Rectangular Tank Mathcad

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Tank Desc:Job Number:Rev Number:

Designed By:Checked By:

Date:

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Rectangular Open Top Tank Design Per AISC 360

Rev # Rev Description Rev By Rev Date

1

2

3

4

Notes

1

2

3

4

5

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Date:

Rectangular Tank Design

This program is used to design large rectangular open top tanks per AISC 360. The tanks consist of plate sides and

bottoms, a horizontal stiffener at the top (Wide Flange or Channel) and vertical stiffeners at some spacing on the sides

(Wide Flange or Channel.)

A. GeometryNumber of crossmembersLength of tank Width of tank Height of tank Design liquid level

Ltank 38.4167 ft⋅:= Btank 12 ft⋅:= Htank 12 ft⋅:= DLL 12 ft⋅:= Ncross 2:=

Thickness oftank walls

Location of horizontalstiffener above bottom

Spacing of tankstiffeners

ts .3125 in⋅:= Hst 11 ft⋅:= Sv 3.167 ft⋅:=

Vertical Stiffener Geometry

Beam Selection (W or C shapes)Stiffener Length

Unbraced Length ofSoil Side Flange

Unbraced Length ofProduct Side Flange

UBLB1 .1 ft⋅:= UBLT1 Htank:= LB1 Htank:=

Horizontal Stiffener Geometry (Long Side)

Beam Selection (W or C shapes) Unbraced Length ofSoil Side Flange

Unbraced Length ofProduct Side Flange Stiffener Length

UBLB2

Ltank

Ncross 1+:= UBLT2

Ltank

Ncross 1+:= LB2

Ltank

Ncross 1+:=

Horizontal Stiffener Geometry (Short Side)

Beam Selection (W or C shapes)Stiffener Length

Unbraced Length ofSoil Side Flange

Unbraced Length ofProduct Side Flange

UBLB3 Btank:= UBLT3 Btank:= LB3 Btank:=

Cross Member GeometryUnbraced Length for

Strong AxisUnbraced Length for

Weak AxisColumn Selection (W shapes) Column Length

LC Btank:= UBLs Btank:= UBLw Btank:=

Eff. length factor forstrong axis

Eff. length factor forweak axis

KxC 1.0:= KyC 1.0:=





Date:


B. Material Properties

Yield strength ofstiffeners

Yield Strength orcross member

Safety factor forplate bendingModulus of elasticity Yield strength of platel

Es 29000 ksi⋅:= Fyp 36 ksi⋅:= FyB 50 ksi⋅:= FyC 50 ksi⋅:= Ωp 1.67:=

Active pressurecoefficient

Height to groundwaterabove bottomDensity of soil Surcharge loading

γe 110 pcf⋅:= Ka .35:= Hgw 5 ft⋅:= Qsur 400 psf⋅:=

Specific gravity

SG 1.0:=





Date:


C. Loading Crteria

Pp DLL SG⋅ γw⋅ 5.20psi=:= Product pressure at bottom of tank

Peb Hgw γw⋅ Hgw γe γw−( )⋅ Ka⋅+ Htank Hgw−( ) γe⋅ Ka⋅+ Qsur Ka⋅+ BURY⋅:=

Peb 5.59psi= Earth pressure at bottom of tank

Pet Qsur Ka⋅ BURY⋅ 0.97psi=:= Earth pressure at top of tank

Pegw Htank Hgw−( ) γe⋅ Ka⋅ Qsur Ka⋅+ BURY⋅ 2.84psi=:= Earth pressure at ground water

