CE 72.52: Advanced Concrete Structures

CE 72.52: Advanced Concrete Structures

Lecture 5-Response and Design of ColumnsAugust 2018

Dr. Naveed AnwarExecutive Director, AIT Solutions|Director, ACECOMS

Affiliated Faculty, Structural Engineering

3

Column Design

CE75.08: Design of Reinforced Concrete Components

• Design of column cross-sections signifies the importance of interaction of axial load and biaxial load bending and efficiency of cross-section shape and reinforcement layout

4

Column-Definition and Usage

• Columns are one of the most important structural components.

• Historically, the symbolic value of columns or pillars has been used inliterature and art as a symbol of strength, stability and support inmany contexts

• The structural significance of columns is evident from their use inalmost every type of structural system.

• Mostly in compression after in conjunction with bending momentand almost always support other structural elements or members


5

Scope, Diversity & Complexity of Column Design

Problem


6

Difference Between Columns and Beams


7

Difference between Beam and Columns

• Generally, It is understood that horizontal load carrying members are beams and vertical members are columns

• What about an inclined member at an angle of 45° subjected to various loading combinations?

• Should that member be designed as beam or column?


8

• Can we distinguish between a column and a beam based on its orientation?



9

• As per ACI-318, if the applied axial load is greater than 10% of the nominal axial load capacity of the cross-section, then the member

should be designed as a column, otherwise as a beam

Definition of Column and Beam for Design Purposes


10

• Difference between detailing of reinforcement between beams and columns. (a) section designed as a beam, (b) same section designed

as a column for same moment

Difference between Detailing of Reinforcement (Beam and Columns)


11


• ACI-318 definition can be used as a general guideline and may bereasonable for members subjected to no axial loads (pure bending)and those subjected to fairly high axial loads.

• A great deal of engineering judgment is needed in borderline caseswhere the distinction between beam and column behavior is notclear.

• As a more general guideline, members with significant bendingmoments, axial force, shear force and torsion is present, should bedesigned to satisfy the more restrictive requirements for both, as abeam and as a column


12

Complexities in Analysis and Design of Columns


13

Types of Columns

Free standing single columns/piers

Column in building frame


14

Types of Columns

Embedded columns

Shear walls as columns

Wall- columns


15

Columns

CE 72.52 - Advanced Concrete Structures

16CE 72.52 - Advanced Concrete Structures

17

Main Design Problem

1. Determine the appropriate dimensions.

2. Determine the cross-section shape

3. Determine the material characteristics,

4. Determine the reinforcement amount

5. Distribution based on a set of applied actions.

6. Column geometry and framing conditions


18

Iterative Design Process


19

Critical Factors for Column Design

Loading type and

level of load

Cross-section

materials, shape and

layout

Column length,

bracing and stability issues

DuctilityAxial

shorteningShear

demand


20

• General 3D column subjected to combined axial load (𝑃𝑥) and biaxial bending moments (𝑀𝑦 and 𝑀𝑥) at both ends

General 3 D Column


21

Complexity in Column Design

• Loading

+P, -P, Mx, My

• Slenderness

• Length (Short, Long, Very Long)• Bracing (Sway, Non-Sway, Braced, Unbraced)• Framing (Pin, Fixed, Free, Intermediate..)

• Section

• Geometry (Rectangular, Circular, Complex..)• Materials (Steel, Concrete, Composite…)


22

Overall Complexity of Column Design Problem


23

Complexity Space between Loading & Section


24

Complexity Space between Loading & Slenderness


25

Slenderness and Stability Issues in Columns


26

Slenderness

𝑀 = 𝑃. 𝑒.

Constant moment

Δ = න𝑎

𝑏 𝑀

𝐸𝐼𝑑𝑥

Deflection

𝑀 = 𝑃∆

Second Order Moment


27

• Curvature distribution along the length of column remains proportional to bending moment as long as moment remains below

yield point.

Slenderness


28

Buckling

• Buckling is a sudden lateral failure of an axially loaded member incompression, under a load value less than the compressive load-carrying capacity of that member.

• The axial compressive load corresponding to this mode of failure isreferred to as critical buckling load.

• A load greater than critical load results in unpredictable and suddendeformation of member in lateral direction.


