Lean Construction

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

• CE-401
• Reinforced Concrete Design-II

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Course Outline

• Analysis design of axially loaded columns,
  Eccentrically loaded columns by USD
• Analysis design of strip footing for wall,
  spread footings for columns and combined footings
  by USD.
• Design of retaining wall.
• Introduction to limit states.
• Detailing of reinforcement.
• Introduction to design of staircases and water
  tanks.

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Columns subjected to eccentric loadings
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Eccentric Compression
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Interaction diagrams of combined bending and
compression
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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
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ACI Design Aids for Columns
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Design Example 8.3
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Bar splicing in Columns
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Assignment No.1 (Total Marks100 each question
carries 50 marks

• Design and Rectangular Column to carry dead load
  of 250K live load of 350K dead load moment
  150ft-K and live load moment of 350ft-K Assume
  material properties.
• Determine the main steel required
• Determine the ties spacing
• Draw final neat to the scale sketch on graph
  paper
• Due Date Sep,17 2012.