Page 252 - Shigley's Mechanical Engineering Design

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Failures Resulting from Static Loading 227

MSS From Eq. (3–16),
σ 1 − σ 3 0 − (−68.0)
τ max = = = 34.0 kpsi
2 2
S y /2 100/2
Answer n = = = 1.47
τ max 34.0
(e) The ordered principal stresses are σ 1 = 30,σ 2 = 30,σ 3 = 30 kpsi
DE From Eq. (5–12),

(30 − 30) + (30 − 30) + (30 − 30)
2 2 2 1/2

σ = = 0 kpsi
2
Answer n = S y = 100 →∞
σ 0

MSS From Eq. (5–3),

Answer n = S y = 100 →∞
σ 1 − σ 3 30 − 30
A tabular summary of the factors of safety is included for comparisons.

(a) (b) (c) (d) (e)

DE 1.43 1.70 1.14 1.70 ∞
MSS 1.43 1.47 1.02 1.47 ∞

Since the MSS theory is on or within the boundary of the DE theory, it will always pre-
dict a factor of safety equal to or less than the DE theory, as can be seen in the table.
For each case, except case (e), the coordinates and load lines in the σ A ,σ B plane are
shown in Fig. 5–11. Case (e) is not plane stress. Note that the load line for case (a) is
the only plane stress case given in which the two theories agree, thus giving the same
factor of safety.

Figure 5–11 B
(a)
Load lines for Example 5–1. S y

(b)
B
A
–S y
S y A
(c)

DE
–S y MSS
Load lines
(d)