are using ASTM A228 wire and the wire diameter is 5mm. Example 13-3 is a good model for you to follow in terms of equations and steps that are necessary for your calculations.
(a) (30%) Determine the desired spring rate, calculate the mean coil diameter and number of active coils. Equation (13.5), (13.7).
Note: The calculated number of active coils need to be rounded to the nearest ¼ coil as the manufacturing tolerance cannot achieve better than that accuracy. As a result, we must now calculate the actual (corrected) spring rate.
(b) (20%) Assume squared and ground ends making the total number of coils, from Figure 13-9. Then, determine the shut height and free length (see Figure 13-8).
(c) (20%) To check for buckling, two ratios need to be calculated, slenderness ratio, Lf/D and Deflection ratio, ymax/Lf. Take these two values to Figure 13-14 and find that their coordinates are safely within the zones that are stable against buckling for either end-condition case.
(d) (30%) Calculate the inside and outside coil diameters and determine the smallest hole and largest pin that should be used with this spring. Calculate the total weight of the spring. List the following parameters of this A228 wire spring: Wire diameter, outside diameter, total coils, and free length.
Problem 14-2 (20%)
Statements: A3/4-6 Acme thread screw is used to lift a 2-kN load. The mean collar diameter is 40 mm. Find the torque to lift and to lower the load using a ball-bearing thrust washer. What are the efficiencies? Is it self-locking?
Assumptions:
1. The thread coefficient of friction is m=0.15
2. The collar coefficient of friction is mc=0.02
Hints:
(a) (10%) Get the thread pitch diameter from Table 14-3. Determine the thread pitch and lead.
(b) (30%) Use equation 14.5 to determine the lifting (up) and lowering (down) torques.
(c) (30%) Use equation 14.7c to determine the lifting (up) and lowering (down) efficiencies.
(d) (30%) Use equation 14.6a to determine if the screw is self-locking.
Problem 14-7 (20%)
Statements: A ½-in dia UNC, class 7 bolt with rolled threads is preloaded to 80% of its proof strength when clamping a 3-in-thick sandwich of solid steel. Find the safety factors against static yielding and joint separation when a static 1000-lb external load is applied. Use 99% reliability.
Hints:
(a) (5%) Determine the load per bolt. Get the tensile stress area from Table 14-1. Then, calculate the preload.
(b) (5%) For a clamp length of 3 in, assume a bolt length of 4 in to allow sufficient protrusion for the nut. Define the bolt length and calculate the shank area.
(c) (20%) Find the lengths of thread lthd and shank ls of the bolt as shown in Figure 14-21, from which we can find the length of thread lt that is the clamp zone. Use lthd=2xd+0.25 in.
(d) (20%) Find the stiffness of the bolt from equation 14.11a. Calculate the material stiffness from equation 14.17, using the constants from Table 14-9a. Find the joint stiffness factor from equation 14.13c.
(e) (10%) The portions of the applied load P felt by the bolt and the material can now be found from equation 14.13.
(f) (20%) Find the resulting loads in bolt and material after the load P is applied. Then, calculate the maximum tensile stress in the bolt.
(g) (10%) This is a uniaxial stress situation, so the principal stress and von Mises stress are identical to the applied tensile stress. Calculate the safety factor against yielding. The yield strength can be found in Table 14-6.
(h) (10%) The load required to separate the joint and the safety factor against joint separation are found from equation 14.14c and 14.14d.