Page 341 - Marks Calculation for Machine Design

P1: Sanjay
15:14
January 4, 2005
Brown.cls
Brown˙C08
MACHINE ASSEMBLY
323
where (A T ) is the cross-sectional area of the threaded portion of the cap screw, which is
also known as the tensile-stress area, and (L T ) is the length of the threaded portion that is
equal to the thickness of the top member plus the thickness of the washer.
As for the bolt, part of its length is threaded and part of it is unthreaded. Therefore, its
stiffness is the series combination of two separate stiffnesses; one for the threaded portion
and one for the unthreaded portion, given by the following two relationships:
A T E
k T = (8.6)
L T
A UT E
k UT = (8.7)
L UT
where (A T ) and (L T ) are the threaded cross-sectional area and threaded length, respectively;
and (A UT ) and (L UT ) are the unthreaded cross-sectional area and unthreaded length, re-
spectively, of the bolt. The two lengths (L T ) and (L UT ) must add up to the thickness of the
members plus the thickness of the washers, not the total length of the bolt. The unthreaded
cross-sectional area (A UT ) is found using the major diameter of the bolt. If a cap screw has
a significant unthreaded length, then treat its stiffness like a bolt.
The two stiffnesses given in Eqs. (8.6) and (8.7) act in series; therefore the overall stiffness
of the bolt is given by Eq. (8.8) as
1 1 1
= + (8.8)
k bolt k T k UT
which can be rearranged as
k T k UT
k bolt = (8.9)
k T + k UT
Note that if one of the stiffnesses is very different from the other, it will dominate the overall
stiffness. Also, use Eq. (8.9) for a cap screw with an unthreaded length.
As mentioned above, the threaded and unthreaded lengths, (L T ) and (L UT ), do not add
up to the total length (L total ) of the threaded and unthreaded portions of a cap screw or bolt.
They add up to what is called the grip, which is the thickness of the unthreaded members
plus the thickness of the washers. This relationship is given in Eq. (8.10) as
L grip = L + L washers = L UT + L T (8.10)
unthreaded
members
For a cap screw assembly, one member is threaded. For a nut and bolt assembly, none
of the members is threaded. Also, washers are recommended to avoid stress concentrations
on the cap screw, bolt, or nut from the sharp edges of machined holes; however, they must
be hardened so as not to compromise the stiffness of the joint, which will be disussed in
the next section. Washers should be installed with the rounded stamped side facing the cap
screw or bolt head, or the washer face of the nut.
The total length (L total ) of a cap screw can therefore be separated into three lengths as
given by Eq. (8.11).

L total = L grip + L hole + L extra (8.11)
where the grip length (L grip ) may only be the threaded length (L T ), and where (L hole ) is
the length of the cap screw in the threaded hole, and (L extra ) is the extra length of the cap
screw past the threaded hole, if any. Cap screws may have a short unthreaded length.