Page 31 - Marks Calculation for Machine Design

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January 4, 2005
Brown.cls
Brown˙C01
U.S. Customary FUNDAMENTAL LOADINGS SI/Metric 13
Example 1. Determine the shear stress (τ) in Example 1. Determine the shear stress (τ) in
one of the four rivets of an overlapping joint, one of the four rivets of an overlapping joint,
where where
P = 10 kip = 10,000 lb P = 45 kN = 45,000 N
D rivet = 0.25 in = 2 r rivet D rivet = 0.6 cm = 0.006 m = 2 r rivet
solution solution
Step 1. Calculate the cross-sectional area (A) Step 1. Calculate the cross-sectional area (A)
of each rivet. of each rivet.
2
2
2
2
A rivet = πr = π(0.125 in) = 0.05 in 2 A rivet = πr = π(0.003 m) = 0.00003 m 2
Step 2. As there are four rivets that must carry Step 2. As there are four rivets that must carry
the force (P), the shear force (V ) for each rivet the force (P), the shear force (V ) for each rivet
is is
P 10,000 lb P 45,000 N
4V = P → V = = 4V = P → V = =
4 4 4 4
= 2,500 lb = 11,250 N
Step 3. Using Eq. (1.13) calculate the shear Step 3. Using Eq. (1.13) calculate the shear
stress (τ). stress (τ).
V 2,500 lb V 11,250 N
τ = = 2 τ = = 2
A rivet 0.05 in A rivet 0.00003 m
2
2
= 50,000 lb/in = 50 kpsi = 375,000,000 N/m = 375 MPa
g
V

FIGURE 1.15 Rectangular plate in shear.

Strain. The shear force (V ) acting on the rectangular plate in Fig. 1.15 will, if one side
of the plate is held fixed, cause the plate to deform into a parallelogram as shown.
◦
The change in the 90 angle, measured in radians, is called the shear strain (γ ). So the
shear strain is dimensionless. If the area of the fixed edge of the plate is labeled (A fix ), then
the shear stress (τ) is given by Eq. (1.14).
V
τ = (1.14)
A fix
Stress-Strain Diagrams. If shear stress (τ) is plotted against shear strain (γ ),itgives
a shear stress-strain diagram as shown in Fig. 1.16, which gives the shear stress-strain
diagram for a ductile material where points A, B, C, D, and F are analogous to the normal