# hmwk7c - ME541 Fatigue of Materials Homework 7 Solutions...

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ME541: Fatigue of Materials Homework 7 Solutions 7.2) At the surface of a thin wall pressure vessel, a plane stress state exists with the axial and hoop directions being principal directions. Then the applied stresses are: Hoop, 1 h σ t pr σ = = and Axial, 3 2 l σ t pr 2t 3rp 2t pr 2tr π π p 3r 2t pr A P 2t pr σ = = + = + = + = Radial, 2 r σ 0 σ = = This stress state is the same as that for pure torsion, such that t pr J Tr τ = = where = = r prJ T 2 4 r π p 7.4) For a material with the following properties, determine the life to failure using the von Mises equivalent stress/strain theory for completely reversed torsional strain “loading” of Δγ /2 = 0.0042 in/in. E = 30,000 ksi, σ f = 120 ksi, b = -0.1, ε f = 1 in/in, c = - 0.5. Direct substitution of material constants and conditions into Eq. 7.9 for G = E/(2*(1+ ν )) = 11,540 ksi for ν = 0.3: () () c f ' f b f ' f 2N ε 3 2N G 3 σ 2 Δγ + = and solving iteratively for N f gives N f = 225,000 cycles. 7.5) (4340 steel shaft) Need to determine the maximum tangential load P for a fatigue life of 10,000 cycles. Also, if a static load of 100 ksi was somehow applied near the bearing, determine the static load P for a fatigue load of 10,000 cycles. Finally, could Sines criteria be used if a zero to maximum (R=0) alternating axial force was applied to the end of the shaft such that the axial force reaches a maximum value every time the shaft completes a half revolution?

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## This note was uploaded on 11/28/2010 for the course ENES enes100 taught by Professor Staff during the Spring '10 term at Maryland.

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hmwk7c - ME541 Fatigue of Materials Homework 7 Solutions...

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