📘 ❞ Reinforced Concrete Deep Beams ❝ كŰȘۧۚ

Ű§Ù„Ù‡Ù†ŰŻŰłŰ© Ű§Ù„Ù…ŰŻÙ†ÙŠŰ© - 📖 كŰȘۧۚ ❞ Reinforced Concrete Deep Beams ❝ 📖

█ _ 0 Ű­Ű”Ű±ÙŠŰ§ كŰȘۧۚ ❞ Reinforced Concrete Deep Beams ❝ 2025 Beams: Beams Reinforced Concrete Deep Beams Edited by PROFESSOR F K KONG Professor of Structural Engineering Department Civil Engineering University Newcastle upon Tyne Published in the United States America by Van Nostrand Reinhold Contents Preface Contributors 1 concrete deep beams F KONG†and†M CHEMROUK Notation 1 1 Introduction 1 2 History†and†development 1 3 Current†design†practice 1 4 CIRIA†Guide†2 1 CIRIA†Guide†ëSimple†RulesĂ­ 1 CIRIA†Guide†ëSupplementary†RulesĂ­ 1 5 Draft†Eurocode†and†CEB FIP†Model†Code 1 Flexural†strength:†simply†supported†deep†beams 1 Flexural†strength:†continuous†deep†beams 1 Shear†strength†and†web†reinforcement 1 6 ACI†Building†Code†318ñ83†(revised†1986) 1 Flexural†strength 1 Shear†strength 1 7 Canadian†Code†CAN3 A23 M84 1 Shear†strength References 2 Strength and behaviour beams M D KOTSOVOS Notation 2 Introduction 2 Current†concepts†for†beam†design 2 Effect†of†transverse†stresses 2 Flexural†capacity 2 Shear†capacity 2 Compressive†force†path†concept 2 Deep†beam†behaviour†at†ultimate†limit†state 2 Causes†of†failure 2 Arch†and†tie†action 2 Effect†of†transverse†reinforcement 2 Design†implications 2 Modelling © 2002 Taylor & Francis Books, Inc CONTENTS xii 2 Design†method 2 Verification†of†design†method References 3 beams with web openings S P RAY Notation 3 Introduction 3 Factors†influencing†behaviour 3 General†behaviour†in†shear†failure†(under†two point†loading) 3 Beam†with†rectangular†web†openings 3 Beam†with†circular†web†openings 3 Flexural†cracks 3 General†behaviour†in†shear†failure†(under†four Effect†of†web†opening 3 Effects†of†main†and†web†reinforcements 3 Diagonal†mode†of†shear†failure†load 3 8 Definitions 3 9 Criterion†of†failure†and†strength†theory 3 10 Ultimate†shear†strength 3 1Evaluation†of†web†opening†parameter 3 2 Ultimate†shear†strength 3 11 Simplified†design†expression 3 12Ultimate†strength†in†flexur 3 13Simplified†expression†for†flexural†strengt 3 14Extension†of†theory†of†ultimate†shear†strength†of†beam to†four point†loading 3 15Extension†for†uniformly†distributed†loading 3 16 Recommendations†for†design†of†beams†for†shear†and†flexure 3 17 Recommendations†for†lever†arm†(Z) 3 18 Design†example References 4 Continuous