154 RESISTANCE OF MATERIALS 



where a denotes the margin or distance from center of rivets to edge of plate, 

 and q' denotes the ultimate shearing strength of the plate. Assuming that q' = |g 



and h = - , and solving the resulting expression for a, we have 



a = 1.5d. 



258. Find the required rivet pitch for a single-riveted lap joint with -in. steel 

 plates and ^-in. steel rivets, in order that the joint shall be of equal strength in 



shear and tension. 



Trd 

 Solution. For a strip of length c the strength in shear is g, and in tension 



is (c d)hp. Hence, to satisfy the given condition, 



?rd 2 

 (c - d) hp = q, 



TT( 5) 2 50,000 

 + d= 4(1)60.000 + i = l-**MayUm. 



Also, efficiency of joint is then 



sectional area through rivet holes c d .75 

 e= = = 50 per cent, 



sectional area unriveted plate c 1.50 



259. Determine the maximum diameter of rivet in terms of thickness of plate so 

 that the crushing strength of the joint shall not be less than its shearing strength. 



Solution. It is customary to assume the ultimate crushing strength of the material 

 as about twice its ultimate shearing strength, or say 100,000 lb./in. 2 Let 



p c = ultimate crushing strength, 

 p t ultimate tensile strength, 

 q = ultimate shearing strength. 



Then, if the shearing strength of the rivets is to equal their crushing strength, we 

 have for lap joints 



Trd 2 



q = dhp c and p c = 2 q ; 

 4 



whence d = 2.54 h. 



A larger rivet than this will crush before it shears, whereas a smaller one will 

 shear before it crushes. Therefore the crushing strength of a lap joint need not 

 be considered when d < 2.54^, as it usually is. 



For a rivet in double shear, assuming that the strength of the rivet in double 

 shear is twice that of the same rivet in single shear,* we have for butt joints 



Trd 2 



2 q = dhp c and p c 2 q ; 



4 



whence d = 1.2 73 7*. 



If the diameter exceeds this value, the rivet will fail by crushing, whereas if it is 

 smaller, it will fail by shear. Consequently the crushing strength of a butt joint 

 need not be considered when d < 1.273 h. 



* This seems to be substantiated by experiment, although the English Board of Trade 

 specifies that a rivet in double shear shall be assumed to be only 1.75 times as strong as 

 if in single shear. 



