Lean Construction

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By Dr. Attaullah ShahSwedish College of
Engineering and Technology Wah Cantt.

• Reinforced Concrete Design-I
• Design of Axial members

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Analysis and Design of Short Columns
General Information
Vertical Structural members Transmits axial
compressive loads with or without moment transmit
loads from the floor roof to the foundation
Column
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Analysis and Design of Short Columns
General Information

• Column Types
• Tied
• Spiral
• Composite
• Combination
• Steel pipe

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Analysis and Design of Short Columns
Tied 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 core
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Analysis and Design of Short Columns
Spiral Columns
Pitch 1.375 in. to 3.375 in. spiral restrains
lateral (Poissons effect) axial load
delays failure (ductile)
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Analysis and Design of Short Columns
Elastic Behavior
An elastic analysis using the transformed section
method would be
For concentrated load, P
uniform stress over section n Es / Ec Ac
concrete area As steel area
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Analysis and Design of Short Columns
Elastic Behavior
The change in concrete strain with respect to
time will effect the concrete and steel stresses
as follows
Concrete stress
Steel stress
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Analysis and Design of Short Columns
Elastic Behavior
An elastic analysis does not work, because creep
and shrinkage affect the acting concrete
compression strain as follows
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Analysis and Design of Short Columns
Elastic Behavior
Concrete creeps and shrinks, therefore we can not
calculate the stresses in the steel and concrete
due to acting loads using an elastic analysis.
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Analysis and Design of Short Columns
Elastic Behavior
Therefore, we are not able to calculate the real
stresses in the reinforced concrete column under
acting loads over time. As a result, an
allowable stress design procedure using an
elastic analysis was found to be unacceptable.
Reinforced concrete columns have been designed by
a strength method since the 1940s.
Creep and shrinkage do not affect the strength of
the member.
Note
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
Initial Behavior up to Nominal Load - Tied and
spiral columns.
1.
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
Let Ag Gross Area bh
Ast area of long steel
fc concrete compressive strength
fy steel yield strength
Factor due to less than ideal consolidation and
curing conditions for column as compared to a
cylinder. It is not related to Whitneys stress
block.
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
Maximum Nominal Capacity for Design Pn (max)

2.
r Reduction factor to account for
accidents/bending r 0.80 ( tied ) r 0.85 (
spiral )
ACI 10.3.6.3
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
Reinforcement Requirements (Longitudinal Steel
Ast)
3.
Let
- ACI Code 10.9.1 requires
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
3.
Reinforcement Requirements (Longitudinal Steel
Ast)
- Minimum of Bars ACI Code 10.9.2
min. of 6 bars in circular arrangement w/min.
spiral reinforcement. min. of 4 bars in
rectangular arrangement min. of 3 bars in
triangular ties
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
3.
Reinforcement Requirements (Lateral Ties)
ACI Code 7.10.5.1
3 bar if longitudinal bar 10 bar
4 bar if longitudinal bar 11 bar 4
bar if longitudinal bars are bundled
size
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
3.
Reinforcement Requirements (Lateral Ties)
Vertical spacing (ACI 7.10.5.2)
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
Arrangement Vertical spacing (ACI 7.10.5.3)
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
Examples of lateral ties.
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
Reinforcement Requirements (Spirals )
ACI Code 7.10.4
3/8 dia. (3/8 f smooth bar, 3 bar dll
or wll wire)
size
clear spacing between spirals
1 in.
3 in.
ACI 7.10.4.3
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
Reinforcement Requirements (Spiral)
Spiral Reinforcement Ratio, rs
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
Reinforcement Requirements (Spiral)
ACI Eqn. 10-5
where
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
4.
Design for Concentric Axial Loads
(a) Load Combination
Gravity
Gravity Wind
and
Check for tension
etc.
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
4.
Design for Concentric Axial Loads
(b) General Strength Requirement
f 0.65 for tied columns f 0.7 for spiral
columns
where,
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
4.
Design for Concentric Axial Loads
(c) Expression for Design
defined
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
or
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Behavior, Nominal Capacity and Design under
Concentric Axial loads
when rg is known or assumed
when Ag is known or assumed
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Example Design Tied Column for Concentric
Axial Load
Design tied column for concentric axial load Pdl
150 k Pll 300 k Pw 50 k
fc 4500 psi fy 60 ksi Design a square column
aim for rg 0.03. Select longitudinal
transverse reinforcement.
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Example Design Tied Column for Concentric
Axial Load
Determine the loading
Check the compression or tension in the column
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Example Design Tied Column for Concentric
Axial Load
For a square column r 0.80 and f 0.65 and r
0.03
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Example Design Tied Column for Concentric
Axial Load
For a square column, AsrAg 0.03(15.2 in.)2
6.93 in2
Use 8 8 bars Ast 8(0.79 in2) 6.32 in2
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Example Design Tied Column for Concentric
Axial Load
Check P0
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Example Design Tied Column for Concentric
Axial Load
Use 3 ties compute the spacing
lt 6 in. No cross-ties needed
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Example Design Tied Column for Concentric
Axial Load
Stirrup design
Use 3 stirrups with 16 in. spacing in the column
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Behavior under Combined Bending and Axial Loads
Usually moment is represented by axial load times
eccentricity, i.e.
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Behavior under Combined Bending and Axial Loads
Interaction Diagram Between Axial Load and Moment
( Failure Envelope )
Concrete crushes before steel yields
Steel yields before concrete crushes
Note
Any combination of P and M outside the envelope
will cause failure.
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Behavior under Combined Bending and Axial Loads
Axial Load and Moment Interaction Diagram
General
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Behavior under Combined Bending and Axial Loads
Resultant Forces action at Centroid
( h/2 in this case )
Moment about geometric center
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Columns in Pure Tension
Section is completely cracked (no concrete
axial capacity)
Uniform Strain
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Columns
Strength Reduction Factor, f (ACI Code 9.3.2)
Axial tension, and axial tension with flexure.
f 0.9 Axial compression and axial compression
with flexure.
(a)
(b)
Members with spiral reinforcement confirming to
10.9.3 f 0.70 Other reinforced members
f 0.65
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Columns
Except for low values of axial compression, f may
be increased as follows
when and
reinforcement is symmetric and ds distance
from extreme tension fiber to centroid of tension
reinforcement.
Then f may be increased linearly to 0.9 as fPn
decreases from 0.10fc Ag to zero.
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Column
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Columns
Commentary
Other sections f may be increased linearly to
0.9 as the strain es increase in the tension
steel. fPb
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Design for Combined Bending and Axial Load (Short
Column)
Design - select cross-section and reinforcement
to resist axial load and moment.
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Design for Combined Bending and Axial Load (Short
Column)
Column Types
Spiral Column - more efficient for e/h lt 0.1,
but forming and spiral expensive Tied Column -
Bars in four faces used when e/h lt 0.2 and for
biaxial bending
1)
2)
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General Procedure
The interaction diagram for a column is
constructed using a series of values for Pn and
Mn. The plot shows the outside envelope of the
problem.
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General Procedure for Construction of ID

