Page 259 - Shigley's Mechanical Engineering Design

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234 Mechanical Engineering Design
Figure 5–17 y

A 120 mm
F
z

P
T
x
(a)

zx

x

x

z
(b)

For accuracy, we choose the distortion-energy theory as the design basis. The von Mises
stress from Eq. (5–15), is
1/2
2 2
σ = σ + 3τ (3)

x zx
On the basis of the given design factor, the goal for σ is

S y 0.276
(4)
σ ≤ = = 0.0690 GPa
n d 4
where we have used gigapascals in this relation to agree with Eqs. (1) and (2).
Programming Eqs. (1) to (3) on a spreadsheet and entering metric sizes from
Table A–8 reveals that a 42 × 5-mm tube is satisfactory. The von Mises stress is found
to be σ = 0.06043 GPa for this size. Thus the realized factor of safety is

Answer n = S y = 0.276 = 4.57
σ 0.06043
For the next size smaller, a 42 × 4-mm tube, σ = 0.07105 GPa giving a factor of

safety of
S y 0.276
n = = = 3.88
σ 0.07105