beams D ROGOWSKY 4 1 Introduction 4 2 Distinguishing†behaviour†of†continuous†deep†beams 4 1 Previous†tests 4 2 Continuous†deep†beams† vs †continuous†shallow†beams 4 3 Continuous†deep†beams† vs †simple†span†deep†beams 4 3 Capacity†predictions†by†various†methods 4 1 Elastic†analysis 4 2 Finite†element†analysis © CONTENTS xiii 4 ACI318 4 Kong,†Robins†and†Sharp 4 Truss†models 4 Truss†models†for†continuous†deep†beams 4 Design†of†continuous†deep†beams 4 Design†example 4 Summary References 5 Flanged beams H SOLANKI†and†A GOGATE Notation 5 Introduction 5 Review†of†current†knowledge 5 Modes†of†failure 5 Mode†of†failure†1:†flexural shear†failure 5 Mode†of†failure†2:†flexural shear compression†failure 5 Mode†of†failure†3:†diagonal†splitting†failure 5 Mode†of†failure†4:†splitting†with†compression†failure 5 Analysis 5 ACI†Building†Code 5 CIRIA†Guide†2 5 Method†of†Taner† et al 5 Method†of†Regan†and†Hamadi 5 Method†of†Subedi†for†flanged†beams†with web†stiffeners 5 Design†example†1:†Beam panel†P311†(Taner† et , †1977) 5 Design†example†2:†ACI†Code References 6 under top bottom loading A R CUSENS Notation 6 Introduction 6 Early†tests†on†deep†beams†under†top†and†bottom†loading 6 Tests†at†Leeds†University 6 Description†of†test†specimens 6 Crack†patterns 6 6Crack†width 6 7 Design†approaches 6 1 American†Concrete†Institute 6 2 Sch ̧ttĂ­s†equations 6 3 CIRIA†Guide © CONTENTS xiv 6 Top loaded†wall beams 6 Bottom Combined†top†and†bottom†loading 6 11 Summary†and†recommendations References 7 Shear strength predictionĂłsoftened truss model S T MAU†and†T C HSU Notation 7 Introduction 7 Modelling†of†deep†beams 7 Shear†element 7 Effective†transverse†compression 7 Softened†truss†model 7 Fundamental†assumptions 7 Stress†transformation†(equilibrium) 7 Strain†transformation†(compatibility) 7 Material†laws 7 Solution†algorithm 7 Accuracy 7 Parametric†study 7 span to height†ratio 7 Longitudinal†reinforcement 7 Transverse†reinforcement 7 Explicit†shear†strength†equation 7 Derivation†of†equation 7 Calibration 7 Conclusions References 8 predictionĂłplastic method M W BRAESTRUP Notation 8 Introduction 8 Plasticity†theory 8 Limit†analysis 8 Rigid,†perfectly†plastic†model 8 Structural†concrete†plane†elements 8 Concrete†modelling 8 Reinforcement†modelling 8 Yield†lines 8 Shear†strength†of†deep†beams 8 Lower†bound†analysis © CONTENTS xv 8 Upper†bound†analysis 8 Experimental†evidence 