29

Euler Buckling Formula

• 𝑃𝑐𝑟 =𝜋2𝐸𝐼

𝑘𝐿 2

• 𝑃𝑐𝑟 is the critical buckling load

• 𝐿 is the length of column

• 𝑘 is the effective length factor

• 𝐸𝐼 is the cross-sectional stiffness

• Interesting Observation:

• There is no role of compressive strength of material in determining thecritical buckling load. It is only dependent on elastic modulus of materialand moment of inertia of cross-section and effective length of column


30

• Ratio of effective length of column to the least radius of gyration of its cross-section.

• 𝜆 =𝑘𝐿

𝑟

Effective Length Factor (K)


31

Determination of K


32

More About Factor K

• How about “I” Gross? Cracked? Effective?

• ACI Rules Beams I = 0.35 Ig, Column I = 0.7Ig

• E for column and beams may be different

IncreasesKIncreaseK

BeamslEI

ColumnslEI C

,

)/(

)/(

=

)(

)(

21

21

BB

CCT

IIE

IIEExample

+

+==

C2

C3

C1

B1 B2

B4B3

Lc


33

Classification of Columns Based on Slenderness Ratio

Short Columns

• Steel columns with slenderness ratio less than 50

• For RC columns, Length/depth < 10

Intermediate Columns

• Steel columns with slenderness ratio between 50-200

Slenderness Columns

• Steel columns with slenderness ratio greater than 50-200

• For RC columns, Length/depth > 10


34

• Based on degree of fixity or release at the ends, a frame can be classified either as “sway” or “non-sway”

Sway and Non-Sway

Sway Conditions

•When the two ends of the column are not significantly braced against lateral movements relative to each other

Non-Sway Conditions

•When the two ends of the column are sufficiently braced against the movement in lateral direction


35

Sway and Non-Sway

• Sway is dependent upon the

• structural configuration

• as well as type of loading


36

Sway and Non-Sway

• Design of columns for sway and non-sway frames will differ due todifferent assumptions for boundary conditions.

• The effective length factor for braced columns varies from 0.5 to 1.0,whereas for un-braced columns, it can vary from 1 to infinity.

• ACI 318 (Section 10) allows the columns to be considered ascomponent of non-sway (braced) frame if the additional momentsinduced by second-order effects are not greater than 5% of the initialend moments.


37

Sway and Non-Sway

• Practically, the distinguishing factors between braced and un-bracedcolumns may not remain constant throughout the intended life ofcolumn.

• In real structures, almost all columns are subjected to normal lateralloads and they undergo some lateral deflections.

• It is difficult to encounter columns that do not undergo any relativedisplacement at the two ends in some stage during the lifetime ofthe structure. However, “very small” lateral displacements may notnecessarily make the column un-braced


38

• Appreciable relative moment of two ends of column

• Sway Limits

Sway

c

BT

lSway

−=0

05.1)

05.0)

6)

0

M

Mc

lV

Pb

EIEIa

m

CU

U

ColumnswallsBracing

DT

DB

lc

Frame considered as “Non-Sway”


39

More on Sway

• Braced Column (Non-Sway)

• Unbraced Column (Sway)

• Most building columns may beconsidered “Non-Sway” forgravity loads

• More than 40% of columns inbuildings are “Non-Sway” forlateral loads

• Moment Magnification for“Sway” case is more significant,more complicated and moreimportant


40

Various Boundary Conditions


41

Idealization of Boundary Conditions

• End boundary conditions for the column in a frame can be represented bya spring system.

• Each spring represents the stiffness of the members attached to the endsof the column.

• The true restraining conditions in a three dimensional building arepractically very difficult to evaluate. However, a simplified model can beconsidered along two principal planes of the structure (or any arbitraryplane for that matter).

• On this restraining plane, the degrees of freedom at ends can be replacedby springs


42

Idealization of Boundary Conditions

(a)Actual Column (b) Full Spring Model(c)Restrained Pin Model (d) Roller Spring Model


43

Columns Embedded in the Soil

Evaluation of Restraining Forced of

Foundations

Determination of Free Length

Columns embedded in soil have 2 main challenges


44


• Challenge 1: Evaluation of Restraining Force of Foundations

• To determine the stiffness of the foundation, we need to realize thatthe foundation and the supporting soil together act as a complexspring system which may be elastic, inelastic or even plastic.

