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Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns
LECTURE # 1
1. COLUMN:
It is a vertical member which is primarily subjected to axial compression in which
major deformation is shortening.
2. TYPES OF COLUMNS:
i. Classification on the Basis of Shape:
• Square section.
• Rectangular section.
• Circular section.
• L-section.
• T-section.
Fig.1 Classification on the Basis of Shape
1
Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns
ii. Classification on the Basis of Reinforcement:
• Tied Columns:
These columns have the bars braced or tied at close intervals by close
loops called ties.
• Spiral Columns:
These columns have the bars and the core concrete wrapped with a closely
spaced helix.
• Composite Columns:
These columns consists of a structural steel or cast iron column encased in
concrete reinforced with both longitudinal and transverse reinforcements.
• Pipe Columns or Concrete Filled Steel Tubes:
These columns are circular, rectangular or square hollow sections filled
with concrete without any additional reinforcement.
Fig.2(a) Classification on the Basis of Reinforcement
2
Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns
Fig.2(b) Classification on the Basis of Reinforcement
iii. Classification on the Basis of Type of Loading:
• Concentrically Loaded Columns:
When the resultant of the load coincides
with the centroid of the cross-section, the column
is said to be concentrically loaded column. Fig. 3
shows a concentrically loaded column.
• Eccentrically Loaded Columns:
When the resultant of the load does Fig.3 Concentrically Loaded
not coincide with the centroid of the Column
cross-section, the column is said to be
eccentrically loaded column. There are two
types of eccentrically loaded columns;
1. Uni-axially eccentrically loaded columns. (Fig. 4(a))
2. Bi-axially eccentrically loaded columns. (Fig. 4(b))
3
Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns
Fig.4 Eccentrically Loaded Columns
• Sources of Eccentricity in Columns:
Eccentricity is due to following three reasons;
1. Eccentric loading. (Fig. 5(a))
2. Initial crookedness. (Fig. 5(b))
3. Out-of-plumbness. (Fig. 5(c))
Fig.5 Sources of Eccentricity in Columns
4
Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns
3. CLASSIFICATION OF COLUMNS ACCORDING TO ACI CODE:
• Short Column:
In short columns there are no 2nd
order effects and the failure is due to
crushing of concrete without any instability. Moment magnification chances are
very less in such columns because radius of gyration is more and length is small.
2
1
1234
M
M
r
lK u
−≤
Where,
K = Effective length factor taken from alignment charts.
M1 = Magnitude of smaller end moment with sign.
M2 = Magnitude of larger end moment with sign.
2
1
M
M
= 0, for concentrically loaded columns.
2
1
M
M
= +ve, when member is bent in single curvature.
2
1
M
M
= −ve, when member is bent in reverse curvature.
• Slender Columns:
These columns fail due to buckling, instability
or 2nd
order effect. The failure load is less than that of
a short column. As length of column increases, the
probability of failure due to buckling increases.
4. TYPES OF REINFORCEMENT IN COLUMNS:
• Longitudinal Steel:
It is that steel which is present along the length of the column. Following
are the various purposes of longitudinal reinforcement;
1. The main function of longitudinal reinforcement is to prevent creep and
shrinkage in concrete.
5
Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns
2. It provides resistance against lateral bending, cracking and reduction of
moment of inertia value.
3. It reduces the size of the column.
• Transverse Steel:
1. It provides confinement to the inner concrete or core concrete i.e. the concrete
which is present inside the longitudinal reinforcement. Confinement provides
ductility and it also increases the strength of the concrete.
2. Transverse steel reduces the chances of buckling of longitudinal steel.
3. It holds the longitudinal steel in position during casting
4. Transverse steel provides resistance against shear.
5. TYPES OF TRANSVERSE REINFORCEMENT:
• Ties or Transverse Ties:
Lateral ties are used in the columns because of lesser construction cost and
ease of placement.
• Spiral Reinforcement:
Spiral columns are used where we need more ductility i.e., in earthquake
zones. Spirals are mostly provided in circular columns. Spiral columns sustain
maximum load at excessive deformation and thus prevent the complete collapse
of the structure before the total redistribution of moments and stresses is
complete. The disadvantage of spiral reinforcement is that it is very difficult to
place in the field, so, due to this reason its use is practically limited.
6. CAPACITY OF CONCENTRICALLY LOADED SHORT COLUMNS:
Steel always yields first because it is lesser in amount and due to pure
compression it is yielded.
