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MUST SOLVE BY HAND AND USING MATLAB CODE. BY HAND IT MEANS THAT THE ENTIRE PROBLEM SHOULD BE STEP-BY-STEP PROCESS LIKE IF THE CODE DID NOT EXIST. YOU ARE ALLOWED TO USE THE CODE AS A MEAN OF CALCULATIONS. Consider the shaft with a shoulder fillet at the middle (r = 1/2). The material is AL2024-T3. Use the loads provided in item 5. The shaft is machined, with a 95 % reliability, subject to an operating temperature of 350F. Assume residual stress effects are important and are taken into account using a factor of 0.7 (this is an added factor to your ks). An additional factor of safety of 1.25 is desired. For a d = 2.15" and a proposed Aluminum (2024-T3) built shaft, D=1.25 d, do fatigue assessment at this location. The fillet has a radius of 0.125-in. You are asked to determine if the substructure will be safe. 1. Write the material properties. 2. Find is K, for all loading conditions. 3. Find is K, for all loading conditions (axial, bending, torsion). Use traditional approach (assuming that plastic strain at notch can be avoided: K = K = R.). 4. What would be the load factors for mean and alternate stress components? (a) Find endurance limit: i. Find is S. ii. Determine ka iii. Calculate Se (b) Determine the stress for N = 100,100 (Sun and Sut). (c) Staying nonconservative (using different curves for low and high cycles), plot the S-N Diagram. Also, the Fatigue Diagram. Do this by hand and compare with MATLAB code. (d) Find the curve constants for high cycle fatigue. In other words, determine the constants a and bin Sn = a (Use the Basquin Equation treatment as posted in Class koctures. Note that Equations 6-14 and 6-15 only apply to materials with an endurance limit at 10%) 5. Use Distortional Energy find all stress values (should be in ksi). (*) The following is the three-loading sequence In a 30-second repetitive data the following sequence is know: i. LOAD CASE A: 5,000 cycles a) The moment load M is fully reversed at 20,000 in-lb. b) Torque T is fully reversed at 5,000 in 1b. ii. LOAD CASE B: 1,000 cycles a) The axial load P is fully reversed at 20,000 lb. b) The moment load M fluctuates in tension at 10,000 in lb. c) Torque T fluctuates in tension at 15,000 in Ib. ii. LOAD CASE C: 2,000 cycles a) Axial load P is alternates from 5,000 to 20,000 lb. b) Torque is fully reversed at 5,000 in-lb. (b) For each load case, find the alternating and mean fatigue stresses (S., S...). These are using the von Mises values from you alternating and mean state of stresses (not Goodman). (Lecture notes) (c) Check for static failure for maximum absolute value of the londs for each loading cycle. (Lecture notes) () Note that is calculated using Son =aN-N- where Sc is the Goodman stress, and a and b are calculated from the MATLAB code (provide hand calculations, as well) 6. How many duty cycles before failure? We need the part in service for 300 days a year. (Lecture notes) B 12 ) SD NNN where B, are duty cycles, n, the service cycles for theith cycle loading conditions, the life cycles for theith cycle loading conditions, and the damage parameter (D = 1, for this homework). 1/ + Example (not values from this homework): Ta + N B, 3 m B + S1 , + NNN B, 1.34761 x 10-5 B, S72705.7 duty cycles 90 sec hr B, S72705.7 duty cycles (1 day 1 duty 60 sec = 75.74 days 60 min 24 hr If 300 days were required, the part for this mini-example would not meet the requirement. Resign is recom- mended 11 TE 13 7. Assume 1 duty cycle for this part (B). If we want to add an additional fully reversed torque load of 5000 Ib-in, how many remaining cycles of life would you predict for the shaft at this final level of londing? (Lecture notes) B; ( NNNN (Hint: We are looking for 14, and Na is found from the given loading condition.) 8. This problem was solved using von Mises stresses. An alternative approach is to use the principal stresses instead. From the MATLAB code, do you see any difference in the calculation of B, (from item 6) when using principal stresses instead of von Mises? Explain. No need to redo the problem by hand. Use may use the code to find the life and then calculate By by hand, 9. 