Page 212 - Handbook of Civil Engineering Calculations, Second Edition

HANGERS, CONNECTORS, AND WIND-STRESS ANALYSIS 1.195

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an allowable stress of 22 kips/sq.in. (151.7 MPa). Thus, L 14 + 12 340 sq.ft. (31.6
sq.in.); L 18.4 ft (5.61 m); r min (18.4 12)/300 0.74 in. (18.8 mm).
Try a 4 4 /4 in. (101.6 101.6 6.35 mm) angle; r 0.79 in. (20.1 mm); A
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1.94 sq.in. (12.52 cm ); P max 1.94(22) 42.7 kips (189.9 kN).
4. Compute the wind drift if the assumed size of bracing is used
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By Eq. 6, P h {196/[(340)(18.4)(12)]} l.94(29)(10) 147 kips (653.9 N). The
wind shear resisted by the columns of the bent is reduced by P h , and the wind drift is re-
duced proportionately.
From the previous calculation procedure, the following values are obtained: without
diagonal bracing, 0.382 in. (9.7 mm); with diagonal bracing, 0.382/(44 – P h )/44
0.382 – 1.28 . Solving gives 0.168 < 0.20 in. (5.1 mm), which is acceptable.
5. Check the axial force in the brace
Thus, P h 147(0.168) 24.7 kips (109.9 kN); P P h L/a 24.7(18.4)/14 32.5 <
42.7 kips (189.9 kN), which is satisfactory. Therefore, the assumed size of the member
is satisfactory.

LIGHT-GAGE STEEL BEAM WITH
UNSTIFFENED FLANGE

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A beam of light-gage cold-formed steel consists of two 7 1 /2 in. (177.8 38.1 mm) by no.
12 gage channels connected back to back to form an I section. The beam is simply supported
on a 16-ft (4.88-m) span, has continuous lateral support, and carries a total dead load of 50
lb/lin ft (730 N/m). The live-load deflection is restricted to 1/360 of the span. If the yield-point
stress f y is 33,000 lb/sq.in. (227.5 MPa), compute the allowable unit live load for this member.

Calculation Procedure:

1. Record the relevant properties of the section
Apply the AISC Specification for the Design of Light Gage Cold-Formed Steel Structural
Members. This is given in the AISC publication Light Gage Cold-Formed Steel Design
Manual. Use the same notational system, except denote the flat width of an element by g
rather than w.
The publication mentioned above provides a basic design stress of 20,000 lb/sq.in.
(137.9 MPa) for this grade of steel. However, since the compression flange of the given
member is unstiffened in accordance with the definition in one section of the publication, it
may be necessary to reduce the allowable compressive stress. A table in the Manual gives
the dimensions, design properties, and allowable stress of each section, but the allowable
stress will be computed independently in this calculation procedure.
Let V maximum vertical shear; M maximum bending moment; w unit load; f b
basic design stress; f c allowable bending stress in compression; v shearing stress;
maximum deflection.
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Record the relevant properties of the section as shown in Fig. 23: I x 12.4 in (516.1
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cm ); S x 3.54 in (58.0 cm ); R /16 in. (4.8 mm).
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2. Compute f c
Thus, g B/2 – t – R 1.1935 in. (30.3 mm); g/t 1.1935/0.105 11.4. From the
Manual, the allowable stress corresponding to this ratio is f c l.667f b – 8640 – l( f b –
12,950)g/t]/15 1.667(20,000) – 8640 – (20,000 – 12,950)11.4/15 19,340 lb/sq.in.
(133.3 MPa).