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Biaxially Loaded Columns

CVE411 Structural Concrete Design

Jamal A. Abdalla

Textbook: Chapter 10

ACI 318-05 Code: Chapter 10

Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons

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Objectives and Outcomes

y Be able to design a column under axial load and biaxial bending

moments and check its strength.

1. Apply theR

eciprocal Load Method to check the strength of columns under axial load and biaxial bending moments

2. Apply the Load Contour Method to check the strength of

columns under axial load and biaxial bending moments

3. Design a column under axial load and biaxial bending moments

using the Equivalent Uniaxial Method

4. Design a column under axial load and biaxial bending moments

using the Equivalent Eccentricity Method

Objectives:

Outcomes:

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Reading Assignment

Textbook:

Read sections 10.1-10.6

ACI 318-02 Code:

Read section 10

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Columns under Axial Load and

Biaxial Bending

Cornercolumns are underaxial load and

biaxial bending

Edge columns and interiorcolumnssupporting unbalance loads are also under

axial load and biaxial bending

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Uniaxial and Biaxial Bending in Columns

Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill

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Interaction Surface of Column under

Axial Load and Biaxial Bending Moment

Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill

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Forces in Column Under Axial

Load and Biaxial Bending

Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons

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The Reciprocal Load MethodThis method is developed by Boris Bresselerofthe University ofCalifornia at Berkeley

Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill

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Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons

Forcolumn with axial load and biaxial moment,

thenominal load isgiven by:

The Reciprocal Load Method

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The Reciprocal Load Method

Alternatively,

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Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons

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Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons

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Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons

lessthen Px,Py, P0 which meansthatthe column is

weakened a lot by being biaxialy loaded

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Equivalent Uniaxial Method

The biaxial moment inthe column is converted to a

uniaxial momentequal tothesum ofthetwo biaxial

moment and the column is design accordingly

!

!!

u

uyuxu

P

MMM

Axial Load

Uniaxial Moment

Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons

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Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons

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Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons

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Load Contour Method

Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill

ex = 0

ey = 0

Used foranalysistosee ifthe column is capableofcarryingthe loads and it dependson

the moments

Use alpha to be 1.5 conservatively

Or

less

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Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill

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`

Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill

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Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill

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Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill

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Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill

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Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill

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Equivalent Eccentricity Method

If

Theequivalenteccentricity isgiven by:

Ref. J. G. MacGreger., Reinforced Concrete Mechanics and Design, 3rd Edition, 1997, Prentice-hall

Ifey/y > ex/x thenthisequation becomese0y ;

afteryou put instead ofevery (x) a (y) and

instead ofevery (y) an (x)

Minvalueof

alpha is 0.6

Minvalueof

alpha is 0.5

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Design of a Column under Axial

Load and Biaxial Moments:

Equivalent Eccentricity Method

Ref. J. G. MacGreger., Reinforced Concrete Mechanics and Design, 3rd Edition, 1997, Prentice-hall

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Ref. J. G. MacGreger., Reinforced Concrete Mechanics and Design, 3rd Edition, 1997, Prentice-hall

Cover= 1.5 in

Tie No. 3

Bars areno. 8

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Ref. J. G. MacGreger., Reinforced Concrete Mechanics and Design, 3rd Edition, 1997, Prentice-hall

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Ref. J. G. MacGreger., Reinforced Concrete Mechanics and Design, 3rd Edition, 1997, Prentice-hall

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Design of a Column under Axial

Load and Biaxial Moments:

Reciprocal Load Method

Ref. J. G. MacGreger., Reinforced Concrete Mechanics and Design, 3rd Edition, 1997, Prentice-hall

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Ref. J. G. MacGreger., Reinforced Concrete Mechanics and Design, 3rd Edition, 1997, Prentice-hall