Review
CIVL3310 STRUCTURAL ANALYSIS
Professor CC Chang
What is Structural Analysis?
Planning
Preliminary design
Load estimation
Structural analysis
Safety/serviceability
Yes
Construction
No
Revised
design
What is Structural Analysis?
Real structure
Factors:
Load, Temperature, etc.
Structure
Performance
Deformation, Stress, etc.
Model
Intended Learning Outcomes
• Ability to analyze the performance of structural
systems under loads or other external effect
• Ability to comprehend and present the structural
analysis results which can support the design of
structural components and systems
• Ability to conduct laboratory tests, validate test
results using various methods, and understand the
discrepancies between the test and the analysis results
What Have Been Covered?




Classification of structural forms, modeling of structural systems
and structural elements and determination of loads
Axial force, shear force and bending moment
Analysis of statistically determinate structures
 Influence lines and their applications
 Deflection
Analysis of statistically indeterminate structures
 Approximate analysis of building frames
 Force method
 Energy method
 Slope-deflection method
 Moment-distribution method
Analysis of Determinate Structures
Influence Lines and Applications
• Definition
• Müller-Breslau’s Principle
• Influence Lines and Distributed Loads
• Influence Lines + Design Load
Calculation of Deflections for
Determinate Structures
• Direct integration
• Moment-area methods
• Conjugate-beam method
• Energy methods
Direct Integration
+ disp
Bernoulli-Euler beam
d2y M

2
dx
EI
M
y  
dx dx
EI
dθ
M

dx EI
θ
M
dx
EI
apply boundary conditions
Moment-Area Methods
1st moment-area theorem
2nd moment-area theorem
+
M
dx
A EI
B/ A  
B
tA/ B 
BM
x A
EI
dx
Conjugate-Beam Method
• Mathematical equivalence
M
-slope-deflection
EI
Load-shear-moment
M
EI
w
θ
V
y
M
Actual beam
Conjugate beam
Energy Methods
• Virtual Work Principle
W  U
Real member deformation
Real deformation
F     f  d
Virtual external load
Trusses =
Beams =
Frames =
Virtual internal loads
fL
EA
M
dx
 M 
EI
 f 
 f 
fL
M
  M  dx
EA
EI
Work-Energy Methods
• Castigliano’s Theorem
U
 i
Pi
Trusses
Beams
Frames
• Betti’s Law
 Pi Qi   Qi Pi
f 2L
U 
2 EA
M2
U 
dx
2 EI
f 2L
M2

dx

2 EA
2 EI
Analysis of Indeterminate Structures
Approximate Analysis of Rectangular
Building Frames
• Vertical Loads
0.1 L
• Horizontal Load
– Portal
- Cantilever
s1
2s1
s1
s1
2s1
s1
CL
Force Methods
• Compatibility
– Choose redundant forces
– Calculate deflection case by case
– Superposition
 B  By  f BB  0
B=0
By
Energy Principle
• Least Work & Castigliano’s principles
P2
P1
F1
 U
 P   P
 U

0
 F

F2
Pm

Fn
Forces thatdo work
Forces thatdo no work
Slope-Deflection Method
• Slope-Deflection Equations
M ij 
2EI ij
L ij
2i   j  3 ij   FEM ij
A
B
MBA
A’
MAB
A
B
 AB
B’

L
Moment-Distribution Method
• Distribution Factors and Carry-Over
• FEM
• Procedure
4 EI
K
L
3EI
K
L
1
CO 
2
CO  0
How to Become
a Good Structural Engineer?
CIVL2110
Statics and Dynamics
ODE, FT, NM
CIVL2120
Mechanics of Materials
CIVL3310
Structural Analysis
CIVL3320
Concrete Design
CIVL4370
Computer Methods
CIVL4320
Steel Design
CIVL4330
Structural Dynamics
?
CIVL5310
Tall Building Design
CIVL5350
Bridge Engineering
CIVL5370
Wind Effects
Shanghai World Finance Center
上海环球金融中心
Taipei 101
Base Isolation
Stonecutters Bridge
Hong Kong-Zhuhai-Macao Bridge
Hong Kong Link Road
Hong Kong-Zhuhai-Macao Bridge
Hong Kong Link Road
Hong Kong-Zhuhai-Macao Bridge
Hong Kong Link Road
Smart Structures
Sense and Respond
Comments are welcome!
ENDING…
HOPE I DON’T SEE YOU AGAIN IN THIS COURSE!