Chapter 12 – Beam Deflection

Notice how deflection diagram (or elastic curve) is different for each beam. How does the support effect slope and deflection? 12.1 The Elastic Curve:

The moment diagram and sign can be a great aid in constructing the elastic curve!

Zero displacement and zero slope Zero displacement Displacement is max either where slope is zero or at end!!

Moment-Curvature Relationship (read 588 – 592): Define x, 

Radius of curvature Internal moment Modulus of elasticity Moment of inertia

Therefore: EI = Flexural Rigidity assume constant throughout beam length 12.2 – Slope and Displacement by Integration!

Or Any of these DE can be used to get  (x). Just integrate and evaluate constants of integration using BC’s. This is called the integration method for getting beam displacement!

OR: Careful! Need M(x) for each span (every time eqn for moment changes).

Sign convention – All Positive!!