bridge_concrete structures

橋梁総合コース Comprehensive Bridge EngineeringOct. 27, 2008

4 Concrete Structures

コンクリート構造

Tatsuya Tsubaki

椿龍哉

MINISTRY OF LAND, INFRASTRUCTURE, TRANSPORT AND TOURISM

JAPAN BRIDGE ASSOCIATION JAPAN INTERNATIONAL COOPERATION AGENCY

Comprehensive Bridge Engineering Concrete Structures

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Concrete Structures

Tatsuya TsubakiDepartment of Civil EngineeringYokohama National University

Comprehensive Bridge Engineering

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ABSTRACT

The properties of concrete, their modeling, and the structural analysis method considering their effects are discussed in relation to the design of concrete structures.

In Part 1, the properties of the materials used for concrete structures are discussed. In particular, the mechanical properties of concrete are outlined.

In Part 2, models to represent the mechanical behavior of the materials used for concrete structures are introduced.

In Part 3, analysis methods for concrete structures are investigated. The analysis method for concrete structural members and the finite element method for two-dimensional and three-dimensional structures are outlined.

The aim of this lecture is to understand the basic theories and the recent developments on the modeling of concrete properties and the structural analysis method. It is intended to obtain the knowledge of the fundamental theory related to the design of concrete structures such as concrete bridge.


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CONTENTS1. Properties of Materials

1.1 Introduction1.2 Strength of Concrete1.3 Stress-Strain Relation of Concrete1.4 Volume Change of Concrete1.5 Fatigue of Concrete1.6 Durability of Concrete1.7 Other Properties of Concrete1.8 Reinforcement

2. Modeling for Structural Analysis and Design2.1 Introduction2.2 Strength of Concrete2.3 Stress-Strain Relation of Concrete2.4 Time Effects for Concrete2.5 Fatigue of Concrete2.6 Temperature Effects for Concrete2.7 Stress and Strain Rate Effects for Concrete

3. Structural Analysis Methods3.1 Introduction3.2 Analysis of Concrete Member3.3 Analysis of 2D and 3D Concrete

Structures

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Cable-Stayed Bridges:Tomei Ashigara Bridge

3-span continuous prestressed concrete cable-stayed bridge, 5-span continuous framed box-girder bridge, road bridge, Shizuoka Pref., Koyama Town, 1991 open.


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Extradosed Bridges:Odawara Blueway Bridge

3-span prestressed continuous extradosed box girder bridge, road bridge, length 270m (73.1 + 122.0 + 73.0), Kanagawa Pref., Odawara City, 1995 open.

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Arch Bridges:Beppu Myoban Bridge

Fixed RC arch bridge, road bridge, length 411m (arch span 235m), Oita Pref., Beppu City, 1989 open.


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Stress Ribbon Bridges:Shiosai Bridge

Stress Ribbon with Prestress

Stress ribbon bridge, pedestrian bridge, length 232m (55+61+61+55), sag ratio 1/10.6, Shizuoka Pref., 1995 open.

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Stress Ribbon Bridges:Yume Tsuribashi Bridge

Stress-ribbon bridge, pedestrian bridge, length 172.6m, span 147.6m, sag ratio 1/42.2, Hiroshima Pref., 1996 open.


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Stress Ribbon Bridges:Yunohana Bashi Bridge

Stress-ribbon bridge, road bridge, length 34.5m, span 22m, sag ratio 1/10, Ehime Pref., 1997 open.

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Problems:Construction of Concrete Structures

□ It is important to prevent rapid moisture loss from the surface by direct sunshine, wind and so on especially in case of early age concrete.

□ Applying vibration, impact or excessive load to insufficiently hardened concrete under curing causes cracking and damage.

□ Curing under high temperature for a long time causes a large increase of long-time strength of concrete.

□ When drying of sheathing is anticipated, drying should be prevented by spraying water.

□ A concrete joint should be placed at the position of bending moment as small as possible and the joint plane should be perpendicular to the direction of compression acting on a member.


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Problems:Construction of Concrete Structures

□ When new concrete is cast at a vertical joint, re-compaction by vibration should not be done after casting concrete.

□ When it is necessary to have a tapered pipe or a curved pipe at the intermediate position, it is recommended to use a concrete pump with large pumping pressure.

□ To make the pumping length longer, it is recommended to have an intermediate pump in the middle and furthermore to remix concrete by an agitator.

□ It is recommended to pump concrete of high mortar ratio to prevent the leak of water and cement paste from the pipe joint.

□ In concrete pumping it is recommended to always keep 4 to 5 agitator trucks standing by in order to prevent interruption of pumping concrete.

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Problems:Construction of Prestressed Concrete Structures

□ In hot weather grouting it is desirable to use water-reducing agent having a function of retarder for an admixture.

□ In hot weather grouting it is better to mix grout materials as quickly as possible to make the grout temperature after mixing low.

□ In making a falsework it should be considered that the distribution of self-weight of concrete member is not the same before and after prestressing.

□ When uplifting of falsework becomes large during prestressing, that part of falsework is to be lowered after prestressing.

□ Considering the deformation of concrete member due to prestressing, a formwork should have suitable camber and some means for shortening.


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Problems:Construction of Prestressed Concrete Structures

□ When the length of tendon is not the same, prestressing should be started from the shortest tendon.

□ At the end section of a member prestressing should be started from the tendon allocated near the centroid of the cross section.

□ The push-out erection method is the commonly used erection method when the ground condition at the erection site is good and there is no particular limitation in choosing an erection method.

□ The cantilever erection method has an advantage in the case of erection over a mountain valley or a road of heavy traffic where the construction of falsework is not possible.

□ The precast block (PC precast segment) erection method can reduce the amount of work at the construction site and is superior in rapid construction because members are prefabricated in a factory.

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URL for Related Documentsand Programs

■ Related Documents and Programs(1) Programs for Structural Analysis and Manuals(2) Program for Quiz on Concrete Structures(3) Database of Creep and Shrinkage of Concrete(4) Other Related Documents

■ URL for Downloadhttp://www.cvg.ynu.ac.jp/G5/tsubaki/conc-struct/


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Concrete Structures

Part 1Properties of Materials


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1.1 Introduction

The properties of materials used in concrete structures such as concrete and reinforcement have considerable significance to designers of concrete structures or products.