• Many engineers use arbitrary values of foundation stiffness, or morecorrectly, the ratio of foundation to column stiffness


45


Challenge 2: Determination of Free Length

Case 1: Single Column

Depending on the size of columns, type of soil andpresence of lateral loads, the column may becomefixed against rotation (or effectively fixed) at a depthof about 3-5 times the average dimension of columncross-section, below the compact or stable soil level.In case of columns or piers in waterways, the soilerosion, silting and scour may keep changing thislevel


46


Case 2: Single Column

The embedded depth less than the fixity depth canbe considered as clear length. Another factor whichmay make the problem more complex is the amountof restraint or fixity provided by back fill andcompacted soils


47


Case 3: Column size below the soil level is largerthan the main column

Effect of larger cross-section as well as larger restraintdue to soil needs to be taken into account. At thesame time because of the larger column near thefooting, it is not immediately clear as to whichcolumn dimensions should be considered indetermining the effective length. In this case,concept of inverse stiffness (or flexibility) to determinethe stiffness of the variable column


48


Case 3: Presence of a concrete floor which is not rigidly connected to the column

The compact and well constrained compactfilling under the floor provide further restraintwhich is numerically difficult to evaluate. In thiscase, consider the column to be hinged fordetermination of slenderness effects. However,this hinged condition should also beconsidered in modeling of the frame to obtainconsistent and compatible moment in thecolumn


49

Importance of Slenderness Effects

• Slenderness effects in columns of very low rise buildings may be more critical than in medium and high-rise buildings.

• Example 1: Medium Rise Buildings

• Column spacing = 6m x 6m

• Story height = 3 m.

• No. of floors = 30 floors,

• Appropriate column size = 0.8m.

• Effective length factor of 1.0

• we get a kl = 20,

• This value is fairly small and also column moment magnification will be small and thus, slenderness effectsare negligible. Also, the column is most likely to be braced due to the presence of shear wall/s, elevationshafts and other bracing systems to resist the lateral loads


50


• For the same example if the No. of floors is 3, the column size is likely tobe about 0.4 m.

• In such case column will most likely to be un-braced in the absence of anyshear walls or elevator shafts and the moments due to lateral loads aregoing to be significant in proportion to the axial load.

• The effective length ratio will be more than 1, e.g. 1.5 or so,

• Therefore the moment magnification in this case will be significant and islikely to affect the column design. Due to high eccentricity, the design willbe moment controlled and hence directly affected by the momentmagnification


51


• In general, the corner and edge columns in buildings are moreaffected by slenderness effects than the interior columns and this isdue to several reasons.

• The corner columns are often subjected to high biaxial moments,due to gravity as well as lateral loads. The axial load is relativelysmall, so the moment governs the design.

• The effective length factor is generally larger due to smaller totalstiffness of beams connected at the ends of the columns. Therefore,the moment magnification may be higher and may affect the designmore significantly than for interior column.


52


• For laterally un-braced frames or sway loading conditions, the momentmagnification may be higher and may affect the design more significantlythan for interior column.

• For braced frames or non-sway load conditions, the interior columns mayexperience greater moment magnification due to the presence of highaxial loads.

• In general, the moment magnification of braced or non-sway columns isgreatly affected by the ratio between the axial load and the criticalbuckling load, whereas for sway or un-braced columns, it is also affectedby the amount of lateral load and the relative lateral drift ratio.


53

Effect of Column Slenderness on Overall Frame Behavior

• Slenderness effects magnify the moments, with a correspondingmagnification of deformations and deflections as well.

• This additional deformation when translated to the ends of aframed structure, will change the elastic or first order deformationcharacteristic of the overall frame, including other column andbeams.

• This will, in turn, change the moments, shear and axial forces inother members of the frame. The beams and columns adjacent tothe column may also undergo the magnification.


54

Effect of Column Slenderness on Overall Frame Behavior

• However, in a real structure several columns may be undergoingthe moment magnification at the same time and hence, theeffects are cumulative.

• The problem is further complicated by the fact that the momentsmodified by moment magnification are further magnified due toslenderness and affect the moments in other member.

• So, the overall 𝑃 − ∆ effect in the frame becomes highly non-linear


55

When Slenderness Should be Considered ?

• The simple answer to this question would be “almost always”.

