Indeterminacy of a Continuous Beam

Equation: for a planar beam, degree of static indeterminacy = r − 3, where r is the number of reaction components and 3 is the number of equilibrium equations (ΣFx, ΣFy, ΣM). Values: the pin at A resists both horizontal and vertical movement, so it gives 2 reactions. Each roller at B and C resists only vertical movement, so each gives 1. Step 1: r = 2 + 1 + 1 = 4. Step 2: degree = 4 − 3 = 1. The beam is indeterminate to the first degree: it has one more unknown than statics can solve. It is stable, because the reactions are neither all parallel nor all concurrent. Calling it determinate counts the pin as one reaction.