8 Shear†reinforcement 8 Conclusion References 9 Finite element analysis Y CHEUNG†and†H CHAN Notation 9 Introduction 9 Concept†of†finite†element†method 9 Triangular†plane†stress†elements 9 Rectangular†plane†stress†elements 9 Isoparametric†quadrilaterals 9 Equivalent†load†vector 9 Stiffness†matrix†of†rectangle†with†sides†2a◊2b 9 Elastic†stress†distribution†in†deep†beam†by†finite element†method 9 Finite†element†model†for†cracked†reinforced†concrete 9 Modelling†of†reinforcing†steel†bars 9 Point†element†or†linkage†element 9 Discrete†cracking†model 9 Smeared†cracking†model 9 Modelling†of†constitutive†relationship†of†concrete 9 12 Constitutive†relationship†of†steel†bars 9 13 Cracking†in†concrete†and†yielding†in†steel 9 14 Stiffness†of†cracked†element 9 15 Solution†procedure 9 Increment†procedure 9 Iterative†procedure 9 Mixed†procedure 9 Flow†chart†of†non linear†analysis†procedure 9 16Example†of†non linear†analysis†of†reinforced†concret deep†beams References 10 Stability slender KONG†and†H H A WONG Notation 10 Introduction 10 Slender†deep†beam†behaviour 10 Elastic†behaviour 10 Ultimate†load†behaviour © CONTENTS xvi 10 Current design methodsĂłCIRIA Guide (1977) 10 CIRIA Simple Rules 10 Supplementary Appendix C: Single Panel Method 10 Two The equivalent column method 10 Theoretical background 10 analysis columns: graphical improved graphical methods 10 analytical beams: column 6Deep beam buckling comparison test result 10 Concluding remarks Reference Ű§Ù„Ù‡Ù†ŰŻŰłŰ© Ű§Ù„Ù…ŰŻÙ†ÙŠŰ© Ù…ŰŹŰ§Ù†Ű§Ù‹ PDF Ű§ÙˆÙ†Ù„Ű§ÙŠÙ† Ù‚ŰłÙ… ۟ۧ۔ ŰšÙƒŰȘŰš للŰȘŰ­Ù…ÙŠÙ„ Ù…ŰŹŰ§Ù„ وهي ŰŁŰ­ŰŻ ÙŰ±ÙˆŰč ÙˆŰ§Ù„Ù…ŰčÙ†ÙŠŰ© ۚۯ۱ۧ۳۩ وŰȘŰ”Ù…ÙŠÙ… وŰȘŰ­Ù„ÙŠÙ„ Ű§Ù„Ù…Ù†ŰŽŰąŰȘ Ű§Ù„Ù…ŰźŰȘÙ„ÙŰ© ÙƒŰ§Ù„ŰŁŰšÙ†ÙŠŰ© Ű§Ù„ŰłÙƒÙ†ÙŠŰ© ÙˆŰ§Ù„ŰźŰŻÙ…ÙŠŰ© ÙˆŰ§Ù„Ű·Ű±Ù‚ ÙˆŰ§Ù„ŰŹŰłÙˆŰ± ÙˆŰ§Ù„ŰŁÙ†ÙŰ§Ù‚ ÙˆŰ§Ù„Ù…Ű·Ű§Ű±Ű§ŰȘ ÙˆŰ§Ù„Ù…ÙˆŰ§Ù†ŰŠ ÙˆŰŽŰšÙƒŰ§ŰȘ Ű„Ù…ŰŻŰ§ŰŻ Ù…ÙŠŰ§Ù‡ Ű§Ù„ŰŽŰ±Űš ÙˆÙ…Ű­Ű·Ű§ŰȘ ۶۟ Ű§Ù„Ù…ÙŠŰ§Ù‡ Ű§Ù„Ű”Ű±Ù Ű§Ù„Ű”Ű­ÙŠ Ű§Ù„ŰȘÙ†Ù‚ÙŠŰ© ومŰčŰ§Ù„ŰŹŰ© ÙˆŰ§Ù„ŰłŰŻÙˆŰŻ ÙˆÙƒŰ°Ù„Ùƒ Ù…ŰŽŰ§Ű±ÙŠŰč Ű§Ù„Ű±ÙŠ ÙˆŰ§Ù„Ű„ŰŽŰ±Ű§Ù Űčمل Ù‡Ű°Ű§ ŰŁŰ«Ù†Ű§ŰĄ فŰȘ۱۩ ۧ۳ŰȘÙ…Ű±Ű§Ű±Ù‡Ű§ Ù„Ű°Ű§ Ù„Ű§ ÙŠŰŹÙˆŰČ Ű­Ű”Ű± Ű§Ù„Űčلم ŰšŰŁÙ†Ù‡ Ű§Ù„Ù…Űčني ŰšŰ§Ù„ŰȘŰ”Ù…ÙŠÙ… ÙˆŰ­ŰŻÙ‡ ÙÙ‚Ű· وهي ÙƒŰŁÙŠ Űčلم ŰȘŰȘŰ·ÙˆŰ± ۚۧ۳ŰȘÙ…Ű±Ű§Ű± ÙˆŰŻÙˆÙ† ŰȘوقف وفي Ű§Ù„ŰąÙˆÙ†Ű© Ű§Ù„Ű­ŰŻÙŠŰ«Ű© ŰȘ۱ۧۚ۷ŰȘ مŰč Ű§Ù„ŰȘŰ·ÙˆŰ± Ű§Ù„Ű”Ù†Ű§Űčي ŰšŰŽÙƒÙ„ ÙƒŰšÙŠŰ± Ù„Ű„Ù†ŰȘۧۏ 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Reinforced Concrete Deep Beams
كŰȘۧۚ

