Download Fundamental Structural Analysis (2) PDF

Page 1

S T R U C T U R A L
A N A L Y S I S

FUNDAMENTAL

Faculty of Engineering
Chulalongkorn University

Jaroon Rungamornrat

Zubizuri Bridge
Bilbao. Biscay, Euskadi, Spain

C

M

Y

CM

MY

CY

CMY

K

Page 315

FUNDAMENTAL STRUCTURAL ANALYSIS
Jaroon Rungamornrat Conjugate Structure Analogy



Copyright © 2011 J. Rungamornrat



299

To obtain the displacement and rotation at point E, we consider a segment AE (containing straight
sub-segments AB and BE) since the displacement and rotation at point A and the relative hinge
rotation B are already known. A corresponding conjugate segment of this segment is shown
below
















where area of the sub-curvature diagram A4 is given by


2 3

4

1 qL L qL
A =

2 3EI 3 18EI

  
    

  



By considering equilibrium of the conjugate structure AE, we obtain


ZΣF = 0 :
AE AE
A 2 3 4 B E+ A + A + A = 0   




3 3 3 3 3

AE
E

7qL qL qL qL 2qL
0

72EI 6EI 3EI 18EI 9EI
      




3

AE
E

7qL

72EI
   CW



XEΣM = 0 :
AE AE AE
A A EU (L) U 0  



  
3

AE
E

7qL
0 L U 0

72EI

 
    
 






4

AE
E

7qL
U

72EI
 Rightward



YEΣM = 0 :
AE AE AE
A A 2 3 4 B EV (2L) A (2L/3) A (7L/12) A (2L/9) (L) V 0       



  
3 3 3 3 3

AE
E

7qL qL 2L qL 7L qL 2L 2qL
0 (2L) L V 0

72EI 6EI 3 3EI 12 18EI 9 9EI

              
                       

              





4

AE
E

11qL
U

162EI
  Downward



3A

AE
AU 0

AE
AV 0

AE
A

AE
EU

AE
EV

AE
E

E

X

Y

A

7L/12

2A B

2L/9

4A

2L/3

Page 316

FUNDAMENTAL STRUCTURAL ANALYSIS
Conjugate Structure Analogy Jaroon Rungamornrat



Copyright © 2011 J. Rungamornrat



300




1. Use the method of conjugate structure analogy to determine the relative hinge rotation (if exists)

and the deflection and rotation at certain points of beams indicated in the figure below. In the
analysis, only bending deformation is considered. Young's modulus and moment of inertia of the
cross section are clearly indicated in the figures.














































Exercises

q

2qL

L/2 L/2

A B 3EI EI

q qL

L 2L L

A
B C D 2EI EI EI

EI EI EI

P 2P

L 2L L

A
B C

D

A
C

B D

q 2qL

2L L 3L

2EI 2EI EI

P

PL

L L L L

B

A C

D

P

EI EI EI EI

Page 629

FUNDAMENTAL STRUCTURAL ANALYSIS
Jaroon Rungamornrat Acknowledgement



Copyright © 2011 J. Rungamornrat



A-1



ACKNOWLEDGEMENT





The author would like to express his greatest gratitude to everyone who advised, supported, and
helped him to complete this book. First of all, he would like to gratefully acknowledge the
Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University for providing
him the great opportunity in teaching of fundamental courses in structural analysis since the first
year he was appointed as a faculty member. The author would also like to express his deepest
appreciation to Mr. Nithi Nikornpakorn and several of his students (Mr. Panupong Boonphennimit,
Mr. Mattana Pinitpanich, Miss Porjan Tuttipongsawat, Mr. Thanachote Techawongsakorn, Mr.
Natdanai Sinsamutpadung, Miss Varanich Chinprapinporn, Miss Sitanan Tanyasakulkit, Mr.
Suttinan Sakulpinyo, Mr. Jessada Sresagoolchai) for their invaluable help in proofreading and
verifying various examples appearing throughout this book. Furthermore, special thanks to his
sister-in-law, Wisa A. Kompayak, for her beautiful design of the book cover.
Last but not least, the author would like to express his sincere gratitude to all family
members, especially his wife and beloved son, for their encouragement and endless love. Without
their continuous support, the author would never finish this writing.