Page 45 - 1

CONCRETE BIAXIAL COLUMN:

COMPOSITE CIRCULAR COLUMN 45 Christy

TANK SUPPORT 07:12

08/31/09

ENGINEERING with the SPREADSHEET

Copyright 2006 American Society of Civil Engineers
21562320.xls
A B C D E F G H I J K L M N
CONCRETE CIRCULAR COLUMN DESIGN Circular, β = 90.00º
L input → 24 in diameter for circular columns
W input ↑ 24 in Rectangular
Shape Circular Circular
FALSE logic
length / diameter 24 in
top

fY 60 ksi area b1,1 1.00 b2,1 1.00 Y top b3,1 1.00 b4,1 1.00
f'C 4 ksi column c1→ 8.1 c2→ 12.0 column c3→ 15.9 c4→ 19.2 row 20
row r1 ↑ 21.4 r1 ↑ 22.1 row r1 ↑ 21.4 r1 ↑ 19.2
Bar Size# 9
1.00 in2 area of bar b1,2 1.00 b2,2 9.24 Composite b3,2 0.00 b4,2 1.00
Bar Qty 16 bars c1→ 4.8 c2→ 12.000 c3→ 12.000 c4→ 21.354
r2 ↑ 19.2 r2 ↑ 20.480 r2 ↑ ­3.520 r2 ↑ 15.875
30.000

27.500
b1,3 1.00 b2,3 0.00 b3,3 9.24 b4,3 1.00
25.000 c1→ 2.6 c2→ ­10.6 c3→ 20.48 c4→ 22.1
22.500 r3 ↑ 15.9 r3 ↑ 5.1 r3 ↑ 12.00 r3 ↑ 12.0
20.000 X left X right
17.500
b1,4 1.00 b2,4 9.24 b3,4 0.00 b4,4 1.00
15.000
c1→ 1.9 c2→ 3.52 c3→ 6.000 c4→ 21.354
12.500

10.000
r4 ↑ 12.0 r4 ↑ 12.0 r4 ↑ 0.00 r4 ↑ 8.125
7.500

5.000 b1,5 1.00 b2,5 0.00 b3,5 9.24 b4,5 1.00

2.500 c1→ 2.6 c2→ 12.0 c3→ 12.00 c4→ 19.2
0.000 r5 ↑ 8.1 r5 ↑ 17.6 r5 ↑ 3.52 r5 ↑ 4.8
0.000 5.000 10.000 15.000 20.000 25.000
COMPRESSION BLOCK
b1,6 1.00 b2,6 1.00 b3,6 1.00 b4,6 1.00
Figure 45-1 Direction of loads col c1→ 4.8 c2→ 8.1 column 3→ 12.0 c4→ 15.9
and reinforcing placement. row r6 ↑ 4.8 r6 ↑ 2.6 Y bottom row r6 ↑ 1.9 r6 ↑ 2.6

Figure 45-2 Input reinforcing and check for placement.

Reinforcing
Lookup Table
Bar Size# Area
10M 0.16
Tied 0 0 = spiral, 1 = tied 15M 0.31
Tie Size# 3 Input rebar areas and check distances for placement. 20M 0.46
0.11 in2 area of tie 25M 0.77
Cover 1.50 in clear distance of rebar from face of column 30M 1.09
See ACI 7.7 clearances, ACI 7.10.4 spirals, ACI 7.10.5 ties, ACI 10.9.3 ρspiral 35M 1.55
45M 2.32
symetrical yes yes = symmetrical in both directions, no = not symmetrical 55M 3.87
0 0
3 0.11
4 0.20
White space is left for your input diagrams/drawings. 5 0.31
6 0.44
7 0.60
8 0.79
9 1.00
10 1.27
11 1.56
14 2.25
18 4.00

row 70
XX COLUMN LENGTHS and LOADS for BENDING ABOUT the X-AXIS Page
Circular, β =45 -2
90.00º
Lx 30.000
14 ft center-to-center beam-column joints
kx 1.0 unitless X bending 27.500
Lu x 13.25 ft unsupported length of column 25.000
22.500
FACTORED LOADS 20.000
Pu 465 k ult factored axial load 17.500
M2ux 1176 k-ft ult factored largest moment, always positive 15.000
12.500 21562320.xls
row 80
10.000
YY COLUMN LENGTHS and LOADS for BENDING ABOUT the Y-AXIS
Ly 14 ft center-to-center beam-column joints 7.500
ky 1.0 unitless 5.000
Luy 13.25 ft unsupported length of column Y bending 2.500
0.000
FACTORED LOADS 0.000 5.000 10.000 15.000 20.000 25.000
M2uy 0 k-ft ult factored largest moment, always positive Y - axis COMPRESSION BLOCK

Figure 45-3 Direction of loads with

reinforcing location and compression
BIAXIAL COLUMN SUMMARY block. row 90
PU required 465 k-ult required axial load
3500.0
Po 4536 k nominal axial load at e = 0
3000.0
Pn 641 k Pn provided
2500.0
ø3Pn provide 481 k-ult OK ø3Pn provided > 465 k-ult required
2000.0
1500.0
MU applied 1176 k-ft ult combined applied moments
1000.0
MC required 1176 k-ft ult magnified moments
500.0
MU provided 1202 k-ft OK Mu provided > 1,176 k-ult Mc required
en 0.0
29.99 in
-500.0 row 100
C_Test 11.000 in input value to determine compression block "a" -1000.0
-1500.0
max diag 24.00 in -2000.0
0 OK k Lu/r 19 ≤ 100 see ACI 10.10.5 braced frame and ACI 10.11.1 -2500.0
0 OK k Lu/r 19 ≤ 34 - 12 * M1/M2 no moment magnifier ACI 10.12.2 -3000.0
ρ 0.0919 unitless A s
/ A gross
density of reinforcing 0 200 400 600 800 1000 1200 1400
logic TRUE OK 0.0100 ρ minimum ≤ 0.0919 ρ provided ACI 10.9.1 Figure 45-4 Axial and moment capacities
logic FALSE !!!  0.0919  ρ provided   ≥  0.0800  ρ maximum  ACI 10.9.1 in the interaction diagram.

OK k Lu/rx 18.9 ≤ 100 see ACI 10.10.1 braced frame ACI 10.11.5 As Mu changes, Mu provided will change row 110
OK 18.9 ≤ 40.0 no moment magnifier in the X direction as a function of en * Pu.
non-sidesway in the X direction ACI 10.22.4.2

OK 18.9 k L/ry ≤ 100 ACI 10.11.5

OK 18.9 ≤ 34.0 no moment magnifier in the Y direction
non-sidesway in the Y direction ACI 10.11.4.2

β 1.571 radians resulting beta from combined, magnified MC2 x and MC2 y 0 row 118
0 ATAN( 1,176 / 0 ) 0
90.0000 degrees rotation of neutral axis counter clockwise from x-axis
0
I g xx ↑ 16286 in4 gross concrete 0
I xx ↑ 18435 in4 includes ± AS
0
0
I g yy → 16286 in4 gross concrete
I yy → 18435 in4 includes ± AS 0

Ec 57000 * f'C 0
3605 ksi Figure 45-5 Strain profile.
57000 * 4,000^0.5 / 1000
row 130
COLUMN SLENDERNESS and MOMENT MAGNIFIER for the X-AXIS Non-Sway Page
Circular, β =45 -3
90.00º
length 24 in referenced from above Mx
Lx 14 ft
kx 1.0 unitless
Pu 465 k ult X - axis
Ec 3605 ksi Move the formulas and explanations and Figure 45-6 Direction of moment icon.
copy-clip and park your math in a convenient cell.
M1 x -838 k-ft ult
smaller factored end moment, + in single curvature bending (, - in double curvature bending () 21562320.xls
M2 x 1176 k-ft ult larger factored end moment, always positive, referenced from above row 140
M1 < M2 OK
Cm 0.400 unitless 0.6 + 0.4 * (M1 / M2) , cannot be less than 0.4
Cm = 1 for transverse loads ACI 10.12.3.1
Cm x 0.400 unitless for transverse loading condition Cm applies to both the minimum e_min PU moment and
the MC2 moments.
FALSE logic Circular
rx 7.2 in 0.3 * h rectangular column ACI 10.11.2 Note: Greek, italic and math symbols from chapter 6 are
0.3 * 24.00 in used as much as possible to avoid format errors in Greek C,
rx 6.0 in 0.25 * diameter for circular columns Symbol SH, and Symbol when things are moved around.
rx ↑ 8.4 in computed ry or input ry as for composite column or Super and subscripting must still be redone -- but those
FOR STEEL COLUMN other section ACI (10 - 21) where the ACI quick errors are more obvious.
calculation in ACI 10.11.2 is overly conservative
Note Also: Symbols from chapter 6 appear as range
k Lux /rx 18.9 unitless kx * LUx / rx names when Insert, Name, Define is used. Use L
1.0 * 13.25 ft / 8.4 in * 12 in/ft instead of ℓ because ℓ does not show up as a range
FALSE logic name.
OK k Lu/rx 18.9 ≤ 100 see ACI 10.10.1 braced frame ACI 10.11.5
Subscript Lux rather than LUX which would be the more
Non-sidesway frames may neglect moment magnifier if: traditional choice. This is because range naming does not
Limit_x 40.0 unitless 34 - 12 * Mu 1 / Mu 2 < 40 ACI 10.12.2 (10-7) recognize formatted characters. A subscripted Lux which
min(40, 34 - 12 * -838 / 1,176 ) looks like Lux is more recognizable as a range name.
FALSE logic
OK 18.9 ≤ 40.0 no moment magnifier in the X direction
EI xx ### k-in2 ((EC * Ig / 5) + 29000 * Is ) / (1 + βd X ) ACI 10.12.3 (10-11)
((3,605 ksi * 16,286 in^4 / 5) + 29 ksi * 2,149.0 in^4) / (1 + 0.00)
EI ### k-in2 0.4 * Ec * Ig /(1 + bd ) ACI 10.12.3 (10 - 12)
0.4 * 3,605 ksi * 16,286 /(1 + 0.00 )
EI min x ### k-in2 min(23,484,413, 11,804,527) row 170