• ACI 318 (Section 10) specifies that the slenderness effects may beignored for compression members braced against side-sway whenthe slenderness ratio 𝜆 = 𝑘𝐿/𝑟 is less than 34-12(𝑀1𝑏/𝑀2𝑏) and forcompression members not braced against side-sway, 𝜆 is less than22.

• For 𝜆 values higher than these prescribed limits, the slendernesseffects must be considered. 𝑀1𝑏 and 𝑀2𝑏 are the smaller and largerfactored end moments respectively


56

General Guidelines to Facilitate the Design of Columns

1. The slenderness effects may be more pronounced in low-risebuildings without shear walls and bracings, and in some casesupper floors of tall buildings.

2. Un-braced frame or sway loading conditions in columns arelikely to produce larger slenderness effects than in braced ornon-sway columns unless the nominal axial stress is higherthan about 50% of buckling stress.

3. Higher slenderness ratio is likely to produce higher slendernesseffects, but not necessarily. The actual amount of axial loadand moment value and distribution are also important.


57

General Guidelines to Facilitate the Design of Columns

4. Most practical column proportion in low to medium rise buildings

will fail in flexural bucking mode and will undergo some moment

magnification when axial load approaches the cross-section

capacity.

5. It is always safer to include the slenderness effects than to exclude

them.

6. Columns of narrow cross-sections, or un-symmetrical cross-sections

may have moment magnification in the lateral direction

7. The presence of transverse bracing beams can affect the primary

moment magnification if the bracing is connected to lateral

bracing systems.


58

Column Design Process Design and Procedures


59

Factors Affecting Selection of Structural System

Architectural Requirements

Aesthetic Considerations

Environmental Consideration

Constructability Concerns

Maintenance Considerations

Economic Considerations


60

Two-step Process; Analysis and Design


61

Column Design Process

(a)Conventional linear-elastic

analysis,

(b) P-Δ analysis

(c)Full non-linear integratedanalysis and design


62

Column Design Procedure (ACI-318 )


63

Moment Magnifier Method

• An Approximate Method to account for Slenderness Effects

• May be used instead of P-D Analysis

• Not to be used when Kl/r > 100

• Separate Magnification for Sway and Non-Sway Load Cases

• Separate Magnification Factors for moment about each axis

• Moment magnification generally 1.2 to 2.5 times

• Mostly suitable for building columns


64

When to Use Moment Magnification

• According to ACI 318-11 Code:

• For Braced Frames (Non-sway)

• Kl/r > 34-12(M1b/M2b)

• For Un-braced Frames (Sway)

• Kl/r > 22

• Or When Secondary Moments become Significant

• These provisions do not consider other factors, such as P, lateral

deflection, lateral loads, section material or properties


65

Design Moment ACI 318-11


66

Moment Magnification-Basic Idea

ssnsnsm MMM +=

Magnification Factor

for Moments that do

not cause sway


67

Calculation of dns (Non-Sway)

C

u

mns

P

P

C

75.01−

=

Moment curvature

Coefficient

Applied column load

2

2

)(

)(

U

CKl

EIP

=

Critical buckling load

Effective Length Factor

Flexural Stiffness

Equation 10-12

ACI 318-11

Equation 10-13

ACI 318-11


68

Moment Magnification

ssnsnsm MMM +=

Magnification Factor for

Moments that cause sway


69

Determination of ds (Sway)

1

75.01

1)

5.1

0.11

1) 0

−

=

=

−=

c

us

s

cu

us

P

Pb

thenIf

lV

PQwhere

Qa

Sway Quotient

Equation 10-10ACI 318-11



Sum of Critical Buckling

Load of all columns in floor


70

Sway Quotient Q and Pc

cu

u

lV

PQ 0=

Sum of column loads in one

floor

Relative displacementDetermined from Frame Analysis

Story shear (sum of shear in

all columns)

Storey height

2

2

)(

)(

U

CKl

EIP

=

Flexural Stiffness

Effective Length Factor


71

Summary of Moment Magnification (ACI-318 )


72

Summary of Moment Magnification (ACI-318 )

• 𝑀𝑛𝑠 Larger non-sway moment

• 𝑀𝑠 Larger sway moment

• 𝛿𝑛𝑠 The moment magnifier for non-sway condition

• 𝛿𝑠 The moment magnifier for sway condition

• 𝐶𝑚 Moment correction factor relating the actual momentdiagram to that of a uniform equivalent moment diagramhaving same peak moment.

