Free Body Diagrams and Reactions

Introduction

Reaction Forces are connections that prevent translation and rotation. There are three main types of reactionary forces: roller supports, pin supports, and fixed supports.

Roller Supports

Rollers only prevent beams from translating in the vertical direction.

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Pin Supports

Pins prevent translating in the horizontal and vertical direction, but allow rotation.

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Fixed Supports

Fixed supports are most restrictive, they prevent translation and rotation.

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Procedure for Solving Reaction Forces

  1. Draw a FBD

  2. Draw Reaction Forces for the type of support

  3. Set up Equilibrium Equations

  4. Solve for Reaction Forces

Important Tips

  • Always draw a FBD to ensure all the forces are accounted for.

  • If a support prevents translation, then a force is exerted on the object.

  • If a support prevents rotation, then a moment is exerted on the object.

Example Problem:

Draw the Reaction Forces and create equilibrium equations

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Equilibrium Equations

→ Σ F X = 0 = − R B x \rightarrow \Sigma F_{X} = 0 = - R_{Bx}

↑ Σ F y = 0 = R A − R B y − 400 N \uparrow \Sigma F_{y} = 0 = R_{A} - R_{By} - 400N

⟲ Σ M B = 0 = 600 N ⋅ m + M B + ( 450 N • 4 m ) − ( R A • 5 m ) ⟲ \Sigma M_{B} = 0 = 600N \cdot m + M_{B} + (450N \bullet 4m) - (R_{A} \bullet 5m)