Handbook of Civil Engineering Calculations

3. Determine whether the selected section is acceptable
   Compute the value OfKxL associated with a uniform-strength column, and compare this
   with the actual effective length. Thus, KxL = 1.73(16.2) = 28.0 > 27.6 ft (8.41 m). There-
   fore, the W8 x 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/in^2 (MPa)

A -46-^2 / 3 (18) = -58(-257.9) 36(248.2)
B -40-^2 / 3 (9) = -^6(-204.6) 33(227.5)
C 1.5(-32 -^3 /4 x g) = -57 (-253.5) 33 (227.5)

2. Select a member for system A and determine if it is adequate
   for system C
   From the AISC Manual, try two angles 4 x y/ 2 x % hi (101.6 x 88.90 x 9.53 mm), with
   long legs back to back; the capacity is 65 kips (289.1 kN). Then A = 5.34 in^2 (34.453
   cm
   2
   ); r = rx = 1.25 in (31.750 mm); KLIr = 11(12)71.25 = 105.6.
   From the Manual, for a yield-point stress of 33 kips/in
   2
   (227.5 MPa),/= 11.76
   kips/in^2 (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 x 31/2 x % hi (101.6 x
   88.90 x 9.53 mm), long legs back to back.