D. Check Plate Thickness

bvf1 CBF BEAM1( ) in⋅ BEAM1 31≤if

WBFBEAM1 31− in⋅ otherwise

5.25 in⋅=:= Flange width of vertical stiffener

Plate moment due to fluid pressure at bottom of

tankMp1

Pp 1⋅ in⋅ Sv bvf1−( )2

⋅

12:= Mp1 38.75 ft lbs⋅⋅=

Mp2 maxDLL Hst−

0 ft⋅

2

γw⋅ SG⋅ 1⋅ in⋅1

2⋅

1

3⋅ max

DLL Hst−

0 ft⋅

⋅:=

Plate moment due to fluid pressure in cantilvered

plate above top stiffenerMp2 0.87 ft lbs⋅⋅=

Plate moment due to earth pressure at bottom

of tankMe1

Peb 1⋅ in⋅ Sv bvf1−( )2

⋅

12:= Me1 41.64 ft lbs⋅⋅=

Me2

Pet Htank Hst−( )2

⋅

2

1

2Htank Hst−( )

2⋅ γe⋅ Ka⋅

1

3⋅ Htank Hst−( )⋅+

1⋅ in⋅:=

Plate moment due to earth pressure in cantilvered

plate above top stiffenerMe2 6.37 ft lbs⋅⋅=

Msmax max

Mp1

Mp2

Me1

Me2

:= Msmax 41.64 ft lbs⋅⋅= Maximum plate moment over a 1" width





Date:


D. Check Plate Thickness

Bending strength of plateMnp

Fyp

Ωp

1 in⋅ ts2

⋅

4⋅:=

Mnp 43.86 ft lbs⋅⋅=

Plate bending strength check - Must be less than

or equal to 100%

Msmax

Mnp

94.95 %⋅=

∆p

max

Pp

Peb

1⋅ in⋅ Sv bvf1−( )4

⋅

384 Es⋅

1 in⋅ ts3

⋅

12⋅

:=

∆p 0.23 in⋅= Deflection of plate

Plate deflection check - Must be less than or equal

to 100%

∆p

ts

72.69 %⋅=





Date:


E. Loading in Vertical Stiffener

Uniform fluid load in stiffener as a function of

height above the bottomqp x( ) Pp Sv⋅ γw SG⋅ x⋅ Sv⋅−:=

qp Htank( ) 0.00 plf⋅=

qp 0 ft⋅( ) 2372.21 plf⋅=

Uniform soil load in stiffener as a function of

height above the bottomqe x( ) Peb

Peb Pegw−( )Hgw

x⋅−

Sv⋅ x Hgw<if

Pegw

Pegw Pet−( ) x Hgw−( )⋅

Htank Hgw−−

Sv⋅ otherwise

:=

x 0 ft⋅

Htank

50, Htank..:=

0 1275 25490

6

12

Uniform Soil Load

Uniform Load

Hei

gh

t A

bo

ve

Bo

tto

m

0 1186 23720

6

12

Uniform Product Load

Uniform Load

Hei

gh

t A

bo

ve

Bo

tto

m





Date:



Reaction at bottom of vertical stiffener due to

soil loadingR2e

0 ft⋅

Htank

xqe x( ) x⋅⌠⌡

d

Htank

:= R2e 5809.49 lbs⋅=

Reaction at top of vertical stiffener due to soil

loadingR1e

0 ft⋅

Htank

xqe x( )⌠⌡

d R2e−:= R1e 9895.76 lbs⋅=

Me x1( ) R1e x1⋅

0 ft⋅

x1

xqe x( ) x1 x−( )⋅⌠⌡

d−:= Moment as a function of x due to

soil loading

MARRAYe

mi MeHtank

100i⋅

←

i 1 100..∈for

m

:=

Mmaxe max MARRAYe( ):= Maximum moment for soil load

Mmaxe 22861.83 ft lbs⋅⋅=

R2p0 ft⋅

Htank

xqp x( ) x⋅⌠⌡

d

Htank

:= R2p 4744.42 lbs⋅= Reaction at bottom of vertical stiffener due to

product loading

Reaction at top of vertical stiffener due to

product loadingR1p

0 ft⋅

Htank

xqp x( )⌠⌡

d R2p−:= R1e 9895.76 lbs⋅=

Mp x1( ) R1p x1⋅

0 ft⋅

x1

xqp x( ) x1 x−( )⋅⌠⌡

d−:=Moment as a function of x due to

product loading

MARRAYp

mi MpHtank

100i⋅

←

i 1 100..∈for

m

:=

Mmaxp max MARRAYp( ):=

Maximum moment for product loadMmaxp 21912.84 ft lbs⋅⋅=





Date:



