Page 126 - Handbook of Civil Engineering Calculations, Second Edition

STRUCTURAL STEEL DESIGN 1.109

3. Determine whether the selected section is acceptable
Compute the value of K x L associated with a uniform-strength column, and compare this
with the actual effective length. Thus, K x L 1.73(16.2) 28.0 > 27.6 ft (8.41 m). There-
fore, the W8 40 is acceptable.

DESIGN OF AN AXIAL MEMBER
FOR FATIGUE

A web member in a welded truss will sustain precipitous fluctuations of stress caused by
moving loads. The structure will carry three load systems having the following character-
istics:

Force induced in member, kips (kN)
__________________________________________ No. of times
System Maximum compression Maximum tension applied
A 46 (204.6) 18 (80.1) 60,000
B 40 (177.9) 9 (40.0) 1,000,000
C 32 (142.3) 8 (35.6) 2,500,000

The effective length of the member is 11 ft (3.4 m). Design a double-angle member.

Calculation Procedure:
1. Calculate for each system the design load, and indicate the
yield-point stress on which the allowable stress is based
The design of members subjected to a repeated variation of stress is regulated by the
AISC Specification. For each system, calculate the design load and indicate the yield-
point stress on which the allowable stress is based. Where the allowable stress is less than
that normally permitted, increase the design load proportionately to compensate for this
reduction. Let + denote tension and – denote compression. Then

System Design load, kips (kN) Yield-point stress, kips/sq.in. (MPa)
2
A –46 – /3(18) –58 (–257.9) 36 (248.2)
2
B –40 – /3(9) –46 (–204.6) 33 (227.5)
3
C 1.5(–32 – /4 8) –57 (–253.5) 33 (227.5)
2. Select a member for system A and determine if it is adequate
for system C
1
From the AISC Manual, try two angles 4 3 /2 /8 in. (101.6 88.90 9.53 mm),
3
with long legs back to back; the capacity is 65 kips (289.1 kN). Then A 5.34 sq.in.
2
(34.453 cm ); r r x 1.25 in. (31.750 mm); KL/r 11(12)/1.25 105.6.
From the Manual, for a yield-point stress of 33 kips/sq.in. (227.5 MPa), f 11.76
kips/sq.in. (81.085 MPa). Then the capacity P 5.34(11.76) 62.8 kips (279.3 kN) > 57
kips (253.5 kN). This is acceptable. Therefore, use two angles 4 3 /2 /8 in. (101.6
1
3
88.90 9.53 mm), long legs back to back.