Page 461 - Shigley's Mechanical Engineering Design

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436 Mechanical Engineering Design
P = external tensile load per bolt
P b = portion of P taken by bolt

P m = portion of P taken by members
F b = P b + F i = resultant bolt load
F m = P m − F i = resultant load on members

C = fraction of external load P carried by bolt
1 − C = fraction of external load P carried by members
N = Number of bolts in the joint
If N bolts equally share the total external load, then

P = P total /N (a)

The load P is tension, and it causes the connection to stretch, or elongate, through
some distance δ. We can relate this elongation to the stiffnesses by recalling that k is
the force divided by the deflection. Thus

P b P m
δ = and δ = (b)
k b k m
or

k m
P m = P b (c)
k b
Since P = P b + P m , we have

k b P
P b = = CP (d)
k b + k m
and

P m = P − P b = (1 − C)P (e)
where

k b
C = (f)
k b + k m
is called the stiffness constant of the joint. The resultant bolt load is

F m < 0 (8–24)
F b = P b + F i = CP + F i
and the resultant load on the connected members is

F m < 0 (8–25)
F m = P m − F i = (1 − C)P − F i
Of course, these results are valid only as long as some clamping load remains in the
members; this is indicated by the qualifier in the equations.
Table 8–12 is included to provide some information on the relative values of the
stiffnesses encountered. The grip contains only two members, both of steel, and no