The physical properties of concrete depend upon a number of factors including mix proportions, aggregates, type of cement, curing conditions, and age. They are also affected by environmental conditions such as temperature and relative humidity.

The durability of concrete is related to these same factors with particular emphasis on the cement content and amount of entrained air.

In addition to the mechanical properties of hardened concrete itself, the mechanical properties of reinforcement and the bond of concrete to steel are summarized in this part.


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Failure of RC Bridge Pier (Case 1)

Gas Pressure Welding

Hoop Reinforcement

Hanshin-Awaji earthquake, 1995.1.17

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• The bridge pier failed in the Kobe earthquake on January 17, 1995.

• It is a bridge pier of the overturned piltz viaduct of the HanshinExpressway Kobe Line.

• The failure of the longitudinal reinforcements is observed.

• The gas pressure welded joints were used for the reinforcement.

• The amount of hoop reinforcement was not sufficient.

Gas pressure welding


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Shear Failure

Shear Force

2-Layer, 3-Span Rigid Frame Viaduct of San-yo Shinkansen.Shear Failure Occurred at Either Lower or Upper Layer.

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• The bridge pier failed by shear in the Kobe earthquake.

• It is a rigid frame 2-story bridge pier of the railway viaduct of the Sanyo Shinkansen.

• The shear failure of the columns occurred either in the upper layer or in the lower layer.

PD


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Limit State Design

・Service Limit State ・Ultimate Limit State・Fatigue Limit State

Safety Factors: ・Material Factor・Load Factor・Structure Factor・Structural Analysis Factor・Member Factor

kfdmkd

dadbddd

di

FFff

FSSfRRR

S

;/

)(;/)(;0.1

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Seismic Design (JSCE2007)

■ Level 1 Earthquake (Several times during lifetime of structure)Seismic Performance 1 :

Stress is less than design strengthNo need of repair

■ Level 2 Earthquake (Very small possibility during lifetime of structure)Seismic Performance 2 :

Displacement is less than limit valueEasy restoring of function, no need of reinforcing

Seismic Performance 3 : No shear failureNo collapse


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Seismic Design (Road Bridge)■ Design Earthquake Motion and Seismic Performance of Structures (Road Bridges)

設計地震動 A種の橋 B種の橋

レベル１地震動耐震性能１

タイプⅠレベル２

地震動タイプⅡ

耐震性能３耐震性能２

Design Earthquake Motion

Type-A Bridge Type-B Bridge

Level-1 Earthquake Motion

Level-2 Earth-quake Motion

Type-I

Type-II

Seismic Performance 1

S.P. 3 S.P. 2

設計地震動 A種の橋 B種の橋

レベル１地震動耐震性能１

タイプⅠレベル２

地震動タイプⅡ

耐震性能３耐震性能２

Design Earthquake Motion

Type-A Bridge Type-B Bridge

Level-1 Earthquake Motion

Level-2 Earth-quake Motion

Type-I

Type-II

Seismic Performance 1

S.P. 3 S.P. 2

■ Response Control Design Method・Passive Control: Passive consumption of seismic energy; anti-seismic show,

TMD (Tuned Mass Damper), oil damper・Active Control: Active consumption of seismic energy; AMD (Active Mass Damper),

Variable Stiffness / Decay Devices

・Type-I: Large scale, plate-boundary type

・Type-II: Inland, local type

・Level-1: Several times during lifetime of structure

・Level-2: Very small possibilityduring lifetime of structure

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1.2 Strength of Concrete

■ Strength of Concrete・Compressive Strength・Tensile Strength・Bond Strength・Bearing Strength・Flexural Cracking Strength・Fatigue Strength

■ Compressive Strength(1) The compressive strength of concrete has a direct influence on the load

carrying capacity of both plain and reinforced structures.(2) Among all the properties of hardened concrete, compressive strength can

usually be determined most easily.(3) The compressive strength can be used as a qualitative indication of other

important qualities of hardened concrete.


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■ Compressive Strength

Strength gain with age: limestone concretes moist cured until tested

■ Influencing Factors・ Quality of Materials・ Curing Temperature・ Entrained Air・ Confining Pressure・ High/Low Temperature・ Impact Loading

Comp. Test

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Self-compactable concrete

■ High-Strength Concrete・ Mix Proportions・ Curing Conditions・ Admixtures

(Superplasticizer)

■ Self-Compactable Concrete


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■ Use of High Strength Concrete

UHSC

Steel Pipe

UHSC

Steel Pipe

Slump flow: 680x675mm, Air content: 1.6% Comp. Strength: 150 MPa, Design Strength: 120 MPa

Conventional HSC: Design Strength: 40 MPa(Top Slab, Web, Bottom Slab)

Ultra HSC: Design Strength: 40 MPa (Top Slab), 120 MPa (Web, Bottom Slab)

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■ Compressive Strength- Curing Temperatures

Effect of low temperatures on concrete compressive strength at various ages

Effect of high temperatures on concrete compressive strength at various ages


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■ Compressive Strength- Confining Pressure

Stress-strain relations of concrete

(a) Biaxial compression (b) Biaxial compression-tension (c) Biaxial tension

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■ Compressive Strength- Effect of High Temperature Exposure

Extremes of the influence of heat exposure on the compressive strength of concrete

■ Influencing Factors

・ Moisture Content・ Evaporation Condition・ Heating/Cooling Rate・ Aggregate

Original strength of the concrete has little effect on the percentage of strength retained after heating and subsequent cooling.


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■ Compressive Strength- Effect of Low Temperature Exposure

Effect of low temperatures on compressive strength:(a) moist concrete; (b) moisture condition

■ Influencing Factors・ Cement Content・ Water-Cement Ratio of Mix・ Aggregate・ Age・ Moisture Condition

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■ Compressive Strength- Impact Loading

Effect of rate of stressing on the compressive strength of concrete


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■ Compressive Strength- Effect of Lateral Tensile Strain

Collins

Seya & Taniguchi

Naganuma & Yamaguchi

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■ Compressive Strength- Effect of Specimen Shape

d

h

d

h


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■ Tensile Strength

Age-strength relations for moist-cured concrete:compressive strength and flexural strength

■ Tensile Strength・ Direct Tensile Strength・ Flexural Tensile Strength・ Splitting Tensile Strength

Splitting test

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■ Tensile Strength- Effect of High Temperature Exposure

Influence of heat exposure on the flexural or tensile strength of concrete

・ Concrete exposed to temperature well above normal room temperature generally shows a deterioration in flexural strength.・ The rate of strength deterioration is highest at temperatures above 400oF (204oC).


