# ECIV 320 Structural Analysis I by vbf10787

VIEWS: 22 PAGES: 13

• pg 1
```									ECIV 320 Structural Analysis I

Deflections
Last Time
Deflection Diagrams & Elastic Curve

ASSUMPTION
Linear Elastic Material Response
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
Last Time - Double Integration Method

Relate Moments to Deflections

d 2u M
2

dx     EI                         Integration
du    M x 
 ( x)               dx          Constants
dx    EI ( x )
Use Boundary
M x  2      Conditions to Evaluate
u( x )              dx   Integration Constants
EI ( x )
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
Conjugate Beam

dV                      d M
 w                   
dx                      dx EI

d 2 M dV               d 2u d M
2
     w           2
   
dx     dx             dx     dx EI
Conjugate Beam

V    wdx                       M     
        dx
 EI   

       
M     wdx dx
 M  
u     dxdx
  EI  

M
Let      w
EI
Conjugate Beam

A “fictitious” beam of the same length as the real beam
loaded with the real beam’s M/EI diagram…

Real Beam = VConjugate Beam

uReal Beam = MConjugate Beam

However...
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
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
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
Examples of Conjugate Beam Supports
Examples of Conjugate Beam Supports
Examples of Conjugate Beam Supports

```
To top