Analysis of Biaxially Loaded Rectangular Columns<Program Created by: Engr. Jeremy E. Caballes>
Units: ksi 3 y d' = 2.5 inMPapsi E = 29000 ksi
ksi 4 ksi
60 ksi
25 in 20 in
Ø = 0.7
8 in
16 ind' = 2.5 in
7.952 sq in 10 in
Yes 15 in2 No
Bending about x Axis:
ρ = Asbh
ρ = 0.02121 < 0.01 Use: ρ = 0.0212058
γ = γhh
γ = 0.800e/h = 0.320
From Interaction Diagram:
0.482 ksi
6,455 kips-in
538 kips-ft
6,455.048 kips-in
806.881 kipsPn = 806.881 kips
Bending about y Axis:
ρ = Asbh
ρ = 0.02121
γ = γhh
γ = 0.667e/h = 1.067
From Interaction Diagram:
0.420 ksi
5,624.416 kips-in
468.701 kips-ft
5,624.416 kips-in
703.052 kips
f'c =
fy =
ex =
ey =
As =
ØMnx/Aghy =
Mnx =
Mnx =
Pnx ey =
Pnx =
ØMny/Aghx =
Mny =
Mny =
Pny ex =
Pny =
0.0 0.5 1.0 1.5 2.0 2.50.0
1.0
2.0
3.0
4.0
5.0
6.0
Interaction Diagram(Rectangular Column, Biaxial Bending)
ØMn/Agh
ØP
n/A
g
0.0 0.5 1.0 1.5 2.0 2.50.0
1.0
2.0
3.0
4.0
5.0
6.0
Interaction Diagram(Rectangular Column, Biaxial Bending)
ØMn/Agh
ØP
n/A
g
Axial Load Capacity:
1752.1294 kips
Determine Pni using Bresler's Equation:1
=1
+1
-1
1=
1+
1-
1
806.881 703.052 1,752.129
478.246 kips
Po = 0.85f'cAg + fyAs
Po =
Pni Pnx Pny Pno
Pni
Pni =
0.0 0.5 1.0 1.5 2.0 2.50.0
1.0
2.0
3.0
4.0
5.0
6.0
Interaction Diagram(Rectangular Column, Biaxial Bending)
ØMn/Agh
ØP
n/A
g
Design of Biaxially Loaded Rectangular Columns<Program Created by: Engr. Jeremy E. Caballes>
Units: MPa 1MPapsi E = 200000 MPa d' = 50 mmksi f'c = 20.7 MPa
fy = 275 MPa
Ø = 0.7
4700 PDL = 4.7 kN 300 mm 200 mm189800 PLL = 189.8 kN500000 MxDL = 0.5 kN-m500000 MxLL = 0.5 kN-m500000 MyDL = 0.5 kN-m500000 MyLL = 0.5 kN-m
d' = 50 mm
20.000 mm 200 mm
12.000 mm300 mm
Optional Values:0 Pn = kN0 ex = mm0 ey = mm
Computing Design Values:Pu = 1.4PDL + 1.7PLLPu = 329,240.000 N
Pu/f'cAg = 0.177 > 0.1Therefore, Ø = 0.7
Pn = Pu/ØPn = 470,342.857 N
Mux = 1.4MxDL + 1.7MxLLMux = 1,550,000.000 N-mmMnx = Mux/ØMnx = 2,214,285.714 N-mm
Muy = 1.4MyDL + 1.7MyLLMuy = 1,550,000.000 N-mmMny = Muy/ØMny = 2,214,285.714 N-mm
Mn = Mnx + MnyMn = 4,428,571.429 N-mm
Required Steel Area:(Bending about x-axis) Required Steel Area:(Bending about y-axis)
ØMn ØMn
4.429E+6 N-mm 4.429E+06 N-mm
9.416 mm 9.416 mm
300.000 mm 300.000 mm
0.031 0.031
γ = γh
γ = γh
h hγ = 0.667 γ = 0.667
0.115 MPa (ØPny/Ag)(ex/hx) = 0.115 MPaFrom Interaction Diagram: From Interaction Diagram:
ρ = 0.01000 < 0.01 Use: ρ = 0.01 ρ = 0.01000 < 0.01 Use: ρ = 0.01
900.000 sq mm 900.000 sq mm
db =
db ties =
Use: ØMnx = Use: ØMny =
ØMnx = ØMny =
ey = Mnx
ex = Mny
Pnx Pny
ey = ex =
hy = hx =
ey/hy = ex/hx =
(ØPnx/Ag)(ey/hy) =
As = ρAg As = ρAg
As = As =
x
y
0.0 2.0 4.0 6.0 8.0 10.0 12.00.0
5.0
10.0
15.0
20.0
25.0
30.0
Interaction Diagram(Rectangular Column, Biaxial Bending)
ØMn/Agh
ØP
n/A
g
900.000 sq mm
n =
n = 2.865 say 3Use: n = 4
200.000 mm
180.000 mm > 25 mm OK!
Spacing of ties:S = 48 x db ties = 576.000 mm 576S = 16 x db = 320.000 mm 320S = Least dim. = 300.000 mm 300
Use: S = 300.000 mm
Use: As =
As
Ab
Soc =
Scl =
0.0 2.0 4.0 6.0 8.0 10.0 12.00.0
5.0
10.0
15.0
20.0
25.0
30.0
Interaction Diagram(Rectangular Column, Biaxial Bending)
ØMn/Agh
ØP
n/A
g