reinforced concrete design - column interaction diagram

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