Page 283 - Shigley's Mechanical Engineering Design

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258 Mechanical Engineering Design
5–19 A brittle material has the properties S ut = 30 kpsi and S uc = 90 kpsi. Using the brittle Coulomb-
Mohr and modified-Mohr theories, determine the factor of safety for the following states of
plane stress.
(a) σ x = 25 kpsi, σ y = 15 kpsi
(b) σ x = 15 kpsi, σ y =−15 kpsi
(c) σ x = 20 kpsi, τ xy =−10 kpsi
(d) σ x =−15 kpsi, σ y = 10 kpsi, τ xy =−15 kpsi
(e) σ x =−20 kpsi, σ y =−20 kpsi, τ xy =−15 kpsi
5–20 Repeat Prob. 5–19 by first plotting the failure loci in the σ A , σ B plane to scale; then for each stress
state, plot the load line and by graphical measurement estimate the factor of safety.
5–21 to For an ASTM 30 cast iron, (a) find the factors of safety using the BCM and MM theories,
5–25 (b) plot the failure diagrams in the σ A , σ B plane to scale and locate the coordinates of the stress
state, and (c) estimate the factors of safety from the two theories by graphical measurements
along the load line.

Problem Number S x (kpsi) S y (kpsi) T xy (kpsi)
5–21 15 10 0
5–22 15 −50 0
5–23 15 0 −10
5–24 −10 −25 −10
5–25 −35 13 −10

5–26 to A cast aluminum 195-T6 exhibits S ut = 36 kpsi, S uc = 35 kpsi, and ε f = 0.045. For the given
5–30 state of plane stress, (a) using the Coulomb-Mohr theory, determine the factor of safety, (b) plot
the failure locus and the load line, and estimate the factor of safety by graphical measurement.

Problem Number S x (kpsi) S y (kpsi) T xy (kpsi)

5–26 15 −10 0
5–27 −15 10 0
5–28 12 0 −8
5–29 −10 −15 10
5–30 15 8 −8

5–31 to Repeat Probs. 5–26 to 5–30 using the modified-Mohr theory.
5–35
Problem number 5–31 5–32 5–33 5–34 5–35

Repeat problem 5–26 5–27 5–28 5–29 5–30
5–36 This problem illustrates that the factor of safety for a machine element depends on the particular
point selected for analysis. Here you are to compute factors of safety, based upon the distortion-
energy theory, for stress elements at A and B of the member shown in the figure. This bar is
made of AISI 1006 cold-drawn steel and is loaded by the forces F = 0.55 kN, P = 4.0 kN,
and T = 25 N · m.