Building Design and Construction Handbook - Merritt - Ventech!

5.30 SECTION FIVE
Hollow Tubes. If a thin-shell hollow tube is twisted, the shearing force per unit
of length on a cross section (shear flow) is given approximately by
T
H � (5.47)
2A
where A is the area enclosed by the mean perimeter of the tube, in 2 , and the unit
shearing stress is given approximately by
H T
v � � (5.48)
t 2At
where t is the thickness of the tube, in. For a rectangular tube with sides of unequal
thickness, the total shear flow can be computed from Eq. (5.47) and the shearing
stress along each side from Eq. (5.48), except at the corners, where there may be
appreciable stress concentration.
Channels and I Beams. For a narrow rectangular section, the maximum shear is
very nearly equal to
1 t ⁄3
v � (5.49)
2 bd
This formula also can be used to find the maximum shearing stress due to torsion
in members, such as I beams and channels, made up of thin rectangular components.
Let J � 1 ⁄3�b 3 d, where b is the thickness of each rectangular component and d the
corresponding length. Then, the maximum shear is given approximately by
Tb�
v � (5.50)
J
where b� is the thickness of the web or the flange of the member. Maximum shear
will occur at the center of one of the long sides of the rectangular part that has the
greatest thickness. (A. P. Boresi, O. Sidebottom, F. B. Seely, and J. O. Smith,
‘‘Advanced Mechanics of Materials,’’ 3d ed., John Wiley & Sons, Inc., New York.)
5.5 STRAIGHT BEAMS
Beams are the horizontal members used to support vertically applied loads across
an opening. In a more general sense, they are structural members that external loads
tend to bend, or curve. Usually, the term beam is applied to members with top
continuously connected to bottom throughout their length, and those with top and
bottom connected at intervals are called trusses. See also Structural System, Art.
1.7.
5.5.1 Types of Beams
There are many ways in which beams may be supported. Some of the more common
methods are shown in Figs. 5.11 to 5.16.