Concrete Column Presentation

RC ColumnRC Column

Presented By:A.B.M Sazzad Hossain

Column Definition:Members that carry axial load, axial load and Bending moment.

Column Types:

1. Tied

2. Spiral

3. Composite

4. Combination

5. Steel sections

Tied Columns 95% of all col mns inTied Columns - 95% of all columns in buildings are tied

Tie spacing h (except for seismic)tie support long bars (reduce buckling)

ties provide negligible restraint to lateral expose of corelateral expose of core

Behavior of Spirally Reinforced and Tied Columns

ConfinementACI spiral reinforcement ratio based on tests by Richart, Brandtzeg and Brown – 1928; using 6” x 12” cylinders,

wheref* =Compressive strength of spirally confined core concretecore concrete0.85 f’c = compressive strength of concrete if unconfinedf’2 = lateral confinement stress in core concretef 2 lateral confinement stress in core concrete produced by spiral

What sort of lateral confinement can a given spiral provide?g p pConsider a length of a spiral--wrapped circular section:for a length “S”:volume of spiral = A π D (approximately)volume of spiral = Aspπ D (approximately)volume of concrete = (πD2/4)S

Ratio of spiral reinforcement

Spacing of Ties to Prevent Longitudinal Bar BucklingSpacing of Ties to Prevent Longitudinal Bar BucklingA. Tied column may fail prior to steel yield if shell spalls and longitudinal bars buckle;B. Insure that bar buckling load is greater than yield load. (σcr >fy)

Assume that bar buckling load is greater than yield load -- Assume a pin--pin bar between ties:

ACI Provisions for Axial Load Capacity of Spiral Columns

ACI Provisions for Axial Load Capacity of Tied Columns

Columns are assigned the following strength reduction factor (ACI 9.3.2.2)Tied column 0 65Tied column -- 0.65Spiral column -- 0.70

Why ?Why ?To allow for the probability of understrength members due to variation in material strengths and dimensionsTo allow for inaccuracies in the design equationsTo reflect the degree of ductility and required reliability of the member under the load effects being considered.gTo reflect the importance of the member in the structure

Effect of Column Tie

Column without Tie/Spiral

Column with Tie/Spiral

ACI Code Provision for Tie and Spiral of Column

16 (bar diameter)

p

For Tied Column: spacing not to be greater than16 (bar diameter)48 tie bar diameterLeast column dimension

For Spiral Column Continuous bar not less th t 3/8 i di tthat 3/8 in. diameterClear spacing < 3 in.Clear spacing > 1 in.

Arrangement Vertical spacing:

At least every other longitudinal bar shall have lateral support from the corner of a tie with an

1.)lateral support from the corner of a tie with an included angle 135o. No longitudinal bar shall be more than 6 in. clear on either side from “support” bar

2.)clear on either side from support bar.

Short Columnwith

Axial Compression and Bending Momentp g

Pure axially Loaded Columns are rarely occur, simultaneously bending y y , y gis always present .Usually moment is represented by axial load times eccentricity,y p y y

Combined Stress due to Axial Compressive plus BendingCombined Stress due to Axial Compressive plus Bending

Strain Compatibility AnalysisSt a Co pat b ty a ys s

For Tension steel For Compression steel For Concrete Stress Depth

For Compressive Resultant Force

Balanced Steel Failure in Column

The load Pb and moment Mb acting in combination to produce failure, with the concrete reaching its limit strain u at precisely thesame instant that thethe concrete reaching its limit strain u at precisely thesame instant that the tensile steel on the far side of the column reaches yield strain. This point on the interaction diagram is the dividing point between

i f il ( ll t i iti ) d t i f il (l

compression failure (small eccentricities) and tension failure (large eccentricities).

Column Interaction CurveInteraction Diagram Between Axial Load and Moment ( Failure Envelope )

Concrete crushesConcrete crushes before steel yields

Steel yields before concrete ycrushes

Any combination of P and M outside the envelope will cause failure.

Column Interaction Curve For Bi axial BendingColumn Interaction Curve For Bi-axial Bending

Column Design By using ACI Interaction Curves

Interaction Diagram For Axial Plus Biaxial bending Moment

Slenderness Slenderness Slenderness of

Slenderness of of

C lof

C lColumnsColumns

Euler Critical Load

The governing equation is a second order homogeneous ordinar differential eq ationordinary differential equation

02

pwwdEI

whereThe Characteristic equation is

02 pwdx

EI

Applying Boundary condition ,0,0

wy

,0,

wLy

Substituting the equation

,0w ,

LxAw sinL

Euler Critical Load

The allowable stress in a compression member depends on the slenderness ratio Leff / rand can be divided into three regions: short, intermediate, and long.and can be divided into three regions: short, intermediate, and long.