PC x 4128 k π2 * EI / (kx braced * Lux)2 Euler buckling load ACI 10.12.3 (10-10)
9.870 * 3,605 * 16,286 k-in² / (1.00 * 14.00 ft * 12 in/ft)²
δns xx 0.471 Cm / (1 - Pu / (0.75 * Pc x) ) ACI 10.12.3 (10-9) Pc, the column critical axial load, is ratioed against Pu. This is
0.40 / [1 - 465 / ( 0.75 * 4,128) ] used to reduce the stiffness factor EI which is important when
δns x 1.000 unitless max( 1.0, dns xx * Limit_x logic) column axial load is high.
max(1, 0.471 * 0)
M magnification factor for braced frame / no sidesway
row 180
e min x ↑ 1.32 in 0.6 + 0.03 * h minimum allowable e ACI 10.12.3.2 (10-14)
0.6 in + 0.03 * 24.00 in
emin Pu 51.15 k-ult dns x * e min x * Pu / 12 in/ft minimum required
1.000 * 1.32 * 465 /12
δns Mc2x 1176 k-ft ult dns M2x required The dns moment magnifier applies to both e_min * Pu moment
1.000 * 1,176 and applied Mc2 moment. The greater moment governs.
1176 k-ft ult
row 190
COLUMN SLENDERNESS and MOMENT MAGNIFIER for the X-AXIS -- SIDESWAY Circular, β = 90.00º
ΣPu x 7749 k ult sum of factored axial loads for all columns resisting sidesway
ΣVu x 1527 k sum of story horizontal shear Mx
M2sx 1174 k-ft ult larger factored moment due to loads causing appreciable sidesway
FALSE !!! input the larger factored end moment
X - axis
Icons are frequently used to help the
Do x 0.8 in relative lateral deflection designer and reviewer identify where
they are in the calculations.
row 200
A story can be considered as non-sidesway if:
Qx 0.02 unitless ΣPU x * ∆ o / (ΣVU x * LC) ≤ 0.05 ACI 10.11.4.2 (10 - 6)
7,749 * 0.80 / (1,527.00 * 14.00 in * 12)
TRUE logic Q < 0.05 is nonsway in the X direction
non-sidesway in the X direction ACI 10.22.4.2
 Page 45 - 4

Member slenderness in a frame not braced against sidesway can be neglected if:
sway x TRUE logic k LU /r ≤ 22 ACI 10.13.2
neglect column slenderness k Lu/r = 18.9 row 210

βd x 0.00 unitless ratio of maximum factored sustained axial load to maximum factored axial load for non-sidesway condition
ratio of the maximum sustained shear to the maximum shear within a story for sidesway condition
21562320.xls
Note: If the column is braced against sidesway or meets the conditions of ACI 10.11.4.2 (10-6)
story sidesway, use the non-sidesway moment magnifier.

row 220

Pcx 4128 k referenced from above

columns 5 each number of columns resisting sway

ΣPcx 20640 k ult sum of PC's for columns in a story resisting sidesway, for ds sidesway calculation

row 230
δs M2s x 1203 k-ft ult M2S /(1 - Q) ACI 12.13.4.2 (10-17)
1,174 /(1 - 0.02417)

ratio 1.023 unitless dS M2S /M2S

1,203 /1,176 The sum of column PC's is ratioed against the sum of column
FALSE logic 1.023 ≤ 1.5 ACI 10.13.4.2 PU's in sidesway calculations to reflect the interaction of all
sway resisting columns in a story.
δs M2s x 2351 unitless max(MS, MS / (1 - ΣPU x / (0.75 * ΣPC x) ) ) ACI 10.13.4.3 (10-18)
max(1,174, 1,174 /(1 - 7,749 /(0.75 * 20,640 + 0.001) ) )
M magnification factor for unbraced frame subject to sidesway

δs M2s x 1203 k-ft ult IF( 0, 2,351, 1,203 )

non-sidesway in the X direction ACI 10.22.4.2

Mc2 x 1176 k-ft ult dns M2x + ds M2Sx
0 + 1,176
row 250
COLUMN SLENDERNESS AND MOMENT MAGNIFIER for the Y-AXIS Non-Sway Page
Circular, β =45 -5
90.00º
width 24.0 in referenced from above
Ly 14 ft My
ky 1.00 unitless
Pu 465 k ult
Ec 3605 ksi Y - axis

M1 y 0 k-ft ult smaller factored end moment, + in single curvature bending (, - in double curvature bending (
)
M2 y 0 k-ft ult larger factored end moment, always positive 21562320.xls
M1 < M2 OK row 260

Cm 0.600 unitless 0.6 + 0.4 * (M1 / M2) , cannot be less than 0.4
Cm = 1 for transverse loads ACI 10.12.3.1
Cm y 1.00 unitless for transverse loading condition

FALSE logic Circular

ry → 7.2 in 0.3 * h rectangular column ACI 10.11.2
0.3 * 24.0 in
ry 6.0 in 0.25 * diameter for circular columns row 230
ry 8.4 in computed ry or input ry as for composite column or
FOR STEEL COLUMN other section ACI (10 - 21) where the ACI quick
calculation in 10.11.2 is overly conservative
k Luy /ry 18.9 unitless ky *LU y / ry * 12
1.00 * 13.25 ft / 8.4 in * 12 in/ft
FALSE logic
OK 18.9 k L/ry ≤ 100 ACI 10.11.5

Non-sidesway frames may neglect moment magnifier if: row 280

Limit_y 34.0 unitless 34 - 12 * Mu 1 / Mu 2 < 40 ACI 10.12.2 (10-7)
min(40, 34 - 12 * 0 / 0 )
FALSE logic
OK 18.9 ≤ 34.0 no moment magnifier in the Y direction

EI yy ### k-in2 ((EC * Ig / 5) + 29000 * Is ) / (1 + Bd y ) ACI 10.12.3 (10-11)

((3,604.997 ksi * 16,286 in^4 / 5) + 29 ksi * 2,149.0 in^4) / (1 + 0.00)
EI ### k-in2 0.4 * Ec * Ig /(1 + bd ) ACI (10 - 12)
0.4 * 3,605 ksi * 16,286 /(1 + 0.00 )
EI min y ### k-in2 min(23,484,413, 11,804,527) row 290

Pc y 4128 k π2 * EI / (k braced * LU)2 Euler buckling load ACI (10-10)

9.870 * 3,605 * 16,286 k-in² / (1.00 * 14.00 ft * 12 in/ft)²
δns yy 1.177 Cm / (1 - PU / (0.75 * PC y) ) ACI 10.12.3 (10-9) PC, the column critical axial load, is ratioed against PU . This
1.00 / [1 - 465 / ( 0.75 * 4,128) ] is used to reduce the stiffness factor EI which is important
δns y 1.000 unitless max( 1.0, dns xx * Limit_x logic) when column axial load is high.
max(1, 1.177 * 0)
M magnification factor for braced frame / no sidesway
row 300
e min y → 1.32 in 0.6 + 0.03 * h minimum allowable e ACI 10.12.3.2 (10-14)
0.6 in + 0.03 * 24.0 in ey → eccentricity distance of load from the
centroid of the gross section contributing
emin Pu 51.15 k-ult dns y * e min y * PU / 12 in/ft to MY moment, inches
1.000 * 1.32 * 465 /12
δns Mc2y 0 k-ft ult dns M2x required The dns moment magnifier applies to both the minimum
1.000 * 0 e_min * PU moment and applied MC2 moment.
51 k-ft ult The greater moment governs.
row 310
COLUMN SLENDERNESS and MOMENT MAGNIFIER for the Y-AXIS -- SIDESWAY Circular, β = 90.00º
ΣPu y 0 k ult for dns no sidesway calculation, sum of PU for all column loads in a story
ΣVu y 0k
M2s y 0 k-ft ult factored load due to loads causing appreciable sidesway My
logic TRUE .larger factored end moment

Y - axis
Doy 0 in

row 320
A story can be considered as non-sidesway if:
Qy 0 unitless ΣPU y * ∆ o / (ΣVU y * LC) ≤ 0.05 ACI 10.11.4.2 (10 - 6)
0.00 k * 0.00 in / (0.00 k * 13.25 in *12)
TRUE logic Q < 0.05 is nonsway in the Y direction
non-sidesway in the Y direction ACI 10.11.4.2
 Page 45 - 6

Member slenderness in a frame not braced againts sidesway can be neglected if:
sway y TRUE logic k Lu /r ≤ 22
neglect column slenderness k Lu/r = 18.9 row 330

βd y 0.00 unitless ratio of maximum factored sustained axial load to maximum factored axial load for non-sidesway condition
ratio of the maximum sustained shear to the maximum shear within a story for sidesway condition
21562320.xls

row 340

Pcy 4128 k referenced from above

columns 0 each number of columns resisting sway

ΣPcy 0 k ult sum of Pc's for columns in a story resisting sidesway, for ds sidesway calculation

row 350
δs M2s y 0 unitless M2S /(1 - Q) ACI 12,13,4,2 (10-17) Σ, sigma this means sum or the sum of
0 /(1 - 0.00000) for you liberal arts majors

ratio 0.000 unitless 0 /0

FALSE logic 0.000 ≤ 1.5 ACI 10.13.4.2 The sum of column Pc's is ratioed against the sum of
column Pu's in sidesway calculations to reflect the
interaction of all sway resisting columns in a story.
δs M2s y 0 k-ft ult max(MS, MS / (1 - ΣPU x / (0.75 * ΣPC x) ) )
ACI 10.13.4.3 (10-18)
max(0, 0 /(1 - 0 /(0.75 * 0 + 0.001) ) ) row 360
M magnification factor for unbraced frame subject to sidesway

δs M2s y 0 k-ft ult IF( 0, 0, 0 )

non-sidesway in the Y direction ACI 10.11.4.2

Mc2 y 51 k-ft ult dns M2y + ds M2Sy
0 + 51
row 370
MOMENT MAGNIFIER LOGIC SIEVE Page
Circular, β =45 -7
90.00º
X Y
emin Pu 51.15 51.15 emin PU is applied to only one axis at a time.
δns Mc2 1176 0 I have interpreted the provisions in ACI 10.12.3.2 to mean that if there is
1176 51 no moment applied in the X or Y axis, emin PU will not be considered in
that unloaded axis.

logic 1 FALSE Where there is no applied moment, the largest emin PU will be used in
Mc req'd 1176 0 the moment magnifier calculations. 21562320.xls
row 380
Mc req'd 1176 k-ft ult 1,176² + 0²

COLUMN COMBINED LOADINGS for BIAXIAL ANALYSIS

30.000
Mu applied 1176 k-ft ult √ 1,176² + 0² applied
27.500
ΣM1 838 k-ft ult √ -838² + 0²
ΣM2 1176 k-ft ult √ 1,176² + 0² braced-frame 25.000 row 390
ΣM2s 1174 k-ft ult √ 1,174² + 0² sway-frame 22.500
20.000
Mc 1176 k-ft ult √ MC x2 + MC y2 17.500
√ 1,176² + 0²)
15.000

