Page 233 - Marks Calculation for Machine Design

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PRINCIPAL STRESSES AND MOHR’S CIRCLE
SI/Metric
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 = 75 MPa σ yy =−25 MPa τ xy =−30 MPa
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 ), that is, (75,−30) and (−25,30)
as in Fig. 5.23.
–75

(75,–30)
–30
–25
s
–75 75 120
30
(–25,30)

75 Scale: 7.5 MPa × 7.5 MPa
t (2θ ccw)

FIGURE 5.23 Plot points (σ xx , t xy ) and (σ xx , −t xy ).

Figure 5.24 shows that a line connecting these two points crosses the (σ) axis at the
average stress (26).

–75

(75,–30)

s
–75 (–25,30) 26 120

75 Scale: 7.5 MPa ¥ 7.5 MPa
t (2q ccw)

FIGURE 5.24 Connect points to find average stress (σ avg ).

Use distance from the average stress to either point as a radius and draw a circle
(Fig. 5.25).