100 points to provide a code run. MUST SOLVE BY HAND AND USING MATLAB CODE. BY HAND IT MEANS THAT THE ENTIRE PROBLEM SHOULD BE STEP-BY-STEP PROCESS LIKE IF THE CODE DID NOT EXIST. YOU ARE ALLOWED TO USE THE CODE AS A MEAN OF CALCULATIONS. Consider the shaft with a shoulder fillet at the middle (r = 1/2). The material is AL2024-T3. Use the loads provided in item 5. The shaft is machined, with a 95 % reliability, subject to an operating temperature of 350F. Assume residual stress effects are important and are taken into account using a factor of 0.7 (this is an added factor to your ks). An additional factor of safety of 1.25 is desired. For a d = 2.15" and a proposed Aluminum (2024-T3) built shaft, D=1.25 d, do fatigue assessment at this location. The fillet has a radius of 0.125-in. You are asked to determine if the substructure will be safe. 1. Write the material properties. 2. Find is K, for all loading conditions. 3. Find is K, for all loading conditions (axial, bending, torsion). Use traditional approach (assuming that plastic strain at notch can be avoided: K = K = R.). 4. What would be the load factors for mean and alternate stress components? (a) Find endurance limit: i. Find is S. ii. Determine ka iii. Calculate Se (b) Determine the stress for N = 100,100 (Sun and Sut). (c) Staying nonconservative (using different curves for low and high cycles), plot the S-N Diagram. Also, the Fatigue Diagram. Do this by hand and compare with MATLAB code. (d) Find the curve constants for high cycle fatigue. In other words, determine the constants a and bin Sn = a (Use the Basquin Equation treatment as posted in Class koctures. Note that Equations 6-14 and 6-15 only apply to materials with an endurance limit at 10%) 5. Use Distortional Energy find all stress values (should be in ksi). (*) The following is the three-loading sequence In a 30-second repetitive data the following sequence is know: i. LOAD CASE A: 5,000 cycles a) The moment load M is fully reversed at 20,000 in-lb. b) Torque T is fully reversed at 5,000 in 1b. ii. LOAD CASE B: 1,000 cycles a) The axial load P is fully reversed at 20,000 lb. b) The moment load M fluctuates in tension at 10,000 in lb. c) Torque T fluctuates in tension at 15,000 in Ib. ii. LOAD CASE C: 2,000 cycles a) Axial load P is alternates from 5,000 to 20,000 lb. b) Torque is fully reversed at 5,000 in-lb. (b) For each load case, find the alternating and mean fatigue stresses (S., S...). These are using the von Mises values from you alternating and mean state of stresses (not Goodman). (Lecture notes) (c) Check for static failure for maximum absolute value of the londs for each loading cycle. (Lecture notes) () Note that is calculated using Son =aN-N- where Sc is the Goodman stress, and a and b are calculated from the MATLAB code (provide hand calculations, as well) 6. How many duty cycles before failure? We need the part in service for 300 days a year. (Lecture notes) B 12 ) SD NNN where B, are duty cycles, n, the service cycles for theith cycle loading conditions, the life cycles for theith cycle loading conditions, and the damage parameter (D = 1, for this homework). 1/ + Example (not values from this homework): Ta + N B, 3 m B + S1 , + NNN B, 1.34761 x 10-5 B, S72705.7 duty cycles 90 sec hr B, S72705.7 duty cycles (1 day 1 duty 60 sec = 75.74 days 60 min 24 hr If 300 days were required, the part for this mini-example would not meet the requirement. Resign is recom- mended 11 TE 13 7. Assume 1 duty cycle for this part (B). If we want to add an additional fully reversed torque load of 5000 Ib-in, how many remaining cycles of life would you predict for the shaft at this final level of londing? (Lecture notes) B; ( NNNN (Hint: We are looking for 14, and Na is found from the given loading condition.) 8. This problem was solved using von Mises stresses. An alternative approach is to use the principal stresses instead. From the MATLAB code, do you see any difference in the calculation of B, (from item 6) when using principal stresses instead of von Mises? Explain. No need to redo the problem by hand. Use may use the code to find the life and then calculate By by hand, 9. 100 points to provide a code run