Ec 57000 * f 'C
2 12.500
3605 k/in 2

57000 * 126.49 / 1000000 10.000

n 8.04 unitless E steel / E concrete 7.500
29000 ksi / 3,605 ksi 5.000
2.500 row 400
0.85 unitless reduce the .85 factor by .05 for each 1000 psi 0.000
over 4000 psi 0.000 5.000 10.000 15.000 20.000 25.000
β1 0.85 unitless but not less than 0.65 ACI 10.2.7.3 COMPRESSION BLOCK
Figure 45-7 Load direction with reinforcing
location and compression block.
RENIFORCING AREA and LAYOUT
Reinforcing Nomenclature Column
b1,1 b2,1 b3,1 b4,1 8.125 12.000 15.875 19.158 in
b1,2 b2,2 b3,2 b4,2 4.842 12.000 12.000 21.354 row 410
b1,3 b2,3 b3,3 b4,3 2.646 ­10.587 20.480 22.125
b1,4 b2,4 b3,4 b4,4 1.875 3.520 6.000 21.354
b1,5 b2,5 b3,5 b4,5 2.646 12.000 12.000 19.158
b1,6 b2,6 b3,6 b4,6 4.842 8.125 12.000 15.875
Row Area steel c1 c2 c3 c4
21.354 22.125 21.354 19.158 in A r1 c1 1.00 1.00 1.00 1.00 in2
19.158 20.480 ­3.520 15.875 r2 1.00 9.24 0.00 1.00
15.875 5.092 12.000 12.000 r3 1.00 0.00 9.24 1.00
12.000 12.000 0.000 8.125 r4 1.00 9.24 0.00 1.00 row 420
8.125 17.625 3.520 4.842 r5 1.00 0.00 9.24 1.00
4.842 2.646 1.875 2.646 r6 1.00 1.00 1.00 1.00
As sum 52.96 in2
P tension 2860 k-ult 0.9 * 52.96 * 60 ksi
A Circ 452 in2
A Rect 576 in2
A gross 452 in2
row 430
PLASTIC CENTROID INERTIA CALCULATIONS Circular,
Pageβ =45
90.00º
-8
For Gross Section Including Steel
-b1,1 b2,1 b3,1 b4,1 A An*dist. An d 2 A*Fy dist.*A*Fy Ad 2

An 8.04 8.04 8.04 8.04 32.18

distance 21.354 22.125 21.354 19.158
An*dist. 171.78 177.98 171.78 154.12 675.67
d 9.35 10.13 9.35 7.16
An d 2
703.94 824.68 703.94 412.21 2644.76
A*Fy 482.66 482.66 482.66 482.66 1930.65
dist.*A*Fy 10307.03 10678.93 10307.03 9247.05 40540.04 row 440
Ad 2
703.94 824.68 703.94 412.21 2644.76 21562320.xls
b1,2 b2,2 b3,2 b4,2
A 8.04 74.33 0.00 8.04 90.42
distance 19.158 20.480 -3.520 15.875
An*dist. 154.12 1522.28 0.00 127.70 1804.10
d 7.16 8.48 15.52 3.87
An d2 412.21 5345.11 0.00 120.78 5878.11
A*Fy 482.66 4459.81 0.00 482.66 5425.14
dist.*A*Fy 9247.05 91336.91 0.00 7662.20 108246.2 row 450
Ad2 412.21 5345.11 0.00 120.78 5878.11
b1,3 b2,3 b3,3 b4,3
A 8.04 0.00 74.33 8.04 90.42
distance 15.875 5.092 12.000 12.000
An*dist. 127.70 0.00 891.96 96.53 1116.20
d 3.87 6.91 0.00 0.00
An d2 120.78 0.00 0.00 0.00 120.78
A*Fy 482.66 0.00 4459.81 482.66 5425.14
dist.*A*Fy 7662.20 0.00 53517.72 5791.96 66971.89 row 460
Ad2 120.78 0.00 0.00 0.00 120.78
b1,4 b2,4 b3,4 b4,4
A 8.04 74.33 0.00 8.04 90.42
distance 12.000 12.000 0.000 8.125
An*dist. 96.53 891.96 0.00 65.36 1053.86
d 0.00 0.00 12.00 3.87
An d2 0.00 0.00 0.00 120.78 120.78
A*Fy 482.66 4459.81 0.00 482.66 5425.14
dist.*A*Fy 5791.96 53517.72 0.00 3921.72 63231.40
Ad2 0.00 0.00 0.00 120.78 120.78 row 470
b1,5 b2,5 b3,5 b4,5
A 8.04 0.00 74.33 8.04 90.42
distance 8.125 17.625 3.520 4.842
An*dist. 65.36 0.00 261.64 38.95 365.95
d 3.87 5.63 8.48 7.16
An d2 120.78 0.00 5345.11 412.21 5878.11
A*Fy 482.66 0.00 4459.81 482.66 5425.14
dist.*A*Fy 3921.72 0.00 15698.53 2336.88 21957.13 row 480
Ad2 120.78 0.00 5345.11 412.21 5878.11
b1,6 b2,6 b3,6 b4,6
A*n 8.04 8.04 8.04 8.04 32.18
distance 4.842 2.646 1.875 2.646
An*dist. 38.95 21.28 15.08 21.28 96.59
d 7.16 9.35 10.13 9.35
An d2 412.21 703.94 824.68 703.94 2644.76
A*Fy 482.66 482.66 482.66 482.66 1930.65
dist.*A*Fy 2336.88 1276.89 904.99 1276.89 5795.65 row 490
Ad2 412.21 703.94 824.68 703.94 2644.76
A*n An*dist. An d2 A*f'c dist.*A*Fy Ad2
cg 12 Ag 452.4 5429 0.000 1809.6 21714.7
d 0.00 ABS(12.00 - 12.00) sum 878.4 10541 17287 4987.2 59845.9 2148.99 I reinforcing only
CG xx 12.00 in
I rectangular 27648 in4 24.0 * 24.0³ /12
I circular 16286 in4 pd4/64 3.14 * 24.0^4 /64
Ig xx ↑ 16286 in4 Circular
PCx 12.00 in plastic centroid which yields uniform strain all across column from bottom fiber
I xx ↑ 18435 in4 gross concrete includes ± AS row 500
PLASTIC CENTROID INERTIA CALCULATIONS -- Continued Circular,
Pageβ =45
90.00º
-9
For Gross Section Including Steel
-b1,1 b2,1 b3,1 b4,1 A An*dist. An d 2 A*Fy dist.*A*Fy Ad 2

A*n 8.04 8.04 8.04 8.04 32.18

distance 8.125 12.000 15.875 19.158
An*dist. 525.80 776.55 1027.30 1239.78 3569.42
d 3.87 0.00 3.87 7.16
An d 2
971.61 0.00 971.61 3316.01 5259.2
A*Fy 482.66 482.66 482.66 482.66 1930.65
dist.*A*Fy 3921.72 5791.96 7662.20 9247.05 26622.93 row 510
Ad 2
120.78 0.00 120.78 412.21 653.78 21562320.xls
b1,2 b2,2 b3,2 b4,2
A *n 8.04 74.33 0.00 8.04 90.42
distance 4.842 12.000 12.000 21.354
An*dist. 313.31 7175.29 0.00 1381.90 8870.50
d 7.16 0.00 0.00 9.35
An d2 3316.01 0.00 0.00 5662.74 8978.74
A*Fy 482.66 4459.81 0.00 482.66 5425.14
dist.*A*Fy 2336.88 53517.72 0.00 10307.03 66161.63 row 520
Ad2 412.21 0.00 0.00 703.94 1116.15
b1,3 b2,3 b3,3 b4,3
A *n 8.04 0.00 74.33 8.04 90.42
distance 2.646 -10.587 20.480 22.125
An*dist. 171.20 0.00 12245.83 1431.76 13848.78
d 9.35 22.59 8.48 10.13
An d2 5662.74 0.00 42998.17 6634.01 55294.92
A*Fy 482.66 0.00 4459.81 482.66 5425.14
dist.*A*Fy 1276.89 0.00 91336.91 10678.93 103292.73 row 530
Ad2 703.94 0.00 5345.11 824.68 6873.72
b1,4 b2,4 b3,4 b4,4
A *n 8.04 74.33 0.00 8.04 90.42
distance 1.875 3.520 6.000 21.354
An*dist. 121.34 2104.75 0.00 1381.90 3607.98
d 10.13 8.48 6.00 9.35
An d2 6634.01 42998.17 0.00 5662.74 55294.92
A*Fy 482.66 4459.81 0.00 482.66 5425.14
dist.*A*Fy 904.99 15698.53 0.00 10307.03 26910.56 row 540
Ad2 824.68 5345.11 0.00 703.94 6873.72
b1,5 b2,5 b3,5 b4,5
A *n 8.04 0.00 74.33 8.04 90.42
distance 2.646 12.000 12.000 19.158
An*dist. 171.20 0.00 7175.29 1239.78 8586.27
d 9.35 0.00 0.00 7.16
An d2 5662.74 0.00 0.00 3316.01 8978.7
A*Fy 482.66 0.00 4459.81 482.66 5425.14
dist.*A*Fy 1276.89 0.00 53517.72 9247.05 64041.66 row 550
Ad2 703.94 0.00 0.00 412.21 1116.15
b1,6 b2,6 b3,6 b4,6
A *n 8.04 8.04 8.04 8.04 32.18
distance 4.842 8.125 12.000 15.875
An*dist. 313.31 525.80 776.55 1027.30 2642.95
d 7.16 3.87 0.00 3.87
An d2 3316.01 971.61 0.00 971.61 5259.23
A*Fy 482.66 482.66 482.66 482.66 1930.65
dist.*A*Fy 2336.88 3921.72 5791.96 7662.20 19712.76 row 560
Ad2 412.21 120.78 0.00 120.78 653.78
Ag An*dist. An d 2 A*Fy dist.*A*Fy Ad2
cg 12 Ag 452.4 5428.7 0.0 27143.4 325720.3
d 0.00 ABS(12.00 - 12.00) sum 878.4 10541.0 139065.8 30321.0 363851.5 2148.99 I reinforcing only
CG yy 12.00 in
I rectangular 27648 in4 24.0 * 24.0³ /12
I circular 16286 in4 pd4/64 3.14 * 24.0^4 /64
Ig yy → 16286 in4 Circular
PCy → 12.00 in plastic centroid which yields uniform strain all across column from left side fiber
I yy → 18435 in4 gross concrete includes ± AS row 570
RADIUS OF GYRATION Circular, β = 90.00º
rx ↑ 4.6 in √ I xx /area ↑

ry → 4.6 in √ I yy /area →

PLASTIC CENTROID STRAIN CALCULATIONS

β 1.5708 radians counter clockwise from the x-axis
90.0000 Idealized strain profile
sin β 1.0000
cos β 0.0000
tan β ### C_Test
r1, c1