• 𝑃𝑢 Total factored vertical load

• 𝑃𝑐 Critical buckling load

• 𝑉𝑢 Horizontal story shear


73

Cm and Moment Magnification for various Cases of End Moments


74

P-Delta Analysis in SAP2000

• The program can include the P-Delta effects in almost all Non-linear analysistypes

• Specific P-Delta analysis can also be carried out

• The P-Delta analysis basically considers the geometric nonlinear effects directly

• The material nonlinear effects can be handled by modification of cross-sectionproperties

• The Buckling Analysis is not the same as P-Delta Analysis

• No magnification of moments is needed if P-Delta Analysis has been carried out


75

Overview of BS 8110 Design Procedure


76

Design of Steel Columns Based on Combined Stress Ratio (AISC Code)


77



78



79

Parametric Study

• Computation of Slenderness Effects for 3 column sections for different axial load and lengths.

• A = 30 x 30 cm

• B = 40 x 40 cm

• C = 80 x 80 cm

• Braced (Non-Sway) frames assuming shear walls prevent large lateral displacements


80

Column Section Shape and Properties

Length


81

A30-Bracing Conditions

• Column Cross-Section = 30cm x 30cm reinforced with 6-d20

• Connecting Members

Beam on Right:

Length = 5 m

Cross-section = 30cmx50cm

Beam on Left:

Length = 3 m


Column Above

Length = 3m


• Fixed at Base

• The column is part of a non-sway structure


82

A30 - Variation in kl/r

kl/r=14.5 kl/r=28.9 kl/r=38.1

kl/r=47.7 kl/r=57.3


83

A30 – Moment Magnification

0

0.5

1

1.5

2

2.5

3

0.20 0.30 0.40 0.50 0.60 0.70 0.80

Mo

me

nt

Ma

gn

ific

atio

n F

ac

tor

Variation of Moment Magnification with Axial Load for

Various kl/r ratios

kl/r=28.9

kl/r=38.1

kl/r=47.7

kl/r=57.3

kl/r=14.5

Normalized Axial Load Pu/Pno

30

cm

30 cmCE75.08: Design of Reinforced Concrete Components

84

B40 - Bracing Conditions

• Column Cross-Section = 40cmx40cm reinforced with 6-d20


• Beam on Right:

• Length = 5 m

• Cross-section = 30cmx50cm

• Beam on Left:

• Length = 3 m• Cross-section = 30cmx50cm

• Column Above

• Length = 3m

• Cross-section = 40cmx40cm

• Fixed at Base



85

B40 - Variation in kl/r

kl/r=29

kl/r=43.4kl/r=36.2

kl/r=22kl/r=11


86

B40 – Moment Magnification

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Mo

me

nt

Ma

gn

ific

atio

n F

ac

tor

Normalized Axial Load Pn/Pu

Variation of Moment Magnification with Axial

Load for Various kl/r ratios

kl/r=11

kl/r=22

kl/r=29

kl/r=36.2

kl/r=43.4

40 cm

40 cm


87

C80 - Bracing Conditions

• Column Cross-Section = 80cm x 80cm reinforced with 6-d20


Beam on Right:

Length = 5 m


Beam on Left:

Length = 3 m


Column Above

Length = 3m


• Fixed at Base



88

C80 - Variation in kl/r

kl/r=11.2kl/r=5.5 kl/r=14.9

kl/r=22.4kl/r=18.6


89

C80 – Moment Magnification

0.99

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

0.20 0.30 0.40 0.50 0.60 0.70 0.80

kl/r=5.5

kl/r=11.2

kl/r=14.9

kl/r=18.6

kl/r=22.4

80 cm

80 cm

Variation of Moment Magnification with Axial Load for Various kl/r ratios

Mo

me

nt

Ma

gn

ific

atio

n F

ac

tor

Normalized Axial Load Pn/Pu


90

Responsibility of Column Design

Architectural requirements and constraint may completely control the design of columns in buildings


91


The aesthetic considerations may over-ride the structural

considerations. (a) Design based on moment demand (b) Design

based on aesthetic demands


92


• Design of columns, and in fact the whole structure, is not really in

the hands of structural engineers and designers.

• Design of members such as columns starts long before the analysis

has been carried out.

• Consideration of moments, axial loads, and slenderness effects

comes in at a much later stage, when not much can be done tooptimize the design or to make it effective and efficient.


