Page 164 - Standard Handbook Of Petroleum & Natural Gas Engineering

Dynamics 149

One of the simplest structures is the truss. A truss consists of straight members
connected at their end points only. All loads, including the weight of the members
themselves, are considered to be supported at the joints. Due to its construction and
the assumption of loading atjoints only, the members of a truss support only loads of
axial tension or axial compression. A rigid truss or a rigid structure will not collapse
and can only deform if its members deform. A simple truss is one that can be
constructed, starting with three members arranged in a triangle, by adding new
members in pairs, first connecting one end of each together to form a new joint, and
then connecting the other ends at separate existing joints of the truss.
Aframe is a structure with at least one member that supports more than two forces.
Members of a frame may support lateral as well as axial forces. Connections in a
frame need not be located at the ends of the members. Frames, like trusses, are
designed to support loads, and are usually motionless. A machine also has multiforce
members. It is designed to modify and transmit forces and, though it may sometimes
be stationary, it always includes parts that move during some phase of operation.
Not all structures can be fully analyzed by the methods of statics. If the number of
discrete equilibrium equations is equal to the number of unknown loads, then the
structure is said to be statically determinate and rigid. If there are more unknowns
than equations, then the structure is statically indeterminate. If there are more equations
than unknowns, then the structure is said to be statically indeterminate and nonrigid.
For further information on this subject, refer to References 1 and 2.
DYNAMICS

Dynamics is the study of the mechanics of rigid bodies in motion. It is usually
subdivided into kinematics, the study of the motion of bodies without reference to the
forces causing that motion or to the mass of bodies, and kinetics, the study of the
relationship between the forces acting on a body, the mass and geometry of the body,
and the resulting motion of the body.
Kinematics

Kinematics is based on one-dimensional differential equations of motion. Suppose
a particle is moving along a straight line, and its distance from some reference point
is S (see Figure 2-6a). Then its linear velocity and linear acceleration are defined by
the differential equations given in the top half of Column 1, Table 2-5. The solutions

Figure 2-6. Diagrams of motion: (a) one-dimensional linear; (b) rotational.