Page 234 - Marks Calculation for Machine Design

P1: Shibu/Sanjay
14:35
January 4, 2005
Brown.cls
Brown˙C05
216
–75 STRENGTH OF MACHINES
Radius
(75,–30)
s
–75 26 120
(–25,30)
75 Scale: 7.5 MPa × 7.5 MPa
t (2q ccw)
FIGURE 5.25 Draw circle.

Graphically from Fig. 5.26, the maximum principal stress is (82.5), and the minimum
principal stress is (−30.5). The radius of the circle is the maximum shear stress, and scales
to (56.5). These are very close to the values found in Example 5.

–75

(75,–30)
–30.5 82.5
s
–75 26 120
(–25,30) 56.5

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

FIGURE 5.26 Principal stresses and radius of circle.

Figure 5.26 also verifies graphically Eqs. (5.15) and (5.16) for the maximum principal
stress (σ 1 ) and a minimum principal stress (σ 2 ),

σ 1 = σ avg + τ max = (26 + 56.5) MPa = 82.5MPa

σ 2 = σ avg − τ max = (26 − 56.5) MPa =−30.5MPa

and as the principal stresses are on the (σ) axis, the shear stress is zero at these
points.
◦
At 90 to the principal stresses are the maximum and minimum shear stresses, (56.5) and
(−56.5), with the normal stress at these points equal to the average stress (Fig. 27).