Page 113 - Handbook of Civil Engineering Calculations, Second Edition

1.96 STRUCTURAL STEEL ENGINEERING AND DESIGN

WT9 27.5, which are presented in
the AISC Manual. Note that the T
section considered is one-half the
wide-flange section being used. See
Fig. 6.
The properties of these sections are
4
4
I w 890 in (37,044.6 cm ); A T 8.10
2
sq.in. (52.261 cm ); t w 0.39 in. (9.906
mm); y m 9.06 – 2.16 6.90 in.
FIGURE 6 (175.26 mm).
2. Calculate the shearing
stress at the centroidal axis
Substituting gives Q 8.10(6.90)
3
55.9 in 3 (916.20 cm ); then v
70,000(55.9)/[890(0.39)] 11,270 lb/
sq.in. (77,706.7 kPa).

SHEARING STRESS IN A BEAM—
APPROXIMATE METHOD

Solve the previous calculation procedure, using the approximate method of determining
the shearing stress in a beam.

Calculation Procedure:
1. Assume that the vertical shear is resisted solely by the web
Consider the web as extending the full depth of the section and the shearing stress as uni-
form across the web. Compare the results obtained by the exact and the approximate
methods.
2. Compute the shear stress
Take the depth of the web as 18.12 in. (460.248 mm), v 70,000/[18.12(0.39)] 9910
lb/sq.in. (68,329.45 kPa). Thus, the ratio of the computed stresses is 11,270/9910 1.14.
Since the error inherent in the approximate method is not unduly large, this method is
applied in assessing the shear capacity of a beam. The allowable shear V for each rolled
section is recorded in the allowable-uniform-load tables of the AISC Manual.
The design of a rolled section is governed by the shearing stress only in those in-
stances where the ratio of maximum shear to maximum moment is extraordinarily large.
This condition exists in a heavily loaded short-span beam and a beam that carries a large
concentrated load near its support.

MOMENT CAPACITY OF A WELDED
PLATE GIRDER

3
A welded plate girder is composed of a 66 /8 in. (1676.4 9.53 mm) web plate and
3
two 20 /4 in. (508.0 19.05 mm) flange plates. The unbraced length of the compres-
sion flange is 18 ft (5.5 m). If C b 1, what bending moment can this member resist?