Handbook of Civil Engineering Calculations

(a) Space diagram and

string polygon

FIGURE 1. Equilibrant of force system.

Calculation Procedure:

1. Construct the system force line
   In Fig. Ib, draw the vector chain A-B-C, which is termed the force line. The vector ex-
   tending from the initial point to the terminal point of the force line represents the resultant
   R. In any force system, the resultant R is equal to and collinear with the equilibrant E, but
   acts in the opposite direction. The equilibrant of a force system is a single force that will
   balance the system.


2. Construct the system rays
   Selecting an arbitrary point O as the pole, draw the rays from O to the ends of the vectors
   and label them as shown in Fig. Ib.


3. Construct the string polygon
   In Fig. Ia, construct the string polygon as follows: At an arbitrary point a on the action
   line of force A, draw strings parallel to rays or and ab. At the point where the string ab in-
   tersects the action line of force B, draw a string parallel to ray be. At the point where
   string be intersects the action line of force C, draw a string parallel to cr. The intersection
   point Q ofar and cr lies on the action line of R.


4. Draw the vector for the resultant and equilibrant
   In Fig. Ia, draw the vector representing R. Establish the magnitude and direction of this
   vector from the force polygon. The action line of R passes through Q.
   Last, draw a vector equal to and collinear with that representing R but opposite in di-
   rection. This vector represents the equilibrant E.

Related Calculations: Use this general method for any force system acting in a

single plane. With a large number offerees, the resultant of a smaller number offerees

can be combined with the remaining forces to simplify the construction.

(b) Force polygon

Force line

Ray

String