Page 237 - Marks Calculation for Machine Design

P1: Shibu/Sanjay
14:35
January 4, 2005
Brown.cls
Brown˙C05
PRINCIPAL STRESSES AND MOHR’S CIRCLE
0
0 219
0
s xx s
s
¨
s xx
0
0 Uniaxial
0
FIGURE 5.30 Uniaxial stress element.
A biaxial element has two nonzero normal stresses (σ xx ) and (σ yy ); however, the shear
stress (τ xy ) is zero. A biaxial stress element is shown in Fig. 5.31. Typically, biaxial stress
elements occur from pressure loadings.
s yy s hoop or s t
0
0
s xx
Æ
s xx s axial or s a s axial or s a
0
0
Biaxial
s yy s hoop or s t

FIGURE 5.31 Biaxial stress element.
A pure shear element has both normal stresses (σ xx ) and (σ yy ) zero, with a nonzero shear
stress (τ xy ). A pure shear element is shown in Fig. 5.32.

0
t xy t
t xy t
0
→
0
t xy t
t xy t
Pure shear
0
FIGURE 5.32 Pure shear stress element.

Consider the Mohr’s circle graphical process for each of these special elements.
Uniaxial Element. For a uniaxial stress element, σ xx = σ, σ yy = 0, and τ xy = 0, where
(σ) is some known stress caused by either a single or combined loading.