Lecture 27 Reinforced Columns

1
Lecture 27 - Reinforced Columns

• March 25, 2002
• CVEN 444

2
Lecture Goals

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

3
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.
4
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.
5
Example
6
Example
Use a series of c values to obtain the Pn verses
Mn.
7
Example
Cb
8
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
9
Design for Combined Bending and Axial Load (short
column)
10
Design for Combined Bending and Axial Load (short
column)
Spices
All bars in compression Use
compression lap splice (ACI 12.16)
11
Design for Combined Bending and Axial Load (short
column)
Column Shear
Recall ( Axial Compression )
Ties must satisfy ACI Ch. 11 and ACI Sec. 7.10.5
12
Design for Combined Bending and Axial Load (short
column)
13
Non-dimensional Interaction Diagrams
or
See Figures A-6 to A-14 or ACI Common 340 Design
Handbook Vol 2 Columns (ACI 340.2R-91)
14
Non-dimensional Interaction Diagrams
15
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.)
16
Design using non-dimensional interaction diagrams
Use appropriate chart (App. A) target rg (for
each governing case) Select
4.)
Calculate required
Read
5.)
17
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.)
18
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. see Ex. 11-2 solve
for rg
8.)
9.)
19
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.
20
Example
21
Example