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■ Splitting Tensile Strength- Effect of Curing Condition

Effect of moist curing and drying time on splitting tensile strength

・ During drying of the concrete, moisture loss progresses at a slow rate into the interior of concrete members, resulting in the probable development of tensile stresses at the exterior faces and balancing compressive stresses in the still moist interior zones.

・ The tensile resistance of drying lightweight concrete will be reduced from that indicated by continuously moist-cured concrete.

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■ Splitting Tensile Strength- Effect of Temperature

Effect of low temperature on splitting strength:(a) moist concrete; (b) moisture condition

Effect of temperature on splitting cylinder tensile strength of a siliceous aggregate concrete


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■ Tensile Strength- Relations between Tests

Relation between direct tensile and splitting strengths of lightweight concrete

・ The ratio between the direct strength and the splitting strength changes with variations in the composition of the concrete and depends to a considerable degree on the type and properties of the aggregates.

・ The ratio of direct tensile strength to modulus of rupture increases with increasing specimen size and compressive strength. When the size of the modulus of rupture beam becomes very large, the strain gradient diminishes, and the modulus of rupture approaches the tensile strength.

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■ Tensile Strength- Relations between Tests

Relation between splitting strength and flexural strength of concrete

Relation between splitting strength and compressive strength of concrete


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■ Shear Strength- Size Effect

Effective DepthSh

ear

Stre

ngth

Rat

io

Flexural Failure

Eq. by Okamura & Higai

Size effect on shear strengthSpecimens for shear test

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1.3 Stress-Strain Relation ofConcrete

Stress-strain curve of normal and lightweight concrete in compression


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■ Stress-Strain Relation

Stress-strain curves for different temperatures

Stress-strain curves forhigh-strength concrete

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■ Stress-Strain Relation (FRC)

Stress-strain curves for fiber-cement composite

Stress-strain curves for fiber-reinforced concrete


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Failure of PC Bridge (Case 1)

■ Koror-Babelthaup Bridge・Center Span 241m・Balanced Cantilever PC Box Girder Type(Palau, 1996.9.27)

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3-span continuous hybrid extradosed bridge(Length 412.7m, Span 82+247+82m, Width 9.2m) 2001.12

Japan-Palau Friendship Bridge (Reconstructed)


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• The bridge is the Koror-Babelthaup Bridge in Palau.

• Description of Bridge:1) Bridge Type: Balanced cantilever PC box girder bridge with movable

joint at the center connecting both sides.2) Center Span: 241m3) Start of Service: 19784) Failure: 1996.9.275) Conditions: Deflection at center was 1.2m in 18 years after completion.

The repair was finished three months before the collapse.

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• The failure of this prestressed concrete bridge happened as follows.

1) The concrete of the upper flange with more than 300 PC tendons inthe longitudinal direction near the bridge pier began to delaminate.

2) The sound of concrete crushing was heard inside the box girder from30 minutes before the collapse.

3) The web of the box girder with 360mm thickness failed in tension atthe top fiber.

4) The bottom slab with 1100mm thickness failed in shear and thecantilever fell down.

5) The other cantilever fell down by being pulled by the external cablewith which it was connected to the cantilever failing first.


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• The bridge was repaired before the collapse occurred.

• The deflection of 1200mm at the movable joint was considered due tocreep.

• The proposed repair methods:1) Replacement of whole bridge2) Replacing the center part of 40m by a PC simple beam3) Connecting both cantilevers by external cables of 310m and lifting up

the center by 300mm; the remaining deflection is filled by additionalconcrete slab.

• The actual repair method was to insert twelve flat jacks at the movablejoint etc. to reduce the stress in the upper flange.

• The possible cause of the failure is considered that the jacking forceexceeding the design value might have caused excessive stress in theupper flange of the box girder at the movable joint.

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1.4 Volume Changes ofConcrete

■ Volume Changes(a) Temperature [thermal expansion](b) Chemical process in hydration [autogeneous shrinkage](c) Drying [drying shrinkage](d) Sustained stress [creep]

■ Thermal Properties(a) Coefficient of expansion or contraction(b) Thermal conductivity; (c) Specific heat; (d) Thermal diffusivity;(e) Adiabatic temperature rise

■ Shrinkage and CreepInfluencing factors:(a) water-cement ratio; (b) physical characteristics of aggregate;(c) cement paste content; (d) age of concrete at drying or loading;(f) amount of steel reinforcement; (g) environmental conditions;(h) curing conditions


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■ Drying Shrinkage and Creep

Relation between shrinkage and drying time for concretes stored at different relative humidities (wet curing until the age of 28 days)

Creep of concrete moist-cured for 28 days, then loaded and stored at different relative humidities

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■ Shrinkage and Creep- High Strength Concrete

Shrinkage

Autogeneous shrinkage

Creep


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Shinsuge Bridge, Kiso Village, Nagano Pref. (1989)

Post-tensioned simple box girder bridge (1965.3),Kiso Village, Nagano Pref. Failure: 1989.6, No casualty, Cause: Failure of PC wire by rust

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• The bridge is the Shinsuge Bridge in Kiso Village, Nagano Pref. Japan.

• Description of Bridge:1) Bridge Type: Post-tensioned simple PC box girder bridge2) Bridge Length: 25.8m3) Start of Service: March 19654) Failure: June 19895) Cross-section: Hollow box type with 27 PC strands (diameter 27mm)

of 37 wires of 3.8mm diameter, 4 diaphragms for deviators ofexternal PC cables

PC CablePC Cable


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Failure of PC Bridge (Case 2)• The bridge failed suddenly in June 1989 at the mid-span when a dump

truck of 9.4t self-weight carrying 10t (7m3) sand about to finish goingthrough the bridge.