Actual strain profile

Neutral Axis
 Plastic Centroid, PCxy a = β1 Page
* xb 45 - 10

Neutral Axis

Figure 45-8 Plan view of compression block Figure 45-9 The strain profile diagram.
and reinforcing.
Distance of Reinforcing from PCxy Es Young's modulus of steel, εS = strain
[ (12.00 - 8.13)^2 + (12.00 - 21.35)^2 ]^0.5 εs strain
21562320.xls
c1 c2 c3 c4 εcu concrete crushing strain, 0.003, unitless
PC r1 c1 10.13 10.13 10.13 10.12 εy strain at first yield, unitless
r2 10.12 8.48 15.52 10.13 ε's strain in compression reinforcing, unitless row 600
r3 10.13 23.62 8.48 10.13 εt allowable tension reinforcing strain, unitless
r4 10.13 8.48 13.42 10.13
r5 10.13 5.63 8.48 10.12 xb ,x bal distance of the neutral axis to the extreme
r6 10.12 10.13 10.13 10.13 fiber in compression noted as
C_test/β1 in this template, inches.
Es * STRAIN
C_TEST 11.000 in referenced from the summary window to the extreme fiber (up and right) perpendicular to the
axis through intersection of PCx and PCy
x bal /d = ε'c = 0.003 Strain Profile See 02 ACI 318 10.3.2 and 10.3.3
ε'c + εt = 0.003 + fy /29,000 row 610
x bal = 87 d /(87 + 60)
8.125 - $Pcx
horizontal c1 c2 c3 c4
r1 -3.875 0.000 3.875 7.158 inch
r2 -7.158 0.000 0.000 9.354
r3 -9.354 -22.587 8.480 10.125
r4 -10.125 -8.480 -6.000 9.354
r5 -9.354 0.000 0.000 7.158 β
r6 -7.158 -3.875 0.000 3.875 PCx ↑ row 620
21.354 - $Pcy PCy →
vertical c1 c2 c3 c4
r1 9.354 10.125 9.354 7.158 inch
r2 7.158 8.480 -15.520 3.875
r3 3.875 -6.908 0.000 0.000
r4 0.000 0.000 -12.000 -3.875
r5 -3.875 5.625 -8.480 -7.158 Figure 45-10 Rotation of the X-axis about PCxy.
r6 -7.158 -9.354 -10.125 -9.354
row 630
REINFORCING LOCATION LOGIC Page
Circular, 4590.00º
β= - 11
Horizontal Direction -β +β
-1 1 1 1
-1 1 1 1
-1 -1 1 1
-1 -1 -1 1
-1 1 1 1
-1 -1 1 1

Vertical Direction row 640

21562320.xls
1 1 1 1
1 1 -1 1
1 -1 1 1 Figure 45-11 Numerical sign notation.
1 1 -1 -1 30.000
-1 1 -1 -1 27.500
-1 -1 -1 -1 25.000
22.500
20.000
add pi()/2 to vertical direction 17.500
0 0 0 0 15.000
0 0 1 0 12.500 row 650
0 -1 0 0 10.000
7.500
0 0 -1 1
5.000
-1 0 1 1 2.500
-1 -1 1 1 0.000
0.000 5.000 10.000 15.000 20.000 25.000
Angle of Reinforcing from PCxy Vertical COMPRESSION BLOCK

ABS(ATAN(IF(0 , 9.354 /(-3.875 + 0.000001), -3.875 /(9.354 + 0.000001))) - PI() /2 * 0) * -1 Figure 45-12 Direction of loads.
angle c1 c2 c3 c4
r1 -0.3927 0.0000 0.3927 0.7854 radians -22.5 0.0 22.5 45.0 degrees
r2 -0.7854 0.0000 3.1416 1.1781 -45.0 0.0 180.0 67.5 row 660
r3 -1.1781 -1.8676 1.5708 1.5708 -67.5 -107.0 90.0 90.0
r4 -1.5708 -1.5708 -2.6779 1.9635 -90.0 -90.0 -153.4 112.5
r5 -1.9635 0.0000 3.1416 2.3562 -112.5 0.0 180.0 135.0
r6 -2.3562 -2.7489 3.1416 2.7489 -135.0 -157.5 180.0 157.5
Difference between β and Reinforcing Angle
$β + R1 C1
1.5708 + -0.3927
c1 c2 c3 c4
r1 1.1781 1.5708 1.9635 2.3562 67.5 90.0 112.5 135.0 degrees row 670
r2 0.7854 1.5708 4.7124 2.7489 radians 45.0 90.0 270.0 157.5
r3 0.3927 -0.2968 3.1416 3.1416 22.5 -17.0 180.0 180.0
r4 0.0000 0.0000 -1.1071 3.5343 0.0 0.0 -63.4 202.5
r5 -0.3927 1.5708 4.7124 3.9270 -22.5 90.0 270.0 225.0
r6 -0.7854 -1.1781 4.7124 4.3197 -45.0 -67.5 270.0 247.5 β

Distance
Distance of Rebar from Rotating X-axis Through PCxy
SIN(r1 c1) * PC_r1_c1 Angle of Reinforcing
SIN(1.1781) * 10.13 row 680
c1 c2 c3 c4
r1 9.354 10.125 9.354 7.158 inch
r2 7.158 8.480 -15.520 3.875
r3 3.875 -6.908 0.000 0.000
r4 0.000 0.000 -12.000 -3.875
r5 -3.875 5.625 -8.480 -7.158
r6 -7.158 -9.354 -10.125 -9.354
Figure 45-13 Distance of reinforcing from the
rotationg vertical axis through PCxy.
row 690
REINFORCING STRAIN Page
Circular, 4590.00º
β= - 12
C_Test 11.000 in reference
β1 0.85 unitless reference
N.A. 12.941 11.000 /0.85 neutral axis N.A. C_Test
PCxy
strain u 0 unitless 60 /29000 strain to first yield, reference
β 1.571 radians reference 90.0000 degrees

21562320.xls
row 700
C_Test to PCxy N.A. to PCxy
x top→pt 12.0000 x begin→ 12.0000 0.0000 x begin→ 12.0000 0.0000 reinf
y top ↑ pt 24.0000 y begin↑ 13.0000 1.0000 y begin↑ 11.0588 -0.9412

add xy 0.9412 in Figure 45-14 The extreme fiber to the neutral

max diag c 24.000 in max circular diagonal axis and the relative strain in the reinforcing.
Max Diag 24.000 in 0
0 0
Relative Strain 0
9.354 /12.941 0
c1 c2 c3 c4 0
0
r1 0.723 0.782 0.723 0.626 unitless
0
r2 0.553 0.655 -1.199 0.299 0
r3 0.299 -0.534 0.000 0.000 0
r4 0.000 0.000 -0.927 -0.299 0
r5 -0.299 0.435 -0.655 -0.553 0
r6 -0.553 -0.723 -0.782 -0.723 0
0
Reinforcing 0
0
Where: 87 = 0.003*29000
87 * 0.723 Figure 45-15 Strain Profile
c1 c2 c3 c4
r1 62.89 68.07 62.89 54.45 k STRAIN DIAGRAM
r2 48.12 57.01 -104.34 26.05 X 0.01 1 1 0.01 0.01
r3 26.05 -46.44 0.00 0.00 Y 0.00360 0 0 0 0.0036
r4 0.00 0.00 -80.67 -26.05
r5 -26.05 37.82 -57.01 -48.12
r6 -48.12 -62.89 -68.07 -62.89
row 730
30.000
LIMIT fy 27.500
25.000
IF(ABS(Reinforcing) > Fy, fs_1, c1 /ABS(fs_1, c1) * Fy, fs_1, c1)
22.500
IF(ABS(62.89) > 60, 62.9 /ABS(62.89) * 60, 62.89) 20.000
c1 c2 c3 c4 17.500
fs_1 c1 60.0 60.0 60.0 54.5 ksi 15.000
fs_2 48.1 57.0 -60.0 26.0 12.500

fs_3 26.0 -46.4 0.0 0.0 10.000

7.500
fs_4 0.0 0.0 -60.0 -26.0
5.000
fs_5 -26.0 37.8 -57.0 -48.1 row 740
2.500
fs_6 -48.1 -60.0 -60.0 -60.0 0.000
0.000 5.000 10.000 15.000 20.000 25.000
COMPRESSION BLOCK

Figure 45-16 Load direction with reinforcing

location and compression block.

row 750
For Pn Page
Circular, 4590.00º
β= - 13
Tension Steel k
A_r1_c1 * fs_1_c1 * (fs_1_c1 < 0) PCx ↑
1.00 * 60.0 * (60.0 < 0) PCy →
c1 c2 c3 c4
Ts_1 0.0 0.0 0.0 0.0 k
Ts_2 0.0 0.0 0.0 0.0
Ts_3 0.0 0.0 0.0 0.0
Ts_4 0.0 0.0 0.0 -26.0 21562320.xls
Ts_5 -26.0 0.0 -526.8 -48.1 row 760
Ts_6 -48.1 -60.0 -60.0 -60.0
30.000
STL_COMP 1 logic 1 for f 'S = ES * eS compression reinforcing compatibility switch 27.500
0 for f 'S = 0 when f 'S < fy 25.000
Compression Steel k 22.500
A_r1_c1 * fs_1_c1 * (fs_1_c1 > 0) 20.000
1.00 * 60.0 * (60.0 > 0) 17.500
c1 c2 c3 c4
15.000
Cs_1 60.000 60.0 60.0 54.5 k
12.500
Cs_2 48.1 526.8 0.0 26.0 row 770
10.000
Cs_3 26.0 0.0 0.0 0.0
7.500
Cs_4 0.0 0.0 0.0 0.0
5.000
Cs_5 0.0 0.0 0.0 0.0
Cs_6 0.0 0.0 0.0 0.0 2.500
0.000
0.000 5.000 10.000 15.000 20.000 25.000
C_Test AS COMPRESSION BLOCK

Area Cc 2.89 unitless Deduct the area of reinforcing As * β1 * f'c of steel for Cc
Figure 45-17 Load direction with
reinforcing location and compression row 780
block.

TS*arm
-Ts_1, c1 * PC_r1_c1 row 790
- 0.0 * 10.1
0.0 0.0 0.0 0.0 k-in
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 263.8
263.8 0.0 4466.9 487.2
487.2 607.5 607.5 607.5

Cs * arm row 800

Cs_1, c1 * PC_r1_c1
60.0 * 10.1
607.5 607.5 607.5 551.2 k-in
487.2 4466.9 0.0 263.8
263.8 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0

row 810
For Pnen Page
Circular, 4590.00º
β= - 14
FALSE logic Circular
TS arm 7791 k-in TS * arm from centroid
CS arm 7855 k-in
CC arm 3577 k-in CC conc * CL area
IF(0, 844.6 * 6.50, 634.6 * 5.64 )

Pnen 19224 k-in Ts_arm + Cs_arm + Cc_arm

1602.0 k-ft
en 29.99 in Pnen / Pn 21562320.xls
row 820
19,224.21 / 640.92

Sym TRUE logic +As = -As symmetry

fy < 60 TRUE logic fy < 60

row 830

Figure 45-18 The Interaction diagram for axial load

and bending moment.

