Page 245 - Marks Calculation for Machine Design

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Brown˙C05
PRINCIPAL STRESSES AND MOHR’S CIRCLE
The important result from this example is that the given stress element is the principal
◦
stress element, and that the maximum shear stress is (σ/2) acting at 45 . 227
Consider now the last of the three special elements, the pure shear element.
Pure Shear Element. For a pure shear stress element, suppose σ xx = 0, σ yy = 0, and
τ xy = τ, where (τ) is a known stress caused by either a single loading or a combination of
loadings.
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 pure shear stress element
these two points are (0,τ) and (0,−τ) as shown in Fig. 5.45.
(0,–t)

s

(0,t)
t (2q ccw)

FIGURE 5.45 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 pure shear element both points are on the (τ) axis, so the average stress is
halfway between, that is (0) as shown in Fig. 5.46.

(0,–t)

s
(0)

(0,t)
t (2q ccw)
FIGURE 5.46 Connect points to find average stress (σ avg ).

The radius of Mohr’s circle will be the shear stress, that is (τ) as shown in Fig. 5.47.