Page 304 - Civil Engineering Formulas

238 CHAPTER NINE

However, the wall material and its attachments to the studs must comply with
the following:
1. Wall sheathing is attached to both faces or flanges of the studs.
2. The spacing in inches of attachments of wall material to each face or flange
of the stud does not exceed a in either:
2
r 2
a max 0.22 k (9.99)
A
L r 2
a max (9.100)
2 r 1
where L length of stud, in
A full cross-sectional area of stud, sq in
r radius of gyration of full cross section of stud about its axis parallel
1
to wall, in
r radius of gyration of full cross section of stud about its axis perpen-
2
dicular to wall, in
k combined modulus of elastic support, or spring constant, of one
attachment of wall material to stud and of wall material tributary to
that attachment, lb per in (kPa)
For any steel other than Grade C, having a yield point f , a computed from
y
2
Eq. (9.99) should be multiplied by (33,000/f ) .
y
For continuous attachment—by an adhesive, for example—a should be
taken as unity in solving Eq. (9.99) for k.
One attachment and the wall material tributary to it should be able to exert
on the stud a force in the plane of the wall at least equal to
kLP
F min (9.101)
2,600,000 I 2 (k/a) 240P
where I moment of inertia of full cross section of stud about its axis perpen-
2
dicular to wall
P load on stud
For continuous attachment, a 1.
Values of k and F for any particular combination of stud, wall material, and
attaching means can only be determined by test.
A satisfactory value of k can be determined from the expression

0.75P ult P 0
k (9.102)
0.5ny
where P ultimate load
ult
P initial or zero load
0
n number of attachments
y average change in length between attachments of each of the stud
pieces from initial load P to 0.75 P ult
0