Page 105 - Handbook of Civil Engineering Calculations, Second Edition

1.88 STRUCTURAL STEEL ENGINEERING AND DESIGN

2. Select the most economic section
Refer to the AISC Manual, and select the most economic section. Use W18 55
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98.2 in (1609.50 cm ); 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 lb (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 55; W allow 52,000 lb (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/sq.in. (344,750.0 kPa) when the
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thickness of the metal is /4 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 L c and L u of that section in order to establish
the allowable bending stress. The variables are defined thus: L c maximum unbraced
length of the compression flange if the allowable bending stress 0.66f y , measured in ft
(m); L u maximum unbraced length of the compression flange, ft (m), if the allowable
bending stress is to equal 0.60f y .
The values of L c and L u 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
L c value is established by applying the definition of a laterally supported member as pre-
sented in the Specification. The value of L u 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
L c 0.66f y
Compact section: L c < L
L u 0.60f y
Noncompact section: L
L u 0.60f y
Apply the Specification formula—use the larger value
L
> L u
obtained when the two formulas given are applied.