εcu = 0.003 (Strain at which concrete crushes)
εy = 0.0015 or 0.0021 (Strain at which steel yields)
6
Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns
After yielding of steel, load is taken by concrete alone and the resistance is
provided by the concrete only. A stage comes when concrete crushes while steel is
already yielded (final stage).
If the bond between concrete and steel is perfect then they equally shorten.
εc = c
c
E
f
and εs = s
s
E
f
εc = εs
c
c
E
f
= s
s
E
f
Modular Ratio, c
s
E
E
n =
fs = n fc
Now,
Ag = Ast + Ac
Pn = Pc + Ps
Pn = Ac fc + Ast fs
Pn = fc ( Ag − Ast ) + Ast (n fc )
Pn = fc [Ag + ( n −1 )Ast ] (within elastic range, service loads)
7. PROBLEM:
A R.C. concentrically loaded short column has a cross-sectional area 450 x 450
mm2
and is reinforced by Grade 420, 8 # 19 bars. If at any stage, concrete stress fc = 10
MPa ( fc’ = 20 MPa), what will be corresponding load carrying capacity of the column.
Solution:
fc << fc’
Therefore, material is within elastic range.
Ec = 4700 'cf = 4700 20 = 21019 MPa
n =
21019
200000
=
c
s
E
E
≈ 10
Now using,
7
Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns
Pn = fc [Ag + ( n −1 )Ast ] Ast = 8 # 19 = 8 x
( )
4
19
2
π
Pn = 10 [ (450 x 450) + ( 10 −1 )2268] Ast = 2268 mm2
Pn = 2229.12 kN
8. RESISTANCE FACTOR AT ULTIMATE STAGE:
When we go to the ultimate stage then the first thing which we have to decide is
the value of ‘φ’ and to do that we must know whether the section of column is tension
controlled or compression controlled.
Section of concentrically loaded column is always compression controlled.
For tied columns, φ = 0.65
For spiral columns, φ = 0.70
As there is always some eccentricity in a column, some additional safety factor is
applied to φ factor,
Additional F.O.S. for tied columns = 0.80
Additional F.O.S. for spiral columns = 0.85
Therefore, total resistance factor for tied and spiral columns are;
For tied columns = 0.80 x 0.65
For spiral columns = 0.85 x 0.70
8

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Columns lecture#1

  • 1. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns LECTURE # 1 1. COLUMN: It is a vertical member which is primarily subjected to axial compression in which major deformation is shortening. 2. TYPES OF COLUMNS: i. Classification on the Basis of Shape: • Square section. • Rectangular section. • Circular section. • L-section. • T-section. Fig.1 Classification on the Basis of Shape 1
  • 2. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns ii. Classification on the Basis of Reinforcement: • Tied Columns: These columns have the bars braced or tied at close intervals by close loops called ties. • Spiral Columns: These columns have the bars and the core concrete wrapped with a closely spaced helix. • Composite Columns: These columns consists of a structural steel or cast iron column encased in concrete reinforced with both longitudinal and transverse reinforcements. • Pipe Columns or Concrete Filled Steel Tubes: These columns are circular, rectangular or square hollow sections filled with concrete without any additional reinforcement. Fig.2(a) Classification on the Basis of Reinforcement 2
  • 3. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns Fig.2(b) Classification on the Basis of Reinforcement iii. Classification on the Basis of Type of Loading: • Concentrically Loaded Columns: When the resultant of the load coincides with the centroid of the cross-section, the column is said to be concentrically loaded column. Fig. 3 shows a concentrically loaded column. • Eccentrically Loaded Columns: When the resultant of the load does Fig.3 Concentrically Loaded not coincide with the centroid of the Column cross-section, the column is said to be eccentrically loaded column. There are two types of eccentrically loaded columns; 1. Uni-axially eccentrically loaded columns. (Fig. 4(a)) 2. Bi-axially eccentrically loaded columns. (Fig. 4(b)) 3
  • 4. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns Fig.4 Eccentrically Loaded Columns • Sources of Eccentricity in Columns: Eccentricity is due to following three reasons; 1. Eccentric loading. (Fig. 5(a)) 2. Initial crookedness. (Fig. 5(b)) 3. Out-of-plumbness. (Fig. 5(c)) Fig.5 Sources of Eccentricity in Columns 4
