231004_ME354_Exam1b_solution

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Purdue University *

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354

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Mechanical Engineering

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Feb 20, 2024

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P URDUE NAME ____________________________________ PUID ________________________________________ Please read the instructions and initial by each statement. ______ Clearly write your name at the top of every page, including any additional blank pages you use. ______ Write only on the front of the exam pages. ______ Show all your work . A correct answer without showing any work may result in zero credit. ______ Ensure that all pages are facing the same direction. ______ Staple any extra pages used to the back of the exam before turning it in. ______ You may have one single-sided 8.5 in x 11 in crib sheet to take this exam. The crib sheet can be handwritten or typed. Staple your crib sheet to the back of the exam (after any extra pages) before turning it in. ______ The only electronic resource allowed on this exam a calculator. ME 354 – Fall 2023 EXAM 1

ME 354 Fa23 Exam 1b Name: PUID: PROBLEM No. 1 (25 points) Problem 1 consists of 10 questions. Each question is worth 2.5 points. (a) You are a designing a component and find that the stress predicted in the part is 50 kPa. Which of the following would appropriate approaches to reduce the predicted stress in the part? Select all that apply. l Increase the part’s dimensions (i.e., make the part bigger) l Decrease the part’s dimensions (i.e., make the part smaller) l Increase the load(s) acting on the part l Decrease the load(s) acting on the part l Choose a stronger material (i.e., a material with higher tensile strength) (b) The Electric Post Hole Digger shown is a tool used to drill through ice or for post hole digging, drilling, or tree planting. During operation, the extension bar shown is loaded with a combination of axial compression and torsion. Select the most appropriate cross-section to achieve a strong stress pattern when the extension bar is being loaded. I-beam Solid round bar Hollow tube Any cross-section will achieve a strong stress pattern (c) What is one reason why fatigue cracks typically initiate from a part’s free surface? Page 1 of 11 M an highest stress most likely location for stress raiser and or surface deflect

ME 354 Fa23 Exam 1b Name: PUID: (d) In the U.S. alone, there are over 700,000 bridges, all of which must be regularly inspected and maintenanced to ensure that they’re safe to use. Practices and regulations vary around the world, but most countries mandate that bridges be inspected at least once every two years. In general, inspectors conducting a bridge inspection will be looking for any flaws, defects, or potential problem areas that may require maintenance. Bridge inspections are an example of which of the following fatigue design approaches? infinite-life design safe-life design fail-safe design damage-tolerant design (e) Consider the turbine blades of a gas turbine. During start-up, the thinner sections of the blade, including the leading edge (LE) and trailing edge (TE), heat up faster than the middle section or core, leading to a temperature gradient in the blade and compressive strains in the blade’s core. The opposite happens during shut-down, leading to tensile strains in the blade’s core. It has been observed that fatigue cracks initiate at the leading edges due to alternating stresses and strains during operation. Which fatigue theory is most appropriate to analyze these turbine blades? Stress-life Linear-elastic fracture mechanics (LEFM) Strain-life (f) When calculating Marin factor k b for the stepped shaft shown below, it is more conservative to use diameter d in the calculation. true false Page 2 of 11 I both accepted as comet

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ME 354 Fa23 Exam 1b Name: PUID: (g) Determine stress concentration factor K t at the location where load F 1 acts. K t “ (h) On the axes provided, sketch and label a sinusoidal cyclic load with σ a “ 70 kpsi and σ m “ 50 kpsi. (i) The Goodman criterion is the most accurate theory for the stress-life method. true false Page 3 of 11 I run Atari 120 8min 29ps i

ME 354 Fa23 Exam 1b Name: PUID: (j) A bucket loader, like the one shown in the figure below, can tip due to heavy bucket loads. The manufacturer of a certain bucket loader claims a factor of safety of 3.0 against tipping when the bucket is loaded with material having a density of 3000 lbf/cubic yard. The bucket capacity is 8 cubic yards. The moment arms to W L and W B are at equal distance from the tipping point. W L is the weight of the bucket loader acting at its center of gravity and W B is the weight of the material in the bucket. Determine the weight of the bucket loader for the factor of safety claimed. W L “ Page 4 of 11 72,000 Ibf sum moments about the tipping point WE 3 WB 3 3000 8 72 eee lbf