0 6 120

11431

22862

Moment in Vertical Stiffener from Soil

Height Above Bottom

Mo

men

t

0 6 120

10956

21913

Moment in Vertical Stiffener from Product

Height Above Bottom

Mo

men

t





Date:


F. Vertical Stiffener Design

1. Beam Loadings

Ultimate Positive Bending Moment

Mup 1.6 Mmaxp⋅:=

Ultimate Negative Bending Moment

Mun 1.6 Mmaxe⋅:=

Ultimate shear in beam

VB 1.6 maxR2e

R2p

⋅:=





Date:



RT

2. Member Properties

UBLT1 12.00ft= UBLB1 0.10 ft=Unbraced length of top flange Unbraced length of bottom flange

Mup 35.06 ft kip⋅⋅= Mun 36.58 ft kip⋅⋅=Ultimate positive moment Ultimate negative moment

IB 61.90 in4

⋅= ZxB 17.00 in3

⋅=Moment of inertia of beam Plastic section modulus

CbB 1.00= ryB 1.23 in⋅=Bending diagram factor Weak axis radius of gyration

CwB 122.00 in6

⋅= IyB 7.97 in4

⋅=Torsional constant Weak axis moment of inertia

SxB 15.20 in3

⋅= rtsB 1.43 in⋅=Strong axis section modulus Torsional radius of gyration

dB 8.14 in⋅= tfB 0.33 in⋅=Beam depth Beam flange thickness

twB 0.23 in⋅= bfB 5.25 in⋅=Beam web thickness Beam flange width

cB 1.00= hoB 7.81 in⋅=Factor used for LTB capacity Center to center of flanges





Date:



3. Bending Strength

Critical unbraced flange length for which

inelastic bukling applies (AISC 360-05, F2-5)LpB 1.76 ryB⋅

Es

FyB

⋅:=

Critical unbraced flange length for which elastic bukling applies (AISC 360-05, F2-6)

LrB 1.95 rtsB⋅

Es

0.7 FyB⋅⋅

JB cB⋅

SxB hoB⋅⋅ 1 1 6.76

0.7 FyB⋅

Es

SxB hoB⋅

JB cB⋅⋅

2

⋅++⋅:=

FcrB UBL( )CbB π

2⋅ Es⋅

UBL

rtsB

21 0.078

JB cB⋅

SxB hoB⋅⋅

UBL

rtsB

2

⋅+⋅:= Critical stress based on LTB (AISC 360-05, F2-4)

Plastic moment strength (AISC 360-05, F2-1)MpB FyB ZxB⋅:=

Nominal moment strength

based on yieldingφMnYB 0.9 MpB⋅:=

φMnLTB UBL( ) 0.9 CbB⋅ MpB

MpB

0.7 FyB⋅ SxB⋅( )−+

...

UBL LpB−

LrB LpB−

⋅

−+

...

⋅:=


based on LTB (AISC 360-05,

F2-2 and F2-3

φMnLTBB UBL( ) 0.9 MpB⋅ UBL LpB≤if

φMnLTB UBL( ) UBL LpB>( ) UBL LrB≤( )⋅if

0.9 FcrB UBL( )⋅ SxB⋅ otherwise

:=


based on LTB with limits

(AISC 360-05, F2-2 and F2-3)





Date:



3. Bending Strength

λB CBFbyTF BEAM1( ) BEAM1 31≤if

WBFby2TFBEAM1 31− otherwise

:= Flange slenderness ratio for local buckling

(AISC 360-05 F3-1)

