civil engineering materials

11

Civil Engineering Materials – CIVE 2110Civil Engineering Materials – CIVE 2110

Concrete Material Concrete Material Stress vs. Strain CurvesStress vs. Strain Curves

Steel Reinforcement Steel Reinforcement

22

Stress-Strain Curve for CompressionStress-Strain Curve for Compression Slightly ductile shape of Stress-Strain curve

A descending branch exists after is reached Due to redistribution of load to un-cracked regions with less stress,

'cf

(MacGregor, 5(MacGregor, 5thth ed., Fig. 3-26) ed., Fig. 3-26)

33

Stress-Strain Curve for CompressionStress-Strain Curve for Compression Strength of Reinforced Concrete structures controlled by,

Size of members, Shape of members, Stress-Strain curves of; - concrete, - reinforcement.Five properties of Stress-Strain curves;(1) - Initial slope, Ec

(2) - Ascending parabola(3) - Strain at max stress,(4) - Descending parabola(5) - Strain at failure

'cf

(Fig. 3-18, MacGregor, 5(Fig. 3-18, MacGregor, 5thth ed.) ed.)

44

Stress-Strain Curve for CompressionStress-Strain Curve for Compression (1) - Initial Slope, Ec ;

ACI 318, Sect. 8.5, 8.6 sensitive to Eaggregate , Ecement .

For normal weight concrete;

For other weight concrete;

Defined as the slope of a line drawn from

As water increases, Ec decreases, because cement paste becomesmore porous, there is less aggregate.

'45.00 cfto (MacGregor, 5(MacGregor, 5thth ed., Fig. 3.17) ed., Fig. 3.17)

'5.1

33

33

16090

ccc

c

fwpsiE

FtLbwFtLb

'

3

000,57

145

cc

c

fpsiE

FtLbw

55

Stress-Strain Curve for CompressionStress-Strain Curve for Compression Lightweight Concrete ;

ACI 318, Sect. 8.5, 8.6 sensitive to Eaggregate .

For all parameters involving Each parameter shall be multiplied by a modification factor

for sand-lightweight conc. for all-lightweight concrete

If splitting tensile strength, fct , is specified, then

This accounts for the reduced capacity of lightweight concrete due to aggregate failure; Such as:

Shear strength Splitting resistance Concrete-rebar bond

For normal weight concrete the averageFor normal weight concrete the averagesplitting tensile strength is;splitting tensile strength is;

0.17.6/ ' cct ff

'cf

'7.6 cct ff

(MacGregor, 5(MacGregor, 5thth ed., Fig. 3.26) ed., Fig. 3.26)

'5.1

33

33

12090

ccc

c

fwpsiE

FtLbwFtLb

75.085.0

66

Stress-Strain Curve for CompressionStress-Strain Curve for Compression (2) – Ascending Parabola;

Curve becomes steeper as increases.'

cf

(Fig. 3.18(Fig. 3.18, MacGregor, 5MacGregor, 5thth ed.,) ed.,)

(3) – Strain ( ) at ; Strain at max stress increases as increases.

'cf

'cf

(4) – Slope of descending branch; Less steep than ascending branch, Slope increases as increases.'

cf

(5) – Strain ( ) at failure; Decreases with increases in '

cf

0

cu

(4 and 5) – depend on; Specimen size; Load, type, rate

ksifc 6'

77

Stress-Strain Curve for Stress-Strain Curve for TensionTension Tensile strength of concrete:

Determined by one of 2 tests: (1) Flexure (Modulus of Rupture) test, (2) Split Cylinder test, fct

2

3

612

2

BHMf

BH

HMf

IMyf

r

r

Flexurer

(1) Flexure (Modulus of Rupture) test; Load until failure due to cracking on tension side, ASTM C78 or ASTM C293,

H = 6”, B = 6” L = 30”

3PL

H

B

P P

3” 3”

8” 8” 8”

