Page 229 - Marks Calculation for Machine Design

P1: Shibu/Sanjay
January 4, 2005
Brown˙C05
Brown.cls
PRINCIPAL STRESSES AND MOHR’S CIRCLE
t 14:35 211
min
(s ,-t )
xy
yy
R = t max
s
s 2 s avg s 1
2f p
(s ,t )
xx xy
t max
t (2q ccw) 2f s
FIGURE 5.15 Maximum shear stress angle (φ s ).
Due to the graphical nature of the process, the following example will be presented first
in the U.S. Customary system of units and then in the SI/metric system.

U.S. Customary
Example 1. Using the stresses below from Example 5, determine the principal stresses,
maximum and minimum shear stresses, and rotation angles by the Mohr’s circle process.
σ xx = 10 kpsi σ yy =−3 kpsi τ xy =−4 kpsi

The first step in the process is to plot two points; one point having the coordinates
(σ xx ,τ xy ) and the other point having the coordinates (σ yy ,−τ xy ), that is (10,−4) and
(−3, 4) as shown in Fig. 5.16.

–10

(10,–4)
–4
–3
σ
–10 10 15
4
(–3,4)

10 Scale: 1 kpsi × 1 kpsi
t (2q ccw)
FIGURE 5.16 Plot points (σ xx , t xy ) and (σ xx , −t xy ).

Figure 5.17 shows that a line connecting these two points crosses the (σ) axis at the
average stress (3.5).