UNIVERSITI TEKNIKAL MALAYSIA MELAKAFACULTY OF MECHANICAL ENGINEERING

DMCD 3523 – ENGINEERING DESIGN

TUTORIAL 2

DESIGN FOR FATIGUE STRENGTH

Q1 A 6-mm 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.

(Ans: Se = 600 MPa)

Q2 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 252 MPa. The known properties are Sut = 463 MPa, σo = 805 MPa, m = 0.22, and f = 0.90.

(Ans: Sf = 374.6 MPa, N = 1.373 x 106 cycles)

Q3 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.

(Ans: Se = 241MPa)

Q4 A rectangular bar is cut from ANSI 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-13-1. The bar is concentrically loaded in push-pull fatigue by axial forces Fa, uniformly distributed across the width. Using the design factor of nd = 1.8, estimate the largest force Fa

that can be applied ignoring column action.(Ans: Fa = 20.1 kN & 98.7 kN)

Q5 A solid square rod is cantilevered at one end as in Figure 1. 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.

(Ans: b = 27.6 mm)

SBMat/FKM/08

Figure 1 A solid square cantilever rodQ6 Bearing reactions R1 and R2 are exerted on the shaft shown in the

Figure 2, which rotates at 1120 rev/min and supports a 45 kN 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.

(Ans: d = 50 mm)

Figure 2 Bearing reactions R1 and R2

Q7 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.

Q8 The cold-drawn AISI 1018 steel bar shown in the Figure 3 is subjected to an axial loading fluctuating between 3.5 kN and 15 kN. Estimate the factor of safety ny and nf using(a)Gerber fatigue failure criterion.(b)ASME-elliptic failure criterion.

SBMat/FKM/08

Figure 3 The cold-drawn AISI 1018 steel bar

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SBMat/FKM/08