P

-P

V

M

0

0

88

Stress-Strain Curve for TensionStress-Strain Curve for Tension

ldPf

ldPf

asistingArePf

ldasistingAre

ct

ct

ct

22

Re

2Re

(2) Split Cylinder test, fct ; Load in compression along long side, ASTM C496,

a standard 6”x12” cylinder is placed on side, Outside surface area,

Load is resisted by only half of surface area,

dlrlArea 2


99

1max Tension

ApC 2

2maxApC

2x90˚

CompressionTension

Concrete always cracks on plane of MaxTension

Split Cylinder Test

Bi-Axial Stress

Stress-Strain Curve for TensionStress-Strain Curve for Tension

1010

Stress-Strain Curve for TensionStress-Strain Curve for Tension Tensile strength of concrete:

Determined by one of 2 tests: (1) Flexure (Modulus of Rupture) test, (2) Split Cylinder test,

rf

Tensile strength from Split Cylinder test is less than that from Flexure (modulus of Rupture) test because;

In Flexure test, only bottom of beam reaches In Split Cylinder test, majority of cylinder reaches

ctf

MaxTension

MaxTension

ctr ff 5.1

H

B

P P

1111

Stress-Strain Curve for TensionStress-Strain Curve for Tension Results from various Split Cylinder

tests vs. are plotted in Fig. 3.10 The mean Split Cylinder strength is:

ACI 318, Sect. R8.6.1 states;

The mean Modulus of Rupture strength is:

ACI 318, Sects. 8.6.1 & 9.5.2.3 state, for deflection calculations:

'3.8 cr ff

'4.6 cct ff


'cf

'7.6 cct ff

0.17.6

5.7

'

'

c

ct

cr

f

fff

concretetlightweighallforconcretetlightweighsandfor

concreteweightnormalfor

75.085.00.1

1212

Stress-Strain Curve for TensionStress-Strain Curve for Tension Tensile strength of concrete:

'' 15.008.0 ct ff

Concrete tensile failure is BRITTLE.

Same factors affect as ; Water/Cement ratio, Type of Cement, Type of Aggregate, Curing Moisture conditions, Curing Temperature, Age, Maturity, Loading rate.

(MacGregor, (MacGregor, 55thth ed., Fig. 3-21) ed., Fig. 3-21)

'tf

'cf

''

''

4.6

8.1

cctt

c

tt

fff

whereEf

E t initi

al =

line

arflexurefor

tensionpurefor

MAX

MAX

t

t

0002.000014.0

0001.0'

'

'5.0 tfFrom: 0

c

tt E

f ''

''5.0 tt ff From: ''5.0 tt ff

'5.0 tf

1313

Steel Reinforcement in ConcreteSteel Reinforcement in Concrete

In any beam (concrete, steel, masonry, wood): Applied loads produce Internal resisting Couple,

Tension and Compression forces form couple.

MacGregor, 5th ed. Fig. 1-4

In a concrete beam:In a concrete beam: - - Cracks occur in areas of occur in areas of Tension,,

- - Beam will have sudden Beam will have sudden Brittle failure failure unless Steel reinforcement reinforcement

is present to take is present to take Tension.

1414

Mohr’s Circle Method – Failure ModesMohr’s Circle Method – Failure Modes

ionslightTensmax

Brittle concrete fails on plane of max normal (tension) Stress.Failure stress located at: 2x90˚=180˚on Mohr Circle

ApC min

2maxApC

2x45˚

2x90˚

tension

Shear Stress Normal Stress Principal Stress

Neutral Axis90˚

tension

Plane of max Tension

Concrete Brittle

1515

Steel Reinforcement in ConcreteSteel Reinforcement in Concrete Steel Reinforcement:

Hot-Rolled deformed bars (rebars)Welded wire fabric

Reinforcement Bars (Rebars):ASTM specs specify;ASTM specs specify;

- diameter, cross-sectional area- diameter, cross-sectional area - sizes in terms of 1/8 inch- sizes in terms of 1/8 inch - #4 rebar, diameter = 4/8 in.- #4 rebar, diameter = 4/8 in.- metallurgical properties- metallurgical properties- mechanical properties- mechanical properties - Grade - Grade min. Tensile Yield Strength min. Tensile Yield Strength - Grade 60, Yield Strength = f- Grade 60, Yield Strength = fyy = 60 = 60

ksiksi

ASTM A 615:ASTM A 615:- made from steel billets- made from steel billets- most commonly used- most commonly used

