Page 238 - Marks Calculation for Machine Design

P1: Shibu/Sanjay
14:35
January 4, 2005
Brown.cls
Brown˙C05
STRENGTH OF MACHINES
220
The first step in the process is to plot two points; one point having the coordinates
(σ xx ,τ xy ) and the other having the coordinates (σ yy ,−τ xy ), where for a uniaxial stress
element these two points are (σ,0) and (0,0) as in Fig. 5.33.
(0,0) (s,0)
s

t (2q ccw)

FIGURE 5.33 Plot points (σ xx , t xy ) and (σ xx , −t xy ).
A line connecting these two points would cross the (σ) axis at the average stress (σ avg );
however, for a uniaxial element both points are on the (σ) axis, so the average stress is
halfway between, or half the given stress, that is (σ/2) as shown in Fig. 5.34.

(0,0) (s,0)
s
(s/2)

t (2q ccw)

FIGURE 5.34 Connect points to find average stress (σ avg ).
The radius of Mohr’s circle will also be half the given stress, that is (σ/2). Note that the
circle in Fig. 5.35 touches the vertical (τ) axis at the origin of the coordinate system.

Radius

(0,0) (s,0)
s
(s/2)

t (2q ccw)
FIGURE 5.35 Draw circle.