1. ECIV 320 Structural Analysis I Deflections

2. Last TimeDeflection Diagrams & Elastic Curve ASSUMPTION Linear Elastic Material Response A structure subjected to a load will return to its original undeformed position after load is removed OBJECTIVE Calculate Slope and Deflection due to Bending at any point on a Beam METHODS • Double Integration Method • Moment Area Theorems • Conjugate Beam

3. Last Time - Double Integration Method Relate Moments to Deflections Integration Constants Use Boundary Conditions to Evaluate Integration Constants

4. Conjugate Beam Method Developed by H. Muller Breslau - 1865 Use to find slopes and deflection due to bending of beams Method is based on Principles of Statics Only

5. Conjugate Beam Beam Theory Internal Loadings

6. Conjugate Beam Beam Theory Internal Loadings Let

7. Conjugate Beam A “fictitious” beam of the same length as the real beam loaded with the real beam’s M/EI diagram… qReal Beam = VConjugate Beam uReal Beam = MConjugate Beam However...

8. Conjugate Beam Supports Shear and Moment at Supports of Conjugate Beam should account for the corresponding slope and deflection of real beam at its supports

9. Conjugate Beam Supports Shear and Moment at Supports of Conjugate Beam should account for the corresponding slope and deflection of real beam at its supports

10. Conjugate Beam Supports Shear and Moment at Supports of Conjugate Beam should account for the corresponding slope and deflection of real beam at its supports

11. Examples of Conjugate Beam Supports

12. Examples of Conjugate Beam Supports

13. Examples of Conjugate Beam Supports