CIVL3310 STRUCTURAL ANALYSISProfessor CC Chang

Review

What is Structural Analysis?

Reviseddesign

No

Planning

Preliminary design

Structural analysis

Load estimation

Safety/serviceability

Construction

Yes

What is Structural Analysis?

Structure

Factors:Load, Temperature, etc.

PerformanceDeformation, Stress, etc.

Real structure

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

Bernoulli-Euler beam

EIM

dxyd

2

2

EIM

dxdθ

dxdxEIMy dx

EIMθ

apply boundary conditions

+ disp

Moment-Area Methods

+

dxEIMB

AAB /

1st moment-area theorem 2nd moment-area theorem

dxEIMxt B

ABA /

Conjugate-Beam Method

• Mathematical equivalence -slope-deflection Load-shear-momentEIM

EIM

θ

y

w

V

M

Actual beam Conjugate beam

Energy Methods• Virtual Work Principle

UW

dfF Virtual external load

Real deformation

Virtual internal loads

Real member deformation

Trusses =

Beams =

Frames =

EAfLf

dxEIMM

dxEIMM

EAfLf

Work-Energy Methods• Castigliano’s Theorem

• Betti’s Law

iiPU

Trusses

Beams

Frames

EALfU

2

2

dxEIMU2

2

dxEIM

EALf

22

22

ii PiQi QP

Analysis of Indeterminate Structures

Approximate Analysis of Rectangular Building Frames

• Vertical Loads

• Horizontal Load– Portal - Cantilever

0.1 L

s1 2s1 s1

s1 2s1 s1

CL

By

B=0

Force Methods• Compatibility

– Choose redundant forces– Calculate deflection case by case– Superposition

0 BByB fB

=

Energy Principle• Least Work & Castigliano’s principles

workno do that Forces0

workdo that Forces

FUPU

P

P1

FnF2F1

PmP2

Slope-Deflection Method• Slope-Deflection Equations

ijijjiij

ijij FEM32

L

EI2M

A B

A’B’

MAB

MBA

AB

AB

L

Moment-Distribution Method• Distribution Factors and Carry-Over

• FEM• Procedure

214

COLEIK

03 CO

LEIK

How to Become a Good Structural Engineer?

CIVL2110Statics and Dynamics

CIVL2120Mechanics of Materials

CIVL3310Structural Analysis

CIVL3320Concrete Design

CIVL4320Steel Design

CIVL4330Structural Dynamics

CIVL5310Tall Building Design

CIVL5350Bridge Engineering

CIVL5370Wind Effects

ODE, FT, NM

?

CIVL4370Computer Methods

Shanghai World Finance Center上海环球金融中心

Taipei 101

Base Isolation

Stonecutters Bridge

Hong Kong-Zhuhai-Macao BridgeHong Kong Link Road

Hong Kong-Zhuhai-Macao BridgeHong Kong Link Road

Hong Kong-Zhuhai-Macao BridgeHong Kong Link Road

Smart StructuresSense and Respond

ENDING…

HOPE I DON’T SEE YOU AGAIN IN THIS COURSE!

Comments are welcome!