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For example, let us consider three ways in which a horizontal
member, such as a beam, is supported at its end. One method consists
of a roller or cylinder, Fig. 1-7,a. Since this support only prevents the
beam from translating in the vertical direction, the roller will only
exert a force on the beam in this direction, Fig. 1-7,b.
The beam can be supported in a more restrictive manner by
using a pin, Fig. 1-7,c.The pin passes through a hole in the beam and
two leaves which are fixed to the ground. Here the pin can prevent
translation of the beam in any direction φ , Fig. 1-7,d, and so the pin
must exert a force F on the beam in this direction. For purposes of
analysis, it is generally easier to represent this resultant force F by its
two rectangular components F and F Fig. 1-7,e. If F and F are
x
y
x
y
known, then F and ψ can be calculated.
The most restrictive way to support the beam would be to use a
fixed support as shown in Fig. 1-7,f. This support will prevent both
translation and rotation of the beam. To do this a force and couple
moment must be developed on the beam at its point of connection, Fig.
1-7,g. As in the case of the pin, the force is usually represented by its
rectangular components F and F .
x
y

Fig. 1-8.

Cables and Pulleys. Unless otherwise stated, throughout this
book, all cables (or cords) will be assumed to have negligible weight
and they cannot stretch. Also, a cable can support only a tension or
“pulling” force, and this force always acts in the direction of the cable.

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