In many cases, all the forces lie in one and the same plane, and if there are any torques aside
from the torques resulting from the forces, those torques are about an axis perpendicular to that
plane. If we define the plane in which the forces lie to be the x-y plane, then for such cases, the
set of six scalar equations reduces to a set of 3 scalar equations (in that the other 3 are trivial 0=0
identities):
∑ F = 0 (23-3)
x
∑F = 0 (23-4)
y
∑τ = 0 (23-5)
z<
Statics problems represent a subset of Newton’s 2nd Law problems. You already know how to
solve Newton’s 2nd Law problems so there is not much new for you to learn here, but a couple of
details regarding the way in which objects are supported will be useful to you.
Many statics problems involve beams and columns. Beams and columns are referred to
collectively as members. The analysis of the equilibrium of a member typically entails some
approximations which involve the neglect of some short distances. As long as these distances
are small compared to the length of the beam, the approximations are very good. One of these
approximations is that, unless otherwise specified, we neglect the dimensions of the cross section
of the member (for instance, the width and height of a beam). We do not neglect the length of
the member.
Pin-Connected Members
A pin is a short axle. A member which is pin-connected at one end, is free to rotate about the
pin. The pin is perpendicular to the direction in which the member extends. In practice, in the
case of a member that is pin-connected at one end, the pin is not really right at the end of the
member, but unless the distance from the pin to the end (the end that is very near the pin) of the
member is specified, we neglect that distance. Also, the mechanism by which a beam is pin-
connected to, for instance, a wall, causes the end of the beam to be a short distance from the
wall. Unless otherwise specified, we are supposed to neglect this distance as well. A pin exerts
a force on the member. The force lies in the plane that contains the member and is perpendicular
to the pin. Beyond that, the direction of the force, initially, is unknown. On a free body diagram
of the member, one can include the pin force as an unknown force at an unknown angle, or one
can include the unknown x and y components of the pin force.
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