93

Column Design Example using CSI COL

𝑓𝑐′ = 40 𝑀𝑃𝑎

𝑓𝑦 = 400 𝑀𝑃𝑎

𝑃𝑢 = 1000 𝑘𝑁 𝑀𝑢𝑥 = 200 𝑘𝑁 (At bottom)

𝑀𝑢𝑥 = 120 𝑘𝑁 (At Top)

𝑀𝑢𝑦 = 250 𝑘𝑁(At bottom)

𝑀𝑢𝑦 = 120 𝑘𝑁(At Top)

Given


94

Step 1: Material & Cross-Section Properties


95

Step 2: Framing and Effective Length Calculations

Column Framing Conditions


96

Step 2: Framing and Effective Length Calculations

Effective Length Calculator


97

Step 3: Loading Conditions


98

Step 4: Calculation of Capacity Ratio

CSI Col evaluates the capacity ratio which is defined as ratio of demand over the

capacity of the cross-section. Is this ratio is less than 1, then design is OK else the

design needs to be revised.


99

Step 5: Moment Curvature Curve


100

Step 6: PM Interaction Curve


101

Step 7: Stress View


102

Practical Considerations for Design of RC Columns


103

Selection of Column Cross-Section

• Size and shape may be restricted due to architectural and space

constraints.

• High axial load in lower floors of high-rise buildings requiring the use

of high-strength concrete

• Consideration of differential axial shortening and slenderness

effects, especially in sway (un-braced) frames, are generally

important.

• Biaxial moments in the corner columns due to gravity loads and all

columns due to diagonal wind or seismic load direction my make

them critical from design point of view


104

Guidelines for Selection of Initial Dimensions

1. Use square, rectangular or circular columns. Circular columns are

especially suitable for seismic prone areas where high strength and

ductility is needed in all directions.

2. Avoid shapes requiring complicated formwork unless it can be reused

several times.

3. Use oblong shapes when the predominant moment in one direction is

clearly much larger than in the other direction, however the aspect ratio

of the cross-section should be reasonable (0.25 < h/b < 4).

4. Use hollow shapes or I shape or H shape when moment is much larger as

compared to axial load


105

Guidelines for Selection of Initial Dimensions

5. Avoid highly unsymmetrical and open shapes (C, Z, L, etc.)

6. For parking and no-wall spaces in buildings, use circular orpolygonal columns whereas use square or rectangular columns forclosed and partitioned spaces

7. For high bridge piers, use hollow rectangular, circular or polygonalbox sections and give special consideration to aesthetic impact ofshape


106

Selection of Concrete Strength

Columns in Tall Buildings

• Generally, highest strength concrete for columns, is used as the primary action is the axial load

For High Bridge Piers & Columns Subjected to Small Load and Large Moments:

• Medium strength concrete is generally used

Columns Submerged in Water or in Aggressive Environments

• Medium strength concrete is generally used.


107

Selection of Steel Strength

• Yield strength of rebars affects moment capacity more than theaxial load capacity, especially for tension-controlled sections.

• Higher strength rebars generally results in a section that has lowerstiffness than a column using lower strength rebars.

• If stiffness is a primary concern, a lower strength steel may beadvantageous, unless a higher than required amount of steel isused for high-strength bars.

• In general, higher strength steel should be used with higher strengthconcrete for greatest overall economy in the design of columns


108

Size and Layout of Longitudinal Bars

• Layout of a specific number of rebars substantially affectsthe moment capacity of section and plastic centroid

• A symmetrical section with unsymmetrical rebararrangement may be subjected to biaxial bending, evenif the loads are concentric or are located along any ofthe principal axis.

• Generally, it is recommended to use the largest practicalbar size because of ease of fabrication, checking andconcreting


109

Size and Layout of Longitudinal Bars

1. Use atleast one bar on each acute angle corner.

2. The bars should be located with due consideration to thepredominant direction and magnitude of moment.

3. Symmetrical rebars should be placed in symmetrical sectionsunless a clear unidirectional moment is present.

4. Generally, large diameter bars are used in the corners and smallerdiameter are used in the sides to maintain maximum spacing limits.

5. At least one bar should be placed on each corner to allow for theproper placement of transverse reinforcement.


110

Size and Layout of Transverse Bars

• Transverse rebars affects the shear capacity of column andconfinement of concrete.

