DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Lectures! Design philosophy ! Action Effects: Bending and axial load! Action Effects: Shear and Torsion! Serviceability: Cracking and deflections! Strut-and-tie method for design! Design and detailing of openings

! Slender column design! Flat slab system! Collapse load methods for slab design! Design of structural systems

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Reinforced Concrete: Mechanics & Design.3 ed.

MacGregor, J.G.Prentice Hall, 1997

Recommended text

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Reinforced Concrete Structures.

Park, R. & Paulay, T. John Wiley & Sons, 199X

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

STRUCTRUALCONCRETE Plain Concrete

Reinforced Concrete

Partially PrestressedConcrete

Prestressed Concrete

INTRODUCTION

Matrix + Reinforcement

Concrete +Steel bars

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Brief History of Structural Concrete

1824 Patent on Portland Cement (Aspdin)1854 Reinforced Concrete (Wilkinson)1886 First prestressing system using tie-rods

(PH Jackson, USA)1910 Various concrete institutes established1920s RC buildings, bridges & liquid containers

constructed; circular prestressing; practical PC; external prestressing

1930s Partial prestressing (Abeles, England)1938 Ultimate strength theories in USSR1940s Bridge design & construction with PC

DEPARTMENT OF CIVIL ENGINEERING

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1956 Ultimate strength theories in England/USA

1960s Working stress design1970s Limit state design1980s Durability issues1990s “Structural concrete” coined;

Unification of codes & theories;Performance-based design;New materials.

1998 Formation of International Federationfor Structural Concrete (fib)

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Design Objectives

!Functionability!Safety!Economy!Restorability

DEPARTMENT OF CIVIL ENGINEERING

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" Working stress design (WSD)!Focus on working load level!Check induced stress against allowable values

" Ultimate strength design (USD)!Focus on ultimate load level!Check factored actions against resistance

" Limit state design (LSD)!Considers both serviceability and ultimate limit

states" Performance-based design (PBD)

DESIGN APPROACHES

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

γγγγfP

MuUltimate strength design (USD)

" Mu ≤≤≤≤ φφφφMn for e.g.

P

fs"Working stress design (WSD)

" fs ≤≤≤≤ fs,allow = fy/1.5 for e.g.!Limit state design (LSD)!∆∆∆∆s ≤≤≤≤ ∆∆∆∆max ; ws ≤≤≤≤ wmax

!Mu ≤≤≤≤ φφφφMnPerformace-based design (PBD)Bridge’s deformation should not affect rail alignmentBridge is able to take a train load of xxx-xx

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Higher loads

Serviceability

Restorability

Safety

WSD

USD

LSD

PBD

Damage Control

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

PIS ≤≤≤≤ PIRe.g.

S(γγγγfFk) ≤≤≤≤ φφφφR(fk/γγγγm)Action effect Resistance

w(γγγγfFk, fk/γγγγm) ≤≤≤≤ w*Crack width Allowable value

Design criteria

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Specifications /Codes of Practice

! BS 8110 Structural Use of Concrete. Parts 1,2,3.British Standards Institution, 1985, 1997 (Part 1)

! CP65 Singapore Standard on Code of Practice for Structural Use of Concrete, 1999

! ACI 318 Building Code Requirements for Structural Concrete and Commentary.American Concrete Institute, 1999, 2002

! Eurocode 2

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Structural Concrete

Matrix ReinforcementConcrete Steel bars

High-strength concrete

Polymer concrete

Light-weight concrete

Self-compacting concrete

Fibrous concrete

Galvanised steel bars

Epoxy-coated bars

Fibre-reinforced polymer bars

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Materials

f y( M

P a)

fc’ (MPa)

1200

800

400

0 30 60 90 120

New RC

conventional

High strengthconcrete

Ultra-high strengthconcrete

Ultra-high strengthsteel

High strengthsteel

highrise RC

Concrete strength

Ste

el s

treng

th

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Characteristic Strength of Materials, fk

fk = fm - ksfrequency

strengthfm

5%e.g. for concrete

fk = fm - 1.64s

depends on reliability/quality

control

fk

k x s (std. dev.)

