Columna de Sotano

7/29/2019 Columna de Sotano

1/38

PROJECT : PAGE :

CLIENT : DESIGN BY :

JOB NO. : DATE : REVIEW BY :

Basement Column Supporting Lateral Resisting Frame Based on CBC 2001/ ACI 318-05

INPUT DATA & DESIGN SUMMARY

CONCRETE STRENGTH f c' = 4.5 ksi

REBAR YIELD STRESS f y = 60 ksi

COLUMN CLEAR HEIGHT h = 14 ft

COLUMN SIZE c1 = 24 in

c2 = 24 in

AMPLIFICATION FACTOR (Tab 16-N) W0 = 2.2

DS = 0 in

LOADS, ASD (ft-kips, kips)

P V M Pground

DL 225 157.5

LL 270 90

E / 1.4 -333.3 131 0.1

( - P for uplift)

LONGITUDINAL REINFORCING

SECTION TOP BOTTOM

LEFT 5 # 10 5 # 10

( d = 21.37 in ) ( d = 21.37 in )

( 1 Layer) ( 1 Layer)

RIGHT 5 # 10 5 # 10

( d = 21.37 in ) ( d = 21.37 in )

( 1 Layer) ( 1 Layer) THE COLUMN DESIGN IS ADEQUATE.

TRANSVERSE REINFORCEMENT FOR CONFINEMENT

4 Legs # 4 @ 5 in, o.c., full height (ACI 318-05 4.4.5 / CBC 1921.4.4.5)

ANALYSIS

DESIGN CRITERIA

1. Since the column supported reaction from lateral resisting frame, CBC 1633.2.4 &1921.4.4.5 apply.

2. Since the column is not part of the lateral force resisting system, CBC 1921.7 apply.

3. Since the transverse reinforcement required 12" at least into footing per CBC 1921.4.4.5,

a condition of pinned top & fixed bottom should be used.

DESIGN LOADS AT TOP OF COLUMN

U1 = 1.2 D + f1 L +1.0 W0Eh , (CBC 1630.8.2.1, 12-17 & 30-2) U2 = 0.9 D 1.0 W0Eh , (CBC 1630.8.2.1, 12-18 & 30-2)

Pu = -432.6 kips Mu = 0.3 ft-kips Pu = -682.3 kips Mu = 0.3 ft-kips

Vu = 403.5 kips f1 = 0.5 Vu = 403.5 kips

U3 = 1.4 D + 1.7 L , (CBC 1909.2.1)

Pu = 994.5 kips Mu = 0.0 ft-kips

Vu = 0.0 kips

24

CHECK CAPACITY SUBJECTED TO BENDING AND AXIAL LOAD 2.2

LOADING U1,top U1,bot U2,top U2,bot U3,top U3,botPu (kips) -432.6 -422.5 -682.3 -674.8 994.5 1006.3

Mu (ft-kips) 0.3 0.2 0.3 0.2 0.0 0.0

dns = Cm/[1-Pu/(0.75Pc)] 1.000 1.000 1.000 1.000 1.168 1.170

dnsMu (ft-kips) 0.3 0.2 0.3 0.2 0.0 0.0

fMn (ft-kips) @ Pu 498.1 822.4 822.4 822.4 822.3 822.3

where EI = 0.4EcIg / (1+bd) = 0.25 EcIg

Pc = p2EI / (kLu)

2

SUMMARY OF LOAD VERSUS MOMENT CAPACITIES (for ACI 318-05 10.2 & 10.3 only)

CAPACITY f Pn (kips) f Mn (ft-kips)AT AXIAL LOAD ONLY 1739 0

AT MAXIMUM LOAD 1739 281

AT 0 % TENSION 1384 487AT 25 % TENSION 1148 580

AT 50 % TENSION 941 648

AT e t = 0.002 605 743

AT BALANCED CONDITION 585 751

AT e t = 0.005 258 943

AT FLEXURE ONLY 0 822

AT TENSION ONLY -1097 0

DESIGN LEVEL BASEMENT DISPLACEMENT


2/38

f Pn (kips) (cont'd)

f Mn (ft-kips)

All load points to be within capacity diagram. [Satisfactory]

DETERMINE INDUCED MOMENT IN THE COLUMN

213.971 ft-kips

where Ec = 57000 (fc')0.5

= 3824 ksi, ACI 318-05 8.5.1 / CBC 1908.5.1

Ig = c1 c23

/ 12 = 27648 in4

Ic = 0.5 Ig = 13824 in4

, CBC 1633.2.4

R = 5.5

DM = MAX( 0.7 R Ds , 0.0025 h) = 0.42 in, CBC (30-17) & 1633.2.4

P = PDL + PLL = 495 kips, CBC 1633.2.4

CHECK REQUIREMENTS OF NOT PART OF THE LATERAL RESISTING SYSTEM

Mu = 1.2 MDL + 1.0 MLL + MD = 213.971 ft-kips, (CBC 1921.7.2, Mu = 1.4 MDL + 1.4 MLL + MD )

< f Mn = 822.3 kips [Satisfactory]

Pu, max = 1006.3 kips > 0.1Agfc' = 259.2 kips [Satisfactory]

Per ACI 318-05 21.11.3.3 / CBC 1921.7.3.3, the column shall satisfy ACI 318-05 21.4.4, 21.4.5 and 21.5.2.1.

CHECK SECTION REQUIREMENTS (ACI 318-05 21.4.1 / CBC 1921.4.1)

cmin =MIN(c1, c2) = 24 in > 12 in [Satisfactory]

cmin / cmax = 1.00 > 0.4 [Satisfactory]

CHECK TRANSVERSE REINFORCING AT BOTTOM OF COLUMN (ACI 318-05 21.4.4 / CBC 1921.4.4)

Ash = 0.80 in2

> MAX[ 0.09shcfc' / fyh , 0.3shc(Ag/Ach-1)fc' / fyh ] = 0.71 in2

[Satisfactory] where s = MAX[MIN(c1/4, 6db, 4+(14-hx)/3, 6), 4] = 5 in

hc = c1 - 2Cover - dt = 20.5 in

Ach = (c1-3)(c2-3) = 441.0 in2

CHECK FLEXURAL REINFORCING (ACI 318-05 21.4.3.1 / CBC 1921.4.3.1)

rtotal = 0.040 > rmin = 0.010 [Satisfactory]

< rmax = 0.060 [Satisfactory]

CHECK SHEAR STRENGTH (ACI 318-05 21.4.5 / CBC 1921.4.5)

Ve = MAX[ (Mpr, left, top + Mpr, right,bot) / h , Vu,max] = 73.4 kips

< 8f(fc')0.5

c2d = 206.4 kips [Satisfactory]

< f[2(fc')0.5

c2d + Avfyd / s] = 205.4 kips [Satisfactory]

where rtop,left = 0.012 > rmin=MIN[3(fc')0.5

/fy, 200/fy ]= 0.003 [Satisfactory]

rbot,left = 0.012 > rmin = 0.003 [Sat isfactory]

Mpr, left, top = 0 ft-kips f = 0.75 (0.85, if CBC 1909.3.2.3)

Mpr, right, bot = 1.25Mn,col,max = 1028 ft-kips Av = 0.8 in2

Vu, max = 0.033 ft-kips

DETERMINE SEISMIC TENSION DEVELOPMENT, Ld, INTO THE FOOTING PER ACI 318-05 21.4.4.5 / CBC 1921.4.4.5

14 db = 17 in, (ACI 318-05 21.5.4.1)

48 db = 61 in, (ACI 318-05 21.5.4.2)

where db = 1.27 in

b = 1.0 , (1.2 for epoxy-coated, ACI 318-05 21.5.4.4 & 12.2.4)

-1500

-1000

-500

0

500

1000

1500

2000

0 200 400 600 800 1000

2

3 MM

E Ic cPM

hD D

D

3.5 , 12d dhMAX inL L b

', , 68

65

b y

dh b

c

fdMAX indL

f


3/38

PROJECT : PAGE :

CLIENT : DESIGN BY :

JOB NO. : DATE : REVIEW BY :

INPUT DATA & DESIGN SUMMARYCONCRETE STRENGTH fc' = 4.5 ksi

REBAR YIELD STRESS fy = 60 ksi

COLUMN DIMENSUINS cx = 24 in

cy = 24 in

FACTORED AXIAL LOAD Pu = -432.6 kFACTORED MOMENT LOAD Mu,x = 0.308 ft-k

Mu,y = 0.0001 ft-k

FACTORED SHEAR LOAD Vu,x = 0 k

Vu,y = 0 k

COLUMN VERT. REINF. 5 # 10 at x dir.

5 # 10 at y dir.

