Page 231 - Marks Calculation for Machine Design

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PRINCIPAL STRESSES AND MOHR’S CIRCLE
Figure 5.19 also verifies graphically Eqs. (5.15) and (5.16) for the maximum principal
stress (σ 1 ) and a minimum principal stress (σ 2 ), 213
σ 1 = σ avg + τ max = (3.5 + 7.5) kpsi = 11 kpsi
σ 2 = σ avg − τ max = (3.5 − 7.5) kpsi =−4 kpsi
and since 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, (7.5) and
(−7.5), with the normal stress at these points equal to the average stress (3.5) as shown in
Fig. 5.20.

–10
–7.5
(10,–4)
–4 11
s
–10 3.5 15
(–3,4) 7.5
7.5
10 Scale: 1 kpsi × 1 kpsi
t (2q ccw)

FIGURE 5.20 Maximum and minimum shear stresses.

The angle between the line connecting points (10,−4) and (−3,4) and the (σ) axis is
the principal stress angle (2φ p ). From Fig. 5.21, this will be a clockwise, or negative,
rotation.

–10
–7.5

(10,–4) 2f p
–4 11
s
–10 3.5 15
(–3,4) 7.5
7.5
10 Scale: 1 kpsi × 1 kpsi
t (2q ccw)
FIGURE 5.21 Principal stresses angle (φ p ).