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Question & Answer:

  • A 1/4 -in drill rod was heat-treated and ground. The measured hardness was found to be 490 Brinell. Estimate the endurance strength if the rod is used in rotating bending.
  • Estimate S′e for the following materials:
    (a) AISI 1020 CD steel.
    (b) AISI 1080 HR steel.
    (c) 2024 T3 aluminum.
    (d) AISI 4340 steel heat-treated to a tensile strength of 250 kpsi.
  • Estimate the fatigue strength of a rotating-beam specimen made of AISI 1020 hot-rolled steel corresponding to a life of 12.5 kilocycles of stress reversal. Also, estimate the life of the specimen corresponding to a stress amplitude of 36 kpsi. The known properties are Sut = 66.2 kpsi, σ0 = 115 kpsi, m = 0.22, and εf = 0.90.
  • Derive Eq. (6–17). For the specimen of Prob. 6–3, estimate the strength corresponding to 500 cycles.
  • For the interval 103 ≤ N ≤ 106 cycles, develop an expression for the axial fatigue strength (S′f ) ax for the polished specimens of 4130 used to obtain Fig. 6–10. The ultimate strength is Sut = 125 kpsi and the endurance limit is (S′e) ax = 50 kpsi.
  • Estimate the endurance strength of a 32-mm-diameter rod of AISI 1035 steel having a machined finish and heat-treated to a tensile strength of 710 MPa.
  • Two steels are being considered for manufacture of as-forged connecting rods. One is AISI 4340 Cr-Mo-Ni steel capable of being heat-treated to a tensile strength of 260 kpsi. The other is a plain carbon steel AISI 1040 with an attainable Sut of 113 kpsi. If each rod is to have a size giving an equivalent diameter de of 0.75 in, is there any advantage to using the alloy steel for this fatigue application?
  • A solid round bar, 25 mm in diameter, has a groove 2.5-mm deep with a 2.5-mm radius machined into it. The bar is made of AISI 1018 CD steel and is subjected to a purely reversing torque of 200 N • m. For the S-N curve of this material, let f = 0.9.
    (a) Estimate the number of cycles to failure.
    (b) If the bar is also placed in an environment with a temperature of 450°C, estimate the number of cycles to failure.
  • A solid square rod is cantilevered at one end. The rod is 0.8 m long and supports a completely reversing transverse load at the other end of ±1 kN. The material is AISI 1045 hot-rolled steel. If the rod must support this load for 104 cycles with a factor of safety of 1.5, what dimension should the square cross section have? Neglect any stress concentrations at the support end and assume that f = 0.9.
  • A rectangular bar is cut from an AISI 1018 cold-drawn steel flat. The bar is 60 mm wide by
    10 mm thick and has a 12-mm hole drilled through the center as depicted in Table A–15–1. The bar is concentrically loaded in push-pull fatigue by axial forces Fa , uniformly distributed across the width. Using a design factor of nd = 1.8, estimate the largest force Fa that can be applied ignoring column action.
  • Bearing reactions R1 and R2 are exerted on the shaft shown in the figure, which rotates at 1150 rev/min and supports a 10-kip bending force. Use a 1095 HR steel. Specify a diameter d using a design factor of nd = 1.6 for a life of 3 min. The surfaces are machined.
  • A bar of steel has the minimum properties Se = 276 MPa, Sy = 413 MPa, and Sut = 551 MPa. The bar is subjected to a steady torsional stress of 103 MPa and an alternating bending stress of 172 MPa. Find the factor of safety guarding against a static failure, and either the factor of safety guarding against a fatigue failure or the expected life of the part. For the fatigue analysis use:
    (a) Modified Goodman criterion.
    (b) Gerber criterion.
    (c) ASME-elliptic criterion.
  • Repeat Prob. 6–12 but with a steady torsional stress of 138 MPa and an alternating bending stress of 69 MPa.
  • Repeat Prob. 6–12 but with a steady torsional stress of 103 MPa, an alternating torsional stress of 69 MPa, and an alternating bending stress of 83 MPa.
  • Repeat Prob. 6–12 but with an alternating torsional stress of 207 MPa.
  • Repeat Prob. 6–12 but with an alternating torsional stress of 103 MPa and a steady bending stress of 103 MPa.
  • The cold-drawn AISI 1018 steel bar shown in the figure is subjected to an axial load fluctuating between 800 and 3000 lbf. Estimate the factors of safety ny and nf using (a) a Gerber fatigue failure criterion as part of the designer’s fatigue diagram, and (b) an ASME-elliptic fatigue failure criterion as part of the designer’s fatigue diagram.
  • Repeat Prob. 6–17, with the load fluctuating between .800 and 3000 lbf. Assume no buckling.
  • Repeat Prob. 6–17, with the load fluctuating between 800 and -3000 lbf. Assume no buckling.
  • The figure shows a formed round-wire cantilever spring subjected to a varying force. The hardness tests made on 25 springs gave a minimum hardness of 380 Brinell. It is apparent from the mounting details that there is no stress concentration. A visual inspection of the springs indicates that the surface finish corresponds closely to a hot-rolled finish. What number of applications is likely to cause failure? Solve using:
    (a) Modified Goodman criterion.
    (b) Gerber criterion.