• Possible causes seem to be the effect of fatigue and corrosion (rust) ofPC wire and collapse of joint. Once prestressing tendons fail, a PC bridgecollapses in a brittle manner. The rust seems to be due to condensationinside steel pipe for PC strand, water leak from anchorage zone, residual chloride ion, and quality of PC tendon. The structure type is notsuitable for inspection for maintenance.

Failed Part

7m

7m

11.8m

Kiso River

Failed Part

7m

7m

11.8m

Kiso River

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1.5 Fatigue of Concrete

S-N curves for plain concrete beams showing various ratios of minimum to maximum stress in the loading cycles


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1.6 Durability of Concrete

Effect of compressive strength on the abrasion resistance of concrete

■ Weathering Resistance

■ Resistance to Deicers

■ Chemical Resistance

■ Abrasion and Skid Resistance

Damage

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■ Allowable Crack Width (JSCE2007)

--0.004cPC Tendon

0.0035c0.004c0.005cDeformed Bar, Round Bar

SevereCorrosiveCondition

CorrosiveCondition

NormalCondition

Environmental ConditionsKind ofSteel

・ c: Cover Length (≦100mm)・ Normal Environment: Ordinary outdoor condition, Underground condition・ Corrosive Environment: More frequent wet-dry cycle, Underground water

with harmful substance, In sea water, Ordinary sea shore environment ・ Severe Corrosive Environment: Harmful effect on steel corrosion,

Tidal zone or splash zone, Severe sea wind


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■ Design for Chloride Attack (JSCE2007)

■ Examination of Chloride Ion Concentration at Steel Position

0.1lim

C

Cdi

γi ： Structure Factor (General: 1.0, Important: 1.1)Clim ： Corrosion Initiation Concentration (1.2kg/m3）Cd ： Design Chloride Ion Concentration at Steel Position

■ Design Chloride Ion Concentration at Steel Position

Cd ： Design Chloride Ion Concentration at Steel PositionC0 ： Chloride Ion Concentration at Concrete Surface (kg/m3)γci ： Safety Factor for Scatter of Cd (1.3 in general)cd ： Reduced Cover (mm) = c – Δcec ： Cover (mm)Δce ： Construction Error (mm)t ： Design Durability Limit (year)(100 yrs at most)Dd ： Design Diffusivity for Chloride Ion (cm2 / yr)

tD

cerfCC

d

cid2

1.010 d

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■ Design Diffusivity for Chloride Ion

0

2

Dw

w

l

wDD

akcd

γc ： Material Factor of Concrete(1.0 in general, 1.3 for Upper Surface)

Dk ： Characteristic Value of Diffusivity for Chloride Ion(cm2 / yr)

D0 ： Constant for Effect of Crack (cm2 / yr)(Only for Flexural Crack) 200 cm2 / yr in general

w ： Crack Width (mm)wa ： Allowable Crack Width (mm)l ： Spacing of Crack (mm)

■ Relationship between Crack Width and Crack Spacing

'3 csd

s

se

El

w w ： Crack Width (mm)l ： Crack Spacing (mm)ε’csd ： Constant for Shrinkage and Creep of Concrete

General：150x10-6 ； High Strength Concrete： 100x10-6

σse ： Stress Increment in Steel from Zero Stress Condition(N/mm2)When steel is PC tendon, replace σse，Es by σpe，Ep.


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W/C

Diff

usi

vity

Dd

(cm

2 /yr

)

No Crack

Allowable Crack Width wa = 0.2mm

W/C

Diff

usi

vity

Dd

(cm

2 /yr

)

No Crack

Allowable Crack Width wa = 0.2mm

Influence of W/C and crack width on diffusivity

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1.7 Other Properties ofConcrete

■ Shear and Torsion

■ Bond of Concrete to Steel

■ Permeability(a) Water Permeability(b) Water Vapor Permeability(c) Air Permeability

■ Acoustical Properties(a) Sound Absorption; (b) Sound Transmission Loss; (c) Impact Noise; (d) Vibration Isolation

■ Electrical Properties


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■ Permeability

Water permeability and capillary porosity of cement paste

Water permeability and water/cement ratio for mature cement paste(93% of cement hydrated)

Permeability

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1.8 Reinforcement

■ Reinforcing Bars(1) Deformed bar

The standards govern strength grades, rib patterns, sizes, andmarkings of bars.All bars are furnished ‘deformed’ – that is, with lugs, ribs orprotrusions rolled into the bar, which increase bond performance with concrete.

(2) Round bar

■ Prestressing Tendons(1) Wire(2) Strand(3) Bar


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■ Reinforcing Bars- Stress-Strain Curves

Typical force-strain curves for rebars

・ Ultimate strength design of reinforced concrete sections is based on the assumption of an ideal elastoplastic (flat-top) stress-strain relation for the reinforcement.

・ The actual stress-strain relation for high-strength reinforcement may not be ideally elastoplastic, not having a well-defined yield point and a flat plateau.

・ Even those steels that have a well-defined yield point exhibit strain-hardening; some of these have a very short flat plateau, and others a considerably long one.

・ The modulus of elasticity for all reinforcing bars is practically the same and is taken as Es = 200GPa.

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■ Reinforcing Bars- Fatigue

Experimental test data on fatigue of deformed bars

■ Influencing Factors・ Range of stress・ Minimum stress・ Bar size・ Deformation

geometry・ Mechanical

characteristics ofthe bar

・ Fabricationprocedures


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■ Prestressing Tendons- Stress-Strain Curve

Effect of postdrawing treatment on wire Typical tensile tests in elastic region on uncoated stress-relieved wire for PC

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■ Prestressing tendons- Creep and Relaxation

Relaxation test in stress-relieved and stabilized (low relaxation), 0.275in. diameter, prestressed concrete wire


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■ Splices

Splicing of reinforcing bars is only for the purpose of providing continuity.

