Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

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EQuILIbRIuM OF bEAMS
y
A x
x
A
A y
(a) Pin support
y
x
A
A y
(b) Roller support
y
M A
A x
x
A
A y
(c) Fixed support
FIGURE 7.1 Types of supports.
• Figure 7.1b shows a roller support. A roller support prevents translation perpendicular
to the longitudinal axis of the beam (i.e., the y direction in Figure 7.1b); however, the
joint is free to translate in the x direction and to rotate about the z axis. Unless
specifically stated otherwise, a roller support should be assumed to prevent joint
displacement both in the +y and −y directions. The roller support in Figure 7.1b
provides a reaction force to the beam in the y direction only.
• Figure 7.1c shows a fixed support. A fixed support prevents both translation and
rotation at the supported joint. The fixed support shown in Figure 7.1c provides
reaction forces to the beam in the x and y directions, as well as a reaction moment in
the z direction. This type of support is sometimes called a moment connection.
Figure 7.1 shows symbols that represent three types of supports commonly associated with
beams. It is important to keep in mind that these symbols are simply graphic shorthand used to
communicate the beam support conditions easily. Actual pin, roller, and fixed supports may
take many configurations. Figure 7.2 shows one possibility for each type of connection.
One type of pin support is shown in Figure 7.2a. In this connection, three bolts are used
to attach the beam to a small component called a clip angle, which in turn is bolted to the
vertical supporting member (called a column). The bolts prevent the beam from moving
either horizontally or vertically. Strictly speaking, the bolts also provide some resistance
against rotation at the joint. Since the bolts are located close to the middle of the beam,
however, they are not capable of fully restraining rotation at the connection. This type of
connection permits enough rotation so that the joint is classified as a pin connection.
Figure 7.2b shows one type of roller connection. The bolts are inserted into slotted
holes in a small plate called a shear tab. Since the bolts are in slots, the beam is free to
deflect in the horizontal direction, but it is restrained from deflecting either upward or
downward. Slotted holes are sometimes used to facilitate the construction process, making
it easier for heavy beams to be quickly attached to columns.
Figure 7.2c shows a welded steel moment connection. Notice that extra plates are
welded to the top and bottom surfaces of the beam and that these plates are connected directly
to the column. These extra plates prevent the beam from rotating at the joint.
Types of Statically Determinate Beams
Beams are further classified by the manner in which the supports are arranged. Figure 7.3
shows three common statically determinate beams. Figure 7.3a shows a simply supported
Column
Column
Beam
Extra plates welded
directly to column
While this connection
restrains deflection, it
does not provide
enough resistance to
completely prevent
rotation.
The slotted bolts
restrain vertical
deflection, but
allow the beam
to move
horizontally.
Deflection is
restrained, and
rotation of the joint
is prevented, by the
extra plates attached
to the top, and
bottom flanges.
Beam
Clip angle
Shear tab with slots
Column
Beam
(a) Pin support
(b) Roller support
(c) Fixed support
FIGURE 7.2 Examples of actual beam supports.