ME 354 Fa23 Exam 1b Name: PUID: PROBLEM No. 2 (25 points) You are working for a major automotive company. There is a 25 mm diameter rotating component that is supported by bearings that your team is responsible for the design of. The rotating shaft is subject to completely reversed axial stress. Your boss wants to know if the following completely reversed axial stresses will cause the component to experience finite or infinite life. (a) 175 MPa (b) 425 MPa (c) 575 MPa If the given completely reversed axial stress is expected to experience finite life , please determine the number of cycles to failure. It is known that the surfaces are polished, the ultimate strength ( S ut ) is 1.0 GPa, and 99.99% reliability is desired. Sketch and label the S - N diagram for this component. Label the diagram with the three loads considered. Page 5 of 11

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Problem 2 Ge Kalutchakede Se 0.5 S ut 500 MPa ka I because surfaces are polished Kb I because subjected to axial stress Kc 0.85 for axial load ked I assume room temp Ke 0.702 for 99.9901 reliability Se 1 I 0.85 I 0.702 500 MPa 298 MPa 1000 mpg MPA 975 MPa 425ha ftp.T pa T Life 103 106 a life for load of 175 MPa because 175 MPa L Se finite life for load of 425 MPa a f g 108248Mt 2145 Mpa

f 0.8 from Fig 6 23 for Shut 1000 MPa b flog feet flog 08.1000mg o 428 N F b Itf 83900 cycles N EEE W 10100 cycles

ME 354 Fa23 Exam 1b Name: PUID: PROBLEM No. 3 (25 points) An elbow with a circular cross section diameter of 30 cm is fixed to a wall at the origin of the coordinate system (Figure 2). The elbow is made of 1030 HR material with S ut “ 470 MPa and S y “ 260 MPa. At the end of the elbow, a cyclic load, F z , varies from 90 ⇡ kN to ´ 70 ⇡ kN in the ´ z direction. You may assume that if fatigue or static failure is to occur, that this would occur at location M on the wall. Further, k b k c k d k e “ 1, transverse shear stress can be neglected, and you do not need to account for a stress raiser at the wall. Determine the following at location M . (a) The factor of safety ( n f ) using Goodman criterion at point M . If infinite life is not predicted, determine the number of cycles to failure for finite life. (b) Check for yielding ( n y ). Figure 1: Loading of a Circular Cross Section Elbow Page 7 of 11

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ME 354 Fa23 Exam 1b Name: PUID: PROBLEM No. 4 (25 points) Below (Figure 2) is a section of a component that is subject to cyclic loading. The torque is steady, with magnitude 6 N-m. The bending moment is fully reversed, with magnitude 12 N-m. The part is made of a material with S ut “ 700 MPa and S y “ 550 MPa. The fully corrected endurance limit is 228 MPa. It is known that D 2 “ 20 mm, D 1 { D 2 “ 1 . 1 and r “ 1 . 0 mm. Determine the following. (a) The factor of safety ( n f ) using Goodman criterion at the notch. If infinite life is not predicted, determine the number of cycles to failure for finite life. (b) Check for yielding ( n y ). Figure 2: Fatigue Loading of a Shaft with Shoulder Fillet Page 9 of 11

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ME 354 Fa23 Exam 1b Name: PUID: Page 10 of 11

ME 354 Fa23 Exam 1b Name: PUID: Page 11 of 11

Problem 4 It It for bending rm o fully reversed ran Iggy IÉqjmgm_ 15.3m Pa KE 1.9 for Ed 1.1 and I I 0.05 9 0.75 from Fig 6 26 Kf It g Kt 1 It 0.75 1.9 1 1.675 or Kf It IFT It 11É 1.688 VT 1,24 2.25 10 3 700 1 6.10 6.7002 4.11 10 10.7003 0.308 for torsion Ta o steady Tm Fifty 6nftcjeth.mn 3.819m Pa

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32 KES 1.33 for Ed 1.1 and I I 0.05 915 0.8 from Fig 6 27 for Saf 700 MPa E Imm Kfs It 9s 16 1 1 0.8 1.3 1 1.24 rat Kf Ta 1.68 15.3 KPa 25.7 kPa rm k V5 Kss Tm V5 I 24 3.82 kpa 8.2 KPa 3ft If he 8 Ny Itm Ifm 254 8.2 16.2