Web slenderness ratio (AISC 360-05 F3-2)HbyTW CHbyTW BEAM1( ) BEAM1 31≤if

WHbyTWBEAM1 31− otherwise

:=

Limiting slenderness for compact flange

(Table B4.1) λpfB 0.38

Es

FyB

⋅:=

Limiting slenderness for non-compact flange

(Table B4.1)λrfB 1.0Es

FyB

⋅:=

kcB 0.354

HbyTW0.35<if

0.764

HbyTW0.76>if

4

HbyTWotherwise

:= (AISC 360-05 F3-2)

φMnFLB 0.9 MpB

MpB

0.7 FyB⋅ SxB⋅( )−+

...

λB λpfB−

λrfB λpfB−

⋅

−+

...

⋅:=

Moment strength based on flange

local buckling (AISC 360-05 F3-1)

φMnFLBB 0.9 MpB⋅ λB λpfB≤if

φMnFLB λB λpfB>( ) λB λrfB≤( )⋅if

0.90.9 Es⋅ kcB⋅ SxB⋅

λB( )2

⋅ otherwise

:=


local buckling with limits (AISC

360-05 F3-1)





Date:



3. Bending Strength

φMnB UBL( ) min

φMnYB

φMnLTBB UBL( )

φMnFLBB

:= Nominal moment strength of beam

0 5 1030

40

50

60

70

Nominal Moment Strength

Positive Moment at Unbraced Length

Negative Moment at Unbraced Length

Beam Capacity as a Function of Unbraced Length

Unbraced Length (ft)

Mo

men

t C

apac

ity

(ft

-kip

s)

All ratios must be at 100% or less -

try another beam shape if over 100%

Mup

φMnB UBLT1( )80.14 %⋅=

Mun

φMnB UBLB1( )57.38 %⋅=





Date:



4. Shear Strength

φVnB 1.0 dB⋅ twB⋅ 0.6⋅ FyB⋅:=Nominal shear strength for beam

φVnB 56.17 kip⋅=

VB

φVnB

16.55 %⋅=Ratio must be less than or equal to 100% - try

another beam shape if over 100%

5. Web Compactness

Limiting slenderness ratio for web compactness

(AISC 360-05, Table B4.1)λpwB 3.76

Es

FyB

⋅:=

λpwB 90.55=

Slenderness ratio for beamHbyTW 29.90=

HbyTW

λpwB

33.02 %⋅= Ratio must be less than or equal to 100%





Date:


G. Loading in Horizontal Stiffener

Horizontal unit load due to soil pressurewhe

R1e

Sv

3124.65 plf⋅=:=

Horizontal unit load due to product pressurewhp

R1p

Sv

2996.16 plf⋅=:=

MheL

whe

Ltank

Ncross 1+

2

⋅

12Ltank Btank=if

whe

Ltank

Ncross 1+( )

2

⋅

8otherwise

:= Moment in long side due to soil pressure

MheL 64.05 ft kip⋅⋅=

MheB

whe Btank2

⋅

12Ltank Btank=if

whe Btank2

⋅

8otherwise

:= Moment in short side due to soil pressure

MheB 56.24 ft kip⋅⋅=

Shear in long direction due to soil pressure

VheL

whe

Ltank

Ncross 1+⋅

2:=

VheL 20006.44 lbs⋅=

Shear in short direction due to soil pressure

VheB

whe Btank⋅

2:=

VheB 18747.88 lbs⋅=





Date:

heB


G. Loading in Horizontal Stiffener

MhpL

whp

Ltank

Ncross 1+( )

2

⋅

12Ltank Btank=if

whp

Ltank

Ncross 1+( )

