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Statically Determinate Beam Members

Key Concept: A beam member where its support reactions as well as internal forces and

moments can be evaluated by the equations of equilibrium is statically determinate.

Otherwise it is statically indeterminate and geometry and load˗deflection must be

considered simultaneously to obtain a solution.

In a Nut Shell: If the bending member is overconstrained (more supports than necessary),

then it is statically indeterminate and more information is needed to determine the support

eactions and internal forces and moments. This same concept also applies to axial and

torsion members.

Consider the two examples shown below. In the top figure the beam is clamped at end

A only. Then the force and bending moment at support A can be determined from

equilibrium by summing forces and moments. In the bottom figure the beam is clamped at A

and simply supported at end B. So there are two unknown reactions at A and two unknown

forces at B. But there are only three equations of equilibrium. So there is insufficient

information provided by equilibrium to determine these reactions and forces. The result is

more information is required to analyze this application.

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