SHEAR REINF. 4 legs,# 4 @ 4 in o.c., x dir. THE COLUMN DESIGN IS ADEQUATE.

2 legs,# 4 @ 4 in o.c., y dir.

ANALYSIS

f Pn (k)

f Pn (kips) f Mn (ft-kips)AT AXIAL LOAD ONLY 1739 0

AT MAXIMUM LOAD 1739 281

AT 0 % TENSION 1384 487

AT 25 % TENSION 1148 580

AT 50 % TENSION 941 648

ATe t = 0.002 605 743

AT BALANCED CONDITION 585 751

f Mn (ft-k) ATe t = 0.005 258 943

AT FLEXURE ONLY 0 822

CHECK FLEXURAL & AXIAL CAPACITY

Mu = ( Mu,x2

+ Mu,y2

)0.5

= ft-k, (combined bending load.) q = 0.02o

, (the direction of combined load.)

f Pmax =0.80 f [ 0.85 fc' (Ag - Ast) + fy Ast] = 1739.2 kips., (at max axial load, ACI 318-02, Sec. 10.3.6.2)

where f = 0.65 (ACI 318-02, Sec.9.3.2.2) > Pu [Satisfactory]

Ag = 576 in2. Ast = 20.32 in

2.

a = Cbb1 = 10 in (at balanced strain condition, ACI 10.3.2)

f = 0.48 + 83 et = (ACI 318-02, Fig. R9.3.2)

where Cb = d ec / (ec + es) = 13 in et= 0.002069 ec= 0.003

d = 21.373 in, (ACI 7.7.1) b1 = 0.825 ( ACI 318-02, Sec. 10.2.7.3 )

fMn = 0.9 Mn = 822 ft-kips @ Pn = 0, (ACI 318-02, Sec. 9.3.2)

fMn = ft-kips @ Pu = -433 kips > Mu [Satisfactory]

rmax = 0.08 (ACI 318-02, Section 10.9) rprovd = 0.035

rmin = 0.01 (ACI 318-02, Section 10.9) [Satisfactory]

CHECK SHEAR CAPACITY (ACI 318-02 Sec. 11.1.1, 11.3.1, & 11.5.6.2)

fVn = f (Vs + Vc) (ACI 318-02 Sec. 11.1.1)

> Vu [Satisfactory]

where f = 0.75 (ACI 318-02 Sec. 9.3.2.3) fy = 60 ksi

d A0 Av Vc = 2 (f c')0.5

A0 Vs = MIN (d fyAv / s , 4Vc) f Vn

x 21.37 513 0.80 68.8 256.4 244

y 21.37 513 0.40 68.8 128.2 148

smax = 12 (ACI 318-02, Section 10.16.8.5) sprovd = 4 in

smin = 1 (ACI 318-02, Section 7.10.4.3) [Satisfactory]

Concrete Column Design Based on ACI 318-02

Daniel

(Total 16 # 10)

0.30801

498

Tian Li

0.652

-1000

-500

0

500

1000

1500

2000

0 200 400 600 800 1000

e

eq

' '

2

'

'

2 0.85, 57 , 29000

0.85 2 , 0

0.85 ,

,

,

C

C

C

C

C

S

fksifE Ec so

Ec

c c forf c of oo

forf c o

forEss s yf

forf s yy

e

e e

ee

ee

ee

eee

ee

-


4/38

R E I N F O R C E M E N T

SIZE DIAM. AREA

# 0 #REF!

3 0.38 0.11

4 0.50 0.20

5 0.63 0.31 Mu,x = 0.30801 ft-k

6 0.75 0.44 Mu,y = 0.00011 ft-k

7 0.88 0.60

8 1.00 0.79

9 1.13 1.0010 1.27 1.27

11 1.41 1.56

14 1.69 2.25

18 2.26 4.00

STRESS STRAIN COMPUTATION AT MAXIMUM LOAD

1ST ESTIMATE

Axial load fPn / f = 2676 k

Distance to neutral axis c = 24 in

Beta factor b = 0.83

Compression block a = 20 in

E = 29000 ksi d = 21.373 in

fy

= 60 ksi D = 24.01 in

fc' = 5 ksi q = 0.02

STA A dist strain stress force arm moment

to end

1 0.00 2.64 0.003 60 0 9 0 qcritial = 45

2 1.27 2.64 0.003 60 71 9 56 dx = 21.365

3 2.54 2.64 0.003 60 143 9 111 dy = 21.365

4 2.54 2.64 0.003 60 143 9 111 sx = 18.730

5 2.54 7.32 0.002 60 143 5 56 sy = 18.730

6 2.54 12.00 0.002 44 101 0 0 Asx = 0.271 in2

/ in

7 2.54 16.69 0.001 27 58 -5 -22 Asx = 0.271 in2

/ in

8 1.90 21.37 0.000 10 11 -9 -9 cx = 24.0

9 1.27 21.37 0.000 10 7 -9 -6 cy = 24.0

10 1.27 21.37 0.000 10 7 -9 -6 20.320

11 1.27 21.37 0.000 10 7 -9 -6 576

12 0.64 21.37 0.000 10 4 -9 -3

CONC 1732 298

S 20.320 2426 582

Ec = 3824 ksi eo = 0.0020

conc sec thick to end b control D ec fc force arm moment to end b to end

1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 6.00 6.01 24.00 143.9486 0.00262 3.825 551 9 413 6.01 24.00 4.01

6 6.00 12.00 24.00 143.9486 0.00187 3.80984 548 3 137 12.00 24.00 8.01

7 6.00 18.00 24.00 143.9486 0.00113 3.09267 445 -3 -111 18.00 24.00 12.01

8 6.00 24.00 24.00 143.9486 0.00038 1.30199 187 -9 -141 24.00 24.00 16.01

9 0.00 24.00 12.00 0.07714 8E-07 0.00307 0 -12 0 24.00 12.00 20.01

10 0.00 24.01 0.00 0.025713 2.7E-07 0.00102 0 -12 0 24.01 0.00 24.01

S 24.01 576 1732 298

3RD ITERATION


Distance to neytral axis c = 27 in



E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 60 143 5 56

6 2.54 12.00 0.002 48 113 0 0

7 2.54 16.69 0.001 33 74 -5 -29

8 1.90 21.37 0.001 18 27 -9 -21

case 1 cas


5/38

9 1.27 21.37 0.001 18 18 -9 -14

10 1.27 21.37 0.001 18 18 -9 -14

11 1.27 21.37 0.001 18 18 -9 -14

12 0.64 21.37 0.001 18 9 -9 -7

CONC 1893 201

S 2669 437

Ec = 3824 ksi eo = 0.0020

conc sec thick to end b control ec fc force arm moment to end b to end

1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.003 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 6.00 6.01 24.00 143.9486 0.00266 3.825 551 9 413 6.01 24.00 4.49

6 6.00 12.00 24.00 143.9486 0.002 3.82498 551 3 138 12.00 24.00 8.98

7 6.00 18.00 24.00 143.9486 0.00133 3.39234 488 -3 -122 18.00 24.00 13.46

8 6.00 24.00 24.00 143.9486 0.00066 2.10563 303 -9 -227 24.00 24.00 17.95

9 0.00 24.00 12.00 0.07714 0.00032 1.14124 0 -12 0 24.00 12.00 22.43

10 0.00 24.01 0.00 0.025713 0.00032 1.13971 0 -12 0 24.01 0.00 26.92

S 24.01 576 1893 201

5TH ITERATION



Beta factor b = 0.83Compression block a = 22 in

E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 60 143 5 56

6 2.54 12.00 0.002 48 113 0 0

7 2.54 16.69 0.001 33 75 -5 -29

8 1.90 21.37 0.001 18 27 -9 -21

9 1.27 21.37 0.001 18 18 -9 -14

10 1.27 21.37 0.001 18 18 -9 -14

11 1.27 21.37 0.001 18 18 -9 -14

12 0.64 21.37 0.001 18 9 -9 -7

CONC 1897 199

S 2676 433

Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 6.00 6.01 24.00 143.9486 0.00267 3.825 551 9 413 6.01 24.00 4.51