Short columns are dominated by the strength limit of the material. Intermediate columns are bounded by the inelastic limit of the member.

Long columns are bounded by the elastic limit (i.e. Euler's formula).g y ( )

The Meta-Equilibrium

Complexity in the Column DesignLoading

Load ComplexityLoad Complexity

P Mx My

P Mx

P

ShapeShape

Shape

Short

ppComplexityComplexity

Long

Most SimpleProblem

V. Long

LengthSlenderness Slenderness

What is Slenderness EffectWhat is Slenderness EffectMoment Amplification

eP

Capacity R d ti

P

I

II

Reduction

( )e

f(Mc)CP

C

M

Column Capacity (P-M)II : Mc = P(e + Long Column

I. Mc = P.eShort Column

Buckling in two major axis Effective length on support conditions:

F i P i FTop End

F i x P i n F r e e

F i x 0 . 5 0 . 8 2 . 0

P i 0 8 1 0 U t b lom

P i n 0 . 8 1 . 0 U n s t a b l e

F r e e 2 . 0 U n s t a b l e U n s t a b l eBot

toEn

d

Alignment charts for effective length factors k.

CC2B1 B2

C1Lc

B4B3Lc

C3

ColumnslEI )/(

IncreasesKIncreaseKBeamslEIColumnslEI C

,)/()/(

Effective length of Non-sway Frame:g yEff ti l th f S FEffective length of Sway Frame

Determination of K

• Members Part of Framed Structure

2120

m GforGGK 21

20 mm GforGK

2)1(90 GfGKUnbracedFrames 2)1(9.0 mm GforGKFrames

010508500.1)(05.07.0

BT

GkGGKBraced

Frames(smaller of)

ColumnsLEI C )/(

0.105.085.0 mGk(smaller of)

T EndTopG

IncreasesKIncreaseGGKBeamsLEIColumnsLEIG C

,)/(

)/(

BTm

B

T

GandGofMinimumGEndBottomG

ndopG

, BTm f

Compression plus Bending, (Bent in single curvature)

Compression plus Bending, (Bent in double curvature)

Fixed portal frame, laterally unbraced.

Fixed portal frame, laterally braced. p , y 1 The strength of concentrically loaded columns decreases with increasing slenderness1. The strength of concentrically loaded columns decreases with increasing slenderness ratio kl/r.

2 In columns that are braced against sidesway or that are parts of frames braced against2. In columns that are braced against sidesway or that are parts of frames braced against sidesway, the effective length kl, i.e., the distance between inflection points, falls between 1/2 and I, depending on the degree of end restraint.

3. The effective lengths of columns that are not braced against sidesway or that are parts of frames not so braced are always larger than l, the more so the smaller the end restraint. In consequence, the buckling load of a frame not braced against sidesway is alwaysconsequence, the buckling load of a frame not braced against sidesway is always substantially smaller than that of the same frame when braced.

C l i

1 In flexural members the presence of axial compression causes additional

Conclusion:

1. In flexural members, the presence of axial compression causes additionaldeflections and additional moments Py. Other things being equal, the additionalmoments increase with increasing slenderness ratio kl/r.

2. In members braced against sidesway and bent in single curvature, the maxima ofboth types of moments, Mo and Py, occur at the same or at nearby locations and

f ll ddi i hi l d l ifi i If h Mare fully additive; this leads to large moment magnifications. If the Mo momentsresult in double curvature (Le., in the occurrence of an inflection point), the oppo-site is true and less or no moment magnification occurs.

3. In members in frames not braced against sidesway, the maximum moments ofboth kinds, Mo and Py, almost always occur at the same locations, the ends of theboth kinds, Mo and Py, almost always occur at the same locations, the ends of thecolumns; they are fully additive, regardless of the presence or absence of aninflection point. Here, too, other things being equal, the additional deflectionsand the corresponding moments increase with increasing kl/rand the corresponding moments increase with increasing kl/r.

Factors Effecting Slenderness Effect

“Effective” Length Actual Length End Framing and Boundary Conditions Lateral Bracing Conditions

“Effective” Stiffness Cross-sections Dimensions and Proportions Reinforcement amount and Distribution

M d l f El i i f C d S l Modulus of Elasticity of Concrete and Steel Creep and Sustained LoadsL d Loads Axial Load End Moments and Moments along the Length End Moments and Moments along the Length

What is Sway …?

