ppt on conjugate

1. Subject Name: Theory of
Structures
Topic Name:Analysis by Conjugate
Beam Lecture No: 25
Dr.Omprakash Netula
Professor & HOD
Department of Civil Engineering
09/28/17Lecture Number, Unit Number1

2. Theory of Structures - ITheory of Structures - I

3. Lecture 16
Deflection
Conjugate-Beam Method

4. Double Integral Method
EI
M
dx
yd
=2
2






++=
===
=
=
∫∫∫∫ ∫∫
21
3
2
2
6
cxc
x
EI
P
y
xdx
EI
P
dx
EI
Px
dx
EI
M
y
EI
M
dx
yd
PxM
Example 1

5. EI
M
dx
yd
=2
2
Conjugate-Beam Method

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

7. EIEI
M
EI
V
BB
BB
5.14062
)25(
5.562
5.562
'
'
−
===∆
−==θ

8. Conjugate-BeamSupports

10. Example 2
Find the deflection at Point C
C

11. EIEIEI
MCC
162
)3(
63
)1(
27
'
−
=−==∆

12. Example 3
Find the deflection at Point D

13. EI
360
EI
720 EI
MDD
3600
' ==∆

14. Example 4
Find the Rotation at A
10ft

15. EI
A
3.33
=θ

16. Group work 1
Find the deflection at Point B

17. Moment Diagrams and Equations for
Maximum Deflection

19. Example 4
Find the Maximum deflection for the following structure based on
The previous diagrams