When a rigid body is acted by two forces: one force remains unchanged, the starting point of the second force is connected to the end point of the other force in translation, and then the starting point of the remaining force and the end point of the other force are connected to form a triangle. The last connected edge is the resultant force of two forces, and the direction is from the starting point of one force to the end point of the other force.
The equilibrium equation of force system is a mathematical equation that represents the equilibrium condition of force system.
When the force system used for a rigid body balances a rigid body, the force system is equivalent to a zero force system, so the necessary and sufficient condition for the balance of the force system is that both the principal vector and the principal moment are zero. Namely: fr = 0mo = 0 (1) or! Fi=0！ Mo (fi) = 0 (2) Projecting the above formula on each coordinate axis of rectangular coordinate system, the balance equations of projected components are obtained, and the number and form of balance equations of different force systems are different.
The equilibrium equation establishes the relationship between the forces acting on the equilibrium object. For statically indeterminate problems, we can try to get all the unknowns from the known. Three-hinged arch ABC is shown in Figure A. Given the load force f and even moment m, the binding force of hinged supports A and B is calculated regardless of the self-weight of the arch.
First of all, consider the overall balance, and try to find out the local binding forces FBy and FAy by using the plane force system balance equation as shown in Figure B, and get the relationship FAX+FBX = 0. Considering the balance of AC arch, as shown in Figure C, FAx can be obtained from the balance equation, and FBx can be obtained by substituting the above relationship. If we continue to write the equilibrium equation of AC arch, we can also get the binding force of hinge C.