1. ECIV 320 Structural Analysis I
Deflections

2. Last Time Deflection 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. Principles of Statics Only
Conjugate Beam Method
Developed by H. Muller Breslau
Use to find slopes and deflection due to
bending of beams
Method is based on
Principles of Statics Only

5. Conjugate Beam
Internal Loadings
Beam Theory

6. Conjugate Beam
Internal Loadings
Beam Theory
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