Practical approximate analysis of beams and frames

Practical

Approximate Analysis of Beams and Frames Nabil Fares, Ph.D.

ASCE

Contents

Preface

1

vii

Approximate Analysis of Beams and Frames no Sidesway 1.1

Introduction to

1.2

Passive Members in Continuous Beams and Frames

1.3

Beam with a Moment

with

Applied

at One End and

at 1.5

Applied

Only One Node

16

Outline of Approximate Method tor with No

Analyzing

Structures 20

Sidesway

1.6

Beam with

1.7

Example:

1.8

Beam with

a

Uniform Load

22

Uniform Load a

39

Point Force

42

1.9

Example:

1.10

Comments and

1.11

Beam with Two or More Internal

1.12

Beam with One Internal Hinge, and

2

11

Continuous Beam with Moment

Example:

Point Force

Resisting

67

Examples

on

Multiple

Loads

71 79

Hinges a

Moment Applied at One End

at the Other

87

1.13

Beam with One Internal

1.14

Beam with One Internal Hinge and

Hinge

and a Uniform Load

Point Force

a

Approximate Analysis of Frames with Sidesway 2.1

The Cantilever and the Single Floor Portal Frame

2.2

Approximate Analysis

of

Single

Floor Frames

2.4

The Column with

2.5

Approximate Analysis

Rotary Springs

105 105

of

Multiple

124

and Moments at Both Ends Floor Frames

131

Subject

to Horizontal Loads

141

2.6

A Note

2.7

Sketching Multiple Floor Frames Subject to Horizontal Loads

2.8

Notes on

Lumped

Sidesway

98

115

Sketching Single Floor Portal Frames

the

94

Subject

to a Horizontal Load

2.3

on

4

Resisting

at the Other 1.4

1 1

Sketching

Mass Model for

Buildings

Due to Vertical Loads or

Applied Couples

152

160 171

v

Practical

vi

3

Approximate Analysis

of Beams and Frames

Estimating Displacements in Beams and Frames 3.1 3.2

Maximum Vertical

Estimating

Displacements

in Beams

191

Displacements

Relative Vertical

3.4

Side

3.5

Obtaining Rotary Stiffness

Displacements

of Frames

versus Strain in Beams

Subject to Side Loads

Factors from

Slope

203 211

Measurements 225

in Beams

4

185 185

Moment of Inertia

3.3

....

Approximate Influence Lines for Indeterminate Beams

235

4.1

Introduction to Influence Lines

235

4.2

Exact Influence Lines for Statically Determinate Beams

242

4.3

Approximate

Influence Lines for

Statically

Indeterminate Structures

270

Appendixes A

B

Beams—End-Moments and Inflection Points Moment End-Loaded Beam

317

A.2

Uniformly Distributed Load

319

A. 3

Point Force

321

Column—Shear Stiffness, End-Moments and Inflection Points

327

B. 1

Cantilever

327

B.2

Column for Single Story Building

328

B.3

Column for Multi-Story Building—First Floor

B.4

Column for Beams

B. 5

C

317

A.1

Multi-Story Building—Top

Floor

330

(Top

and Bottom

Similar)

Column for

332

Multi-Story

Building—General Case

Beams—Deflections and Rotations

333

335

C. 1

Displacements at Any

C.2

Rotations at Any Location

C.3

Uniform Load—Mid

C.4

Point

C.5

Point force—Loaded Anywhere—Mid Displacements

344

C.6

Point Moment—Loaded Anywhere—Mid

347

C.7

Cantilever—Various Special Cases—Displacements

Location

335 338

Displacements

340

Force—Centrally Loaded—Mid Displacements Displacements

342

350

Practical

D

Approximate Analysis of

Beams and Frames

vii

Useful Results for Influence Lines

353

D.1

Influence Lines for Vertical Force Reactions

353

D.2

Influence Lines for Shear Forces

355

D.3

Influence Lines for Bending Moments

355

D.4

Transition Member

357

Index

359