Sway is dependent upon the structural configuration as well as type of loadingas well as type of loading

N S S Ma be S a

0.1

Non Sway Sway May be Sway

For Non-sway Frames (Very rigid or braced) 0.10.1

ns

s

For Sway Frames (Open frames, not braced, Depends on loads also) 01

0.1s

Depends on loads also) 0.1ns

… More on Sway

Braced Column (Non-Sway)

• Most building columns may be considered “Non-Sway” for gravity loads

Unbraced Column (Sway)

• More than 40% of columns in buildings are “Non-Sway” for lateral loads• Unbraced Column (Sway) lateral loads

• Moment Magnification forMoment Magnification for “Sway” case is more significant, more complicated and more i t timportant

Criteria for Braced or Non Braced

P

CU

U

lVPQ 0

PPPP UUUU ......321 PU1 PU2 PU3 PU4

T

VVVV

BT

0

VU1VU1VU1VU1

lC

averageheightstoreyClearlVVVV

C

UUUU

.......321

B

CSQcaseswayNonQIf

050:05.0

CaseSwayQ :05.0

ACI CRITERIA FOR SLENDERNESS EFFECTS IN COLUMNS

1. For compression members braced against sidesway (i.e., in nonswaystructures) the effects of slenderness may be neglected when k1/r=34 -structures), the effects of slenderness may be neglected when k1/r=34 -12M1/M2, where 34 - 12M1/M2 is not taken greater than 40.

2. For compression members not braced against sidesway (i.e., in sway structures), the effects of slenderness may be neglected when k1u/r is less than 22than 22.

ACI Moment Magnification For Non-Sway Frame

nsnsm MM

g y

Where Moment Magnification Factor ns Is-

1C 1

75.01

C

u

mns

PP

C

Where

2

2

)()(

UC Kl

EIP

Where

4.014.06.0 MCm

Moment Correction Factor

2Mm

12 MM and

“+’ When bent in single c r at re“+’ When bent in single curvature“-’ When bent in single curvature

ACI Code provides that the factored moment M2ACI Code provides that the factored moment M2 not be taken less than M2,min = Pu(0.6 + 0.03h)

The Cm Factorm

The Moment and StressThe Moment and Stress Amplification Factors are derived on the basis of pin-

4.0214.06.0

MMCm

M1 M1

derived on the basis of pinended columns with single moment curvature.

2M

M1 1(Cm = 1.0)

F th M t

M2 M2

For other Moment Distribution, the correction factor C needs to be

M1/M2Positive

M1/M2Negative

factor Cm needs to be computed to modify the stress amplification.

M1 is the smaller End MomentM2 is the larger End Moment

stress amplification.

Cm = 0.4 to 1.0 M2 is the larger End Moment

More about Cm Factor 4.014.06.0 MCmm

M1M1

M2M2

2Mm

M1

M M M 0 M M M 0

M2 M1 M1 M2

M1= -M M1 = 0 M1 =M M1 =0M2 = M M2 = M M2 = M M2 = M

11 MM

01 M 11

M 01 MM

2M2M 2M 2M

Cm = 1.0 Cm = 0.6 Cm = 0.2 Cm = 0.6

Determination of Stiffness EI

AbsesgC IEIEEI

2.0

hybC

d

IE

EI

4.01

b

d

gC IEor

14.0

Attempt to include, Cracking, Variable E, Creep effect

b

3Cracking, Variable E, Creep effect Geometric and material non linearity

12

3bhIg

Ig = Gross Moment of Inertia Ise = Moment of Inertia of rebars 2

. bbse yAI

d = Effect of creep for sustained loads. = Pud/Pu

ACI Moment Magnification For Non-Sway Frame

Larger Sway Moment

Larger Non- Sway MomentFinalDesign

M t

ssnsnsm MMM g yMoment

The maximum magnified moments caused by sway loading occur at the ends of the column but those due to gravity loads may occur somewhere in theof the column, but those due to gravity loads may occur somewhere in the mid height of the column, the exact location of the latter varying depending on the end moments.

Because magnified gravity moments and magnified sway moments do not occur at the same location for this reasontwo cases involved

ssns

MMMMMM

111

ssns MMM 222

ss

ss MPMMa

) s

cu

uss

lVP

1)

0

s

cu

thenIf 5.1

ss

ss MPMMb

)

c

uP

P

75.01