Calculation Procedure:- Record the basic values of the previous calculation procedure
The beam-column factors were devised in an effort to reduce the labor entailed in analyz-
ing a given member as a beam column whenfa/Fa > 0.15. They are defined by B = AIS per
inch (decimeter); a = 0.149 x 106 /in^4 (6201.9/dm^4 ).
Let P denote the applied axial load and -Pauow the axial load that would be permitted in
the absence of bending. The equations given in the previous procedure may be trans-
formed to P + BMCm(Fa/Fb)a/[a - P(KL)^2 ] < Pallow, and PFJQ.6fy) + BMFJFb < Pallow,
where KL, B 9 and a are evaluated with respect to the plane of bending.
The basic values of the previous procedure are P = 160 kips (711.7 kN); M= 31.5
ft-kips (42.71 kN-m); Fb = 22 kips/in^2 (151.7 MPa); Cm = 0.793. - Obtain the properties of the section
From the Manual for a W12 x 53, A = 15.59 in^2 (100.587 cm^2 ); Bx = 0.221 per inch (8.70
per meter); ax = 63.5 x 10
6
in
4
(264.31 x 1Q
3
dm
4
). Then when KL = 20 ft (6.1 m),Pallow =
209 kips (929.6 kN). - Substitute in the first transformed equation
Thus, F 0 = Pallow/A = 209/15.59 = 13.41 kips/in^2 (92.461 MPa), P(KL)^2 = 160(24O)^2 =
9.22 x 106 kip-in^2 (2.648 x 104 kN-m^2 ), and aj[ax - P(KL)^2 ] = 63.57(63.5 - 9.22) =1.17;
then 160 + 0.221(31.5)(12)(0.793)(13.41/22)(1.17) = 207 < 209 kips (929.6 kN). This is
acceptable. - Substitute in the second transformed equation
Thus, 160(13.41/22) + 0.221(31.5)(12)(13.41/22) = 148 < 209 kips (929.6 kN). This is
acceptable. The Wl2 x 53 section is therefore satisfactory.
NET SECTION OF A TENSION MEMBERThe 7 x % in (177.8 x 6.35 mm) plate in Fig. 17 carries a tensile force of 18,000 Ib
(80,064.0 N) and is connected to its support with three^3 /4-in (19.05-mm) rivets in the
manner shown. Compute the maximum tensile stress in the member.
Calculation Procedure:- Compute the net width
of the member at each section
of potential rupture
The AISC Specification prescribes the man-
ner of calculating the net section of a tension
member. The effective diameter of the holes
is considered to be Vs in (3.18 mm) greater
than that of the rivets.
After computing the net width of each
section, select the minimum value as the ef-
fective width. The Specification imposes an
upper limit of 85 percent of the gross width.
Refer to Fig. 17. From B to D 9 s = 1.25 in
FIGURE 17 (31.750 mm), g = 2.5 in (63.50 mm); from D