6 6.00 12.00 24.00 143.9486 0.002 3.825 551 3 138 12.00 24.00 9.01

7 6.00 18.00 24.00 143.9486 0.00133 3.40006 489 -3 -122 18.00 24.00 13.51

8 6.00 24.00 24.00 143.9486 0.00067 2.12719 306 -9 -230 24.00 24.00 18.01

9 0.00 24.00 12.00 0.07714 0.00033 1.17203 0 -12 0 24.00 12.00 22.51

10 0.00 24.01 0.00 0.025713 0.00033 1.17051 0 -12 0 24.01 0.00 27.01

S 24.01 576 1897 199

7TH ITERATION





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 60 143 5 56

6 2.54 12.00 0.002 48 113 0 0

case 1 cas

case 1 cas


6/38

7 2.54 16.69 0.001 33 75 -5 -29

8 1.90 21.37 0.001 18 27 -9 -21

9 1.27 21.37 0.001 18 18 -9 -14

10 1.27 21.37 0.001 18 18 -9 -14

11 1.27 21.37 0.001 18 18 -9 -14

12 0.64 21.37 0.001 18 9 -9 -7

CONC 1897 199

S 2676 433

Ec = 3824 ksi eo = 0.0020

conc sec thick to end b controlD e

cfc force arm moment to end b to end

1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 6.00 6.01 24.00 143.9486 0.00267 3.825 551 9 413 6.01 24.00 4.51

6 6.00 12.00 24.00 143.9486 0.002 3.825 551 3 138 12.00 24.00 9.01

7 6.00 18.00 24.00 143.9486 0.00133 3.40006 489 -3 -122 18.00 24.00 13.51

8 6.00 24.00 24.00 143.9486 0.00067 2.12719 306 -9 -230 24.00 24.00 18.01

9 0.00 24.00 12.00 0.07714 0.00033 1.17203 0 -12 0 24.00 12.00 22.51

10 0.00 24.01 0.00 0.025713 0.00033 1.17052 0 -12 0 24.01 0.00 27.01

S 24.01 576 1897 199

STRESS-STRAIN COMPUTATIONS AT POINT OF 0% TENSION

Stress at last row of bars fs = 0 ksi




E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

case 1 ca


7/38

5 2.54 7.32 0.002 57 135 5 53

6 2.54 12.00 0.001 38 87 0 0

7 2.54 16.69 0.001 19 39 -5 -15

8 1.90 21.37 0.000 0 -7 -9 6

9 1.27 21.37 0.000 0 -5 -9 4

10 1.27 21.37 0.000 0 -5 -9 4

11 1.27 21.37 0.000 0 -5 -9 4

12 0.64 21.37 0.000 0 0 -9 0

CONC 1532 417

S 2129 750Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 3.56 3.57 24.00 85.45624 0.00275 3.825 327 10 278 6.01 24.00 3.57

6 3.56 7.13 24.00 85.45624 0.00225 3.825 327 7 181 12.00 24.00 7.13

7 3.56 10.69 24.00 85.45624 0.00175 3.76461 322 3 83 18.00 24.00 10.69

8 3.56 14.25 24.00 85.45624 0.00125 3.28577 281 0 -11 24.00 24.00 14.25

9 3.56 17.81 24.00 85.45624 0.00075 2.32952 199 -4 -67 22.69 3702.44 17.81

10 3.56 21.37 24.00 85.45624 0.00025 0.89586 77 -8 -48 21.37 7380.87 21.37

S 21.37 513 1532 417






E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 47 109 5 43

6 2.54 12.00 0.001 21 44 0 0

7 2.54 16.69 0.000 -4 -11 -5 4

8 1.90 21.37 -0.001 -30 -57 -9 45

9 1.27 21.37 -0.001 -30 -38 -9 30

10 1.27 21.37 -0.001 -30 -38 -9 30

11 1.27 21.37 -0.001 -30 -38 -9 30

12 0.64 21.37 -0.001 -30 -19 -9 15

CONC 1139 523

S 1448 997

Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 2.65 2.66 24.00 63.53559 0.00275 3.825 243 11 216 6.01 24.00 2.66

6 2.65 5.30 24.00 63.53559 0.00225 3.825 243 8 163 12.00 24.00 5.30

7 2.65 7.95 24.00 63.53559 0.00175 3.76449 239 5 107 18.00 24.00 7.95

8 2.65 10.60 24.00 63.53559 0.00125 3.28552 209 3 47 24.00 24.00 10.60

9 2.65 13.25 24.00 63.53559 0.00075 2.32927 148 0 1 19.95 11374.91 13.25

10 2.65 15.89 24.00 63.53559 0.00025 0.89574 57 -3 -12 15.89 22725.82 15.89

S 15.89 381 1139 523

STRESS-STRAIN COMPUTATIONS AT BALANCED CONDITION





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 60 0 9 0

2 1.27 2.64 0.002 60 71 9 56

case 1 cas

case 1 cas


8/38

3 2.54 2.64 0.002 60 143 9 111

4 2.54 2.64 0.002 60 143 9 111

5 2.54 7.32 0.001 37 83 5 32

6 2.54 12.00 0.000 4 2 0 0

7 2.54 16.69 -0.001 -28 -70 -5 27

8 1.90 21.37 -0.002 -60 -114 -9 89

9 1.27 21.37 -0.002 -60 -76 -9 59

10 1.27 21.37 -0.002 -60 -76 -9 59

11 1.27 21.37 -0.002 -60 -76 -9 59

12 0.64 21.37 -0.002 -60 -38 -9 30CONC 907 516

S 897 1152

Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 2.11 2.12 24.00 50.5618 0.00275 3.825 193 11 176 6.01 24.00 2.12

6 2.11 4.22 24.00 50.5618 0.00225 3.825 193 9 142 12.00 24.00 4.22

7 2.11 6.33 24.00 50.5618 0.00175 3.76437 190 7 107 18.00 24.00 6.33

8 2.11 8.44 24.00 50.5618 0.00125 3.28527 166 5 64 24.00 24.00 8.44

9 2.11 10.54 24.00 50.5618 0.00075 2.32902 118 3 25 18.32 15915.88 10.5410 2.11 12.65 24.00 50.5618 0.00025 0.89563 45 0 2 12.65 31807.77 12.65

S 12.65 303 907 516

STRESS-STRAIN COMPUTATIONS AT Pu = 0.1 * f'c * Ag < = = Not used

1ST ESTIMATE

Axial load Pn = 259 k




E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 60 0 9 0

2 1.27 2.64 0.002 60 71 9 56

3 2.54 2.64 0.002 60 143 9 111

4 2.54 2.64 0.002 60 143 9 111

5 2.54 7.32 0.001 37 83 5 32

6 2.54 12.00 0.000 4 2 0 0

7 2.54 16.69 -0.001 -28 -70 -5 27

8 1.90 21.37 -0.002 -60 -114 -9 89

9 1.27 21.37 -0.002 -60 -76 -9 59

10 1.27 21.37 -0.002 -60 -76 -9 59

11 1.27 21.37 -0.002 -60 -76 -9 59

12 0.64 21.37 -0.002 -60 -38 -9 30

CONC 907 516

S 897 1152

Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 2.11 2.12 24.00 50.5618 0.00275 3.825 193 11 176 6.01 24.00 2.12

6 2.11 4.22 24.00 50.5618 0.00225 3.825 193 9 142 12.00 24.00 4.22

7 2.11 6.33 24.00 50.5618 0.00175 3.76437 190 7 107 18.00 24.00 6.33

8 2.11 8.44 24.00 50.5618 0.00125 3.28527 166 5 64 24.00 24.00 8.44

9 2.11 10.54 24.00 50.5618 0.00075 2.32902 118 3 25 18.32 15915.88 10.54

10 2.11 12.65 24.00 50.5618 0.00025 0.89563 45 0 2 12.65 31807.77 12.65

S 12.65 303 907 516

3RD ITERATION

Axial load Pu = 259 k




E = 29000 ksi d = 21 in

case 1 cas

case 1 cas


9/38

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 60 0 9 0

2 1.27 2.64 0.002 60 71 9 55

3 2.54 2.64 0.002 60 142 9 111

4 2.54 2.64 0.002 60 142 9 110

5 2.54 7.32 0.000 11 18 5 7

6 2.54 12.00 -0.001 -38 -95 0 07 2.54 16.69 -0.003 -60 -152 -5 59

8 1.90 21.37 -0.005 -60 -114 -9 89

9 1.27 21.37 -0.005 -60 -76 -9 59

10 1.27 21.37 -0.005 -60 -76 -9 59

11 1.27 21.37 -0.005 -60 -76 -9 59

12 0.64 21.37 -0.005 -60 -38 -9 30

CONC 601 429

S 344 1070

Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.014 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 1.40 1.40 24.00 33.49523 0.00275 3.825 128 11 121 6.01 24.00 1.40

