27.5, which are presented in the AISC
Manual. Note that the T section consid-
ered is one-half the wide-flange section
being used. See Fig. 6.
The properties of these sections are Iw
= 890 in^4 (37,044.6 cm^4 ); AT = 8.10 in^2
(52.261 cm^2 ); tw = 0.39 in (9.906 mm);
ym = 9.06 - 2.16 = 6.90 in (175.26 mm).
- Calculate the shearing FIGURE 6
stress at the centroidal axis
Substituting gives Q = 8.10(6.90) = 55.9
in
3
(916.20 cm
3
); then v = 70,000(55.9)/
[890(0.39)] = 11,270 lb/in^2 (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:- 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. - 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/in^2 (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
A welded plate girder is composed of a 66 x^3 / 8 in (1676.4 x 9.53 mm) web plate and two
20 x^3 /4 in (508.0 x 19.05 mm) flange plates. The unbraced length of the compression
flange is 18 ft (5.5 m). If Cb = 1, what bending moment can this member resist?