Yxx↑ 0.844 unitless (h - d' - ds) /h > 0.70 ACI 9.3.2.2 Where:
Yyy→ 0.844 unitless (h - d' - ds) /h > 0.70 fy < 60 ksi
and reinforcing is symmetrical row 840
Y 1 logic Yxx and Yyy > 0.70 (h - d' - ds) /h > 0.70
ø may be increased linearly to 0.90
as øPn decreases from 0.10 f'c Ag to 0
ACI 9.3.2.2
ø1 0.75 unitless Tied columns = 0.7, Spiral tied columns = 0.75 ACI 9.3.2.2
ø1Pn 480.7 k ø1 * Pn
0.75 * 640.9

Tie 0.15 Tied columns = 0.2, Spiral tied columns = 0.15

(0 = 1) * 0.2 + (0 = 0) * 0.15 row 850

_.1Agf'c 230 k 0.10 * length * width * f'C ACI 9.3.2.2

0.10 * 24.00 * 24.00 * 4

ø2 0.75 unitless max (ø1 , 0.90 - (Tie * ø1Pn /_.1Agf'C )) ACI 9.3.2.2
MAX(0.75, (0.9 - (0.15 * 481 /230 )))

ø2Pn 481 k ø2 * Pn
0.75 * 640.9
row 860
ø3 0.75 max (ø1 , 0.90 - (Tie * ø2Pn /_.1Agf'C))
MAX(0.75, (0.9 - (0.15 * 481 /230)))

ø3Pn 480.7 k ø3 * Pn * (sum(Sym + [fy < 60] + Y) = 3)

0.75 * 641 * ((1 + 1 + 1) = 3)
where conditions of symmetry, fy < 60, and Yxx & Yyy > 0.70 are met

row 870
MATH for RECTANGULAR ROTATING COMPRESSION BLOCK Page
Circular, 4590.00º
β= - 15
L 24.00 in referenced from above
W 24.00 in reference
βinput 1.5708 radians reference
90.0000 degrees
tan β ### unitless
sin β 1.0000 unitless 1111 0110 0110 0110 0110
cos β 0.0000 unitless 0111 0111 1110 1110
1 2 0110 3 4
PCx 12.00 in PCx top 12.00 in Figure 45-19 30.000
Area computation logic diagrams. 21562320.xls
row 880
PCy 12.00 in PCy right 12.00 in 27.500
25.000
A diag 0.785 rad 22.500
45.000 deg 20.000
diag 16.971 in PC x, y to top right corner 17.500
sweep TRUE logic βinput > A diag 15.000
12.500
diff 0.7854 rad difference between diagonal and load direction 10.000
45.0000 deg 7.500
5.000 row 890
x top→pt 12.0000 0.0000 12.0000 pt the extreme fiber up and right 2.500
0.000
y top ↑ pt 12.0000 12.0000 24.0000
0.000 5.000 10.000 15.000 20.000 25.000
COMPRESSION BLOCK
C_Test 11.000
For 0 pressure line intersection with perimeter Figure 45-20 Load direction and compression block.
x top→pt 12.000 x diag→ 0.0000
y top ↑ pt 24.000 y diag↑ 11.0000 x begin→ 12.000 x top→ ### x top→ 0 FALSE
y begin↑ 13.000 y top ↑ 0.000 y top ↑ 13 TRUE
x bot→ 24.000 x bot→ 24 TRUE
logic 0110 0110 y bot ↑ 0.000 y bot ↑ 13 TRUE
logic 0111 1110 A triangle
x→ 24.00 0.00 1111 0111 0110 1110
y ↑ 11.000 24 24.000 24.000 24.000 24.000
A rect 264.0 0.0 11.000 0.000 13.000 24.000
132.0 0.0 156.0 288.0
logic TRUE FALSE 0 1 0 0
logic 0 2 0 0 sum A 2
A rect 264.0 0.0 0.0 0.0 0.0 0.0 264.00 in² area of compression block
row 910
CG y→ 12.00 24.00 16.00 16.00 16.00 16.00 in
CG x ↑ 18.50 12.00 20.33 13.00 8.67 16.00 in
sum Ad CG from bottom left CG from top right
Ad y→ 3168.0 0.0 0.0 0.0 0.0 0.0 3168 in³ 12 in→ 12 in←
Ad x ↑ 4884.0 0.0 0.0 0.0 0.0 0.0 4884 in³ 18.5 in ↑ 5.5 in ↓
CG PCy→ 0.0000 in→
CG PCx↑ 6.5000 in ↑
CG PCxy 6.5000 in sum(d*A) / AREA from PCx and y
row 920
CC concrete 845 k 0.85 * f'C * AREA -sum(d < C_TEST AS ) w/o deduct for comp st'l area
0.85 * 4.00 * 264.00 - SUM(52.96)

Pn 851 k T s + C s + C c the nominal axial load strength

19,946 k + 78,679 k + 845 k
Conc 1778 k 0.85 * f'C * (Lxx * Wyy - sum(Area steel))
Steel rect 3177.6 k fy * sum(Area steel)
Po 4956 k Conc + Steel rectangular
Pn max 3402 k Po*ø1 (Design Strength Factor)
row 930
MATH for SEMICIRCULAR ROTATING COMPRESSION BLOCK Page
Circular, 4590.00º
β= - 16
Lxx 24.0 in referenced from above
W yy 24.0 in
24.0 in
33.9 in
max diag 24.0 in
C Test 11 in compress block reference
For a bearing area as a partially loaded semicircle to full semicircle 12.00
leg b 11.96 in ((24.00 /2 )^2 - (24.00 /2 - 11.000)^2 )^0.5 0.00 21562320.xls
chord 23.92 in 11.00 row 940
leg c 12.00 in radius
angle α 1.4874 radians atan(11.96 /(24.00 /2 - 11.00))
A segment 202.2 in2 (24.00 /2)^2 * (1.4874 - SIN(1.4874) * COS(1.4874))

c
A semi c 226.2 in2 area of semicircle

leg
A bearing 1 202.2 in2 11.96

xc 5.64 in cg of bearing area 1 α A

xc semi c 5.09 in
xc bearing 1 5.64 in
row 950
For a bearing area as a loaded semicircle to fully loaded circle
angle α 4.6290 radians
A segment 202.2 in2
A bearing 2 428.4 in2 A semi c - A segment
xc seg -5.64 in CL Tank 5.64 xc centroid
xc bearing 2 5.35 in

A sum 202.2 in2 Figure 45-21 Diagram of a circular segment

xc sum -5.70 in
row 960
CL area 5.64 in to CG of compression area
CC concrete 635 k 0.85 * f'C * AREA -sum(d < C_TEST AS ) w/o deduct for comp st'l area
0.85 * 4.00 * 202.22 - SUM(52.96)
30.000
Pn 641 k Ts + Cs + Cc nominal axial load strength 27.500
25.000
-855 k + 861 k + 635 k
22.500
Conc Circular 20.000
Circular 1358 k 0.85 * f'C * (p r2 - sum(Area steel)) 17.500
Rectangle 1905 15.000 row 970
1358 12.500
10.000
7.500
Steel 3178 k fy * sum(Area steel)
5.000
Po 4536 k Conc + Steel circular 2.500
Pn max 3402 k Po*ø1 (Design Strength Factor) 0.000
0.000 5.000 10.000 15.000 20.000 25.000

Rectangular / Circular Switch Figure 45-22 Direction of loads.

Shape C alpha Circular row 980
FALSE Logic 0 = Circular, 1 = Rectangular
CL area 5.64
CC concrete 635
Pn 641 k
Conc 1358 k
St'l 3178 k
Po 4536 k
Pn max 3402 k
row 990
LOTUS MACRO LANGUAGE Page 45 - 17
VBA is Microsoft's Visual Basic for Applications. Microsoft refers to this as a macro language but it is, in truth,
computer code which requires a bit of time to learn.

The Lotus 1-2-3 r2.01 macro language was tailored specifically for the spreadsheet. It is flexible and relatively
easy to learn.

Microsoft's Excel for Microsoft office '97 allows the use of Lotus 1-2-3 macros. The range names to activate
a macro must be created in Lotus 1-2-3 r2.01, however. At the top of this template are several macro range
names that can be used to activate a macro. 21562320.xls
row 1000

The \a is the range name for the cell to the right. Hold down the [Ctrl] key and press a to start the macro.

These macros make use of string concantenation to wright values into cells and branch to other macros.

The graphing macro activated by [Ctrl] [Shift] x is written in VBA. The value range must be adjusted in the
VBA code.

\a {goto}Testing~ row 1010

{Let M_Compare,3.486}
{calc}
{branch M_BranchB1}

M branch {Let Testing,11.120} M_BranchB1 {Let Testing,10.880} converge 0

above {Let M_Compare,3.486} {Let M_Compare,3.486} M conv TRUE
{calc} {calc} M copy 0.120
{Branch M_Branch} {Branch M_BranchB1}
M Compare 3.486
Branch 7.514 row 1020
M Branch2 {Let Testing,11.118} M_BranchB2 {Let Testing,10.882}
below {Let M_Compare,11.120} {Let M_Compare,11.000}
{calc} {calc}
{Let Testing,24.000} {Let Testing,11.000}
{beep} {beep}