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Concretefc’ (MPa) W/C ratio

Normal structuralconcrete

20 - 45 0.40 – 0.45

High strengthconcrete

45 - 70 0.35 – 0.40

70 - 85 0.30 – 0.35Ultra-highstrength concrete 85 - 140 0.22 – 0.30

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Normal structural concrete

" Compressive strength : fcu or fc’(≈ 0.8fcu)(28-day characteristic)

" Tensile strength: ft’ = 0.1~0.2 fc’

" Modulus of rupture: fr = 0.623√fc’> ft’ (ACI)

" Modulus of elasticity: Ec= 4730 √fc’ (MPa)

DEPARTMENT OF CIVIL ENGINEERING

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An ↑↑↑↑ in fc’ leads to:

↓↓↓↓ in εεεεcu↑↑↑↑ in linear portion↓↓↓↓ in ductility↑↑↑↑ in Ec

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Stress-strain relation of concrete

fc/fc’ = 2εεεεc/εεεεc’ - (εεεεc/εεεεc’)2 (fc’≤≤≤≤45 MPa)

fc

fc’

0.4fc’Ec

εcεo’ εcu

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

High strength concrete

" Tensile strength: ft’ = 0.615√fc’ (fc’≤85 MPa)

" Modulus of rupture: fr = (0.623~1)√fc’ (MPa)

" Modulus of elasticity: Ec= (3323√fc’ + 6895)(wk/2323) (MPa)where wk: weight in kg/m3

DEPARTMENT OF CIVIL ENGINEERING

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Reinforcement

Es=200,000 MPa

f y(M

Pa)

strain

Steel

0.005 0.010 εεεεs

DEPARTMENT OF CIVIL ENGINEERING

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FRP Reinforcement

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

PC Strand

Rebar

Tens

ile s

treng

th (M

Pa)

Strain %

CFRPAFRP

GFRP

0

2000

4 6 8 10

1000

2

FRP

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Design stress-strain relations

Concrete

BS8110, EC2, JSCE, CEB-FIP …similar

0.67fcu/γγγγmst

ress

(MP a

)

strain0.0035

5.5√√√√(fcu/γγγγm) kN/mm2

2.4x10-4√√√√(fcu/γγγγm)

DEPARTMENT OF CIVIL ENGINEERING

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Steel

BS8110, ACI, JSCE, AS, CEB-FIP …similar

fy/γγγγm

fy/γγγγm

strain

200 kN/mm2

compression

tension

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Partial safety factors

1.5 (BS 1997)Concrete

1.15 (BS 1985)1.05 (BS 1997)

Steel

γγγγm

Design strength = Characteristic strength / γγγγm

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Loads (Actions)

Characteristicsload Fk

• Dead loads• Imposed loads• Dynamic loads• Accidental loads• Construction loads

• Earth loads• Wind loads• Seismic loads• Snow loads

⇒⇒⇒⇒ BS6399, ASCE7-98, AS1170

load

freq

uenc

y

5%

Fm Fk

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Load Combinations

LC = ΣγΣγΣγΣγkFk

" Ultimate limit state:e.g. 1.4Gk+1.6Qk (BS8110)

1.4Gk+1.7Qk (ACI318-99)

" Serviceability limit state:!short term effects! long term effects

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Limit state Load Comb. BS8110 ACI318-99

Dead & Live 1.4DL+1.6LL orDL+LL

1.4DL+1.7LL

Ultimatelimit state

Dead & Wind 1.4(DL+WL) or DL + 1.4WL

0.75(1.4DL+1.7WL)

Dead & wind & live

1.2(DL+LL+WL) 0.75(1.4DL+1.7LL+1.7WL) or

0.9DL+ 1.3WL

Serviceability Dead & Live short-term effects,

limit state Dead & Wind long-term effects, etc.

(Deflection, Cracking, etc)

Dead & wind & Iive

to be considered

Load Combinations

DEPARTMENT OF CIVIL ENGINEERING

Tan K H, NUS

Summary

Designobjectives

ResistanceActioneffects

PIS≤≤≤≤PIR

ActionsMaterial

properties

•numerical•analytical*•simplified*

•analytical*•formulae*•tests