Page 280 - Shigley's Mechanical Engineering Design

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Failures Resulting from Static Loading 255
Yield design equation, p. 224
S y
(5–19)
σ =
n
Shear yield strength, p. 225
(5–21)
S sy = 0.577 S y
Coulomb-Mohr Theory
1
σ 1 σ 3
p. 225 − = (5–26)
S t S c n
where S t is tensile yield (ductile) or ultimate tensile (brittle), and S t is compressive
yield (ductile) or ultimate compressive (brittle) strengths.

Modified Mohr (Plane Stress)

S ut
σ A = σ A ≥ σ B ≥ 0
n
(5–32a)

σ B
and ≤ 1
σ A ≥ 0 ≥ σ B
σ A

1
(S uc − S ut )σ A σ B
p. 236 − = σ A ≥ 0 ≥ σ B and σ B > 1 (5–32b)
S uc S ut S uc n σ A
S uc
σ B =− 0 ≥ σ A ≥ σ B (5–32c)
n
Failure Theory Flowchart
Fig. 5–21, p. 239

Brittle behavior Ductile behavior

< 0.05 ≥ 0.05
f

No Yes No Yes
·
Conservative? S yt = S yc ?

Mod. Mohr Brittle Coulomb-Mohr Ductile Coulomb-Mohr
(MM) (BCM) (DCM)
Eq. (5–32) Eq. (5–31) Eq. (5–26) No Yes
Conservative?

Distortion-energy Maximum shear stress
(DE) (MSS)
Eqs. (5–15) Eq. (5–3)
and (5–19)