6 1.40 2.80 24.00 33.49523 0.00225 3.825 128 10 106 12.00 24.00 2.80

7 1.40 4.20 24.00 33.49523 0.00175 3.76408 126 9 89 18.00 24.00 4.20

8 1.40 5.59 24.00 33.49523 0.00125 3.28465 110 7 65 24.00 24.00 5.59

9 1.40 6.99 24.00 33.49523 0.00075 2.32841 78 6 37 16.19 21889.38 6.99

10 1.40 8.38 24.00 33.49523 0.00025 0.89534 30 4 11 8.38 43754.75 8.38

S 8.38 201 601 429

5TH ITERATION





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 58 0 9 0

2 1.27 2.64 0.002 58 69 9 53

3 2.54 2.64 0.002 58 137 9 107

4 2.54 2.64 0.002 58 137 9 107

5 2.54 7.32 0.000 6 5 5 2

6 2.54 12.00 -0.002 -46 -117 0 0

7 2.54 16.69 -0.003 -60 -152 -5 59

8 1.90 21.37 -0.005 -60 -114 -9 89

9 1.27 21.37 -0.005 -60 -76 -9 59

10 1.27 21.37 -0.005 -60 -76 -9 59

11 1.27 21.37 -0.005 -60 -76 -9 59

12 0.64 21.37 -0.005 -60 -38 -9 30

CONC 562 412

S 259 1038

Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 1.31 1.31 24.00 31.34965 0.00275 3.825 120 11 113 6.01 24.00 1.31

6 1.31 2.62 24.00 31.34965 0.00225 3.825 120 10 100 12.00 24.00 2.62

7 1.31 3.93 24.00 31.34965 0.00175 3.76403 118 9 86 18.00 24.00 3.93

8 1.31 5.23 24.00 31.34965 0.00125 3.28453 103 7 64 24.00 24.00 5.23

9 1.31 6.54 24.00 31.34965 0.00075 2.32828 73 6 37 15.92 22640.36 6.54

10 1.31 7.85 24.00 31.34965 0.00025 0.89528 28 5 11 7.85 45256.71 7.85

S 7.85 188 562 412

7TH ITERATION



case 1 cas

case 1 cas


10/38



E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 58 0 9 0

2 1.27 2.64 0.002 58 69 9 53

3 2.54 2.64 0.002 58 137 9 1074 2.54 2.64 0.002 58 137 9 107

5 2.54 7.32 0.000 6 5 5 2

6 2.54 12.00 -0.002 -46 -117 0 0

7 2.54 16.69 -0.003 -60 -152 -5 59

8 1.90 21.37 -0.005 -60 -114 -9 89

9 1.27 21.37 -0.005 -60 -76 -9 59

10 1.27 21.37 -0.005 -60 -76 -9 59

11 1.27 21.37 -0.005 -60 -76 -9 59

12 0.64 21.37 -0.005 -60 -38 -9 30

CONC 562 412

S 259 1038

Ec = 3824 ksi eo = 0.0020

conc sec thick to end b control D ec

fc

force arm moment to end b to end

1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 1.31 1.31 24.00 31.35378 0.00275 3.825 120 11 113 6.01 24.00 1.31

6 1.31 2.62 24.00 31.35378 0.00225 3.825 120 10 100 12.00 24.00 2.62

7 1.31 3.93 24.00 31.35378 0.00175 3.76403 118 9 86 18.00 24.00 3.93

8 1.31 5.23 24.00 31.35378 0.00125 3.28453 103 7 64 24.00 24.00 5.23

9 1.31 6.54 24.00 31.35378 0.00075 2.32828 73 6 37 15.92 22638.91 6.54

10 1.31 7.85 24.00 31.35378 0.00025 0.89528 28 5 11 7.85 45253.82 7.85

S 7.85 188 562 412

STRESS STRAIN COMPUTATION AT PURE MOMENT CONDITION

1ST ESTIMATE

Axial load Pu = 0 k




E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 60 0 9 0

2 1.27 2.64 0.002 60 71 9 56

3 2.54 2.64 0.002 60 143 9 111

4 2.54 2.64 0.002 60 143 9 111

5 2.54 7.32 0.001 42 98 5 38

6 2.54 12.00 0.000 14 25 0 0

7 2.54 16.69 -0.001 -15 -38 -5 15

8 1.90 21.37 -0.001 -43 -83 -9 65

9 1.27 21.37 -0.001 -43 -55 -9 43

10 1.27 21.37 -0.001 -43 -55 -9 43

11 1.27 21.37 -0.001 -43 -55 -9 43

12 0.64 21.37 -0.002 -44 -28 -9 22

CONC 1021 526

S 1187 1072

Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 2.37 2.38 24.00 56.9594 0.00275 3.825 218 11 196 6.01 24.00 2.38

6 2.37 4.76 24.00 56.9594 0.00225 3.825 218 8 153 12.00 24.00 4.76

7 2.37 7.13 24.00 56.9594 0.00175 3.76444 214 6 108 18.00 24.00 7.13

8 2.37 9.50 24.00 56.9594 0.00125 3.28541 187 4 58 24.00 24.00 9.50

9 2.37 11.88 24.00 56.9594 0.00075 2.32916 133 1 15 19.12 13676.65 11.88

10 2.37 14.25 24.00 56.9594 0.00025 0.89569 51 -1 -4 14.25 27329.31 14.25

case 1 ca

case 1 ca


11/38

S 14.25 342 1021 526

3RD ITERATION

Axial load Pu = 0 k




E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02

STA A dist strain stress force arm momentto end

1 0.00 2.64 0.002 50 0 9 0

2 1.27 2.64 0.002 50 58 9 45

3 2.54 2.64 0.002 50 116 9 91

4 2.54 2.64 0.002 50 116 9 91

5 2.54 7.32 -0.001 -17 -42 5 -16

6 2.54 12.00 -0.003 -60 -152 0 0

7 2.54 16.69 -0.005 -60 -152 -5 59

8 1.90 21.37 -0.007 -60 -114 -9 89

9 1.27 21.37 -0.007 -60 -76 -9 59

10 1.27 21.37 -0.007 -60 -76 -9 59

11 1.27 21.37 -0.007 -60 -76 -9 59

12 0.64 21.37 -0.007 -60 -38 -9 30CONC 441 348

S 3 916

Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 1.02 1.03 24.00 24.55893 0.00275 3.825 94 11 90 6.01 24.00 1.03

6 1.02 2.06 24.00 24.55893 0.00225 3.825 94 10 82 12.00 24.00 2.06

7 1.02 3.08 24.00 24.55893 0.00175 3.76377 92 9 73 18.00 24.00 3.08

8 1.02 4.10 24.00 24.55893 0.00125 3.28399 81 8 57 24.00 24.00 4.10

9 1.02 5.13 24.00 24.55893 0.00075 2.32774 57 7 35 15.07 25017.19 5.13

10 1.02 6.15 24.00 24.55893 0.00025 0.89503 22 6 12 6.15 50010.37 6.15

S 6.15 147 441 348

5TH ITERATION

Axial load Pu = 0 k




E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 50 0 9 0

2 1.27 2.64 0.002 50 58 9 45

3 2.54 2.64 0.002 50 116 9 91

4 2.54 2.64 0.002 49 116 9 90

5 2.54 7.32 -0.001 -17 -43 5 -17

6 2.54 12.00 -0.003 -60 -152 0 0

7 2.54 16.69 -0.005 -60 -152 -5 59

8 1.90 21.37 -0.007 -60 -114 -9 89

9 1.27 21.37 -0.007 -60 -76 -9 59

10 1.27 21.37 -0.007 -60 -76 -9 59

11 1.27 21.37 -0.007 -60 -76 -9 59

12 0.64 21.37 -0.007 -60 -38 -9 30

CONC 439 347

S 0 914

Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 1.02 1.03 24.00 24.46923 0.00275 3.825 94 11 90 6.01 24.00 1.03

6 1.02 2.05 24.00 24.46923 0.00225 3.825 94 10 82 12.00 24.00 2.05

7 1.02 3.07 24.00 24.46923 0.00175 3.76377 92 9 73 18.00 24.00 3.07

8 1.02 4.09 24.00 24.46923 0.00125 3.28398 80 8 56 24.00 24.00 4.09

case 1 cas

case 1 cas


12/38

9 1.02 5.11 24.00 24.46923 0.00075 2.32773 57 7 35 15.06 25048.58 5.11

10 1.02 6.13 24.00 24.46923 0.00025 0.89502 22 6 12 6.13 50073.16 6.13

S 6.13 147 439 347

7TH ITERATION

Axial load Pu = 0 k




E = 29000 ksi d = 21 in

fy

=60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 50 0 9 0

2 1.27 2.64 0.002 50 58 9 45

3 2.54 2.64 0.002 50 116 9 91

4 2.54 2.64 0.002 49 116 9 90

5 2.54 7.32 -0.001 -17 -43 5 -17

6 2.54 12.00 -0.003 -60 -152 0 0

7 2.54 16.69 -0.005 -60 -152 -5 59

8 1.90 21.37 -0.007 -60 -114 -9 89

9 1.27 21.37 -0.007 -60 -76 -9 59

10 1.27 21.37 -0.007 -60 -76 -9 5911 1.27 21.37 -0.007 -60 -76 -9 59

12 0.64 21.37 -0.007 -60 -38 -9 30

CONC 439 347

S 0 914

Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 1.02 1.03 24.00 24.46922 0.00275 3.825 94 11 90 6.01 24.00 1.03