• Compute P0 and determine maximum Pn in
  compression
• Select a c value (multiple values)
• Calculate the stress in the steel components.
• Calculate the forces in the steel and
  concrete,Cc, Cs1 and Ts.
• Determine Pn value.
• Compute the Mn about the center.
• Compute moment arm,e Mn / Pn.

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General Procedure for Construction of ID

• Repeat with series of c values (10) to obtain a
  series of values.
• Obtain the maximum tension value.
• Plot Pn verse Mn.
• Determine fPn and fMn.
• Find the maximum compression level.
• Find the f will vary linearly from 0.65 to 0.9
  for the strain values
• The tension component will be f 0.9

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Example Axial Load vs. Moment Interaction
Diagram
Consider an square column (20 in x 20 in.) with 8
10 (r 0.0254) and fc 4 ksi and fy 60 ksi.
Draw the interaction diagram.
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Example Axial Load vs. Moment Interaction
Diagram
Given 8 10 (1.27 in2) and fc 4 ksi and fy
60 ksi
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Example Axial Load vs. Moment Interaction
Diagram
Given 8 10 (1.27 in2) and fc 4 ksi and fy
60 ksi
Point 1
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Example Axial Load vs. Moment Interaction
Diagram
Determine where the balance point, cb.
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Example Axial Load vs. Moment Interaction
Diagram
Determine where the balance point, cb. Using
similar triangles, where d 20 in. 2.5 in.
17.5 in., one can find cb
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Example Axial Load vs. Moment Interaction
Diagram
Determine the strain of the steel
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Example Axial Load vs. Moment Interaction
Diagram
Determine the stress in the steel
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Example Axial Load vs. Moment Interaction
Diagram
Compute the forces in the column
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Example Axial Load vs. Moment Interaction
Diagram
Compute the forces in the column
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Example Axial Load vs. Moment Interaction
Diagram
Compute the moment about the center
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Example Axial Load vs. Moment Interaction
Diagram
A single point from interaction diagram,
(585.6 k, 556.9 k-ft). The
eccentricity of the point is defined as
Point 2
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Example Axial Load vs. Moment Interaction
Diagram
Now select a series of additional points by
selecting values of c. Select c 17.5 in.
Determine the strain of the steel. (c is at the
location of the tension steel)
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Example Axial Load vs. Moment Interaction
Diagram
Compute the forces in the column
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Example Axial Load vs. Moment Interaction
Diagram
Compute the forces in the column
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Example Axial Load vs. Moment Interaction
Diagram
Compute the moment about the center
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Example Axial Load vs. Moment Interaction
Diagram
A single point from interaction diagram,
(1314 k, 351.1 k-ft). The
eccentricity of the point is defined as
Point 3
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Example Axial Load vs. Moment Interaction
Diagram
Select c 6 in. Determine the strain of the
steel, c 6 in.
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Example Axial Load vs. Moment Interaction
Diagram
Compute the forces in the column
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Example Axial Load vs. Moment Interaction
Diagram
Compute the forces in the column
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Example Axial Load vs. Moment Interaction
Diagram
Compute the moment about the center
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Example Axial Load Vs. Moment Interaction Diagram
A single point from interaction diagram,
(151 k, 471 k-ft). The eccentricity
of the point is defined as
Point 4
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Example Axial Load vs. Moment Interaction
Diagram
Select point of straight tension. The maximum
tension in the column is
Point 5
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Example Axial Load vs. Moment Interaction
Diagram
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Example Axial Load vs. Moment Interaction
Diagram
Use a series of c values to obtain the Pn verses
Mn.
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Example Axial Load vs. Moment Interaction
Diagram
Cb