2

⋅

8otherwise

:= Moment in long side due to product pressure

MhpL 61.41 ft kip⋅⋅=

MhpB

whp Btank2

⋅

12Ltank Btank=if

whp Btank2

⋅

8otherwise

:= Moment in short side due to product pressure

MhpB 53.93 ft kip⋅⋅=

Shear in long direction due to product pressure

VhpL

whp

Ltank

Ncross 1+( )⋅

2:=

VhpL 19183.76 lbs⋅=

Shear in short direction due to product pressureVhpB

whp Btank⋅

2:=

VhpB 17976.96 lbs⋅=





Date:


H. Horizontal Stiffener Design (Long Side)

1. Beam Loadings


Mup 1.6 MhpL⋅:=


Mun 1.6 MheL⋅:=


VB 1.6 max

VheL

VhpL

⋅:=





Date:



RT


UBLT1 12.81ft= UBLB1 12.81ft=Unbraced length of top flange Unbraced length of bottom flange


IB 291.00 in4

⋅= ZxB 47.30 in3



CwB 887.00 in6

⋅= IyB 19.60 in4


SxB 42.00 in3









Date:



3. Bending Strength



Es

FyB

⋅:=


LrB 1.95 rtsB⋅

Es

0.7 FyB⋅⋅

JB cB⋅

SxB hoB⋅⋅ 1 1 6.76

0.7 FyB⋅

Es

SxB hoB⋅

JB cB⋅⋅

2

⋅++⋅:=

FcrB UBL( )CbB π

2⋅ Es⋅

UBL

rtsB

21 0.078

JB cB⋅

SxB hoB⋅⋅

UBL

rtsB

2

⋅+⋅:=Critical stress based on LTB (AISC 360-05, F2-4)





MpB

0.7 FyB⋅ SxB⋅( )−+

...

UBL LpB−

LrB LpB−

⋅

−+

...

⋅:=



F2-2 and F2-3




:=



(AISC 360-05, F2-2 and F2-3)





Date:



3. Bending Strength




(AISC 360-05 F3-1)



:=



Es

FyB

⋅:=



FyB

⋅:=

kcB 0.354

HbyTW0.35<if

0.764

HbyTW0.76>if

4

HbyTWotherwise

:= (AISC 360-05 F3-2)

φMnFLB 0.9 MpB

MpB

0.7 FyB⋅ SxB⋅( )−+

...

λB λpfB−

λrfB λpfB−

⋅

−+

...

⋅:=






λB( )2

⋅ otherwise

:=



360-05 F3-1)





Date:



3. Bending Strength

φMnB UBL( ) min

φMnYB

φMnLTBB UBL( )

φMnFLBB


0 5 1080

100

120

140

160

180






Mo

men

t C

apac

ity

(ft

-kip

s)



Mup

φMnB UBLT2( )78.82 %⋅=

Mun

φMnB UBLB2( )82.20 %⋅=





Date:



4. Shear Strength


φVnB 111.78 kip⋅=

VB

φVnB



5. Web Compactness



Es

FyB

⋅:=

λpwB 90.55=


HbyTW

λpwB


6. Beam Deflection

∆L 5

max

whe

whp

Ltank

Ncross 1+

4

⋅

384 Es⋅ IB⋅⋅ 0.22 in⋅=:= Beam deflection at top of tank

∆maxL

Ltank

1802.56 in⋅=:= Allowable beam deflection at top of tank

∆L

∆maxL






Date:


I. Horizontal Stiffener Design (Short Side)

1. Beam Loadings


Mup 1.6 MhpB⋅:=


Mun 1.6 MheB⋅:=


VB 1.6 max

VheB

VhpB

⋅:=





Date:



RT


UBLT1 12.00ft= UBLB1 12.00ft=Unbraced length of top flange Unbraced length of bottom flange


IB 291.00 in4

⋅= ZxB 47.30 in3



CwB 887.00 in6

⋅= IyB 19.60 in4


SxB 42.00 in3









Date:



3. Bending Strength



Es

FyB

⋅:=


LrB 1.95 rtsB⋅

Es

0.7 FyB⋅⋅

JB cB⋅

SxB hoB⋅⋅ 1 1 6.76

0.7 FyB⋅

Es

SxB hoB⋅

JB cB⋅⋅

2

⋅++⋅:=

FcrB UBL( )CbB π

2⋅ Es⋅

UBL

rtsB

21 0.078

JB cB⋅

SxB hoB⋅⋅

UBL

rtsB

2






MpB

0.7 FyB⋅ SxB⋅( )−+

...

