MET313: Applied Strength of Materials Week-5 Guided Practice Problem 1 (Columns) A round compression member with both ends pinned and made of AISI 1020 cold-drawn steel is to be used in a machine. Its diameter is 25 mm, and its length is 950 mm. What maximum load can the member take before buckling would be expected? Also compute the allowable load on the column for a design factor of N = 3. Solution Objective Compute the critical buckling load for the column and the allowable load for a design factor of N = 3. Given L = 950 mm. Cross section is circular; D = 25 mm. Pinned ends. Column is steel; AISI 1020 cold-drawn. From Appendix A-14: sy = 441 MPa; E = 207 GPa = 207 109 N/m Analysis Use the Method of Analyzing Columns from the texbtook. Results Step 1. Determine the end-fixity factor. For the pinned-end column, K = 1.0. Step 2. Compute the effective length. Le=KL = 1.0(L) = 950 mm Step 3. Compute the smallest value of the radius of gyration. From Appendix A-1, for any axis of a circular cross section, r = D/4. Then, 25 mm 6.25 mm 4 Step 4. Compute the slenderness ratio, SR = Le/r. Le SR = Step 5. Compute the column constant, Cc. = 950 mm 152 6.25 mm Ce = 2ZE Sy 2(207 10 N/m) 441 x 106 N/m = 96.3 Step 6. Compare Cc with SR and decide if column is long or short. Then use the appropriate column formula to compute the critical buckling load. Since SR is greater than Cc, Euler's formula applies. The area is Then EA Per = (SR) D 4 (25 mm)2 = 491 mm 4 Por = (207 x 10 N/m)(491 mm) (152) Step 7. A design factor of N = 3 is specified. Step 8. The allowable load, Pa, is 1 m (10 mm) 43.4 kN Per 43.4 kN = 14.5 kN Pa = N 3 Solve the above problem with different input parameters as given below (Please, keep other input parameters the same): Problem Case Column diameter (mm) Column Length (mm) Allowable Load (kN) Guided 50 1200 ? Practice 1. What is the objective of the solution? 2. Which input is provided in the problem? 3. Which equations will be employed to develop the solution, i.e. provide the equations to obtain the solution? 4. What are the results? Week-5 Guided Practice Problem 2 (Pressure Vessels) Compute the magnitude of the maximum longitudinal, hoop, and radial stresses in a cylinder carrying helium at a steady pressure of 10 000 psi. The outside diameter is 8.00 in and the inside diameter is 6.40 in. Specify a suitable material for the cylinder. Solution Objective Compute the maximum stresses and specify a material. Given Pressure = p = 10 000 psi. Do = 8.00 in. Di = 6.40 in. Analysis Use Procedure C from this section in Chapter 12 from the textbook. Results Step 1. Dm = (Do + Di)/2 = (8.00 + 6.40)/2 = 7.20 in = Step 2. t (Do Di)/2 = (8.00 - 6.40)/2 = 0.80 in Dm/t = 7.20/0.80 = 9.00 - Step 3. This step does not apply. Cylinder is thick. Step 4. Use equations from Table 12-1 from the textbook. a = Di/2 = 6.40/2 = 3.20 in b = Do/2 = 8.00/2 = 4.00 in P(b + a) (10000 psi)(4.002 + 3.202) in 45 560 psi hoop b - a (4.00 - 3.20) in pa (10000 psi)(3.20 in) 02 b-a (4.00 - 3.20) in = 17780 psi longitudinal 03 = -p=-10000 psi radial All three stresses are a maximum at the inner surface of the cylinder. Step 5. Let the design stress = Od = Sy/4. Step 6. The maximum stress is the hoop stress, 1 = 45 560 psi. Then the required yield strength for the material is Sy = d x 4 = 45,560 4 = 182,240 psi or use 183 ksi Step 7. From Appendix A-14, we can specify AISI 4140 OQT 700 steel that has a yield strength of 212 ksi since 212ksi > the 183 ksi limit. Solve the above problem with different input parameters as given below (Please, keep other input parameters the same): Problem Case Pressure (psi) (in) Outside Diameter Inside Diameter Max Hoop Stress (psi) (in) Guided 15000 Practice 7.5 5 ? 1. What is the objective of the solution? 2. Which input is provided in the problem? 3. Which equations will be employed to develop the solution, i.e. provide the equations to obtain the solution? 4. What are the results?