Splices are needed because of(a) limitations set up by the physical length of the bar(b) transitions from a larger to a smaller bar(c) construction requirements, i.e., construction joints

Traditional methods:(a) lap splices by bond(b) welded lap or butt splices

Newer methods:(a) couplers (for tension or compression)(b) end-bearing (for compression only)(c) semiautomatic butt-welded splices with commercially available

equipmentSplice

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■ Corrosion of Steel and NonferrousMetals

■ Galvanic corrosion is influenced by differences in:(a) the composition of the solution at the two electrodes(b) the nature of the metals of the electrodes(c) environmental conditions, such as the presence of oxygen

chloride concentration, alkalinity, moisture, temperature,or large air- or liquid filled spaces next to the metals

(d) permeability, thickness, or uniformity of concrete

■ Stress-Assisted Corrosion

■ Stress-Corrosion

■ Corrosion-Fatigue

■ Corrosion Protection(a) Coating (Metal, Non-metal)(b) Cathodic Protection(c) Anticorrosive Steel

Corrosion


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■ Durability Improvement ofConcrete Bridge by New Materials

Coated PC tendon

Pre-grouted PC tendon

Plastic sheath

FRP tendon

Carbon

Aramid

Glass

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■ Life Cycle Cost of Structure

LCC = I + M + R

Cost

Time

L.C.C.

Scenario 1

Scenario 2

Scenario 3

Initial Cost (I) Maintenance Cost (M) Renewal Cost (R)

Cost

Time

L.C.C.

Scenario 1

Scenario 2

Scenario 3

Initial Cost (I) Maintenance Cost (M) Renewal Cost (R)


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Problems:Materials for Concrete Structures

□ Steel PC tendon has about the same Young's modulus as steel reinforcing bar, but its elongation at rupture is smaller than that of steel reinforcing bar.

□ The shape and spacing of the ribs and indentations of deformed steel PC wires influences the bond with concrete and the fatigue strength of wire itself.

□ The pre-grout steel PC tendon is covered with polyethylene sheet and thehardening behavior of the resin inside the sheet is not influenced by ambient temperature.

□ When PC wire or PC strand is shipped in the form of coil, it is recommended that the diameter of the coil is no less than 150 times as long as the steel diameter so as not to have permanent deformation.

□ The rapid hardening portland cement is used for prestressed concrete and manufactured products because of early strength development.

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□ The low-alkali-type portland cement is the one specified as cement with total alkali amount of Na2O equivalent no more than 0.6%, and is used to suppress alkali-aggregate reaction.

□ The concrete using blast-furnace cement has smaller diffusion coefficient against chloride ion penetration than that using ordinary portland cement, and is suitable for marine structures.

□ The moderate heat portland cement has higher chemical resistance against various salts than the low-heat portland cement, and is suitable for underground structures.

□ The reinforced concrete structures which are always in sea water suffers less salt damage than those exposed in the coastal atmosphere.

□ The rate of carbonation development is accelerated with time.


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□ The diffusion coefficient of chloride ion is larger for concrete with smaller water cement ratio.

□ When phenolphthalein 1% ethanol solution is sprayed on the split surface of concrete, the color of the concrete under carbonation changes to red violet.

□ The expansion of concrete by the alkali aggregate reaction becomes large as the amount of reactive aggregate increases.

□ The frost resistance of concrete becomes high as the air content of concrete increases.

□ The flexural strength of concrete is 1/5 to 1/7 of the compressive strength.

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□ The Poisson's ratio of concrete in the elastic range is 1/5 to 1/6.

□ The drying shrinkage of concrete is large as the strength increases.

□ The creep coefficient of concrete becomes small as the strength increases.

□ The tensile strength of the continuous fiber reinforced material (rods) using carbon or aramid fibers is larger than that of steel reinforcing bar.

□ The corrosion resistance against chloride ion of the continuous fiber reinforced material (rods) using carbon or aramid fibers is more superior to that of steel reinforcing bar or steel PC tendon.


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Exercise 1The stress-strain curve of concrete subjected to compression is given as follows.

where cdf '

ckf '

cu'8052.0

: characteristic comp. strength (N/mm2): design comp. strength (N/mm2): strain at the peak stress (=0.002)0'c

Show the flexural capacity of a singly reinforced rectangular section by using the rectangular equivalent stress block based on the above stress-strain curve.

1k ;

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References

[1.1] Fintel, M.(Ed.): Handbook of Concrete Engineering, Second Ed., Van Nostrand Reinhold Company, New York, 1985.

[1.2] Neville, A.M.: Properties of Concrete, Fourth Ed., Prentice Hall, 1995.

[1.3] Zia, P.(Ed.): International Workshop on High Performance Concrete, Bangkok, Thailand(1994), ACI SP-159, 1996.

[1.4] JSCE: Standard Specifications for Concrete Structures-2007, Design,JSCE, 2007.

[1.5] JSCE: Standard Specifications for Concrete Structures-2007, Materialsand Construction, JSCE, 2007.

[1.6] JSCE: Recommendations for Design, Fabrication and Evaluation ofAnchorages and Joints in Reinforcing Bars [2007], JSCE, 2007.


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Concrete Structures

Part 2Modeling for Structural Analysis and Design


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2.1 Introduction

The mechanical properties of materials are modeled in the form of design formula to analyze concrete structures for design.

In the following, the formulas mainly in CEB Model Code 1990 are introduced for the representative mechanical properties of materials.

In addition to those, some formulas of other design codes are introduced.

The following equations for concrete apply to concrete with normal weight aggregates so composed and compacted as to retain no appreciable amount of entrapped air other than intentionally entrained air.

Though the following relations in principle also apply for heavy weight concrete, special consideration may be necessary for such concrete.


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2.2 Strength of Concrete

■ Stress Rate and Strain RateThe information given in this section is valid for monotonically increasing compressive stresses or strains at stress rate ～ 1.0MPa/s or strain rate ～ 30×10-6s-1, respectively.

For tensile stresses or strains it is valid for stress rate ～ 0.1MPa/s or strain rate ～ 3.3×10-6s-1, respectively.

■ Characteristic Compressive StrengthStrength below which 5% of all possible strength measurements forspecified concrete may be expected to fall.

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■ Test and SpecimenThe uniaxial compressive strength fc of cylinders, 150mm in diameter and 300mm in height stored in water at 20±2℃, and tested at the ageof 28 days.