  • 5. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns 3. CLASSIFICATION OF COLUMNS ACCORDING TO ACI CODE: • Short Column: In short columns there are no 2nd order effects and the failure is due to crushing of concrete without any instability. Moment magnification chances are very less in such columns because radius of gyration is more and length is small. 2 1 1234 M M r lK u −≤ Where, K = Effective length factor taken from alignment charts. M1 = Magnitude of smaller end moment with sign. M2 = Magnitude of larger end moment with sign. 2 1 M M = 0, for concentrically loaded columns. 2 1 M M = +ve, when member is bent in single curvature. 2 1 M M = −ve, when member is bent in reverse curvature. • Slender Columns: These columns fail due to buckling, instability or 2nd order effect. The failure load is less than that of a short column. As length of column increases, the probability of failure due to buckling increases. 4. TYPES OF REINFORCEMENT IN COLUMNS: • Longitudinal Steel: It is that steel which is present along the length of the column. Following are the various purposes of longitudinal reinforcement; 1. The main function of longitudinal reinforcement is to prevent creep and shrinkage in concrete. 5
  • 6. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns 2. It provides resistance against lateral bending, cracking and reduction of moment of inertia value. 3. It reduces the size of the column. • Transverse Steel: 1. It provides confinement to the inner concrete or core concrete i.e. the concrete which is present inside the longitudinal reinforcement. Confinement provides ductility and it also increases the strength of the concrete. 2. Transverse steel reduces the chances of buckling of longitudinal steel. 3. It holds the longitudinal steel in position during casting 4. Transverse steel provides resistance against shear. 5. TYPES OF TRANSVERSE REINFORCEMENT: • Ties or Transverse Ties: Lateral ties are used in the columns because of lesser construction cost and ease of placement. • Spiral Reinforcement: Spiral columns are used where we need more ductility i.e., in earthquake zones. Spirals are mostly provided in circular columns. Spiral columns sustain maximum load at excessive deformation and thus prevent the complete collapse of the structure before the total redistribution of moments and stresses is complete. The disadvantage of spiral reinforcement is that it is very difficult to place in the field, so, due to this reason its use is practically limited. 6. CAPACITY OF CONCENTRICALLY LOADED SHORT COLUMNS: Steel always yields first because it is lesser in amount and due to pure compression it is yielded. εcu = 0.003 (Strain at which concrete crushes) εy = 0.0015 or 0.0021 (Strain at which steel yields) 6
  • 7. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns After yielding of steel, load is taken by concrete alone and the resistance is provided by the concrete only. A stage comes when concrete crushes while steel is already yielded (final stage). If the bond between concrete and steel is perfect then they equally shorten. εc = c c E f and εs = s s E f εc = εs c c E f = s s E f Modular Ratio, c s E E n = fs = n fc Now, Ag = Ast + Ac Pn = Pc + Ps Pn = Ac fc + Ast fs Pn = fc ( Ag − Ast ) + Ast (n fc ) Pn = fc [Ag + ( n −1 )Ast ] (within elastic range, service loads) 7. PROBLEM: A R.C. concentrically loaded short column has a cross-sectional area 450 x 450 mm2 and is reinforced by Grade 420, 8 # 19 bars. If at any stage, concrete stress fc = 10 MPa ( fc’ = 20 MPa), what will be corresponding load carrying capacity of the column. Solution: fc << fc’ Therefore, material is within elastic range. Ec = 4700 'cf = 4700 20 = 21019 MPa n = 21019 200000 = c s E E ≈ 10 Now using, 7
  • 8. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns Pn = fc [Ag + ( n −1 )Ast ] Ast = 8 # 19 = 8 x ( ) 4 19 2 π Pn = 10 [ (450 x 450) + ( 10 −1 )2268] Ast = 2268 mm2 Pn = 2229.12 kN 8. RESISTANCE FACTOR AT ULTIMATE STAGE: When we go to the ultimate stage then the first thing which we have to decide is the value of ‘φ’ and to do that we must know whether the section of column is tension controlled or compression controlled. Section of concentrically loaded column is always compression controlled. For tied columns, φ = 0.65 For spiral columns, φ = 0.70 As there is always some eccentricity in a column, some additional safety factor is applied to φ factor, Additional F.O.S. for tied columns = 0.80 Additional F.O.S. for spiral columns = 0.85 Therefore, total resistance factor for tied and spiral columns are; For tied columns = 0.80 x 0.65 For spiral columns = 0.85 x 0.70 8