Page 106 - Handbook of Civil Engineering Calculations, Second Edition

STRUCTURAL STEEL DESIGN 1.89

The values of allowable uniform load given in the AISC Manual apply to beams of
A36 steel satisfying the first or third condition above, depending on whether the section is
compact or noncompact.
Referring to the table in the Manual, we see that the most economic section made of
A36 steel is W16 45; W allow 46 kips (204.6 kN), where W allow allowable load on
the beam, kips (kN). Also, L c 7.6 > 5. Hence, the beam is acceptable.
2. Compute the equivalent load for a member of A242 steel
To apply the AISC Manual tables to choose a member of A242 steel, assume that the
shape selected will be compact. Transform the actual load to an equivalent load by apply-
ing the conversion factor 1.38, that is, the ratio of the allowable stresses. The conversion
factors are recorded in the Manual tables. Thus, equivalent load 45/1.38 32.6 kips
(145.0 N).
3. Determine the highest satisfactory section
Enter the Manual allowable-load table with the load value computed in step 2, and select
the lightest section that appears to be satisfactory. Try W16 36; W allow 36 kips (160.1
N). However, this section is noncompact in A242 steel, and the equivalent load of 32.6
kips (145.0 N) is not valid for this section.
4. Revise the equivalent load
To determine whether the W16 36 will suffice, revise the equivalent load. Check the L u
value of this section in A242 steel. Then equivalent load 45/1.25 36 kips (160.1 N),
L u 6.3 ft (1.92 m) > 5 ft (1.5 m); use W16 36.
5. Verify the second part of the design
To verify the second part of the design, calculate the bending stress in the W16 36,
3
using S 56.3 in 3 (922.76 cm ) from the Manual. Thus M (1/8)WL
(1/8)(45,000)(25)(12) 1,688,000 in·lb (190,710.2 N·m); f M/S 1,688,000/56.3
30,000 lb/sq.in. (206,850.0 kPa). This stress is acceptable.

DESIGN OF A BEAM WITH REDUCED
ALLOWABLE STRESS

The compression flange of the beam in Fig. 1a will be braced only at points A, B, C, D,
and E. Using AISC data, a designer has selected W21 55 section for the beam. Verify
the design.

Calculation Procedure:

1. Calculate the reactions; construct the shear
and bending-moment diagrams
The results of this step are shown in Fig. 1.
2. Record the properties of the selected section
Using the AISC Manual, record the following properties of the 21WF55 section:
3
3
4
4
S 109.7 in (1797.98 cm ); I y 44.0 in (1831.41 cm ); b f 8.215 in. (208.661 mm);
t f 0.522 in. (13.258 mm); d 20.80 in. (528.32 mm); t w 0.375 in. (9.525 mm);
d/A f 4.85/in. (0.1909/mm); L c 8.9 ft (2.71 m); L u 9.4 ft (2.87 m).
Since L
> L u , the allowable stress must be reduced in the manner prescribed in the
Manual.