• A well-confined concrete may have as much as twice thefailure strength than that of an unconfined concrete.

• Performance of columns subjected to cyclic loads can beenhanced significantly by using proper transverse rebars.

• Spacing & diameter of transverse bars also controls thebuckling of the longitudinal bars and hence, preventspremature failure.


111

Size and Layout of Transverse Bars

1. Start the transverse rebar design based on shear demand.

2. Select lateral ties based on the relative magnitude of loads and moments(tension or compression control).

3. Provide closer longitudinal & lateral spacing in the moment hinging regions forbetter ductility.

4. Spiral reinforcement is more effective than ties for enhancing the axial loadcapacity.

5. For large columns, it is not necessary to provide full length intermediate ties.Embedment of ties should be just enough to anchor the tie in the compressedarea.

6. Use smaller diameter ties for smaller bond and anchorage requirement andcloser spacing.

7. Generally, a transverse bar should tie alternate longitudinal bar


112

Factors Producing Bending Moment in Columns

1•Rotation of frame joints due to loads applied to beams

2•Rotation of frame joints due to lateral load on frames or direct application of force to

the ends of cantilever column

3•Direct application of loads within the column height in a frame

4•Eccentricity of axial loads supported by columns

5•Unsymmetrical shape and reinforcement layout in column cross-sections subjected to

concentric loads

6•Secondary P-∆ moment due to the slenderness effects

7•Eccentricity of load due to imperfections in column construction


113

Effect of Loading in Column Design

• In building and frame design for gravity loads only, shearforce is often not critical for a column.

• Tension is generally not critical and often not consideredin design, except for special tie or hanger columns.

• Torsion may be present in some columns, but because ofthe enhanced shear strength of concrete undercompression, design for torsion is usually not carried out


114

Effect of Loading in Column Design

• For frames resisting lateral loads, shear in columns could besignificant and may need to be explicitly considered anddesigned for such column may also be subjected to tension insome cases.

• Due to the direct axial-flexural interaction, the capacity of thecolumn depends on the absolute values, relative magnitudesand directions of the axial loads and the moments.

• The column shape, proportion, arrangement of rebars etc.,should be selected on the basis of predominant loading


115

Strength Vs Stability in Columns

• Strength relates to the materialfailure.

• Failure in strength is defined interms of the load carryingcapacity of the member orcross-section and is computedfrom the material and cross-section parameters

• Stability relates to the overallmember or structural failure.

• Failure in stability is defined asdeformations of a structuralmember or structuralcomponent, becomes so largethat it becomes un-useable,

STRENGTH STABILITY


116

Designing for Strength

• Strength capacity ratio should be less than one, meaning

that the section capacity for all action sets should be

more than the applied actions.

• Entails the proportioning of the cross-section, selection of

appropriate materials, and proper placement of

reinforcement etc.

• Proportioning for strength, does not ensure proper

serviceability, stability, ductility and performance.


117

Designing for Stability

Stability of a column is

governed by the framing and

bracing congestions on the

weaker axis


118

Special Cases and Considerations


119

Design of Bridge Piers

Loading Considerations

Framing Considerations

Cross-Section Considerations


120

Design Shear Walls as Columns

• Main consideration is the validity of the basic assumptions made inthe derivation of capacity or stress resultant equations.

• Main assumptions is that the plane sections remains plane afterdeformation, or in other words the assumption of linear straindistribution across the entire cross-section.

• Strain tends to be higher near the edges and corners and hencehigher concentration of rebar at the corners and edges producesmore efficient shear wall design


121

Design of Piles

• Soil profile

• Pile end bearing and soil condition at base

• Construction method

• Shape of pile

• Pile Inclination

• Pile to Pile spacing

• Lateral load and negative skin friction

• Scour depth

• Pile cross section

• Pre-Stressing

• Framing conditions

• Large variation in moment

Geotechnical Aspects Structural Aspects


122

Conclusion

• The effective, economic, aesthetic and safe design ofcolumn cross-sections is one of the fundamental featuresof overall structural design and detailing process.

• Overall design process as well as the code-basedprocedures are intended to follow ultimate strengthdesign philosophy.

• One of the key parameter for safe design of columns,subjected to lateral dynamic loads, is the provision ofductility


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CE 72.52: Advanced Concrete Structures

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