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Report of Engr. Ferrer, Engr. Magallanes, and Engr. Matias... :) download a coppy now on SCRIBD. :) haha
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COLUMN INTERACTION
DIAGRAM
CE514D2-REINFORCED CONCRETE DESIGN
• TO DISCUSS HOW THE COLUMN INTERACTION DIAGRAM WAS MADE.
• TO DISCUSS THE IMPORTANT POINTS OF THE DIAGRAM.
• TO DISCUSS HOW IT IS BEING USED.
OBJECTIVES
COLUMN INTERACTION DIAGRAM
The COLUMN STRENGTH INTERACTION DIAGRAM is a curve plot of points; where each point has two ordinates. The first ordinate is bending moment strength and the second is the corresponding axial force. Both ordinates are linked with eccentricity. The shape of the curve, or the strength interaction diagram, can be defined by finding the ordinates of major seven points.
COLUMN INTERACTION DIAGRAM
Calculation of Pn and Mn for a given strain distribution
COLUMN INTERACTION DIAGRAM
Point 1: axial compression at zero moment. Point 2: maximum axial compression load permitted by code at zero eccentricity. Point 3: maximum moment strength at the maximum axial compression load permitted by code. Point 4: compression and moment strength at zero strain in the tension side reinforcement. Pont 5: compression and moment strength at 50% strain in the tension side reinforcement. Point 6: compression and moment strength at balanced conditions. Point 7: moment strength at zero axial force.
The seven major points of the diagram are as follows:
COLUMN INTERACTION DIAGRAM
Strain Distribution corresponding to points on the Interaction Diagram
COLUMN INTERACTION DIAGRAM
COLUMN INTERACTION DIAGRAM
Concrete crushes before steel yields
Steel yields before concrete crushes
Note: Any combination of P and M outside the envelope will cause failure.
COLUMN INTERACTION DIAGRAM
NON- DIMENSIONALINTERACTION
DIAGRAM
COLUMN INTERACTION DIAGRAM
COLUMN INTERACTION DIAGRAM
COLUMN INTERACTION DIAGRAM
COLUMN INTERACTION DIAGRAM
COLUMN INTERACTION DIAGRAM
Computations of the Major Seven Points of
the Diagram
COLUMN INTERACTION DIAGRAM
Point 1 – Axial Compression at Zero Moment
Point 2– Maximum Permissible Axial Compression at Zero Eccentricity
TIED SPIRAL
COLUMN INTERACTION DIAGRAM
Point 3 – Maximum Moment Strength at Maximum Permissible Compression
COLUMN INTERACTION DIAGRAM
∑ Fv = 0
∑ M = 0
COLUMN INTERACTION DIAGRAM
Point 4 – Axial Compression and Zero Moment at Zero Strain
COLUMN INTERACTION DIAGRAM
Point 5 – Axial Compression and Moment Strength at 50% Strain
COLUMN INTERACTION DIAGRAM
COLUMN INTERACTION DIAGRAM
Point 6 – Axial Compression and Moment Strength at Balanced Conditions
COLUMN INTERACTION DIAGRAM
COLUMN INTERACTION DIAGRAM
Point 7 – Moment Strength at Zero Axial Force
COLUMN INTERACTION DIAGRAM
COLUMN INTERACTION DIAGRAM
DESIGN USING NON-DIMENSIONAL INTERACTION DIAGRAMS
1. Calculate factored loads (Pu , Mu ) and e for relevant load combinations
2. Select potentially governing case(s)
3. Use estimate h to calculate gh, e/h for governing case(s)
4. Use appropriate chart (App. A) target rg
(for each governing case)
5. Select
n
c g
P
f A
u cg
n
c g
P fA
P
f A
Read Calculate required
COLUMN INTERACTION DIAGRAM
6. If dimensions are significantly different from estimated (step 3), recalculate ( e / h ) and redo steps 4 & 5.
Revise Ag if necessary.
7. Select steel gst AA
8. Using actual dimensions & bar sizes to check all load combinations ( use charts or “exact: interaction diagram).
9. Design lateral reinforcement.
COLUMN INTERACTION DIAGRAM
EXAMPLE PROBLEM(Comparison between Static
Equation and Interaction Diagram)
COLUMN INTERACTION DIAGRAM
References:•Strunet•Reinforced Concrete, Mechanics and Design ( Fourth Edition )
( James MacGregor, James K. Wight)•Fundamentals of Reinforced Concrete ( Gillesania )•books.google.com.ph/•www.tcd.ie/civileng/Staff/Biswajit.Basu/3A2/3A2LEC16.pdf•www.philjol.info/index.php/JRSCE/article/viewPDFInterstitial/.../580•www.tpub.com/content/NAVFAC/.../dm2_080107.htm
COLUMN INTERACTION DIAGRAM
Presented by:
Ferrer, DarylMagallanes III, Benjamin
Matias, Herj
Presented to:
Engr. Rhonnie Estores
COLUMN INTERACTION DIAGRAM