■ Mean Value of Compressive Strength

where

: Characteristic compressive strength


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83

■ Tensile Strength

■ Test MethodThe term ‘tensile strength’ refers to the axial tensile strength fctdetermined in accordance with RILEM CPC7.

■ Mean Value of Tensile Strength

where;

where

: Mean splitting tensile strength

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■ Strength under Multiaxial Statesof Stress

Biaxial strength of concrete

■ Failure Criterion


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85

■ Strength under Multiaxial Statesof Stress

Biaxial failure envelope

■ Stress Invariants and Constants

86

■ Strength under Multiaxial States of Stress

Failure envelope for triaxial compression

■ Biaxial Comp. and Tens.-Comp.for

■ Biaxial Tension

■ Biaxial Tens.-Comp. for


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87

2.3 Stress-Strain Relation ofConcrete

■ Stress Rate and Strain RateThe information given in this section is valid for monotonically increasing compressive stresses or strains at stress rate ～ 30MPa/sor strain rate ～ 30×10-6s-1, respectively.

For tensile stresses or strains it is valid for stress rate ～ 0.03MPa/sor strain rate ～ 3×10-6s-1, respectively.

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■ Elastic Constants

■ Modulus of Elasticity

■ Poisson’s Ratio

: Modulus of Elasticity (MPa) at a concrete age of 28 days

; ;

= 0.1～0.2

for a range of stresses


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89

■ Stress-Strain Relations for Short-Term Loading

Stress-strain diagram for uniaxial compression

■ Stress-Strain Curve in Compression

■ Limit Strain

90

■ Stress-Strain Relations for Short-Term Loading

Stress-strain and stress-crack opening diagram in uniaxial tension

■ Stress-Strain Curve in Tension

for

for

■ Stress-Crack Opening Relation fora Cracked Section

for

for

;


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91

■ Multiaxial States of Stress

Equivalent uniaxial stress-strain diagram

■ Stress-Strain Relation in Principal Stress Direction

■ Stress-Strain Relation Using EquivalentUniaxial Strain

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■ Stress-Strain Relations for SeismicDesign (JSCE2007)

Simplified hysteresis model of concrete in compression

■ Stress-Strain Relation for Seismic Design in the Analysis of a Linear Member (for fc<50MPa)


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93

■ Stress-Strain Relations for SeismicDesign (JRA2002)

Stress-strain curve of concrete in compression

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■ Stress-Strain Relations for Seismic Design (JSCE2007)

Stress-strain relation of concretein tension

■ Stress-Strain Relation in Tension(1) Linear member

In the analysis of a linear member the stress-strain relation in tension may be neglected. Even if the tensile stress is neglected, the effect to the response of structures is small because the nonlinear region is limited in a certain portion of a linear member.

(2) Planar memberIn the tensile zone perpendicular to the direction of a crack, tension stiffening effect due to bond on the average stress-strain relation is considered to apply to tension field of reinforced concrete with sufficient amount of reinforcement.


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95

■ Equivalent Stress Block

d

b

x x

f'c d

TAs

Neutral Axis

x

uccdc xydybC0

'''' //

x

cdcc ydybCyx0

'')(

■ Moment w.r.t Neutral Axis → yc, β

■ Compressive Stress Resultant → α, k1

yc : Position of Compressive Stress Resultant

The compressive stress distribution of concrete may be assumed to be a rectangular distribution (equivalent stress block) except for the case of compressive strain all over the cross-section.

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2.4 Time Effects for Concrete

■ Development of Strength with Time

■ Strength under Sustained Loads

■ Development of Modulus of Elasticity with Time

;

;


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97

■ Creep and Shrinkage

■ DefinitionsThe total strain at time t of a concrete member uniaxially loaded at time t0 with a constant stress may be expressed as follows.

where

: initial strain at loading

: creep strain at time t>t0

: shrinkage strain: thermal strain

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■ Creep (CEB1990 Model)

: creep function, creep compliance

: creep coefficient

;


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99


■ Shrinkage (CEB1990 Model)

;

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2.5 Fatigue of Concrete

S-N relations

■ S-N RelationFor a constant stress amplitude the number N of cycles causing fatigue failure of plain concrete may be estimated by the S-N relations.

■ Fatigue Relation for Pure Compression

■ Fatigue Relation for compression-tension

■ Fatigue Relation for Pure Tension


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101

2.6 Temperature Effects forConcrete

■ Range of Temperature・ Normal temperature: -20℃～+40℃・ Deviation from a mean concrete temperature of 20℃

for the range of approximately 0℃ to +80℃

■ Maturity

■ Thermal Expansion

;

■ Temperature Effects on Other Material Properties・ Modulus of Elasticity・ Creep and Shrinkage

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2.7 Stress and Strain RateEffects for Concrete

Type of Loading Strain Rate(s-1)

Traffic 10-6～10-4

Gas Explosion 5x10-5～5x10-4

Earthquake 10-2～5x100

Pile Driving 10-2～100

Airplane Impact 5x10-3～5x10-2

Hard Impact 100～102

High-Vel. Plate Impact 102～106

Strain rate of various loading■ Compressive Strength・ Effect of Stress Rate

・ Effect of Strain Rate


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103

■ Effect of Strain and Stress Rates

Effect of strain rate Effect of stress rate

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■ Impact Loading on RC Structures

Penetration

Punching Shear Failure

Response of Structure(Flexure)

SpallingScabbing

Penetration

Punching Shear Failure

Response of Structure(Flexure)

SpallingScabbing

Impact loading

Static

Dynamic(1)

Dynamic(2)

Dynamic(3)

Dynamic(4)

Dynamic(5)

RC beam under impact loading


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105

2.8 Stress-Strain Relation ofReinforcing Steel

Stress-strain relation of reinforcing steel under cyclic loading (JSCE2007)

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Problems:Design of Concrete Structures

□ The deformation increases and the stress resultants develops due to creep of concrete even in the case where the structural system does not change in during and after construction as in erecting a continuous girder at once.

□ In a PC bridge pier subjected to reversed cyclic loading, the energy absorption capacity decreases, and the residual displacement and the damage become smaller, as the amount of prestress increases.

