Page 30 - Marks Calculation for Machine Design

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January 4, 2005
Brown.cls
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12
V
P STRENGTH OF MACHINES
FIGURE 1.12 Free-body-diagram.
A shear force (V ) acts over the cross section of the rivet and by static equilibrium equals
the magnitude of the force (P). As a consequence a shear stress (τ) is developed in the
rivet as given by Eq. (1.12).
V P
τ = = (1.12)
A A rivet
The unit of shear stress (τ) is the same as that for normal stress (σ), that is, pound per
square inch (psi) in the U.S. Customary System and newton per square meter, or pascal
(Pa), in the metric system.
Suppose the overlapping joint is held together by two rivets as in Fig. 1.13.

P P

FIGURE 1.13 Two-rivet joint (top view).

If both the rivets are cut in half at the overlap to expose the cross-sectional areas A of the
rivets, then Fig. 1.14 shows the resulting free-body-diagram.

V
P

V
FIGURE 1.14 Free-body-diagram.

A shear force (V ) acts over the cross section of each rivet and so by static equilibrium
these two shear forces together equal the magnitude of the force (P), which means each
is half the force (P). The shear stress (τ) that is developed in each rivet is given by
Eq. (1.13).

V P/2 P
τ = = = (1.13)
A A rivet 2A rivet
As the number of rivets increase, the shear stress in each rivet is reduced.