6 1.02 2.05 24.00 24.46922 0.00225 3.825 94 10 82 12.00 24.00 2.05

7 1.02 3.07 24.00 24.46922 0.00175 3.76377 92 9 73 18.00 24.00 3.07

8 1.02 4.09 24.00 24.46922 0.00125 3.28398 80 8 56 24.00 24.00 4.09

9 1.02 5.11 24.00 24.46922 0.00075 2.32773 57 7 35 15.06 25048.58 5.11

10 1.02 6.13 24.00 24.46922 0.00025 0.89502 22 6 12 6.13 50073.17 6.13

S 6.13 147 439 347

STRESS STRAIN COMPUTATION AT MAXIMUM LOAD

1ST ESTIMATE

Axial load Pu = -433 k




E = 29000 ksi d = 21.373 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 60 143 5 56

6 2.54 12.00 0.002 44 101 0 0

7 2.54 16.69 0.001 27 58 -5 -22

8 1.90 21.37 0.000 10 11 -9 -9

9 1.27 21.37 0.000 10 7 -9 -6

10 1.27 21.37 0.000 10 7 -9 -6

11 1.27 21.37 0.000 10 7 -9 -6

12 0.64 21.37 0.000 10 4 -9 -3

CONC 1732 298

S 2426 582

Ec = 3824 ksi eo = 0.0020

conc sec thick to end b control DA ec fc force arm moment to end b to end

1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

case 1 cas

case 1 cas


13/38

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 6.00 6.01 24.00 143.9486 0.00262 3.825 551 9 413 6.01 24.00 4.01

6 6.00 12.00 24.00 143.9486 0.00187 3.80984 548 3 137 12.00 24.00 8.01

7 6.00 18.00 24.00 143.9486 0.00113 3.09267 445 -3 -111 18.00 24.00 12.01

8 6.00 24.00 24.00 143.9486 0.00038 1.30199 187 -9 -141 24.00 24.00 16.01

9 0.00 24.00 12.00 0.07714 8E-07 0.00307 0 -12 0 24.00 12.00 20.01

10 0.00 24.01 0.00 0.025713 2.7E-07 0.00102 0 -12 0 24.01 0.00 24.01

S 24.01 576 1732 298

3RD ITERATION





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 60 143 5 56

6 2.54 12.00 0.002 46 106 0 0

7 2.54 16.69 0.001 30 65 -5 -25

8 1.90 21.37 0.000 13 18 -9 -14

9 1.27 21.37 0.000 13 12 -9 -10

10 1.27 21.37 0.000 13 12 -9 -10

11 1.27 21.37 0.000 13 12 -9 -10

12 0.64 21.37 0.000 13 6 -9 -5

CONC 1811 251

S 2543 512

Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.00

3 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 6.00 6.01 24.00 143.9486 0.00264 3.825 551 9 413 6.01 24.00 4.22

6 6.00 12.00 24.00 143.9486 0.00193 3.82036 550 3 137 12.00 24.00 8.43

7 6.00 18.00 24.00 143.9486 0.00122 3.24112 467 -3 -117 18.00 24.00 12.64

8 6.00 24.00 24.00 143.9486 0.00051 1.69307 244 -9 -183 24.00 24.00 16.85

9 0.00 24.00 12.00 0.07714 0.00015 0.55483 0 -12 0 24.00 12.00 21.06

10 0.00 24.01 0.00 0.025713 0.00015 0.55303 0 -12 0 24.01 0.00 25.27

S 24.01 576 1811 251

5TH ITERATION


Distance to neutral axis c = -13 in


Compression block a = -11 in

E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.004 60 0 9 0

2 1.27 2.64 0.004 60 71 9 56

3 2.54 2.64 0.004 60 143 9 111

4 2.54 2.64 0.004 60 143 9 111

5 2.54 7.32 0.005 60 143 5 56

6 2.54 12.00 0.006 60 143 0 0

7 2.54 16.69 0.007 60 143 -5 -56

8 1.90 21.37 0.008 60 107 -9 -83

9 1.27 21.37 0.008 60 71 -9 -56

10 1.27 21.37 0.008 60 71 -9 -56

case 1 cas


14/38

11 1.27 21.37 0.008 60 71 -9 -56

12 0.64 21.37 0.008 60 36 -9 -28

CONC 602314 967320

S 603455 967320

Ec = 3824 ksi eo = 0.0020


1 -1.30 -1.30 -3640.60 0.00 2366.699 0.00285 3.825 9053 13 9546 0.00 6.00 0.00

2 -1.30 -2.60 -7281.19 0.01 7100.097 0.00255 3.825 27158 14 31581 0.00 12.00 0.00

3 -1.30 -3.90 ####### 24.00 11833.49 0.00225 3.825 45263 15 57540 0.01 18.00 0.014 -1.30 -5.20 ####### 24.01 16566.89 0.00195 3.82254 63328 17 87365 0.01 24.00 0.01

5 -1.30 -6.50 ####### 23666.99 0.00165 3.70748 87745 18 130557 6.01 24.00 -2.16

6 -1.30 -7.80 ####### 28400.39 0.00135 3.4204 97141 19 155063 12.00 24.00 -4.33

7 -1.30 -9.10 ####### 33133.79 0.00105 2.96132 98120 20 167257 18.00 24.00 -6.50

8 -1.30 -10.40 ####### 37867.18 0.00075 2.33024 88240 22 159975 24.00 24.00 -8.66

9 -1.30 -11.70 ####### 40233.88 0.00045 1.52715 61443 23 118051 5.50 51828.07 -10.83

10 -1.30 -13.00 ####### 44967.28 0.00015 0.55205 24824 24 50385 -13.00 103632.14 -13.00

S -13.00 246137 602314 967320

7TH ITERATION





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 60 143 5 56

6 2.54 12.00 0.002 48 113 0 0

7 2.54 16.69 0.001 33 75 -5 -29

8 1.90 21.37 0.001 18 28 -9 -22

9 1.27 21.37 0.001 18 18 -9 -14

10 1.27 21.37 0.001 18 18 -9 -14

11 1.27 21.37 0.001 18 18 -9 -14

12 0.64 21.37 0.001 18 9 -9 -7

CONC 1899 198

S 2679 431

Ec = 3824 ksi eo = 0.0020


1 0.00 0.00 6.00 0.00 0.006428 0.003 3.825 0 12 0 0.00 6.00 0.00

2 0.00 0.00 12.00 0.01 0.019285 0.003 3.825 0 12 0 0.00 12.00 0.003 0.00 0.01 18.00 24.00 0.032142 0.003 3.825 0 12 0 0.01 18.00 0.01

4 0.00 0.01 24.00 24.01 0.044999 0.003 3.825 0 12 0 0.01 24.00 0.01

5 6.00 6.01 24.00 143.9486 0.00267 3.825 551 9 413 6.01 24.00 4.52

6 6.00 12.00 24.00 143.9486 0.002 3.825 551 3 138 12.00 24.00 9.03

7 6.00 18.00 24.00 143.9486 0.00134 3.40352 490 -3 -122 18.00 24.00 13.53

8 6.00 24.00 24.00 143.9486 0.00067 2.13687 308 -9 -231 24.00 24.00 18.04

9 0.00 24.00 12.00 0.07714 0.00034 1.18586 0 -12 0 24.00 12.00 22.55

10 0.00 24.01 0.00 0.025713 0.00034 1.18435 0 -12 0 24.01 0.00 27.06

S 24.01 576 1899 198

f Pn (kips) f Mn (ft-kips)-1097 0 0

0 822 258

258 943 585

585 751 605

case 1 cas

case 1 cas


15/38

605 743 941

941 648 1148

1148 580 1384

1384 487 1739

1739 281 1739

1739 0

f Pn (kips) f Mn (ft-kips)-1097 0

-433 498

0 822

f Pn (kips) f Mn (ft-kips)-1097 0 0

0 822 258

258 943 585

585 751 605

605 743 941

941 648 1148

1148 580 1384

1384 487 1739

1739 281 1739

1739 0

f Pn (kips) f Mn (ft-kips)POINT 1 -1097 0

-433 498

0 822

f Pn (kips) f Mn (ft-kips)POINT 2 0 822

0 822

258 943


0 822

258 943


0 822

258 943


0 822

258 943


0 822

258 943


16/38

2ND ESTIMATE





E = 29000 ksi d = 21 in

fy

= 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 60 143 5 56

6 2.54 12.00 0.002 48 111 0 0

7 2.54 16.69 0.001 32 72 -5 -28

8 1.90 21.37 0.001 17 25 -9 -19

9 1.27 21.37 0.001 17 16 -9 -13

10 1.27 21.37 0.001 17 16 -9 -13

11 1.27 21.37 0.001 17 16 -9 -13

12 0.64 21.37 0.001 17 8 -9 -6

CONC 1873 214

S 2638 455

Ec = 3824 ksi eo = 0.0020

b to end b conc sec thick to end b control ec fc force arm moment to end

6.00 2.40 6722.62 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 4.80 13445.24 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 7.20 20167.86 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 9.60 26890.47 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 12.00 33613.09 5 6.00 6.01 24.00 143.949 0.00266 3.825 551 9 413 6.01

