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Chapter 12 – Beam Deflection

Chapter 12 – Beam Deflection. 12.1 The Elastic Curve:. Notice how deflection diagram (or elastic curve) is different for each beam. How does the support effect slope and deflection?. The moment diagram and sign can be a great aid in constructing the elastic curve!.

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Chapter 12 – Beam Deflection

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  1. Chapter 12 – Beam Deflection

  2. 12.1 The Elastic Curve: Notice how deflection diagram (or elastic curve) is different for each beam. How does the support effect slope and deflection?

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

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

  5. Moment-Curvature Relationship (read 588 – 592): Define x, u

  6. Internal moment Moment of inertia Modulus of elasticity Radius of curvature

  7. 12.2 – Slope and Displacement by Integration! Therefore: EI = Flexural Rigidity assume constant throughout beam length

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

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

  10. Sign convention – All Positive!!

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