Page 154 - Handbook of Civil Engineering Calculations, Second Edition

STRUCTURAL STEEL DESIGN 1.137

DETERMINING IF A GIVEN BEAM
IS COMPACT OR NON-COMPACT

A designer plans to use a W6 15 and a W12 65 beam in (a) A6 steel [F y 36 ksi
(248 MPa)], and (b) with F y 50 ksi 344.5 MPa and wishes to determine if the beams are
compact or non-compact.

Calculation Procedure:
For the W6 15 beam
1. Analyze the W6 15 beam
Referring to the AISC Manual table, namely “Limiting Width-Thickness Ratios for
Beams” and its illustration “Definition of widths (b and h) and thickness,” the flanges of a
W shape are given by
65
p
F y
where p limiting width-thickness ratio for compact section.
Substituting for each of the two beams, we have
65

36
65 10.8 if F y 36 ksi (248 MPa)
p = =
F y
65

50 9.2 if F y 50 ksi (344.5 MPa)
2. Compute the data for the web of a W shape
Using the same equation as in Step 1, for the web of a W shape
640

36
640 106.7 if F y 36 ksi (248 MPa)
p = =
F y
640

50 90.5 if F y 50 ksi (344.5 MPa)
3. Determine if the beam is compact
From the Properties Tables for W Shapes, in Part 1 of the AISC LRFD Manual (Compact
Section Criteria): for a W6 15
b b f
flange 11.5
t 2t f
h c
web 21.6
t w
Since flange (b/t 11.5) > ( p 10.8), the W 15 beam is noncompact in A36 steel.
Likewise, it is noncompact if F y 50 ksi (344.4 Mpa).
For the W12 65 beam
4. Compute the properties of the beam shape
From the AISC Manual “Properties Tables for W Shapes,” for a W12 65