Reinforced Concrete Deep Beams

Reinforced Concrete Deep Beams
كŰȘۧۚ

Reinforced Concrete Deep Beams

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Űčن كŰȘۧۚ Reinforced Concrete Deep Beams:
Reinforced Concrete Deep Beams

Reinforced Concrete
Deep Beams
Edited by
PROFESSOR F.K.KONG
Professor of Structural Engineering
Department of Civil Engineering
University of Newcastle-upon-Tyne

Published in the United States of America by
Van Nostrand Reinhold

Contents
Preface
Contributors
1 Reinforced concrete deep beams
F.K.KONG†and†M.CHEMROUK
Notation
1.1 Introduction
1.2 History†and†development
1.3 Current†design†practice
1.4 CIRIA†Guide†2
1.4.1 CIRIA†Guide†ëSimple†RulesĂ­
1.4.2 CIRIA†Guide†ëSupplementary†RulesĂ­
1.5 Draft†Eurocode†and†CEB-FIP†Model†Code
1.5.1 Flexural†strength:†simply†supported†deep†beams
1.5.2 Flexural†strength:†continuous†deep†beams
1.5.3 Shear†strength†and†web†reinforcement
1.6 ACI†Building†Code†318ñ83†(revised†1986)
1.6.1 Flexural†strength
1.6.2 Shear†strength
1.7 Canadian†Code†CAN3-A23.3-M84
1.7.1 Flexural†strength
1.7.2 Shear†strength
References
2 Strength and behaviour of deep beams
M.D.KOTSOVOS
Notation
2.1 Introduction
2.2 Current†concepts†for†beam†design
2.3 Effect†of†transverse†stresses
2.3.1 Flexural†capacity
2.3.2 Shear†capacity
2.4 Compressive†force†path†concept
2.5 Deep†beam†behaviour†at†ultimate†limit†state
2.5.1 Causes†of†failure
2.5.2 Arch†and†tie†action
2.5.3 Effect†of†transverse†reinforcement
2.6 Design†implications
2.6.1 Modelling
© 2002 Taylor & Francis Books, Inc.
CONTENTS
xii
2.6.2 Design†method
2.6.3 Verification†of†design†method
References
3 Deep beams with web openings
S.P.RAY
Notation
3.1 Introduction
3.2 Factors†influencing†behaviour
3.3 General†behaviour†in†shear†failure†(under†two-point†loading)
3.3.1 Beam†with†rectangular†web†openings
3.3.2 Beam†with†circular†web†openings
3.3.3 Flexural†cracks
3.4 General†behaviour†in†shear†failure†(under†four-point†loading)
3.5 Effect†of†web†opening
3.6 Effects†of†main†and†web†reinforcements
3.7 Diagonal†mode†of†shear†failure†load
3.8 Definitions
3.9 Criterion†of†failure†and†strength†theory
3.10 Ultimate†shear†strength
3.10.1Evaluation†of†web†opening†parameter
3.10.2
Ultimate†shear†strength
3.11
Simplified†design†expression
3.12Ultimate†strength†in†flexur
3.13Simplified†expression†for†flexural†strengt
3.14Extension†of†theory†of†ultimate†shear†strength†of†beam
to†four-point†loading.
3.15Extension†for†uniformly†distributed†loading
3.16
Recommendations†for†design†of†beams†for†shear†and†flexure
3.17
Recommendations†for†lever†arm†(Z)
3.18
Design†example.
References
4
Continuous deep beams
D.ROGOWSKY
4.1
Introduction
4.2
Distinguishing†behaviour†of†continuous†deep†beams
4.2.1
Previous†tests
4.2.2
Continuous†deep†beams†
vs
†continuous†shallow†beams
4.2.3
Continuous†deep†beams†
vs
†simple†span†deep†beams
4.3
Capacity†predictions†by†various†methods
4.3.1
Elastic†analysis
4.3.2
Finite†element†analysis
© 2002 Taylor & Francis Books, Inc.
CONTENTS
xiii
4.3.3 ACI318
4.3.4 Kong,†Robins†and†Sharp
4.3.5 Truss†models
4.4 Truss†models†for†continuous†deep†beams
4.5 Design†of†continuous†deep†beams
4.6 Design†example
4.7 Summary
References
5 Flanged deep beams
H.SOLANKI†and†A.GOGATE
Notation
5.1 Introduction
5.2 Review†of†current†knowledge
5.3 Modes†of†failure
5.3.1 Mode†of†failure†1:†flexural-shear†failure
5.3.2 Mode†of†failure†2:†flexural-shear-compression†failure
5.3.3 Mode†of†failure†3:†diagonal†splitting†failure
5.3.4 Mode†of†failure†4:†splitting†with†compression†failure
5.4 Analysis
5.4.1 ACI†Building†Code
5.4.2 CIRIA†Guide†2
5.4.3 Method†of†Taner†
et al.
5.4.4 Method†of†Regan†and†Hamadi
5.4.5 Method†of†Subedi†for†flanged†beams†with