24.00 14.41 40335.71 6 6.00 12.00 24.00 143.949 0.00198 3.82458 551 3 138 12.00

24.00 16.81 47058.33 7 6.00 18.00 24.00 143.949 0.0013 3.35587 483 -3 -121 18.0024.00 19.21 53780.95 8 6.00 24.00 24.00 143.949 0.00062 2.00446 289 -9 -216 24.00

24.00 21.61 60503.57 9 0.00 24.00 12.00 0.07714 0.00028 0.99695 0 -12 0 24.00

24.00 24.01 67226.19 10 0.00 24.01 0.00 0.02571 0.00028 0.99535 0 -12 0 24.01

S 24.01 576 1873 214

4TH ITERATION





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 60 143 5 56

6 2.54 12.00 0.002 48 113 0 0

7 2.54 16.69 0.001 33 75 -5 -29

8 1.90 21.37 0.001 18 27 -9 -21

case 3 case 2


17/38

9 1.27 21.37 0.001 18 18 -9 -14

10 1.27 21.37 0.001 18 18 -9 -14

11 1.27 21.37 0.001 18 18 -9 -14

12 0.64 21.37 0.001 18 9 -9 -7

CONC 1897 199

S 2676 433

Ec = 3824 ksi eo = 0.0020


6.00 2.69 7536.91 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 5.38 15073.82 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.0018.00 8.07 22610.72 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 10.77 30147.63 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 13.46 37684.54 5 6.00 6.01 24.00 143.949 0.00267 3.825 551 9 413 6.01

24.00 16.15 45221.45 6 6.00 12.00 24.00 143.949 0.002 3.825 551 3 138 12.00

24.00 18.84 52758.36 7 6.00 18.00 24.00 143.949 0.00133 3.3998 489 -3 -122 18.00

24.00 21.53 60295.27 8 6.00 24.00 24.00 143.949 0.00067 2.12648 306 -9 -229 24.00

24.00 24.22 67832.17 9 0.00 24.00 12.00 0.07714 0.00033 1.17101 0 -12 0 24.00

24.00 26.92 75369.08 10 0.00 24.01 0.00 0.02571 0.00033 1.16949 0 -12 0 24.01

S 24.01 576 1897 199

6TH ITERATION



Beta factor b = 0.83Compression block a = 22 in

E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 60 143 5 56

6 2.54 12.00 0.002 48 113 0 0

7 2.54 16.69 0.001 33 75 -5 -29

8 1.90 21.37 0.001 18 27 -9 -21

9 1.27 21.37 0.001 18 18 -9 -14

10 1.27 21.37 0.001 18 18 -9 -14

11 1.27 21.37 0.001 18 18 -9 -14

12 0.64 21.37 0.001 18 9 -9 -7

CONC 1897 199

S 2676 433

Ec = 3824 ksi eo = 0.0020

b to end b conc sec thick to end b control D ec fc force arm moment to end

6.00 2.70 7564.17 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 5.40 15128.33 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 8.10 22692.50 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 10.81 30256.66 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 13.51 37820.83 5 6.00 6.01 24.00 143.949 0.00267 3.825 551 9 413 6.01

24.00 16.21 45384.99 6 6.00 12.00 24.00 143.949 0.002 3.825 551 3 138 12.00

24.00 18.91 52949.16 7 6.00 18.00 24.00 143.949 0.00133 3.40006 489 -3 -122 18.00

24.00 21.61 60513.32 8 6.00 24.00 24.00 143.949 0.00067 2.12719 306 -9 -230 24.00

24.00 24.31 68077.49 9 0.00 24.00 12.00 0.07714 0.00033 1.17203 0 -12 0 24.00

24.00 27.01 75641.65 10 0.00 24.01 0.00 0.02571 0.00033 1.17052 0 -12 0 24.01

S 24.01 576 1897 199

8TH ITERATION





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 60 143 5 56

6 2.54 12.00 0.002 48 113 0 0

case 3 case 2

e 2 case 3 cas


18/38

7 2.54 16.69 0.001 33 75 -5 -29

8 1.90 21.37 0.001 18 27 -9 -21

9 1.27 21.37 0.001 18 18 -9 -14

10 1.27 21.37 0.001 18 18 -9 -14

11 1.27 21.37 0.001 18 18 -9 -14

12 0.64 21.37 0.001 18 9 -9 -7

CONC 1897 199

S 2676 433

Ec = 3824 ksi eo = 0.0020

b to end b conc sec thick to end b controlD e

cfc force arm moment to end

6.00 2.70 7564.17 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 5.40 15128.34 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 8.10 22692.51 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 10.81 30256.68 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 13.51 37820.85 5 6.00 6.01 24.00 143.949 0.00267 3.825 551 9 413 6.01

24.00 16.21 45385.03 6 6.00 12.00 24.00 143.949 0.002 3.825 551 3 138 12.00

24.00 18.91 52949.20 7 6.00 18.00 24.00 143.949 0.00133 3.40006 489 -3 -122 18.00

24.00 21.61 60513.37 8 6.00 24.00 24.00 143.949 0.00067 2.12719 306 -9 -230 24.00

24.00 24.31 68077.54 9 0.00 24.00 12.00 0.07714 0.00033 1.17203 0 -12 0 24.00

24.00 27.01 75641.71 10 0.00 24.01 0.00 0.02571 0.00033 1.17052 0 -12 0 24.01

S 24.01 576 1897 199






E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

e 2 case 3 cas


19/38

5 2.54 7.32 0.002 52 122 5 48

6 2.54 12.00 0.001 30 66 0 0

7 2.54 16.69 0.000 7 9 -5 -4

8 1.90 21.37 -0.001 -15 -29 -9 22

9 1.27 21.37 -0.001 -15 -19 -9 15

10 1.27 21.37 -0.001 -15 -19 -9 15

11 1.27 21.37 -0.001 -15 -19 -9 15

12 0.64 21.37 -0.001 -15 -10 -9 7

CONC 1307 495

S 1766 892Ec = 3824 ksi eo = 0.0020


6.00 2.14 5984.53 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 4.27 11969.06 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 6.41 17953.59 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 8.55 23938.12 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 10.69 29922.66 5 3.04 3.05 24.00 72.8841 0.00275 3.825 279 10 243 6.01

24.00 12.82 35907.19 6 3.04 6.08 24.00 72.8841 0.00225 3.825 279 7 173 12.00

24.00 14.96 41891.72 7 3.04 9.12 24.00 72.8841 0.00175 3.76455 274 4 101 18.00

24.00 17.10 47876.25 8 3.04 12.16 24.00 72.8841 0.00125 3.28565 239 1 27 24.00

24.00 19.24 53860.78 9 3.04 15.19 24.00 72.8841 0.00075 2 .3294 170 -2 -24 21.11

24.00 21.37 59845.31 10 3.04 18.23 24.00 72.8841 0.00025 0.8958 65 -5 -26 18.23

S 18.23 437 1307 495

STRESS-STRAIN COMPUTATIONS AT POINT OF et = 0.002





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 60 0 9 0

2 1.27 2.64 0.002 60 71 9 56

3 2.54 2.64 0.002 60 143 9 111

4 2.54 2.64 0.002 60 143 9 111

5 2.54 7.32 0.001 37 85 5 33

6 2.54 12.00 0.000 6 4 0 0

7 2.54 16.69 -0.001 -26 -67 -5 26

8 1.90 21.37 -0.002 -58 -110 -9 86

9 1.27 21.37 -0.002 -58 -74 -9 57

10 1.27 21.37 -0.002 -58 -74 -9 57

11 1.27 21.37 -0.002 -58 -74 -9 58

12 0.64 21.37 -0.002 -58 -37 -9 29

CONC 919 518

S 931 1143

Ec = 3824 ksi eo = 0.0020


6.00 1.59 4450.04 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 3.18 8900.07 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 4.77 13350.11 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 6.36 17800.14 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 7.95 22250.18 5 2.14 2.14 24.00 51.26 0.00275 3.825 196 11 179 6.01