\e {goto}Testing~
{Let P_Compare,11.000} row 1030
{calc}
{Branch P_BranchB1}

P branch {Let Testing,10.952} P_BranchB1 {Let Testing,10.814} converge 0

above {Let P_Compare,11.000} {Let P_Compare,11.000} P conv TRUE
{calc} {calc} P copy 0.187
{Branch P_Branch} {Branch P_BranchB1}
P Compare 23.913
P Branch2 {Let Testing,10.815} P_BranchB2 {Let Testing,10.815} Branch 0.000
below {Let P_Compare,11.091} {calc} row 1040
{calc} {Let P_Compare,10.998}
{Let Testing,11.000} {Let Testing,11.001}
{beep} {beep}

row 1050
 VERIFYING GRAPHS Graphing Ctrl Shift x Page 45 - 18
24" circular column with 16 - #7's. Combined M2ux and M2uy = Mu provided. Pu = 200 k-ult.
β 1.571 aa 0 0 0.03 0.13 0.25 0.38 0.52 0.68 0.74 0.79 0.83
C_Test 11 15.22 15.57 15.59 15.63 15.57 15.39 15.45 15.4 15.34 15.29 15.34
M2Ux 1176 0 1 10 50 100 150 200 250 270 282.84 295.13
M2Uy 0 400 400 399.87 396.86 387.3 370.81 346.41 312.25 295.13 282.84 270
ø3Pn provided/10 48.069 76.42 79.69 79.76 79.84 79.26 77.97 78.14 77.77 77.38 77.04 77.38

area b1,1 0.60 b2,1 0.60 b3,1 0.60 b4,1 0.60 80 21562320.xls
column c1→ 8.2 c2→ 12.0 column c3→ 15.8 c4→ 19.1
75
row r1 ↑ 21.2 r1 ↑ 22.0 row r1 ↑ 21.2 r1 ↑ 19.1
70
b1,2 0.60 b2,2 0.00 Composite b3,2 0.00 b4,2 0.60 65
c1→ 4.9 c2→ 12.000 c3→ 12.000 c4→ 21.239
60
r2 ↑ 19.07 r2 ↑ 20.48 r2 ↑ ­3.52 r2 ↑ 15.83
55
b1,3 0.60 b2,3 0.00 b3,3 0.00 b4,3 0.60 50
c1→ 2.8 c2→ ­10.6 c3→ 20.48 c4→ 22.0 45
r3 ↑ 15.8 r3 ↑ 5.1 r3 ↑ 12.00 r3 ↑ 12.0 40
35
b1,4 0.60 b2,4 0.00 b3,4 0.00 b4,4 0.60
c1→ 2.0 c2→ 3.52 c3→ 6.000 c4→ 21.239 30
r4 ↑ 12.0 r4 ↑ 12.0 r4 ↑ 0.00 r4 ↑ 8.173 25
20
b1,5 0.60 b2,5 0.00 b3,5 0.00 b4,5 0.60
15
c1→ 2.8 c2→ 12.0 c3→ 12.00 c4→ 19.1
0 0.25 0.5 0.75 1 1.25 1.5 1.75
r5 ↑ 8.2 r5 ↑ 17.6 r5 ↑ 3.52 r5 ↑ 4.9
C_Test ø3Pn
b1,6 0.60 b2,6 0.60 b3,6 0.60 b4,6 0.60 provided/1
col c1→ 4.9 c2→ 8.2 column 3→ 12.0 c4→ 15.8 0
row r6 ↑ 4.9 r6 ↑ 2.8 row r6 ↑ 2.0 r6 ↑ 2.8
Figure 45-23 Curves for M2Ux and M2Uy.
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
Colum Colum Colum Colum Colum Colum Colum Colum Colum Colum Colum Colum Colum Colum Colum Colum Colum Colum
nD nE nF nG nH nI nJ nK nL nM nN nO nP nQ nR nS nT nU

ø3Pn provided/10

Figure 45-24 M2Ux versus C_Test.

VERIFYING GRAPHS -- Continued Page 45 - 19
24" square column with 16 - #7's. Combined M2ux and M2uy. Pu = 200 k-ult.
C_Test aa 18.71 19.02 19.25 20.15 21.02 21.57 22.01 22.26 22.28 22.26 22.28
M2Ux 0 1 10 50 100 150 200 250 270 282.84 295.13
M2Uy 400 400 399.87 396.86 387.3 370.81 346.41 312.25 295.13 282.84 270
ø3Pn provided/10 113.75 117 117 116 114.52 113 113 113 113 113 113
10 en 4.22 4 4 4 4.19 4 4 4 4 4 4
100 β 1.67 1.667 1.667 1.667 1.67 1.667 1.667 1.667 1.667 1.667 1.667
21562320.xls
400
375
350
325
300
275
250
225
200
175
150
125
100
75
50
25
0
18.5 18.75 19 19.25 19.5 19.75 20 20.25 20.5 20.75 21 21.25 21.5 21.75 22 22.25 22.5

Row 1114 Row 1115 Row 1116

Figure 45-25 Combined M2ux and M2uy.

24 x 24 COLUMN WITH 8 - #8's C_TEST ADJUSTED FOR ø3Pn provided = PU required = 900 k ult
C_Test 11.000 aaa 14.786 14.58 14.85 15.94 17.1 18.01 18.62 18.9 18.91 18.91 18.62
M2Ux 1176.000 0.00 1 10 50 100 150 200 270 282.84 295.13 346.41
M2Uy 0.00 400 400 399.87 396.86 387.3 370.81 346.41 295.13 282.84 270 200
MU provided 1202 464.80 481.63 480.41 475.04 467.93 459.94 450.7 437.21 435.32 437.2 450.7
β*100 1.57 0.0000 0.25 2.5 12.53 25.27 38.44 52.36 74.1 78.54 82.98 104.72
logic 2 4 4 4 4 4 4 4 3 3 3 2

0 25 250.03 1253.28 2526.8 3843.97 5235.99 7409.65 7853.99 8298.32 10471.98

400

300

200

100

0
14.500 15.000 15.500 16.000 16.500 17.000 17.500 18.000 18.500 19.000

Row 1149 Row 1150

Figure 45-26 The rotation of β through 1/4 π radians (90º) to check M2Ux, M2Uy, and Mu provided.
VERIFYING GRAPHS -- Continued Page 45 - 20
24 x 24 COLUMN WITH 8 - #8's C_TEST ADJUSTED FOR M provided = M required Pu = 200
C_Test 11 aaa 4.56 5.17 5.34 6.14 7.42 8.92 8.92 10.08 11.11 11.44 11.59
M2Ux 1176 0 1 10 50 100 150 150 200 250 270 282.84
M2Uy 0 400 400 399.87 396.86 387.3 370.81 370.81 346.41 312.25 295.13 282.84
β*100 157.08 0 0.25 2.5 12.53 25.27 38.44 38.44 52.36 67.51 74.1 78.54
ø3Pn provide/10 48.069
logic 2 4 4 4 4 4 1 1 1 1 1 1
21562320.xls
400

375

350

325
300

275

250

225

200

175

150

125

100

75

50

25
0
4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5

M2Ux M2Uy β*100

Figure 45-27 C_Test compression block versus M2Ux and M2Uy.

VERIFYING GRAPHS -- Continued Page 45 - 21
24 x 24 COLUMN WITH 8 - #8's C_TEST VARIES WITH MOMENT Pu = 50 k-ult
C_Test 11 aaa 1.95 2.26 3.25 4.21 4.59 5.15 6.5 8.37
M2Ux 1176.000 325 340 350 360 375 400 450 500
MU provided 1201.51 327.034 340.03 350.01 360.01 375.06 400.02 450.011 500.006
ø3Pn provided 481 50.018 71.28 152.77 219.44 244.89 284.63 375.892 497.501
en*10 299.95 784.594 572.42 274.92 196.87 183.79 168.65 143.662 120.604

area b1,1 0 b2,1 0.79 b3,1 0 b4,1 0.79 21562320.xls

column c1→ 8.17 c2→ 12 column c3→ 15.83 c4→ 19.07
row r1 ↑ 21.24 r1 ↑ 22 row r1 ↑ 21.24 r1 ↑ 19.07

b1,2 0.79 b2,2 0 Composite b3,2 0 b4,2 0

c1→ 4.93 c2→ 12 c3→ 12 c4→ 21.24
r2 ↑ 19.07 r2 ↑ 20.48 r2 ↑ -3.52 r2 ↑ 15.83

b1,3 0 b2,3 0 b3,3 0 b4,3 0.79

c1→ 2.76 c2→ -10.59 c3→ 20.48 c4→ 22
r3 ↑ 15.83 r3 ↑ 5.09 r3 ↑ 12 r3 ↑ 12

b1,4 0.79 b2,4 0 b3,4 0 b4,4 0

c1→ 2 c2→ 3.52 c3→ 6 c4→ 21.24
r4 ↑ 12 r4 ↑ 12 r4 ↑ 0 r4 ↑ 8.17

b1,5 0 b2,5 0 b3,5 0 b4,5 0.79

c1→ 2.76 c2→ 12 c3→ 12 c4→ 19.07
r5 ↑ 8.17 r5 ↑ 17.56 r5 ↑ 3.52 r5 ↑ 4.93

b1,6 0.79 b2,6 0 b3,6 0.79 b4,6 0

col c1→ 4.93 c2→ 8.17 column 3→ 12 c4→ 15.83
row r6 ↑ 4.93 r6 ↑ 2.76 row r6 ↑ 2 r6 ↑ 2.76

C_Test Varies vs Moment

800
750
700
650
600
550
500
450
400
350
300
250
200
150
100
50
1 2 2 2.5 2 3 3 3.5 3 4 4 4.5 4 5 5 5.5 5 6 6 6.5 6 7 7 7.5 7 8 8 8.5
.75 .25 .75 .25 .75 .25 .75 .25 .75 .25 .75 .25 .75 .25

Row 1234 Row 1235 Row 1236 Row 1237

Figure 45-28 C_Test versus moment.

VERIFYING GRAPHS -- Continued Page 45 - 22
24" square column with 16 - #7's in a circular cage as for 24" diameter column. Combined M2ux and M2uy. Pu = 200 k-ult, Mu = Mu provided
C_Test 11.000 aaa 18.71 19.02 19.25 20.15 21.02 21.57 22.01 22.26 22.28 22.26 22.28
M2Ux 1176 0 1 10 50 100 150 200 250 270 282.84 295.13
M2Uy 0 400 400 399.87 396.86 387.3 370.81 346.41 312.25 295.13 282.84 270
ø3Pn provided 48 113.75 116.94 116.71 115.73 114.52 113.28 113.2 112.96 112.74 112.54 112.74
MU provided 1201.51 400.03 400.06 400.05 400.06 400.04 400.04 400.03 400.01 400.01 400.01 400.01
10 en 299.95 42.2 41.05 41.13 41.48 41.92 42.38 42.4 42.49 42.58 42.65 42.58
100 β 157.08 0 0.25 2.5 12.53 25.27 38.44 52.36 67.51 74.1 21562320.xls
78.54 82.98

450
21.57
400 200
346.41
350 110.36
300
414.81
250 45.1
52.36
200

150

100

50

0
18.5 18.75 19 19.25 19.5 19.75 20 20.25 20.5 20.75 21 21.25 21.5 21.75 22 22.25 22.5

Row 1294 Row 1295 Row 1296 Row 1297 Row 1298 Row 1299

Figure 45-29 The rotation of β through 1/4 π radians (90º) to check M2Ux, M2Uy, and Mu provided.

24" square column with 16 - #7's in a rectangular configuration. Combined M2ux and M2uy. Pu = 200 k-ult, Mu = Mu provided
β degrees 90.000 aaa 0 0.14 0.29 1.43 7.18 14.48 22.02 30 38.68 45 51.32
C_Test 11 18.56 18.87 18.89 19.08 19.91 20.68 21.22 21.52 21.61 21.5 21.61
M2Ux 1176 0 1 2 10 50 100 150 200 250 282.84 312.25
M2Uy 0 400 400 399.99 399.87 396.86 387.3 370.81 346.41 312.25 282.84 250
ø3Pn provided/10 48.069 112.85 115.66 115.62 115.32 113.85 111.99 110.52 109.62 108.48 107.4 108.48
10 en 299.95 42.53 41.51 41.52 41.63 42.16 42.87 43.43 43.79 44.25 44.69 44.25
MU provided 1201.51 400.02 400.05 400.05 400.05 400.03 400.04 400.02 400.03 400.01 400.02 400.01
600

500

400
Row 1325
300
Row 1327
200 Row 1328
Row 1329
100 Row 1330

0
Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co
lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu lu
mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn mn

Figure 45-30 C_Test and β rotation.

