Calculation Procedure:
- Record the properties of the
individual channel
Since x and y are axes of symmetry, they are
the principal centroidal axes. However, it is
not readily apparent which of these is the mi-
nor axis, and so it is necessary to calculate
both rx and ry. The symbol r, without a sub-
script, is used to denote the minimum radius
of gyration, in inches (centimeters).
Using the AISC Manual, we see that the
channel properties are A = 11.70 in
2
(75.488
cm
2
); h = 0.78 in (19.812 mm); T 1 - 5.44 in
(138. 176 mm); r 2 = 0.89 in (22.606 mm).
- Evaluate the minimum radius _ ^ M
of gyration of the built-up FIGURE 11. Built-up column
section; determine the
slenderness ratio
Thus, rx = 5.44 in (138.176 mm); ry = (r\ +
5.78^2 )^0 -^5 > 5.78 in (146.812 mm); therefore, r
= 5.44 in (138.176 mm); KLIr = 22(12)75.44
= 48.5.
- Determine the allowable stress in the column
Enter the Manual slenderness-ratio allowable-stress table with a slenderness ratio of 48.5
to obtain the allowable stress/= 18.48 kips/in
2
(127.420 MPa). Then, the column capaci-
ty = P = Af= 2(11.7O)(18.48) = 432 kips (1921.5 kN).
CAPACITY OF A DOUBLE-ANGLE
STAR STRUT
A star strut is composed of two 5 x 5 x^3 / 8 in (127.0 x 127.0 x 9.53 mm) angles intermit-
tently connected by^3 /s-in (9.53-mm) batten plates in both directions. Determine the ca-
pacity of the member for an effective length of 12 ft (3.7 m).
Calculation Procedure:
- Identify the minor axis
Refer to Fig. 12a. Since p and q are axes of symmetry, they are the principal axes; p is
manifestly the minor axis because the area lies closer to p than q.
- Determine r
Refer to Fig. 126, where v is the major and z the minor axis of the angle section. Apply
I? = Ix' cos
2
O + Iy> sin
2
S - Px'y' sin 26, and set Pvz = O to get r^ = r
2
cos
2
Q + r} sin
2
0;
therefore, r sec
2
6-r} tan
2
- For an equal-leg angle, B = 45°, and this equation reduces
tor
2
= 2^
2
-r
2
.
Locing-