24.00 9.54 26700.22 6 2.14 4.28 24.00 51.26 0.00225 3.825 196 9 144 12.00

24.00 11.12 31150.25 7 2.14 6.42 24.00 51.26 0.00175 3.76438 193 7 107 18.00

24.00 12.71 35600.29 8 2.14 8.55 24.00 51.26 0.00125 3.28529 168 5 63 24.00

24.00 14.30 40050.32 9 2.14 10.69 24.00 51.26 0.00075 2.32904 119 2 24 18.41

24.00 15.89 44500.36 10 2.14 12.82 24.00 51.26 0.00025 0.89564 46 0 1 12.82

S 12.82 308 919 518

STRESS-STRAIN COMPUTATIONS AT POINT OF et = 0.005





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 58 0 9 0

2 1.27 2.64 0.002 58 69 9 54

e 2

e 2 case 3 cas

case 3 cas


20/38

3 2.54 2.64 0.002 58 139 9 108

4 2.54 2.64 0.002 58 138 9 108

5 2.54 7.32 0.000 8 9 5 4

6 2.54 12.00 -0.001 -43 -110 0 0

7 2.54 16.69 -0.003 -60 -152 -5 59

8 1.90 21.37 -0.005 -60 -114 -9 89

9 1.27 21.37 -0.005 -60 -76 -9 59

10 1.27 21.37 -0.005 -60 -76 -9 59

11 1.27 21.37 -0.005 -60 -76 -9 59

12 0.64 21.37 -0.005 -60 -38 -9 30CONC 574 418

S 287 1048

Ec = 3824 ksi eo = 0.0020


6.00 1.26 3541.84 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 2.53 7083.68 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 3.79 10625.52 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 5.06 14167.37 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 6.32 17709.21 5 1.33 1.34 24.00 32.0247 0.00275 3.825 122 11 116 6.01

24.00 7.59 21251.05 6 1.33 2.68 24.00 32.0247 0.00225 3.825 122 10 102 12.00

24.00 8.85 24792.89 7 1.33 4.01 24.00 32.0247 0.00175 3.76404 121 9 87 18.00

24.00 10.12 28334.73 8 1.33 5.35 24.00 32.0247 0.00125 3.28457 105 7 64 24.00

24.00 11.38 31876.57 9 1.33 6.68 24.00 32.0247 0.00075 2.32832 75 6 37 16.0124.00 12.65 35418.41 10 1.33 8.01 24.00 32.0247 0.00025 0.8953 29 5 11 8.01

S 8.01 192 574 418

2ND ESTIMATE

Axial load Pn = 259 k




E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.001 24 0 9 0

2 1.27 2.64 0.001 24 26 9 20

3 2.54 2.64 0.001 24 52 9 40

4 2.54 2.64 0.001 24 52 9 40

5 2.54 7.32 -0.003 -60 -152 5 -59

6 2.54 12.00 -0.007 -60 -152 0 0

7 2.54 16.69 -0.011 -60 -152 -5 59

8 1.90 21.37 -0.015 -60 -114 -9 89

9 1.27 21.37 -0.015 -60 -76 -9 59

10 1.27 21.37 -0.015 -60 -76 -9 59

11 1.27 21.37 -0.015 -60 -76 -9 59

12 0.64 21.37 -0.015 -60 -38 -9 30

CONC 262 229

S -447 627

Ec = 3824 ksi eo = 0.0020


6.00 1.26 3541.84 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 2.53 7083.68 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 3.79 10625.52 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 5.06 14167.37 4 0.00 0.01 24.00 24.01 0.045 0.00299 3.825 0 12 0 0.01

24.00 6.32 17709.21 5 0.61 0.62 24.00 14.5876 0.00274 3.825 56 12 54 6.01

24.00 7.59 21251.05 6 0.61 1.22 24.00 14.5876 0.00224 3.825 56 11 52 12.00

24.00 8.85 24792.89 7 0.61 1.83 24.00 14.5876 0.00175 3.76296 55 10 48 18.00

24.00 10.12 28334.73 8 0.61 2.44 24.00 14.5876 0.00125 3.28228 48 10 39 24.00

24.00 11.38 31876.57 9 0.61 3.05 24.00 14.5876 0.00075 2.32603 34 9 26 13.83

24.00 12.65 35418.41 10 0.61 3.66 24.00 14.5876 0.00025 0.89423 13 9 9 3.66

S 3.66 88 262 229

4TH ITERATION





E = 29000 ksi d = 21 in

e 2 case 3 cas

e 2 case 3 cas


21/38

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 58 0 9 0

2 1.27 2.64 0.002 58 69 9 54

3 2.54 2.64 0.002 58 137 9 107

4 2.54 2.64 0.002 58 137 9 107

5 2.54 7.32 0.000 6 6 5 2

6 2.54 12.00 -0.002 -46 -116 0 07 2.54 16.69 -0.003 -60 -152 -5 59

8 1.90 21.37 -0.005 -60 -114 -9 89

9 1.27 21.37 -0.005 -60 -76 -9 59

10 1.27 21.37 -0.005 -60 -76 -9 59

11 1.27 21.37 -0.005 -60 -76 -9 59

12 0.64 21.37 -0.005 -60 -38 -9 30

CONC 564 413

S 264 1040

Ec = 3824 ksi eo = 0.0020


6.00 0.84 2347.14 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 1.68 4694.29 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 2.51 7041.43 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.0124.00 3.35 9388.57 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 4.19 11735.71 5 1.31 1.32 24.00 31.4643 0.00275 3.825 120 11 114 6.01

24.00 5.03 14082.86 6 1.31 2.63 24.00 31.4643 0.00225 3.825 120 10 101 12.00

24.00 5.87 16430.00 7 1.31 3.94 24.00 31.4643 0.00175 3.76403 118 9 86 18.00

24.00 6.71 18777.14 8 1.31 5.25 24.00 31.4643 0.00125 3.28453 103 7 64 24.00

24.00 7.54 21124.28 9 1.31 6.56 24.00 31.4643 0.00075 2.32829 73 6 37 15.94

24.00 8.38 23471.43 10 1.31 7.87 24.00 31.4643 0.00025 0.89528 28 5 11 7.87

S 7.87 189 564 413

6TH ITERATION





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 58 0 9 0

2 1.27 2.64 0.002 58 69 9 53

3 2.54 2.64 0.002 58 137 9 107

4 2.54 2.64 0.002 58 137 9 107

5 2.54 7.32 0.000 6 5 5 2

6 2.54 12.00 -0.002 -46 -117 0 0

7 2.54 16.69 -0.003 -60 -152 -5 59

8 1.90 21.37 -0.005 -60 -114 -9 89

9 1.27 21.37 -0.005 -60 -76 -9 59

10 1.27 21.37 -0.005 -60 -76 -9 59

11 1.27 21.37 -0.005 -60 -76 -9 59

12 0.64 21.37 -0.005 -60 -38 -9 30

CONC 562 412

S 259 1038

Ec = 3824 ksi eo = 0.0020


6.00 0.78 2196.95 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 1.57 4393.89 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 2.35 6590.84 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 3.14 8787.79 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 3.92 10984.73 5 1.31 1.31 24.00 31.3538 0.00275 3.825 120 11 113 6.01

24.00 4.71 13181.68 6 1.31 2.62 24.00 31.3538 0.00225 3.825 120 10 100 12.00

24.00 5.49 15378.63 7 1.31 3.93 24.00 31.3538 0.00175 3.76403 118 9 86 18.00

24.00 6.28 17575.58 8 1.31 5.23 24.00 31.3538 0.00125 3.28453 103 7 64 24.00

24.00 7.06 19772.52 9 1.31 6.54 24.00 31.3538 0.00075 2.32828 73 6 37 15.92

24.00 7.85 21969.47 10 1.31 7.85 24.00 31.3538 0.00025 0.89528 28 5 11 7.85

S 7.85 188 562 412

8TH ITERATION



e 2

e 2 case 3 cas

case 3 cas


22/38



E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 58 0 9 0

2 1.27 2.64 0.002 58 69 9 53

3 2.54 2.64 0.002 58 137 9 1074 2.54 2.64 0.002 58 137 9 107

5 2.54 7.32 0.000 6 5 5 2

6 2.54 12.00 -0.002 -46 -117 0 0

7 2.54 16.69 -0.003 -60 -152 -5 59

8 1.90 21.37 -0.005 -60 -114 -9 89

9 1.27 21.37 -0.005 -60 -76 -9 59

10 1.27 21.37 -0.005 -60 -76 -9 59

11 1.27 21.37 -0.005 -60 -76 -9 59

12 0.64 21.37 -0.005 -60 -38 -9 30

CONC 562 412

S 259 1038

Ec = 3824 ksi eo = 0.0020

b to end b conc sec thick to end b control D ec

fc

force arm moment to end

6.00 0.78 2197.24 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 1.57 4394.47 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 2.35 6591.71 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 3.14 8788.94 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 3.92 10986.18 5 1.31 1.31 24.00 31.3538 0.00275 3.825 120 11 113 6.01