web†stiffeners
5.5 Design†example†1:†Beam-panel†P311†(Taner†
et al.,
†1977)
5.6 Design†example†2:†ACI†Code
References
6 Deep beams under top and bottom loading
A.R.CUSENS
Notation
6.1 Introduction
6.2 Early†tests†on†deep†beams†under†top†and†bottom†loading
6.3 Tests†at†Leeds†University
6.4 Description†of†test†specimens
6.5 Crack†patterns
6.6Crack†width
6.7
Design†approaches
6.7.1
American†Concrete†Institute
6.7.2
Sch ̧ttĂ­s†equations
6.7.3
CIRIA†Guide
© 2002 Taylor & Francis Books, Inc.
CONTENTS
xiv
6.8 Top-loaded†wall-beams
6.9 Bottom-loaded†wall-beams
6.10 Combined†top†and†bottom†loading
6.11 Summary†and†recommendations
References
7 Shear strength predictionĂłsoftened truss model
S.T.MAU†and†T.T.C.HSU
Notation
7.1 Introduction
7.2 Modelling†of†deep†beams
7.2.1 Shear†element
7.2.2 Effective†transverse†compression
7.3 Softened†truss†model
7.3.1 Fundamental†assumptions
7.3.2 Stress†transformation†(equilibrium)
7.3.3 Strain†transformation†(compatibility)
7.3.4 Material†laws
7.3.5 Solution†algorithm
7.3.6 Accuracy
7.4 Parametric†study
7.4.1 Shear-span-to-height†ratio
7.4.2 Longitudinal†reinforcement
7.4.3 Transverse†reinforcement
7.5 Explicit†shear†strength†equation
7.5.1 Derivation†of†equation
7.5.2 Calibration
7.6 Conclusions
References
8 Shear strength predictionĂłplastic method
M.W.BRAESTRUP
Notation
8.1 Introduction
8.2 Plasticity†theory
8.2.1 Limit†analysis
8.2.2 Rigid,†perfectly†plastic†model
8.3 Structural†concrete†plane†elements
8.3.1 Concrete†modelling
8.3.2 Reinforcement†modelling
8.3.3 Yield†lines
8.4 Shear†strength†of†deep†beams
8.4.1 Lower†bound†analysis
© 2002 Taylor & Francis Books, Inc.
CONTENTS
xv
8.4.2 Upper†bound†analysis
8.4.3 Experimental†evidence
8.4.4 Shear†reinforcement
8.5 Conclusion
References
9 Finite element analysis
Y.K.CHEUNG†and†H.C.CHAN
Notation
9.1 Introduction
9.2 Concept†of†finite†element†method
9.3 Triangular†plane†stress†elements
9.4 Rectangular†plane†stress†elements
9.4.1 Isoparametric†quadrilaterals
9.4.2 Equivalent†load†vector
9.4.3 Stiffness†matrix†of†rectangle†with†sides†2a◊2b
9.5 Elastic†stress†distribution†in†deep†beam†by†finite
element†method
9.6 Finite†element†model†for†cracked†reinforced†concrete
9.7 Modelling†of†reinforcing†steel†bars
9.8 Point†element†or†linkage†element
9.9 Discrete†cracking†model
9.10 Smeared†cracking†model
9.11 Modelling†of†constitutive†relationship†of†concrete
9.12 Constitutive†relationship†of†steel†bars
9.13 Cracking†in†concrete†and†yielding†in†steel
9.14 Stiffness†of†cracked†element
9.15 Solution†procedure
9.15.1 Increment†procedure
9.15.2 Iterative†procedure
9.15.3 Mixed†procedure
9.15.4 Flow†chart†of†non-linear†analysis†procedure
9.16Example†of†non-linear†analysis†of†reinforced†concret
deep†beams
References
10 Stability and strength of slender concrete deep beams
F.K.KONG†and†H.H.A.WONG
Notation
10.1 Introduction
10.2 Slender†deep†beam†behaviour
10.2.1 Elastic†behaviour
10.2.2 Ultimate†load†behaviour
© 2002 Taylor & Francis Books, Inc.
CONTENTS
xvi
10.3 Current design methodsĂłCIRIA Guide 2 (1977)
10.3.1 CIRIA Guide Simple Rules
10.3.2 CIRIA Guide Supplementary Rules
10.3.3 CIRIA Guide Appendix C: Single-Panel Method
10.3.4 CIRIA Guide Appendix C: Two-Panel Method
10.4 The equivalent-column method
10.4.1 Theoretical background
10.4.2 Stability analysis of columns: graphical method
10.4.3 Stability analysis of columns: improved
graphical methods
10.4.4 Stability analysis of columns: analytical method
10.5 Stability analysis of slender deep beams: the equivalent-
column method
10.6Deep beam buckling comparison with test result
10.7 Concluding remarks
Reference
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