. 
72 APPLIED MECHANICS 
16. Taking the stress at the elastic limit as 16,000 Ibs, per aoa. inch, cal- 
culate the resilience of the bar referred to in Exercise 10. 
17. Re-work Exercise 15, assuming that there is a steady load of 1 ton hanging 
from the lower end of the par before the blow is applied. 
18. If the maximum crushing stress of a punch is four times the maximum 
shearing stress of a plate, show that the smallest hole which can be punchag in 
the plate has a diameter equal to the thickness of the plate, 
89. Riveted Joints.—Considering first a simple form of riveted joint, 
such as the double riveted lap joint shown in Fig. 82. When this joint 
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is subjected to tension it may give way (1) by the tearing of the plates 
between the rivets, as shown at (a) ; (2) by the shearing of the rivets, as 
shown at (b) ; (3) by the crushing of the rivets or of the parts of the plates 
in contact with them ; (4) by the breaking of the plates between their 
outer edges and the rivet holes, as shown at (c). 
p= pitch of rivets. J, = tensile stress in plates. 
d= diameter of rivets. J, =shearing stress in rivets. 
t= thickness of plates. J, = crushing stress in rivets or plates. 
Considering a strip of the joint equal in width to the pitch p, 
Resistance of this strip to tearing = (p — d)tf;. 
“a ‘5 »  Shearing= Th x 2. 
95 =) » crushing = dtf, x 2. 
In the last of these expressions the bearing area of the rivet on the 
plate is taken as its projected area on a plane containing the axis of the 
rivet and perpendicular to the direction of the pressure. > 
If the values of the stresses f;, f,, and f, be given, then the three 
expressions above must be equal to one another. This gives two equations 
to determine p andd. Solving these equations, 
Atf, nadie 6 +2), 
oath Aeiee 
The stresses f,and /, can usually be definitely settled, but for materials 
used in riveted joints the value of the stress f, is more difficult to decide. 
Very often the diameter of the rivets is fixed empirically, and the 
resistance to tearing is then equated to the resistance to shearing to deter- 
mine the pitch. In that case the crushing stress should then be calculated 
