Page 138 - Shigley's Mechanical Engineering Design

bud29281_ch03_071-146.qxd 11/25/09 4:55PM Page 113 ntt 203:MHDQ196:bud29281:0073529281:bud29281_pagefiles:

Load and Stress Analysis 113
Answer σ max = K t σ 0 = 2.5(156) = 390 MPa

Though the stress concentration is higher with the 4-mm hole, in this case the increased
nominal stress with the 8-mm hole has more effect on the maximum stress.
For the fillet,

F 10 000
σ 0 = = = 147 MPa
A (34)2
From Table A–15–5, D/d = 40/34 = 1.18, and r/d = 1/34 = 0.026. Then K t = 2.5.

Answer σ max = K t σ 0 = 2.5(147) = 368 MPa

Answer The crack will most likely occur with the 8-mm hole, next likely would be the 4-mm
hole, and least likely at the fillet.

3–14 Stresses in Pressurized Cylinders
Cylindrical pressure vessels, hydraulic cylinders, gun barrels, and pipes carrying fluids
at high pressures develop both radial and tangential stresses with values that depend
upon the radius of the element under consideration. In determining the radial stress σ r
and the tangential stress σ t , we make use of the assumption that the longitudinal
elongation is constant around the circumference of the cylinder. In other words, a right
section of the cylinder remains plane after stressing.
Referring to Fig. 3–31, we designate the inside radius of the cylinder by r i, the out-
side radius by r o, the internal pressure by p i, and the external pressure by p o. Then it can
be shown that tangential and radial stresses exist whose magnitudes are 10

2 2
2
2
p i r − p o r − r r (p o − p i )/r 2
i
i o
o
σ t =
2
p r − r 2
o
o i
(3–49)
2
2 2
2
p i r − p o r + r r (p o − p i )/r 2
dr σ r = i o i o
2
r − r 2
r o i
p i
As usual, positive values indicate tension and negative values, compression.
For the special case of p o = 0, Eq. (3–49) gives
r i r
o
2 2
r p i r o
i
σ t = 2 1 +
2
r − r i r 2
o
Figure 3–31 (3–50)
2 r 2
A cylinder subjected to both r p i o
i
σ r = 2 1 −
2
internal and external pressure. r − r r 2
o i
10 See Richard G. Budynas, Advanced Strength and Applied Stress Analysis, 2nd ed., McGraw-Hill, New
York, 1999, pp. 348–352.