□ In the internal cable method, the loss due to the friction by the angle change of PC tendon only has to be considered for the frictional loss of prestress in PC tendon.

□ As an effect of prestress to the shear force in the external cable method, the force component of the tension in PC tendon in the direction of shear force can be taken into consideration, but the shear force supported by concrete does not increase.


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107


□ The examination of the diagonal tensile stress for suppressing the diagonal cracking in the member designed as a PC structure is recommended to be done for the section of the maximum normal stress at the bottom fiber of the member cross section.

□ The balanced reinforcement ratio is the tensile reinforcement ratio of a section where the main tensile reinforcement reaches the design yield strength and the strain of concrete at the compressive top fiber becomes the ultimate compressive strain at the same time.

□ A PRC(PPC) structure is a structure which allows cracking in a serviceability limit state condition and controls the crack width by using deformed steel bars and prestressing.

108


□ Once cracking occurs in concrete, the tensile stress of PC tendon suddenly increases compared to that of the state where the whole cross section is effective.

□ The spacing between sheaths in a post-tensioned member should be no less than 4/3 times the maximum aggregate size and sufficient to insert a vibrator.

□ It is recommended to arrange PC tendons at the centroid of cross section in sections close to the section in which the sign of bending moment for various load combinations is different.


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109

Problems:Quality Control and Test Methods

□ The alkali-aggregate reaction is a phenomenon in which cracking occurs in concrete by the chemical reaction between hydroxide alkali in concrete and the alkali-reactive minerals in aggregate, and it becomes active when concrete is in a dry condition.

□ The salt damage is a phenomenon in which corrosion occurs in steel reinforcing bars and steel PC tendons by the action of chloride ion in concrete, causing damage of the structure, and it considerably develops if water and oxygen are supplied.

□ The carbonation is a phenomenon in which the alkalinity of concrete decreases by the action of the carbon dioxide in air, and its development is slow for concrete with dense internal structure.

110


□ The frost damage is a phenomenon in which concrete fails by the hydraulic pressure due to volume expansion and subsequent water flow by freezing of water, and it is closely related to the air content of concrete.

□ The compressive strength of concrete becomes large as the ratio h/d (h: height, d: diameter) of a cylindrical specimen increases.

□ The strength of a cubic specimen is about equal to the strength of a cylindrical specimen with diameter equal to the side length of the cube and height twice as long as the diameter.

□ The strength of concrete becomes larger as the loading rate increases.


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111


□ It is recommended that concrete is moist-cured by covering with sheet to prevent direct sunshine, wind, cold air and so on immediately after completing casting concrete.

□ Higher temperature of concrete at casting is in general advantageous for long-time strength development of concrete if the water cement ratio is the same.

□ In general the slump value becomes larger due to decrease of viscosity when the temperature of concrete increases.

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Exercise 2For the rubber support used in a PC bridge, the size and the thickness are determined by the reaction and the horizontal displacement respectively.The design horizontal displacement of a movable support is calculated as follows.

; ;

; ;

;

In case of symmetric deflection of a simple beam, calculate the horizontaldisplacement for ΔT=±40℃, α=10×10-6, l=30m, εcs=-200×10-6, Pt/Ac=-6.5N/mm2, φ=2.0, Ec=3.1×104N/mm2, h=1.0m, θ=1/300(rad).


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References

[2.1] ACI Committee 209: Prediction of Creep, Shrinkage, and Temperature Effects inConcrete Structures, ACI SP-76, Designing for Creep and Shrinkage in ConcreteStructures, American Concrete Institute, pp.193-301, 1982.

[2.2] BSI: British Standards: Structural Use of Concrete, BS8110, Part 2, Section 7,British Standards Institution, pp.7/1-7/5, 1985.

[2.3] CEB: CEB-FIP Model Code 1990, Thomas Telford, pp.53-58, 61-65, 1993.

[2.4] Chen, W.F.: Plasticity in Reinforced Concrete, McGraw-Hill, 1982.

[2.5] DIN: Prestressed Concrete: Structural Components Made of Ordinary Concretewith Partial or Total Prestressing DIN 4227, Part 1, DIN, pp.10-14, 1975.

[2.6] JSCE: Standard Specifications for Concrete Structures-2002, “StructuralPerformance Verification,” JSCE Guidelines for Concrete, No.3, Chap.3, DesignValues for Materials, Japan Society of Civil Engineers, pp.22-51, Jan. 2005.

114

References (cont.)

[2.7] JSCE: Standard Specifications for Concrete Structures-2002 “SeismicPerformance Verification,” JSCE Guidelines for Concrete, No.5, Chap.4,Analytical Model, Japan Society of Civil Engineers, pp.24-39, Mar. 2005.

[2.8] JRA: Specifications for Highway Bridges, Part V, Seismic Design, Chap.10,Lateral Strength and Ductility Capacity of Reinforced Concrete Columns,Japan Road Association, pp.174-230, Mar. 2002.

[2.9] JSCE: Standard Specifications for Concrete Structures-2007, Design,JSCE, 2007.

[2.10] JSCE: Standard Specifications for Concrete Structures-2007, Materialsand Construction, JSCE, 2007.


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Concrete Structures

Part 3Structural Analysis Methods


116

3.1 Introduction

For the design of concrete structures with various shapes, numerical structural analysis is conducted. In order to assure the satisfactory performance under severe loading conditions, nonlinear numericalstructural analysis is necessary.In this part, the structural analysis method for a prismatic concrete member and that for two-dimensional and three-dimensional concrete structures are discussed.

Conc. Struct.

