ce 72.52: advanced concrete structures
TRANSCRIPT
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
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Scope, Diversity & Complexity of Column Design
Problem
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Difference Between Columns and Beams
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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?
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• Can we distinguish between a column and a beam based on its orientation?
Difference between Beam and Columns
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• 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
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• 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)
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Difference between Beam and Columns
• 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
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Complexities in Analysis and Design of Columns
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Types of Columns
Free standing single columns/piers
Column in building frame
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Types of Columns
Embedded columns
Shear walls as columns
Wall- columns
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Columns
CE 72.52 - Advanced Concrete Structures
16CE 72.52 - Advanced Concrete Structures
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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
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Iterative Design Process
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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
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• General 3D column subjected to combined axial load (𝑃𝑥) and biaxial bending moments (𝑀𝑦 and 𝑀𝑥) at both ends
General 3 D Column
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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…)
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Overall Complexity of Column Design Problem
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Complexity Space between Loading & Section
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Complexity Space between Loading & Slenderness
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Slenderness and Stability Issues in Columns
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Slenderness
𝑀 = 𝑃. 𝑒.
Constant moment
Δ = න𝑎
𝑏 𝑀
𝐸𝐼𝑑𝑥
Deflection
𝑀 = 𝑃∆
Second Order Moment
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• Curvature distribution along the length of column remains proportional to bending moment as long as moment remains below
yield point.
Slenderness
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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.
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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
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• Ratio of effective length of column to the least radius of gyration of its cross-section.
• 𝜆 =𝑘𝐿
𝑟
Effective Length Factor (K)
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Determination of K
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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
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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
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• 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
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Sway and Non-Sway
• Sway is dependent upon the
• structural configuration
• as well as type of loading
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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.
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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
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• 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”
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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
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Various Boundary Conditions
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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
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Idealization of Boundary Conditions
(a)Actual Column (b) Full Spring Model(c)Restrained Pin Model (d) Roller Spring Model
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Columns Embedded in the Soil
Evaluation of Restraining Forced of
Foundations
Determination of Free Length
Columns embedded in soil have 2 main challenges
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Columns Embedded in the Soil
• 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
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Columns Embedded in the Soil
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
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Columns Embedded in the Soil
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
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Columns Embedded in the Soil
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
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Columns Embedded in the Soil
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
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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
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Importance of Slenderness Effects
• 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
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Importance of Slenderness Effects
• 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.
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Importance of Slenderness Effects
• 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.
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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.
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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
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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
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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.
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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.
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Column Design Process Design and Procedures
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Factors Affecting Selection of Structural System
Architectural Requirements
Aesthetic Considerations
Environmental Consideration
Constructability Concerns
Maintenance Considerations
Economic Considerations
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Two-step Process; Analysis and Design
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Column Design Process
(a)Conventional linear-elastic
analysis,
(b) P-Δ analysis
(c)Full non-linear integratedanalysis and design
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Column Design Procedure (ACI-318 )
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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
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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
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Design Moment ACI 318-11
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Moment Magnification-Basic Idea
ssnsnsm MMM +=
Magnification Factor
for Moments that do
not cause sway
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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
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Moment Magnification
ssnsnsm MMM +=
Magnification Factor for
Moments that cause sway
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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
Equation 10-20ACI 318-11
Equation 10-21ACI 318-11
Sum of Critical Buckling
Load of all columns in floor
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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
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Summary of Moment Magnification (ACI-318 )
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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
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Cm and Moment Magnification for various Cases of End Moments
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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
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Overview of BS 8110 Design Procedure
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Design of Steel Columns Based on Combined Stress Ratio (AISC Code)
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Design of Steel Columns Based on Combined Stress Ratio (AISC Code)
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Design of Steel Columns Based on Combined Stress Ratio (AISC Code)
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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
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Column Section Shape and Properties
Length
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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
Cross-section = 30cmx50cm
Column Above
Length = 3m
Cross-section = 40cmx40cm
• Fixed at Base
• The column is part of a non-sway structure
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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
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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
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B40 - Bracing Conditions
• Column Cross-Section = 40cmx40cm reinforced with 6-d20
• Connecting Members
• 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
• The column is part of a non-sway structure
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B40 - Variation in kl/r
kl/r=29
kl/r=43.4kl/r=36.2
kl/r=22kl/r=11
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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
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C80 - Bracing Conditions
• Column Cross-Section = 80cm x 80cm reinforced with 6-d20
• Connecting Members
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
• The column is part of a non-sway structure
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C80 - Variation in kl/r
kl/r=11.2kl/r=5.5 kl/r=14.9
kl/r=22.4kl/r=18.6
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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
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Responsibility of Column Design
Architectural requirements and constraint may completely control the design of columns in buildings
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Responsibility of Column Design
The aesthetic considerations may over-ride the structural
considerations. (a) Design based on moment demand (b) Design
based on aesthetic demands
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Responsibility of Column Design
• 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.
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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
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Step 1: Material & Cross-Section Properties
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Step 2: Framing and Effective Length Calculations
Column Framing Conditions
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Step 2: Framing and Effective Length Calculations
Effective Length Calculator
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Step 3: Loading Conditions
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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.
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Step 5: Moment Curvature Curve
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Step 6: PM Interaction Curve
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Step 7: Stress View
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Practical Considerations for Design of RC Columns
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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
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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
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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
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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.
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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
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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
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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.
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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.
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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
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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
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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
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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
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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
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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.
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Designing for Stability
Stability of a column is
governed by the framing and
bracing congestions on the
weaker axis
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Special Cases and Considerations
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Design of Bridge Piers
Loading Considerations
Framing Considerations
Cross-Section Considerations
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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
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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
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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
CE75.08: Design of Reinforced Concrete Components
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