VERIFYING GRAPHS -- Continued Page 45 - 23
C_Test 18.56 18.87 18.89 19.08 19.91 20.68 21.22 21.52 21.61 21.56 21.5
β degrees 0 0.14 0.29 1.43 7.18 14.48 22.02 30 38.68 42.45 45
M2Ux 0 1 2 10 50 100 150 200 250 270 282.84
M2Uy 400 400 399.99 399.87 396.86 387.3 370.81 346.41 312.25 295.13 282.84
ø3Pn provided/10 112.85 115.66 115.62 115.32 113.85 111.99 110.52 109.62 108.48 107.86 107.4
10 en 42.53 41.51 41.52 41.63 42.16 42.87 43.43 43.79 44.25 44.51 44.69
MU provided 400.02 400.05 400.05 400.05 400.03 400.04 400.02 400.03 400.01 400.04 400.02
21562320.xls
400

350

300

250

200

150

100

50

0
18.5 18.75 19 19.25 19.5 19.75 20 20.25 20.5 20.75 21 21.25 21.5 21.75

β degrees M2Ux M2Uy ø3Pn provided/10

Figure 45-31 C_Test and β rotation.

400
area b1,1 0.6 b2,1 0.6 b3,1 0.6 b4,1 0.6
375
column c1→ 3 c2→ 9 column c3→ 15 c4→ 21
row r1 ↑ 21 r1 ↑ 21 row r1 ↑ 21 r1 ↑ 21 350
325
b1,2 0.6 b2,2 0.6 Composite b3,2 0.6 b4,2 0.6
c1→ 3 c2→ 9 c3→ 15 c4→ 21 300
r2 ↑ 15 r2 ↑ 15 r2 ↑ 15 r2 ↑ 15
275
b1,3 0.6 b2,3 0.6 b3,3 0.6 b4,3 0.6 250
c1→ 3 c2→ 9 c3→ 15 c4→ 21
225 β degrees
r3 ↑ 9 r3 ↑ 9 r3 ↑ 9 r3 ↑ 9
M2Ux
200
b1,4 0.6 b2,4 0.6 b3,4 0.6 b4,4 0.6 M2Uy

c1→ 3 c2→ 9 c3→ 15 c4→ 21 175 ø3Pn

provided/10
r4 ↑ 3 r4 ↑ 3 r4 ↑ 3 r4 ↑ 3 150

b1,5 0 b2,5 0 b3,5 0 b4,5 0 125

c1→ 2.65 c2→ 12 c3→ 12 c4→ 19.16 100
r5 ↑ 8.13 r5 ↑ 17.63 r5 ↑ 3.52 r5 ↑ 4.84
75
b1,6 0 b2,6 0 b3,6 0 b4,6 0 50
col c1→ 4.84 c2→ 8.13 column 3→ 12 c4→ 15.87
row r6 ↑ 4.84 r6 ↑ 2.65 row r6 ↑ 1.88 r6 ↑ 2.65 25
0
4 5 6 7 8 9 10

Figure 45-32 C_Test and β rotation.

 VERIFYING GRAPHS -- Continued Page 45 - 24
Circular column 24" Mu required versus Pu allowed
C_Test 11.00 aaa 10.85 11.23 11.26 11.62 12 12.39 13.16 13.96 14.77 15.6 16.45
MU provided 1201.51 563.92 562.33 562.18 557.9 551.53 544.53 526.36 506 483.26 458.34 430.94
ø3Pn provided 481 500 525.02 527.04 550.04 575.05 600.03 650.05 700.03 750.02 800.04 850.06
100 en 2999.46 1353.4 1285.28 1280.01 1217.16 1150.93 1089 971.68 867.39 773.2 687.48 608.34

area b1,1 0.79 b2,1 0.79 b3,1 0.79 b4,1 0.79

column c1→ 8.2 c2→ 12.0 column c3→ 15.8 c4→ 19.1 21562320.xls
row r1 ↑ 21.2 r1 ↑ 22.0 row r1 ↑ 21.2 r1 ↑ 19.1

b1,2 0.79 b2,2 0.00 Composite b3,2 0.00 b4,2 0.79

c1→ 4.9 c2→ 12.000 c3→ 12.000 c4→ 21.2
r2 ↑ 19.1 r2 ↑ 20.48 r2 ↑ ­3.52 r2 ↑ 15.8

b1,3 0.79 b2,3 0.00 b3,3 0.00 b4,3 0.79

c1→ 2.8 c2→ ­10.6 c3→ 20.48 c4→ 22.0
r3 ↑ 15.8 r3 ↑ 5.1 r3 ↑ 12.00 r3 ↑ 12.0

b1,4 0.79 b2,4 0.00 b3,4 0.00 b4,4 0.79

c1→ 2.0 c2→ 3.52 c3→ 6.000 c4→ 21.2
r4 ↑ 12.0 r4 ↑ 12.0 r4 ↑ 0.00 r4 ↑ 8.2

b1,5 0.79 b2,5 0.00 b3,5 0.00 b4,5 0.79

c1→ 2.8 c2→ 12.0 c3→ 12.00 c4→ 19.1
r5 ↑ 8.2 r5 ↑ 17.6 r5 ↑ 3.52 r5 ↑ 4.9

b1,6 0.79 b2,6 0.79 b3,6 0.79 b4,6 0.79

col c1→ 4.9 c2→ 8.2 column 3→ 12.0 c4→ 15.8
row r6 ↑ 4.9 r6 ↑ 2.8 row r6 ↑ 2.0 r6 ↑ 2.8

1400
1300
1200
1100
1000
900
800
700
600
500
400
300
200
100
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

MU provided ø3Pn provided 100 en

Figure 45-33 Mu required versus Pu allowed.

VERIFYING GRAPHS -- Continued Page 45 - 25
Circular Column 24" Lx versus Mux allowed 16 - #8's Ly = 5', C_Test Constant, M1ux = M2ux = 100 k-ft ult, Pu = 575
Lxy, Lu xy 13.25 aaa 10 11 11.1 12 14 15 16 17 18 19 20
MC required 1176 100 100 113.27 115.87 122.91 127.23 132.19 137.91 144.54 152.29 161.41
k LUx /rx *10 189.29 200 220 222 240 280 300 320 340 360 380 400
ø3Pn provided 481 575.05 575.05 575.05 575.05 575.05 575.05 575.05 575.05 575.05 575.05 575.05
10 MU provided 1202 551.53 551.53 551.53 551.53 551.53 551.53 551.53 551.53 551.53 551.53 551.53
100 en 2999.46 1150.93 1150.93 1150.93 1150.93 1150.93 1150.93 1150.93 1150.93 1150.93 1150.93 1150.93
c_test 11 12 12 12 12 12 12 12 12 12 21562320.xls
12 12

700
650
600
550
500
450
MC required
400
k LUx /rx *10
350 ø3Pn provided

300
250
200
150
100
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Figure 45-34 Lx versus Mux allowed.

24" Circular Column 16 - #8's C_Test Variable, M2ux versus Pu

C_Test 11 aaa 2.8 2.86 2.99 3.12 3.41 4.19 5.05 5.98 6.91 7.74 8.55
ø3Pn provided 465.00 0 10 20 30 50 100 150 200 250 300 350
MU provided 1201.513 553.46 552.21 549.65 547.43 543.9 539.17 545.11 538.14 539.92 552.6 563.48
en 29.99 1202.6 661.45 328.72 218.61 130.41 64.69 43.58 32.29 25.91 22.1 19.32

1400

1200

1000

800

600

400

200

0
2 4 6 8 10 12 14 16 18 20 22 24

ø3Pn provided MU provided en

Figure 45-35 C_Test variable, M2ux versus Pu.

VERIFYING GRAPHS -- Continued Page 45 - 26
24" Square Column 16 - #8's C_Test Variable, M2ux versus Pu
C_Test 11 aaa 1.5 1.52 1.56 1.63 1.8 2.3 2.92 3.67 4.46 5.21 5.97
ø3Pn provided 480.69 13.33 15.08 20.82 30.09 50.01 100.07 150.07 200.06 250.07 300.01 350.06
MU provided 1201.513 597.9 597.66 594.89 590.7 582.93 570.47 581.29 601.93 598.36 611.09 625.04
en 29.99 538.09 475.46 342.91 235.6 139.89 68.41 46.48 36.11 28.71 24.44 21.43

1500
21562320.xls
1400
1300
1200
1100
1000
900 #REF!
800
700
600
500
400
300
200
100
0
0 2 4 6 8 10 12 14 16 18 20 22 24

ø3Pn provided en

Figure 45-36 C_Test variable, M2ux versus Pu.

 Page 45 - 27
\d {u} \o {u} \u {u}

\m {u} \s {u} \w {u}

45

21562320.xls

COLUMN CROSS SECTIONAL GRAPHING

24.00 circular column cross section
logic 0 1 2 3 4 5 6 7 8 9
FALSE 0 1 2 3 4 5 6 7 8 9
X-Axis 24.000 23.276 21.193 18.000 14.084 9.916 6.000 2.807 0.724 0.000
E outline 12.000 16.104 19.713 22.392 23.818 23.818 22.392 19.713 16.104 12.000
E data
D reinforcing
D labels
A text 26.4
A data width = 24.00"
B lines
B data

COLUMN LOADING AND SLENDERNESS GRAPHING XX Column Outline ========= ========= =======> =========
X-Axis 0 6.3 1 1 1.2 1.2 1
E outline 0 28.51 3 21.93 21.93 3 3
E data
D reinforcing
D labels
A text
A data
B lines
B data
 Page 45 - 28

21562320.xls

Graph
Moment u 0 1201.5 1201.5 1201.5 0 0 1201.5
P ultimate 3402 480.7 480.7 0 -2859.8 480.7 480.7

24

000 1200 1400

Page 45 - 29

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 Page 45 - 44

0.9 1.05 1.19 1.32 1.45 1.57 1.57

15.4 15.45 15.39 15.57 15.63 15.57 15.57
312.25 346.41 370.81 387.3 396.86 400 400
250 200 150 100 50 1 0
77.77 78.14 77.97 79.26 79.84 79.69 79.68

