Page 128 - Handbook of Civil Engineering Calculations, Second Edition

STRUCTURAL STEEL DESIGN 1.111

Calculation Procedure:

1. 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 when f a /F a > 0.15. They are defined by B A/S
4
4
6
per inch (decimeter); a 0.149 10 I in (6201.9I dm ).
Let P denote the applied axial load and P allow the axial load that would be permitted in
the absence of bending. The equations given in the previous procedure may be trans-
2
formed to P + BMC m (F a /F b )a/[a – P(KL) ] P allow , and PF a /(0.6f y ) + BMF a /F b P allow ,
where KL, B, 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); F b 22 kips/sq.in. (151.7 MPa); C m 0.793.
2. Obtain the properties of the section
2
From the Manual for a W12 53, A 15.59 sq.in. (100.587 cm ); B x 0.221 per inch
6
4
3
4
(8.70 per meter); a x 63.5 10 in (264.31 10 dm ). Then when KL 20 ft (6.1 m),
P allow 209 kips (929.6 kN).
3. Substitute in the first transformed equation
Thus, F a P allow /A 209/15.59 13.41 kips/sq.in. (92.461 MPa), P(KL) 160(240)
2
2
2
6
2
9.22 10 kip·sq.in. (2.648 10 kN·m ), and a x /[a x – P(KL) ] 63.5/(63.5 – 9.22)
4
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.
4. 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 W12 53 section is therefore satisfactory.
NET SECTION OF A TENSION MEMBER
1
The 7 /4 in. (177.8 6.35 mm) plate in Fig. 17 carries a tensile force of 18,000 lb
3
(80,064.0 N) and is connected to its support with three /4-in. (19.05-mm) rivets in the
manner shown. Compute the maximum tensile stress in the member.
Calculation Procedure:
1. Compute the net width
of the member at each section
of potential rupture
The AISC Specification prescribes
the manner of calculating the net
section of a tension member. The
effective diameter of the holes is
considered to be /8 in. (3.18 mm)
1
greater than that of the rivets.
After computing the net width of
each section, select the minimum
value as the effective width. The
Specification imposes an upper limit
of 85 percent of the gross width. FIGURE 17