Building Design and Construction Handbook - Merritt - Ventech!

5.62 SECTION FIVE
5.8 GRAPHIC-STATICS FUNDAMENTALS
A force may be represented by a straight line of fixed length. The length of line to
a given scale represents the magnitude of the force. The position of the line parallels
the line of action of the force. And an arrowhead on the line indicates the direction
in which the force acts.
Forces are concurrent when their lines of action meet. If they lie in the same
plane, they are coplanar.
5.8.1 Parallelogram of Forces
The resultant of several forces is a single forces that would produce the same effect
on a rigid body. The resultant of two concurrent forces is determined by the parallelogram
law:
If a parallelogram is constructed with two forces as sides, the diagonal represents
the resultant of the forces (Fig. 5.45a).
The resultant is said to be equal to the sum of the forces, sum here meaning,
of course, addition by the parallelogram law. Subtraction is carried out in the same
manner as addition, but the direction of the force to be subtracted is reversed.
If the direction of the resultant is reversed, it becomes the equilibrant, a single
force that will hold the two given forces in equilibrium.
5.8.2 Resolution of Forces
To resolve a force into two components, a parallelogram is drawn with the force
as a diagonal. The sides of the parallelogram represent the components. The procedure
is: (1) Draw the given force. (2) From both ends of the force draw lines
parallel to the directions in which the components act. (3) Draw the components
along the parallels through the origin of the given force to the intersections with
the parallels through the other end. Thus, in Fig. 5.45a, P 1 and P 2 are the components
in directions OA and OB of the force represented by OC.
5.8.3 Force Polygons
Examination of Fig. 5.45a indicates that a step can be saved in adding the two
forces. The same resultant could be obtained by drawing only the upper half of the
parallelogram. Hence, to add two forces, draw the first force; then draw the second
FIGURE 5.45 Addition of forces by (a) parallelogram law; (b) triangle
construction; (c) polygon construction.