Appl. FEM


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117

■ Analysis for Seismic Design

■ Seismic Performance (JSCE 2007)(1) SP1: Sound Function; No Need of Repair(2) SP2: Easy Restoring Function; No Need of Reinforcing(3) SP3: No Collapse

■ Structural Models for Examination of Performance(1) SP1: Frame Model, Linear Model(2) SP2, SP3: 3D Finite Element Model; Nonlinear Material Properties

■ Analysis Methods of Seismic Design(1) Static Analysis Method (Level1: Elastic / Level2: Elastoplastic)

Seismic Intensity Method (High-Stiffness Structures)Design Earthquake Force = Mass x Design Seismic Intensity

Modified Seismic Intensity Method (Low-Stiffness Structures)Dynamic Characteristics of Structure → Design Seismic Intensity

(2) Dynamic Analysis Method (Level1: Elastic / Level2: Elastoplastic)

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■ Static Analysis Method forSeismic Design of Road Bridge (2002)

■ Level 1 Earthquake Motion(Seismic Intensity Method)Standard Seismic Intensity = 0.2 – 0.3Foundation Type: I, II, III

■ Level 2 Earthquake Motion(Limit State Design Method)Type-1 (Large-Scale, Plate-Boundary Type) → 0.7 – 1.0Type-2 (Inland, Local) → 1.5 – 2.0


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119

■ Linear and Nonlinear AnalysisLoad

Displacement0

F1

U1

K

1

K U 1 = F 1

Load

Displacement0

F2

F1

U1 U2

K2

K1

dF2

dF1

dU1

dU2

Ki dU i = dF i

(i=1,2)

Load

Displacement0

F0

K0

K1

U0 U1

t=t0 t=t1

dU1

(t1>t0)

U1 = (1 + p) U0

K1 = K0 / (1 + p)

Creep Coefficient (p)

Load

Displacement0

F0

K0

K1

U0 U1

t=t0 t=t1

dU1

(t1>t0)

U1 = (1 + p) U0

K1 = K0 / (1 + p)

Creep Coefficient (p)

(a) Linear analysis (b) Nonlinear analysis(incremental method)

(c) Analysis for time-dependent materials

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3.2 Analysis of a Concrete Member■ Constitutive Relation of Concrete

Stress-strain relation of concrete

The incremental stress-strain relation of concrete is given in the following form to express the nonlinear behavior.

where

(Stress increment)

(Inelastic stress increment)

(Strain increment)


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121

■ Inelastic Behavior of Reinforcing Steel

Stress-strain diagram for reinforcing steel

The Bauschinger effect in the cyclic response of a reinforcing steel bar is modeled by Agrawal, G.L. et al. (ACI Journal, Vol.62, No.7, 1965) and Brown, R.H. et al. (ACI Journal, Vol.68, No.5, 1971).

where

εu: strain at ultimate stress σu in the first loadingεip: strain between successive points of zero stress immediately preceding a given cycle

122

■ Internal Force-Displacement Relations for a Beam

Geometry, discrete cross sections, and mode ofdeformation of a concrete beam: Inelastic force

increment

Force increment:

Stiffness matrix:

Curvature and strain:


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123

■ Internal Force-Displacement Relations for a Beam

Moment-curvature relation for a concrete beam

124

■ Layered Beam Element Model

x

yz

z

y

0

1 i nynz

j

1Centroidal Axis

Element and Coordinate Cross Section

x

yz

z

y

0

1 i nynz

j

1Centroidal Axis

Element and Coordinate Cross Section

DiscretizedSection - i

φ+Δφ

εo+Δεo

ε i+Δε i

M

N

φ

ε o

εｉ

CentroidalAxis

zi

(1) Bernoulli-Euler Assumption

(2) Perfect Bond between Concrete and Steel

DiscretizedSection - i

φ+Δφ

εo+Δεo

ε i+Δε i

M

N

φ

ε o

εｉ

CentroidalAxis

zi

(1) Bernoulli-Euler Assumption

(2) Perfect Bond between Concrete and Steel

25

75

75

25

25 75 75 25 (mm)

N

N

E

W

W

E

S

S

(1)

(2)

–20 0 20

–50

0

50

Displacement (mm)

Load

(kN

)

Spec. U8–0

ModelTest

（Li, Otani, Aoyama, 1986）

25

75

75

25

25 75 75 25 (mm)

N

N

E

W

W

E

S

S

(1)

(2)

–20 0 20

–50

0

50

Displacement (mm)

Load

(kN

)

Spec. U8–0

ModelTest

（Li, Otani, Aoyama, 1986）


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125

3.3 Analysis of 2D and 3D Concrete Structures

Experimental crack patterns of beams failing in shear

Analytical model of beams failing in shear

■ Modeling of Concrete Member

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Analytical models and linkage elements

■ Linkage Element・ The bond between steel reinforcement and surrounding concrete is modeled by bond link elements. The position of crack is assumed along the inter-element boundary.・ A linkage element has two nodes and is made up of two springs, i.e., normal spring and tangential spring, connecting its nodes.・ A linkage element is used to represent the bond of reinforcement and the shear transfer across crack surfaces.


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Finite elements for analysis of prestressed reactor vessels

To model a three-dimensional concrete structure, solid elements are used. Examples of axisymmetricelements and three-dimensional elements used to model prestressedconcrete reactor vessels are shown.

128

■ Stiffness Equation and Solution Technique

Isoparametric finite element

: Global stiffness matrix

: Global nodal displacement vector

: Global nodal force vector

■ Stiffness Equation


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129


Iterative solution techniques for nonlinear analysis

130


Solution techniques for nonlinear analysis:(a) unbalanced load iteration method – total equilibrium approach; (b) direct forward marching strategy – incremental equilibrium approach


66

131Simple flow chart for a typical nonlinear finite element program


132

■ Modeling of Crack

Possible crack configurations for multiple cracking models


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133

■ Modeling by Finite ElementMethod

134

■ Finite Elements


68

135

■ Modeling of Concrete

Stress-strain curve Cracking properties

Failure envelope Crack model

136

■ Example of FEM Analysis- RC Shear Wall under Shear


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■ Example of FEM Analysis- Shear Failure of RC Beam

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■ Example of FEM Analysis- Pullout of Anchor Bolt


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Exercise 3An example of 2D FEM analysis of RC beam is shown in the figure using triangular elements.Complete the input data shown below.

①

②

③④

⑤

① nodal coordinates; ② element data;③ nodal load; ④ displacement boundary condition;⑤ material data

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References

[3.1] Chen, W.F.: Plasticity in Reinforced Concrete, McGraw-Hill, 1982.

[3.2] Zienkiewicz, O.C. and Taylor, R.L.: The Finite Element Method, Fourth Ed., Vol.1, 1994, Vol.2, 1991, McGraw-Hill.