Page 49 - Marks Calculation for Machine Design

P1: Shibu
January 4, 2005
12:26
Brown.cls
Brown˙C01
FUNDAMENTAL LOADINGS
31
From equilibrium, the two shear forces (V ) are equal to the applied force (2P),soa
single shear force (V ) equals a single applied force (P) and the shear stress (τ) is given by
Eq. (1.44) as
V P
τ = = (1.44)
A A rivet
[Note that the applied force (P) in Eq. (1.44) is twice the applied force (P) in Eq. (1.43).]
Consider a modification of the overlapping joint in Fig. 1.33, where now there are gaps
between the plates as shown in Fig. 1.35, and the rivet is no longer under direct shear
loading but shear owing to bending. This means the rivet is acting like a beam and so the
shear stress (τ) is given by Eq. (1.45).
VQ
τ = (1.45)
Ib
P
2P
Gaps
P
FIGURE 1.35 Shear owing to bending.

Rivets, as well as pins and bolts, have circular cross sections like that shown in Fig. 1.36.
Using the definition of the first moment, and the nomenclature of Fig. 1.35, the maximum
first moment (Q max ) for a circular cross section is given by Eq. (1.46).

2
πR 4R 2 3
Q max = A max y max = = R (1.46)
2 3π 3
The area moment of inertia (I) for a circular cross section about the neutral axis that
passes through the centroid of the area, is given by Eq. (1.47),
1 4
I = πR (1.47)
4
and the maximum width (b max ) of a circular cross-section beam is the diameter, or (2R).

pR 2
A max =
2
4R
y max =
3p
y = 0

2R
FIGURE 1.36 Maximum first moment.