ASTM A 706:ASTM A 706:- made from steel billets- made from steel billets- for seismic applications- for seismic applications

- better - ductility- better - ductility - -

bendabilitybendability - -

weldabilityweldability

1616

Steel Reinforcement in ConcreteSteel Reinforcement in ConcreteReinforcement Bars (Rebars):

Upper Limit on

dStrengthactualYielygthnsileStrenUltimateTe f 25.1

(MacGregor, 5(MacGregor, 5thth ed., Table 3-4) ed., Table 3-4)

1717


Rebars in US customary units:- Grade 60,

- # 11

Rebars in metric units:Rebars in metric units:- just numerical conversions- just numerical conversions

of US customary sizes.of US customary sizes. - #36 - #36

- Grade 420, - Grade 420, MPaf y 420

ksif y 60


"41.1"375.18"11

d "409.1"14.25

8.35

mmmmd

1818

Steel Reinforcement in ConcreteSteel Reinforcement in ConcreteReinforcement Bars (Rebars): (MacGregor, 5(MacGregor, 5thth ed., Table A-1) ed., Table A-1)

1919

Steel Reinforcement in ConcreteSteel Reinforcement in ConcreteReinforcement Bars (Rebars): (MacGregor, 5(MacGregor, 5thth ed., Table A-1M) ed., Table A-1M)

2020


- modulus of Elasticity, ES = 29,000,000 psi

ACI 318, Sect. 8.5.2

- for rebars with fy > 60,000 psi

must use fy = ES x ( ) ACI 318, Sect. 3.5.3.2

0035.0S


2121


- at temperatures > 850at temperatures > 850˚F˚F ffyy and f and fultimateultimate

drop significantlydrop significantly - concrete cover- concrete cover over the rebarsover the rebars helps to delay losshelps to delay loss loss during firesloss during fires


2222

Steel Reinforcement in ConcreteSteel Reinforcement in ConcreteFatigue Strength of rebars:- Bridge decks subjected to large number of load cycles - Stress Range, Sr =

(MacGregor, 5(MacGregor, 5thth ed., Fig. 3-33) ed., Fig. 3-33)- Fatigue failure may

occur if at least one stress is tensile

and Sr > 20 ksi- Fatigue failure will not

occur if;

cyclesanycyclesiniteksi

Max

Max

000,20inf20

- Fatigue strength reduced at: Bends, Welds

cyclesameinMinStresscycleainStressMaxTensile

2323


Example: Fatigue Failure not possible;

Fatigue Strength of rebars: - Stress Range, Sr =

cyclesameinMinStresscycleainStressMaxTensile

ksiS

ksiksiS

r

cyclesameincycleainr

21

165

ksiS

ksiksiS

r

cyclesameincycleainr

21

265

Example: Fatigue Failure possible;

2424

Steel Reinforcement in ConcreteSteel Reinforcement in ConcreteWelded-Wire Reinforcement: - used in: Walls, Slabs, Pavements. - due to cold-working process used in drawing the wire strain-hardening occurs, so wire is BRITTLE. - Plain wire; ASTM A82; A185; ACI 318, Sect. R3.5.3.6 fy = 60,000 psi

- mechanical anchorage in concrete provided by - cross-wires

- Deformed wire; ASTM A496; A497; ACI 318, Sect. R3.5.3.7 fy = 60,000 psi

- mechanical anchorage in concrete provided by

- cross-wires- deformations

2525

Steel Reinforcement in ConcreteSteel Reinforcement in ConcreteWelded-Wire Reinforcement:- Wire diameter = 0.125” 0.625” - Wire area increments of 0.01 in2 .

- Plain wire; W - Deformed wire: D - ACI 318, Sect. 3.5.3.5 D-4 wire size D-31area = 0.04 in2 area = 0.031 in2 .

-

(MacGregor, 5(MacGregor, 5thth ed., Table A-2a) ed., Table A-2a)

2626

Steel Reinforcement in ConcreteSteel Reinforcement in ConcreteWelded-Wire Reinforcement:- Wire area increments of 0.01 in2 .- Wire center-center spacing a x b , inches

- Plain wire; W

-

(MacGregor, 5(MacGregor, 5thth ed., Table A-2b) ed., Table A-2b)