21562320.xls

25 1.5 1.75

/1
 Page 45 - 45

22.26 22.01 21.55 21.02 20.15 19.25 19.02 18.99

312.25 346.41 370.81 387.3 396.86 399.87 400 400
250 200 150 100 50 10 1 0
113 113 113.09 114.52 115.73 116.71 116.94 116.97
4 4 4.26 4.19 4.15 4.11 4.11 4.1
1.667 1.667 1.67 1.67 1.67 1.67 1.67 1.67
21562320.xls

18.01 17.1 15.94 14.85 14.581 14.55

370.81 387.3 396.86 399.87 400.00 400
150 100 50 10 1 0
459.94 467.93 475.02 480.41 482 481.76
118.64 131.81 144.55 154.58 156.83 157.08
2 2 2 2 2.0000 2

11864 13181.16 14454.68 15457.94 15682.96 15707.96

 Page 45 - 46

11.44 11.11 10.08 8.92 7.42 6.14 5.34 5.17 5.15 0 17.18 17.66
295.13 312.25 346.41 370.81 387.3 396.86 399.87 400 400 0 1
270 250 200 150 100 50 10 1 0 400 400
82.98 89.57 104.72 118.64 131.81 144.55 154.58 156.83 157.08 0 0.25

1 1 1 1 2 2 2 2 2 4 4
21562320.xls
Page 45 - 47

21562320.xls
 Page 45 - 48

22.26 22.01 22.26 22.01 21.57 21.02 20.15 19.25 19.02 18.99
312.25 346.41 312.25 346.41 370.81 387.3 396.86 399.87 400 400
250 200 250 200 150 100 50 10 1 0
112.96 113.2 112.96 113.2 113.28 114.52 115.73 116.71 116.94 116.97
400.01 400.03 400.01 400.03 400.04 400.04 400.06 400.05 400.06 400.06
42.49 42.4 42.49 42.4 42.38 41.92 41.48 41.13 41.05 41.04
89.57 104.72 89.57 104.72 118.64 131.81 144.55 154.58 156.83 157.08 21562320.xls

60 67.98 75.52 82.82 88.57 89.71 89.86 90.00 0 14.48 22.02 38.68
21.52 21.22 20.68 19.91 19.08 18.89 18.87 18.84 4.24 5.21 8.54
346.41 370.81 387.3 396.86 399.87 399.99 400 400.00 100.00 150.00 250
200 150 100 50 10 2 1 0.00 387.30 370.81 312.25
109.62 110.52 111.95 113.85 115.32 115.62 115.66 115.70 8.03 8.93 18.56
43.79 43.43 42.91 42.16 41.63 41.52 41.51 41.49 597.51 537.82 258.58
400.03 400.02 400.26 400.03 400.05 400.05 400.05 400.01 400.03 400.02 400.01
 Page 45 - 49
21.56 21.61 21.52 21.22 20.68 19.91 19.08 18.89 18.87 18.84 4.24
47.55 51.32 60 67.98 75.52 82.82 88.57 89.71 89.86 90.00 14.48
295.13 312.25 346.41 370.81 387.3 396.86 399.87 399.99 400 400.00 100.00
270 250 200 150 100 50 10 2 1 0.00 387.30
107.86 108.48 109.62 110.52 111.95 113.85 115.32 115.62 115.66 115.70 8.03
44.51 44.25 43.79 43.43 42.91 42.16 41.63 41.52 41.51 41.49 597.51
400.04 400.01 400.03 400.02 400.26 400.03 400.05 400.05 400.05 400.01 400.03
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17.33 18.25 19.22 20.27 21.46 23.01 24

400.82 367.57 330.94 290.4 245.14 193.19 171.83
900.01 950.05 1000.03 1050.01 1100.02 1150.02 1166.75
534.42 464.28 397.12 331.88 267.42 201.59 176.73

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21 22 23 24 25 26 27 28 29 30
172.25 185.3 201.27 221.17 246.58 280.09 326.13 393.22 499.76 694.54
420 440 460 480 500 520 540 560 580 600
575.05 575.05 575.05 575 575.05 575.05 575.05 575.05 575.05 575.05
551.53 551.53 551.53 552 551.53 551.53 551.53 551.53 551.53 551.53
1150.93 1150.93 1150.93 1150.93 1150.93 1150.93 1150.93 1150.93 1150.93 1150.93
12 12 12 12 12 12 12 12 12 12 21562320.xls

MC required
k LUx /rx *10
ø3Pn provided

9.32 10.09 10.85 11.62 12.39 13.16 13.96 15.6 16.45 17.33 18.25 19.22
400 450 500 550 600 650 700 800 850 900 950 1000
565.97 565.71 563.92 557.9 544.51 526.36 506 458.34 430.94 400.82 367.57 330.94
16.98 15.08 13.53 12.17 10.89 9.72 8.67 6.87 6.08 5.34 4.64 3.97
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6.75 7.53 8.33 9.14 9.96 10.78 11.57 12.35 13.14 13.93 14.72 15.51
400.08 450.09 500.01 550.01 600.01 650.07 700.07 750.09 800.04 850.02 900.02 950.05
638.76 651.37 662.07 669.55 674.68 677.23 667.75 651.23 633.55 614.31 593.26 570.13
19.16 17.37 15.89 14.61 13.49 12.5 11.45 10.42 9.5 8.67 7.91 7.2

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22 24
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rectangular column cross section

10 11 12 13 14 15 16 17 18
10 11 12 13 14 15 16 17 18
0.724 2.807 6.000 9.916 14.084 18.000 21.193 23.276 24.000 0 0
7.896 4.287 1.608 0.182 0.182 1.608 4.287 7.896 12.000 0 0

========= ========= ========= ========= ========= ========= ========= ========= ========= ========= =========
1.2 0.5 1.2 1.2 0.5 0.5
12.46
kLx/rx = 18.9

28.51 14.96 17.45 26.31 24.12

P = 0.0k at exdb_x
= 29.99"
= 1.00 Mc x = 1176 M1b
k-ft = 0 k-ft M2b + M2s = 0 k-ft

eY → 30.0 in =SIN(b ) * e
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0 1176.0 0 1176.0
640.9 465
0 465
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17.9 18.87 19.82 20.46 20.75 20.77 20.72 20.66 20.72 20.77 20.75 20.46
10 50 100 150 200 250 270 282.84 295.13 312.25 346.41 370.81
399.87 396.86 387.3 370.81 346.41 312.25 295.13 282.84 270 250 200 150
2.5 12.53 25.27 38.44 52.36 67.51 74.1 78.54 82.98 89.57 104.72 118.64

4 4 4 4 4 3 3 3 3 3 2 2
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42.45 45 47.55 51.32 67.98 75.52

9.28 9.69 9.28 8.54 5.21 4.24
270 282.84 295.13 312.25 370.81 387.3
295.13 282.84 270 250 150 100
21.31 22.98 21.31 18.56 8.93 8.03
225.29 208.9 225.29 258.58 537.82 597.51
400.01 400 400.01 400.01 400.02 400.03
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5.21 8.54 9.28 9.69 9.28 8.54 5.21 4.24
22.02 38.68 42.45 45 47.55 51.32 67.98 75.52
150.00 250 270 282.84 295.13 312.25 370.81 387.3
370.81 312.25 295.13 282.84 270 250 150 100
8.93 18.56 21.31 22.98 21.31 18.56 8.93 8.03
537.82 258.58 225.29 208.9 225.29 258.58 537.82 597.51
400.02 400.01 400.01 400 400.01 400.01 400.02 400.03
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20.27 21.46 23.01 23.99

1050 1100 1150 1166.7
290.4 245.14 193.19 171.91
3.32 2.67 2.02 1.77
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16.31 17.11 17.91 18.71 19.51 20.32 21.12 21.93 22.73 23.54 24
1000 1050.03 1100.02 1150.05 1200.06 1250.06 1300 1350.02 1400.05 1450.03 1478.38
544.81 517.05 486.79 453.87 418.24 379.81 338.56 294.33 247.11 196.91 167.08
6.54 5.91 5.31 4.74 4.18 3.65 3.13 2.62 2.12 1.63 1.36

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ular column cross section

Reinforcing
0 0 0 24 8.125 12.000 15.875 19.158 4.842
0 0 0

21.35 22.13 21.35 19.16 19.16

1
12 25.2 25.2 25.2 25.2
h = 24.00"

YY Column Outline ========= ========= =======>

4 4 4.2 4.2 4 4.2 3.5 4.2
3 18.93 18.93 3 3 12.46

24.61 14.96

eX ↑ 0.0
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19.82 18.87 17.9 17.66 17.63

387.3 396.86 399.87 400 400
100 50 10 1 0
131.81 144.55 154.58 156.83 157.08
109.06 109.21 109.23
2 2 2 2 2
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12.000 0.000 21.354 2.646 0.000 20.480 22.125 1.875 3.520 0.000 21.354 2.646

20.48 0.00 15.87 15.87 0.00 12.00 12.00 12.00 12.00 0.00 8.13 8.13
9.24 0 1 1 0 9.24 1 1 9.24 0 1 1

4.2 3.5 3.5

17.45 22.71 20.82

in
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w 24 in width in Y direction
L 24 in length in X direction
45.00 aspect 1
Beta 1.57 comp block 9.35 PC x & y
β1*C 9.35 in β1 reduction factor *C_test

0.000 12.000 19.158 4.842 8.125 12.000 15.875 24 24 24 24 24

0.00 3.52 4.84 4.84 2.65 1.88 2.65

0 9.24 1 1 1 1 1
15.87 19.16 21.35 22.13 21.35
8.13" 4.84" 2.65" 1.88" 2.65"
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25.000

22.500

20.000

17.500

15.000

12.500

10.000

7.500

5.000

2.500

0.000
0.000 2.500 5.000 7.500 10.00 12.50 15.00 17.50 20.00 22.50 25.00
0 0 0 0 0 0 0
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β inp 1.5708 rad FALSE logic Circular
90.0 deg
[tan β ] ### Err:502
[sin β ] 1.0000
β1 reduction factor *C_test [cos β ] 0.0000
X-Sect Whitney's Stress Block diagonal
mid-diag end lt side rt side cross - hairs
24 0.0 24.0000 12.000

19.2
4.84"
13.000 13.0 12.000
B = 90.0000 degrees a block = 9.3"
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max diagonal load vector

cross - hairs CG plastic centroid
12.000 12.000 12.000 9.600 14.400 12.000

14.4 9.6 12 12 12 12.000

PCx = 12.0" PCy = 12.0" net
30.000
27.500
25.000
22.500
20.000
17.500
15.000
12.500
10.000
7.500
5.000
2.500
0.000
0.000 5.000 10.000 15.000 20.000 25.000

circular compression block coordinates

b 23.92
13 0 13 13
12 11.96 0.04 23.96
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16.971 1.2
12.000 12.575 11.425 12.000

28.971 27.917 27.917 28.971

0.000
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