Structure Analysis I

Structure Analysis I

Lecture 16Deflection

Conjugate-Beam Method

Double Integral Method

EI

M

dx

yd

2

2

21

3

2

2

6cxc

x

EI

Py

xdxEI

Pdx

EI

Pxdx

EI

My

EI

M

dx

yd

PxM

Example 1

EI

M

dx

yd

2

2

Conjugate-Beam Method

Example 1Find the Max. deflection Take E=200Gpa, I=60(106)

EIEIM

EIV

BB

BB

5.14062)25(

5.562

5.562

'

'

Con

jug

ate

-Beam

Su

pp

ort

s

Example 2Find the deflection at Point C

C

EIEIEIMCC

162)3(

63)1(

27'

Example 3Find the deflection at Point D

EI

360

EI

720 EIM DD

3600'

Example 4Find the Rotation at A

10 ft

EIA

3.33

Group work 1Find the deflection at Point B

Moment Diagrams and Equations for Maximum Deflection

Example 4 Find the Maximum deflection for the following structure based onThe previous diagrams