biaxially loaded columns
TRANSCRIPT
-
8/3/2019 Biaxially Loaded Columns
1/34
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
-
8/3/2019 Biaxially Loaded Columns
2/34
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:
-
8/3/2019 Biaxially Loaded Columns
3/34
Reading Assignment
Textbook:
Read sections 10.1-10.6
ACI 318-02 Code:
Read section 10
-
8/3/2019 Biaxially Loaded Columns
4/34
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
-
8/3/2019 Biaxially Loaded Columns
5/34
Uniaxial and Biaxial Bending in Columns
Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill
-
8/3/2019 Biaxially Loaded Columns
6/34
Interaction Surface of Column under
Axial Load and Biaxial Bending Moment
Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill
-
8/3/2019 Biaxially Loaded Columns
7/34
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
-
8/3/2019 Biaxially Loaded Columns
8/34
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
-
8/3/2019 Biaxially Loaded Columns
9/34
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
-
8/3/2019 Biaxially Loaded Columns
10/34
The Reciprocal Load Method
Alternatively,
-
8/3/2019 Biaxially Loaded Columns
11/34
Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons
-
8/3/2019 Biaxially Loaded Columns
12/34
Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons
-
8/3/2019 Biaxially Loaded Columns
13/34
-
8/3/2019 Biaxially Loaded Columns
14/34
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
-
8/3/2019 Biaxially Loaded Columns
15/34
-
8/3/2019 Biaxially Loaded Columns
16/34
-
8/3/2019 Biaxially Loaded Columns
17/34
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
-
8/3/2019 Biaxially Loaded Columns
18/34
Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons
-
8/3/2019 Biaxially Loaded Columns
19/34
Ref. McCormac, J. C. and Nelson Jr., J. K., Design of Reinforced Concrete, 6th Edition, 2005, John Wiley and Sons
-
8/3/2019 Biaxially Loaded Columns
20/34
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
-
8/3/2019 Biaxially Loaded Columns
21/34
Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill
-
8/3/2019 Biaxially Loaded Columns
22/34
`
Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill
-
8/3/2019 Biaxially Loaded Columns
23/34
Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill
-
8/3/2019 Biaxially Loaded Columns
24/34
Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill
-
8/3/2019 Biaxially Loaded Columns
25/34
Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill
-
8/3/2019 Biaxially Loaded Columns
26/34
Ref. Nilson, A. M., Design of Concrete Structures, 12th Edition, 1997, McGraw-Hill
-
8/3/2019 Biaxially Loaded Columns
27/34
-
8/3/2019 Biaxially Loaded Columns
28/34
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
-
8/3/2019 Biaxially Loaded Columns
29/34
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
-
8/3/2019 Biaxially Loaded Columns
30/34
Ref. J. G. MacGreger., Reinforced Concrete Mechanics and Design, 3rd Edition, 1997, Prentice-hall
Cover= 1.5 in
Tie No. 3
Bars areno. 8
-
8/3/2019 Biaxially Loaded Columns
31/34
Ref. J. G. MacGreger., Reinforced Concrete Mechanics and Design, 3rd Edition, 1997, Prentice-hall
-
8/3/2019 Biaxially Loaded Columns
32/34
Ref. J. G. MacGreger., Reinforced Concrete Mechanics and Design, 3rd Edition, 1997, Prentice-hall
-
8/3/2019 Biaxially Loaded Columns
33/34
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
-
8/3/2019 Biaxially Loaded Columns
34/34
Ref. J. G. MacGreger., Reinforced Concrete Mechanics and Design, 3rd Edition, 1997, Prentice-hall