"In this chapter we will analyze beams in which the number of reactions exceeds the number of independent equations of equilibrium. Since the reactions of such beams cannot be determined by statics alone, the beams are said to be statically indeterminate. The analysis of statically indeterminate beams is quite diferent from that of statically determinate beams. When a beam is statically determinate, we can determine all reactions, shear forces, and bending moments from free-body diagrams and equations of equilibrium. Then knowing the shear forces and bending moments, we can obtain the stresses and deflections. However, when a beam is statically indeterminate, the equilibrium equations are not sufficient and additional equations are needed. The most fundamental method for analyzing a statically indeterminate beam is to solve the differential equations of the deflection curve... Although this method serves as a good starting point in our analysis, it is practical for only the simplest types of statically indeterminate beams. Therefore, we also discuss the method of superposition, a method that is applicable to a wide variety of structures. In the method of superposition, we supplement the equilibrium conditions with compatibility equations and force-displacement equations."

BEAM
A SUPPORT THAT IS USED TO TRANSMIT AND SUPPORT FORCES

CANTILEVER BEAM
A BEAM THAT IS FIXED AT ONE END AND HANGS FREE AT THE OTHER END.

EQUATION
A MATHEMATICAL EQUALITY RELATING PARAMETERS OR MEASUREMENTS

EQUILIBRIUM
A STEADY-STATE CONDITION IN WHICH FORCES, TORQUES, FLOWS MAY BE HAPPENING BUT THE SYSTEM UNDER STUDY IS NOT CHANGING WITH TIME.

EQUILIBRIUM
A STATE OF BALANCE. FORCES, MOMENTS, FLOWS MAY BE OCCURRING IN A SYSTEM BUT NO NET CHANGE IS OCCURRING IN THE SYSTEM.

EQUILIBRIUM EQUATION
THERE ARE TWO KINDS OF EQUILIBRIUM BALANCE SOUGHT FOR STATIC STRUCTURES: ROTATIONAL AND TRANSLATIONAL EQUILIBRIUM. AN OBJECT IS IN ROTATIONAL EQUILIBRIUM IF THE SUM OF ALL MOMENTS (TORQUES) ON THE OBJECT EQUALS ZERO (THE MOMENTS ACT TO CANCEL EACH OTHER). AN OBJECT IS IN TRANSLATIONAL EQUILIBRIUM IF THE SUM OF ALL FORCES ON THE OBJECT EQUALS ZERO (THE FORCES ACT TO CANCEL EACH OTHER).

PROPPED CANTILEVER BEAM
A BEAM PINNED AT ONE END, EXTENDED AWAY FROM THE PIN AND SUPPORTED BY A STRUCTURAL MEMBER (PROP).