Page 124 - Handbook of Civil Engineering Calculations, Second Edition

STRUCTURAL STEEL DESIGN 1.107

Calculation Procedure:

1. Draw schematic diagrams to indicate the restraint conditions
Show these conditions in Fig. 14b. The cross bracing prevents sidesway at the top solely
with respect to the minor axis, and the rigid beam-to-column connections afford partial
fixity with respect to the major axis.
2. Record the I x values of the column and beams

I x
Section in 4 cm 4
W14 95 1064 44,287
W24 76 2096 87,242
W21 68 1478 61,519

3. Calculate the rigidity of the column relative to that
of the restraining members at top and bottom
Thus, I c /L c 1064/28 38. At the top, (I g /L g ) 2096/40 + 1478/30 101.7. At the
top, the rigidity G t 38/101.7 0.37.
In accordance with the instructions in the Manual, set the rigidity at the bottom G b 10.

4. Determine the value of K x
Using the Manual alignment chart, determine that K x 1.77.
5. Compute the slenderness ratio with respect to both principal
axes, and find the allowable stress
Thus, K x L/r x 1.77(28)(12)/6.17 96.4; K y L/r y 28(12)/3.71 90.6.
Using the larger value of the slenderness ratio, find from the Manual the allowable ax-
ial stress in the absence of bending f 13.43 kips/sq.in. (92.600 MPa).

LACING OF BUILT-UP COLUMN

Design the lacing bars and end tie plates of the member in Fig. 15. The lacing bars will be
1
connected to the channel flanges with /2-in. (12.7-mm) rivets.

Calculation Procedure:

1. Establish the dimensions of the lacing system to conform
to the AISC Specification
The function of the lacing bars and tie plates is to preserve the integrity of the column and
to prevent local failure.
Refer to Fig. 15. The standard gage in 15-in. (381.0-mm) channel 2 in. (50.8 mm),
from the AISC Manual. Then h 14 < 15 in. (381.0 mm); therefore, use single lacing.
Try 60°; then, v 2(14) cos 60° 16.16 in. (410.5 mm). Set v 16 in. (406.4
mm); therefore, d 16.1 in. (408.94 mm). For the built-up section, KL/r 48.5; for the
single channel, KL/r 16/0.89 < 48.5. This is acceptable. The spacing of the bars is
therefore satisfactory.