Lecture 29 Reinforced Columns

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Lecture 29- Reinforced Columns

• April 7, 2002
• CVEN 444

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Lecture Goals

• Columns
• Short Column Design
• Column Example
• Interaction Diagrams

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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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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
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Example
Use a series of c values to obtain the Pn verses
Mn.
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Example
Cb
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Design for Combined Bending and Axial Load (short
column)
Column Types
Tied Column - Bars in 2 faces (furthest from axis
of bending.
3)
- Most efficient when e/h gt 0.2 - rectangular
shape increases efficiency
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Design for Combined Bending and Axial Load (short
column)
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Design for Combined Bending and Axial Load (short
column)
Spices
All bars in compression Use
compression lap splice (ACI 12.16)
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Design for Combined Bending and Axial Load (short
column)
Column Shear
Recall ( Axial Compression )
Ties must satisfy ACI 11 and ACI Sec. 7.10.5
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Design for Combined Bending and Axial Load (short
column)
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Non-dimensional Interaction Diagrams
or
See Figures B-12 to B-26 or ACI Common 340 Design
Handbook Vol 2 Columns (ACI 340.2R-91)
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Non-dimensional Interaction Diagrams
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Design using non-dimensional interaction diagrams
Calculate factored loads (Pu , Mu ) and e for
relevant load combinations Select potentially
governing case(s) Use estimate h to calculate gh,
e/h for governing case(s)
1.)
2.)
3.)
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Design using non-dimensional interaction diagrams
Use appropriate chart (App. A) target rg (for
each governing case) Select
4.)
Calculate required
Read
5.)
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Design using non-dimensional interaction diagrams
If dimensions are significantly different from
estimated (step 3), recalculate ( e / h ) and
redo steps 4 5. Revise Ag if
necessary. Select steel
6.)
7.)
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Design using non-dimensional interaction diagrams
Using actual dimensions bar sizes to check all
load combinations ( use charts or exact
interaction diagram). Design lateral
reinforcement.
8.)
9.)
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Example Column design using Interaction Diagrams
Determine the tension and compression
reinforcement for a 16 in x 24 in. rectangular
tied column to support Pu 840 k and Mu 420
k-ft. Use fc 4 ksi and fy 60 ksi. Using the
interaction diagram.
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Example Interaction Diagrams
Compute the initial components
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Example Interaction Diagrams
Compute the initial components
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Example Interaction Diagrams
Compute the coefficients of the column
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Example Interaction Diagrams
Using an interaction diagram, B-13
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Example Interaction Diagrams
Using an interaction diagram, B-14
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Example Interaction Diagrams
Using linear interpolation to find the r of the
column
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Example Interaction Diagrams
Determine the amount of steel required Select
the steel for the column, using 11 bars
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Example Interaction Diagrams
The areas of the steel The loading on the
column
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Example Interaction Diagrams
The compression components are
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Example Interaction Diagrams
The tension component is
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Example Interaction Diagrams
Take the moment about the tension steel
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Example Interaction Diagrams
The first equation related to Pn
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Example Interaction Diagrams
The second equation comes from the equilibrium
equation and substitute in for Pn
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Example Interaction Diagrams
Substitute the relationship of c for the stress
in the steel. The problem is now a cubic
solution c fs RHS 15
in. 37.7 -10.38 19 in. 11.45
2.64 19.5 in. 8.92 4.63 20.0 in.
6.52 6.70 19.98 in. 6.62 6.62
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Example Interaction Diagrams
Compute Pn Compute Mn about the center
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Example Interaction Diagrams
Compute Mn about the center
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Example Interaction Diagrams
Check that Mn is greater than the required Mu
Check the Pn is greater than the required Pu
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Example Interaction Diagrams
Determine the tie spacing using 4 bars
Use 16 in.
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Homework
Due 4/18/03 Problem 9.6, part a using at least 10
points Using the interaction diagram, design a
column with h 28 in., g 0.84 and b 18 in.,
PD 240 k and PL 480 k and Mu 704 k-ft.
Determine the amount of reinforcement and type of
ties and their spacing for fy 60 ksi and fc
5 ksi
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Project
Part A3 Due 4/18/03 Part B1 Due 4/23/03
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Exam 2
November ? (19 or 26)