Lecture 27 Columns

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Lecture 27- Columns

• March 31, 2003
• CVEN 444

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Lecture Goals

• Definitions
• Columns

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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
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Analysis and Design of Short Columns
Tie 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
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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
1 in. 3 in.
- clear spacing between spirals
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
Determine the loading
Check the compression or tension in the column
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Example Design Tied Column
For a square column r 0.80 and f 0.65 and r
0.03
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Example Design Tied Column
For a square column, As rAg 0.03(15 in.)2
6.75 in2
Use 8 8 bars Ast 8(0.79 in2) 6.32 in2
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Example Design Tied Column
Check P0
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Example Design Tied Column
Use 3 ties compute the spacing
lt 6 in. No cross-ties needed
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Example Design Tied Column
Stirrup design
Use 3 stirrups with 16 in. spacing in the column
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Homework Due 4/4/03
Problem 9.1