Page 50 - Marks Calculation for Machine Design

P1: Shibu
12:26
January 4, 2005
Brown.cls
Brown˙C01
32
STRENGTH OF MACHINES
Substituting the maximum first moment (Q max ) from Eq. (1.46), the area moment of
inertia (I) from Eq. (1.47), and the maximum width (b max ) equal to (2R) into the expression
for shear stress (τ) owing to bending in Eq. (1.45) gives

2 3
V R
VQ max 3 4 V 4 V
τ max = = = 2 = (1.48)
Ib max 1 π R 4 (2R) 3 πR 3 A
4
The importance of Eq. (1.48) is that it shows the maximum shear stress owing to bending
is greater by one third (33 percent) of the maximum shear stress owing to direct shear
loading. This is a nontrivial difference and great care should be taken if a rivet, pin, or bolt
is in bending rather than in direct shear.