UBL LpB−

LrB LpB−

⋅

−+

...

⋅:=



F2-2 and F2-3




:=



(AISC 360-05, F2-2 and F2-3)





Date:



3. Bending Strength




(AISC 360-05 F3-1)



:=



Es

FyB

⋅:=



FyB

⋅:=

kcB 0.354

HbyTW0.35<if

0.764

HbyTW0.76>if

4

HbyTWotherwise

:= (AISC 360-05 F3-2)

φMnFLB 0.9 MpB

MpB

0.7 FyB⋅ SxB⋅( )−+

...

λB λpfB−

λrfB λpfB−

⋅

−+

...

⋅:=






λB( )2

⋅ otherwise

:=



360-05 F3-1)





Date:



3. Bending Strength

φMnB UBL( ) min

φMnYB

φMnLTBB UBL( )

φMnFLBB


0 5 1080

100

120

140

160

180






Mo

men

t C

apac

ity

(ft

-kip

s)



Mup

φMnB UBLT3( )66.23 %⋅=

Mun

φMnB UBLB3( )69.07 %⋅=





Date:



4. Shear Strength


φVnB 111.78 kip⋅=

VB

φVnB



5. Web Compactness



Es

FyB

⋅:=

λpwB 90.55=


HbyTW

λpwB


6. Beam Deflection

Deflection of beam at top of tank∆B 5

max

whe

whp

Btank4

⋅

384 Es⋅ IB⋅⋅ 0.17 in⋅=:=

Allowable deflection of beam∆maxB

Btank

1800.80 in⋅=:=

∆B

∆maxB






Date:


J. Cross Stiffener Design

1. Member Loadings

Ultimate Axial Load

PC 1.6 2 VheL⋅ 64020.61 lbs⋅=:=

Ultimate strong axis shear in column

VxC 0 kip⋅:=

Ultimate weak axis shear in column

VyC 0 kip⋅:=

Ultimate Strong Axis Bending Moment at Top

MusT 0 ft⋅ kip⋅:=

Ultimate Strong Axis Bending Moment at Bottom

MusB 0 ft⋅ kip⋅:=

Ultimate Weak Axis Bending Moment at Top

MuwT 0 ft⋅ kip⋅:=

Ultimate Weak Axis Bending Moment at Bottom

MuwB 0 ft⋅ kip⋅:=

Ultimate Tensile Load

TC 1.6 2 VhpL⋅:=





Date:


J. Cross Stiffener DesignRT

2. Member PropertiesUnbraced length of

compression flange for flexureUBLF 12.00ft= ZyC 4.75 in

3⋅=

Plastic section modulus-weak axis

IC 29.30 in4

⋅= Moment of inertia of

columnZxC 10.80 in

3⋅=

Plastic section modulus-strong axis

AC 4.45 in2

⋅= Area of column ryC 1.45 in⋅=Weak axis radius of gyration

CwC 76.50 in6

⋅= rxC 2.56 in⋅=Torsional constant Weak axis radius of gyration

SxC 9.77 in3

⋅= IyC 9.32 in4

⋅=Strong axis section modulus Weak axis moment of inertia

SyC 3.11 in3

⋅= rtsC 1.65 in⋅=Weak axis section modulus Torsional radius of gyration

dC 5.99 in⋅= tfC 0.26 in⋅=Beam depth Beam flange thickness

twC 0.23 in⋅= bfC 5.99 in⋅=Beam web thickness Beam flange width

cC 1.00= hoC 5.73 in⋅=Factor used for LTB capacity Center to center of flanges





Date:



3. Strong Axis Bending Strength


inelastic bukling applies (AISC 360-05, F2-5)LpC 1.76 ryC⋅

Es

FyC

⋅:=


LrC 1.95 rtsC⋅

Es

0.7 FyC⋅⋅

JC cC⋅

SxC hoC⋅⋅ 1 1 6.76

0.7 FyC⋅

Es

SxC hoC⋅

JC cC⋅⋅

2

⋅++⋅:=

FcrC UBL( )CbC π

2⋅ Es⋅

UBL

rtsC

21 0.078

JC cC⋅

SxC hoC⋅⋅

UBL

rtsC

2


Plastic moment strength (AISC 360-05, F2-1)MpC FyC ZxC⋅:=


based on yieldingφMnYC 0.9 MpC⋅:=

φMnLTB UBL( ) 0.9 CbC⋅ MpC

MpC

0.7 FyC⋅ SxC⋅( )−+

...

UBL LpC−

LrC LpC−

⋅

−+

...

⋅:=



F2-2 and F2-3

φMnLTBC UBL( ) 0.9 MpC⋅ UBL LpC≤if

φMnLTB UBL( ) UBL LpC>( ) UBL LrC≤( )⋅if

0.9 FcrC UBL( )⋅ SxC⋅ otherwise

:=



(AISC 360-05, F2-2 and F2-3)





Date:




λC WBFby2TFCOL 31−:= Flange slenderness ratio for local buckling

(AISC 360-05 F3-1)

Web slenderness ratio (AISC 360-05 F3-2)HbyTW WHbyTWCOL 31−:=


(Table B4.1) λpfC 0.38

Es

FyC

⋅:=


(Table B4.1)λrfC 1.0Es

FyC

⋅:=

kcC 0.354

HbyTW0.35<if

0.764

HbyTW0.76>if

4

HbyTWotherwise

:= (AISC 360-05 F3-2)

φMnFLB 0.9 MpC

MpC

0.7 FyC⋅ SxC⋅( )−+

...

λC λpfC−

λrfC λpfC−

⋅

−+

...

⋅:=



φMnFLBC 0.9 MpC⋅ λC λpfC≤if

φMnFLB λC λpfC>( ) λC λrfC≤( )⋅if

0.90.9 Es⋅ kcC⋅ SxC⋅

λC( )2

⋅ otherwise

:=



360-05 F3-1)





Date:




φMnC UBL( ) min

φMnYC

φMnLTBC UBL( )

φMnFLBC


φMnC LC( ) 31.72 ft kip⋅⋅=

Maximum strong axis moment in columnMusC max

MusB

MusT

:=

MusC 0.00 ft kip⋅⋅=





Date:



4. Weak Axis Bending Strength

MpwC FyC ZyC⋅:= Plastic moment strength (AISC 360-05, F6-1)


based on yieldingφMnwYC 0.9 MpwC⋅:=

φMnwFLB 0.9 MpwC

MpwC

0.7 FyC⋅ SyC⋅( )−+

...

λC λpfC−

λrfC λpfC−

⋅

−+

...

⋅:=



φMnwFLBC 0.9 MpwC⋅ λC λpfC≤if

φMnwFLB λC λpfC>( ) λC λrfC≤( )⋅if

0.90.69 Es⋅ SyC⋅

λC( )2

⋅ otherwise

:=



360-05 F6)

φMnwC min

φMnYC

φMnFLBC

:= Nominal weak axis moment strength of

column

φMnwC 38.16 ft kip⋅⋅=

MuwC max

MuwB

MuwT

:=

MuwC 0.00 ft kip⋅⋅=Maximum weak axis bending moment





Date:



5. Column Axial Strength

λfxC

KxC UBLs⋅

rxC

:= λfyC

KyC UBLw⋅

ryC

:= Slenderness ratio for Y-axis and X-axis

FexC

π2

Es⋅

λfxC( )2

:= FeyC

π2

Es⋅

λfyC( )2

:=Elastic critical buckling stress for X-axis and

Y-axis - AISC 360-05 E3-4

Critical compressive stress for X-axis

without consideration to local buckling AISC

360-05 E3-2 and E3-3

FcrxC 0.658

FyC

FexCFyC⋅ λfxC 4.71

Es

FyC

⋅≤if

0.877 FexC⋅ otherwise

:=

Critical compressive stress for Y-axis

without consideration to local buckling AISC

360-05 E3-2 and E3-3FcryC 0.658

FyC

FeyCFyC⋅ λfyC 4.71

Es

FyC

⋅≤if

0.877 FeyC⋅ otherwise

:=

Controlling critical compressive stress

FcrC min

FcryC

FcrxC

:=

QsC 1 λC 0.56Es

FyC

⋅≤if

1.415 0.74 λC⋅

Es

FyC

⋅− λC 0.56Es

FyC

⋅>

λC 1.03

Es

FyC

⋅≤

⋅if

0.69 Es⋅

FyC λC( )2

⋅

otherwise

:=

QsC 1.00=Local buckling factor for unstiffened elements,

AISC 360-05 E7-4, E7-5, E7-6





Date:



5. Column Axial Strength

Effective width of web, AISC

360-05 E7-17bewC min

max 1.92 twC⋅

Es

FcrC

⋅ 1.34

HbyTW

Es

FcrC

⋅−

⋅ 0

HbyTW twC⋅

:=

AeffC AC HbyTW twC( )2

⋅− bewC twC⋅+:= AeffC 4.45 in2

⋅=

QaC

AeffC

AC

:= QaC 1.00= Local buckling factor for stiffened elements,

AISC 360-05 E7-16

QC QsC QaC⋅:= QC 1.00= Combined factor for determining critical

compressive stress including local buckling

FcrxQC QC 0.658

QC FyC⋅

FexC⋅ FyC⋅ λfxC 4.71

Es

QC FyC⋅⋅≤if

0.877 FexC⋅ otherwise

:= Critical compressive stress

for X-axis with consideration

to local buckling AISC

360-05 E3-2 and E3-3

Critical compressive stress

for Y-axis with

consideration to local

buckling AISC 360-05 E3-2

and E3-3

FcryQC QC 0.658

QC FyC⋅

FeyC⋅ FyC⋅ λfyC 4.71

Es

QC FyC⋅⋅≤if

0.877 FeyC⋅ otherwise

:=

Controlling critical compressive stress

with consideration to local bucklingFcrQC min

FcryC

FcrxC

:=

FcrQC 24310.31 psi=

φPnC 0.9 FcrQC⋅ AC⋅:= Compressive strength of column section AISC

360-05 E7-1

φPnC 97.36 kip⋅=





Date:



6. Check Interaction

INTC

PC

φPnC

8

9

MusC

φMnC LC( )

MuwC

φMnwC

+

⋅+

PC

φPnC

0.2≥if

PC

2 φPnC⋅

MusC

φMnC LC( )

MuwC

φMnwC

+

+ otherwise

:=

Interaction of bending and compression per AISC

360-05 H1-1a and H1-1b. Moments and axial force

must consider 2nd order effects.INTC 65.75 %⋅=

7. Shear Strength

φVnxC 1.0 dC⋅ twC⋅ 0.6⋅ FyC⋅:=Nominal shear strength for column

φVnxC 41.33 kip⋅=

VxC

φVnxC


another column shape if over 100%

φVnyC 1.0 2⋅ bfC⋅ tfC⋅ 0.6⋅ FyC⋅:=Nominal shear strength for column

φVnyC 93.44 kip⋅=

VyC

φVnyC


another column shape if over 100%

8. Web Compactness


(AISC 360-05, Table B4.1)λpwC 3.76

Es

FyC

⋅:=

λpwC 90.55=


HbyTW

λpwC



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Rectangular Tank Mathcad