Handbook of Civil Engineering Calculations

98.2 in^3 (1609.50 cm^3 ); section compact. The disparity between the assumed and actual

beam weight is negligible.

A second method for making this selection is shown below.

3. Calculate the total load on the member
   Thus, the total load = W= 30(1700) = 51,000 Ib (226,848.0 N).


4. Select the most economic section
   Refer to the tables of allowable uniform loads in the Manual, and select the most econom-
   ic section. Thus use W18 x 55; fFallow = 52,000 Ib (231,296.0 N). The capacity of the
   beam is therefore slightly greater than required.

MOST ECONOMIC SECTION FOR A BEAM

WITH INTERMITTENT LATERAL SUPPORT

UNDER UNIFORM LOAD

A beam on a simple span of 25 ft (7.6 m) carries a uniformly distributed load, including

the estimated weight of the beam, of 45 kips (200.2 kN). The member is laterally support-

ed at 5-ft (1.5-m) intervals. Select the most economic member (a) using A36 steel; (b) us-

ing A242 steel, having a yield-point stress of 50,000 lb/in^2 (344,750.0 kPa) when the

thickness of the metal is^3 A in (19.05 mm) or less.

Calculation Procedure:

1. Using the AISC allowable-load tables, select the most economic
   member made of A36 steel
   After a trial section has been selected, it is necessary to compare the unbraced length L' of
   the compression flange with the properties Lc and Lu of that section in order to establish
   the allowable bending stress. The variables are defined thus: L 0 = maximum unbraced
   length of the compression flange if the allowable bending stress = 0.66/J,, measured in ft
   (m); L 14 = maximum unbraced length of the compression flange, ft (m), if the allowable
   bending stress is to equal 0.60/J,.
   The values of L 0 and Lu associated with each rolled section made of the indicated
   grade of steel are recorded in the allowable-uniform-load tables of the AISC Manual. The
   Lc value is established by applying the definition of a laterally supported member as pre-
   sented in the Specification. The value of L 14 is established by applying a formula given in
   the Specification.
   There are four conditions relating to the allowable stress:

Condition Allowable stress
Compact section: L' < Lc 0.66/J,
Compact section: L 0 < L' < Lu 0.60/J,
Noncompact section: L' ^ Lu 0.60/J,
L' > Lu Apply the Specification formula—use the larger value
obtained when the two formulas given are applied.

The values of allowable uniform load given in the AISC Manual apply to beams of