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