Introduction

statically determinate beams

the number of reactions equals the number of independent equilibrium equations

1. determine reactions
2. determine shear forces and bending moments
3. determine stresses and deflections

 

statically indeterminate beams

the number of reactions exceeds the number of independent equilibrium equations

Most of the structures we encounter in everyday life (automobile frames, buildings, aircraft) are statically indeterminate. However, they are much more complex than beams and must be designed by sophisticated analytical techniques. Many of these techniques rely on the concepts presented in this chapter.

 

degree of static indeterminacy

the number of reactions in excess of the number of equilibrium equations

 

static redundants

the excess reactions

 

released structure or primary structure

the structure that remains when the redundants are released

• must be stable -- can carry loads
• must be statically determinate -- all force quantities can be determined from equilibrium alone

Types of Statically Indeterminate Beams

Propped cantilever beam		Fixed-end beam		Continuous beam

Analysis by the Differential Equations of the Deflection Curve

This technique involves symbolically solving the differential equations of the deflection curve, just as for a statically determinate beam. However, unknown quantities will now include integration constants and redundant reactions. Various conditions must be applied to solve for all of the unknowns.

This technique is only useful for simple beam and loading situations.