24.00 4.71 13183.42 6 1.31 2.62 24.00 31.3538 0.00225 3.825 120 10 100 12.00

24.00 5.49 15380.65 7 1.31 3.93 24.00 31.3538 0.00175 3.76403 118 9 86 18.00

24.00 6.28 17577.89 8 1.31 5.23 24.00 31.3538 0.00125 3.28453 103 7 64 24.00

24.00 7.06 19775.12 9 1.31 6.54 24.00 31.3538 0.00075 2.32828 73 6 37 15.92

24.00 7.85 21972.36 10 1.31 7.85 24.00 31.3538 0.00025 0.89528 28 5 11 7.85

S 7.85 188 562 412

2ND ESTIMATE

Axial load Pu = 0 k




E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 55 0 9 0

2 1.27 2.64 0.002 55 65 9 51

3 2.54 2.64 0.002 55 129 9 101

4 2.54 2.64 0.002 55 129 9 101

5 2.54 7.32 0.000 -2 -6 5 -2

6 2.54 12.00 -0.002 -60 -151 0 0

7 2.54 16.69 -0.004 -60 -152 -5 59

8 1.90 21.37 -0.006 -60 -114 -9 89

9 1.27 21.37 -0.006 -60 -76 -9 59

10 1.27 21.37 -0.006 -60 -76 -9 59

11 1.27 21.37 -0.006 -60 -76 -9 59

12 0.64 21.37 -0.006 -60 -38 -9 30

CONC 510 387

S 143 993

Ec = 3824 ksi eo = 0.0020


6.00 1.42 3989.69 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 2.85 7979.37 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 4.27 11969.06 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 5.70 15958.75 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 7.12 19948.44 5 1.19 1.19 24.00 28.4626 0.00275 3.825 109 11 103 6.01

24.00 8.55 23938.12 6 1.19 2.38 24.00 28.4626 0.00225 3.825 109 10 93 12.00

24.00 9.97 27927.81 7 1.19 3.57 24.00 28.4626 0.00175 3.76393 107 9 81 18.00

24.00 11.40 31917.50 8 1.19 4.75 24.00 28.4626 0.00125 3.28433 93 8 61 24.00

24.00 12.82 35907.19 9 1.19 5.94 24.00 28.4626 0.00075 2.32808 66 7 37 15.56

24.00 14.25 39896.87 10 1.19 7.12 24.00 28.4626 0.00025 0.89519 25 5 12 7.12

e 2 case 3 cas

e 2 case 3 cas


23/38

S 7.12 171 510 387

4TH ITERATION

Axial load Pu = 0 k




E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


1 0.00 2.64 0.002 50 0 9 0

2 1.27 2.64 0.002 50 58 9 45

3 2.54 2.64 0.002 49 116 9 91

4 2.54 2.64 0.002 49 116 9 90

5 2.54 7.32 -0.001 -17 -43 5 -17

6 2.54 12.00 -0.003 -60 -152 0 0

7 2.54 16.69 -0.005 -60 -152 -5 59

8 1.90 21.37 -0.007 -60 -114 -9 89

9 1.27 21.37 -0.007 -60 -76 -9 59

10 1.27 21.37 -0.007 -60 -76 -9 59

11 1.27 21.37 -0.007 -60 -76 -9 59

12 0.64 21.37 -0.007 -60 -38 -9 30CONC 439 347

S 0 914

Ec = 3824 ksi eo = 0.0020


6.00 0.61 1721.58 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 1.23 3443.16 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 1.84 5164.74 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 2.46 6886.32 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 3.07 8607.90 5 1.02 1.03 24.00 24.4627 0.00275 3.825 94 11 90 6.01

24.00 3.69 10329.49 6 1.02 2.05 24.00 24.4627 0.00225 3.825 94 10 82 12.00

24.00 4.30 12051.07 7 1.02 3.07 24.00 24.4627 0.00175 3.76377 92 9 72 18.00

24.00 4.92 13772.65 8 1.02 4.09 24.00 24.4627 0.00125 3.28398 80 8 56 24.00

24.00 5.53 15494.23 9 1.02 5.10 24.00 24.4627 0.00075 2.32773 57 7 35 15.06

24.00 6.15 17215.81 10 1.02 6.12 24.00 24.4627 0.00025 0.89502 22 6 12 6.12

S 6.12 147 439 347

6TH ITERATION

Axial load Pu = 0 k




E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 50 0 9 0

2 1.27 2.64 0.002 50 58 9 45

3 2.54 2.64 0.002 50 116 9 91

4 2.54 2.64 0.002 49 116 9 90

5 2.54 7.32 -0.001 -17 -43 5 -17

6 2.54 12.00 -0.003 -60 -152 0 0

7 2.54 16.69 -0.005 -60 -152 -5 59

8 1.90 21.37 -0.007 -60 -114 -9 89

9 1.27 21.37 -0.007 -60 -76 -9 59

10 1.27 21.37 -0.007 -60 -76 -9 59

11 1.27 21.37 -0.007 -60 -76 -9 59

12 0.64 21.37 -0.007 -60 -38 -9 30

CONC 439 347

S 0 914

Ec = 3824 ksi eo = 0.0020


6.00 0.61 1715.30 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 1.23 3430.60 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 1.84 5145.91 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 2.45 6861.21 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 3.06 8576.51 5 1.02 1.03 24.00 24.4692 0.00275 3.825 94 11 90 6.01

24.00 3.68 10291.81 6 1.02 2.05 24.00 24.4692 0.00225 3.825 94 10 82 12.00

24.00 4.29 12007.12 7 1.02 3.07 24.00 24.4692 0.00175 3.76377 92 9 73 18.00

24.00 4.90 13722.42 8 1.02 4.09 24.00 24.4692 0.00125 3.28398 80 8 56 24.00

e 2

e 2 case 3 cas

case 3 cas


24/38

24.00 5.51 15437.72 9 1.02 5.11 24.00 24.4692 0.00075 2.32773 57 7 35 15.06

24.00 6.13 17153.02 10 1.02 6.13 24.00 24.4692 0.00025 0.89502 22 6 12 6.13

S 6.13 147 439 347

8TH ITERATION

Axial load Pu = 0 k




E = 29000 ksi d = 21 in

fy

=60 ksi D = 24 infc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.002 50 0 9 0

2 1.27 2.64 0.002 50 58 9 45

3 2.54 2.64 0.002 50 116 9 91

4 2.54 2.64 0.002 49 116 9 90

5 2.54 7.32 -0.001 -17 -43 5 -17

6 2.54 12.00 -0.003 -60 -152 0 0

7 2.54 16.69 -0.005 -60 -152 -5 59

8 1.90 21.37 -0.007 -60 -114 -9 89

9 1.27 21.37 -0.007 -60 -76 -9 59

10 1.27 21.37 -0.007 -60 -76 -9 5911 1.27 21.37 -0.007 -60 -76 -9 59

12 0.64 21.37 -0.007 -60 -38 -9 30

CONC 439 347

S 0 914

Ec = 3824 ksi eo = 0.0020


6.00 0.61 1715.30 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 1.23 3430.60 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 1.84 5145.90 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 2.45 6861.21 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 3.06 8576.51 5 1.02 1.03 24.00 24.4692 0.00275 3.825 94 11 90 6.01

24.00 3.68 10291.81 6 1.02 2.05 24.00 24.4692 0.00225 3.825 94 10 82 12.00

24.00 4.29 12007.11 7 1.02 3.07 24.00 24.4692 0.00175 3.76377 92 9 73 18.00

24.00 4.90 13722.41 8 1.02 4.09 24.00 24.4692 0.00125 3.28398 80 8 56 24.00

24.00 5.51 15437.71 9 1.02 5.11 24.00 24.4692 0.00075 2.32773 57 7 35 15.06

24.00 6.13 17153.01 10 1.02 6.13 24.00 24.4692 0.00025 0.89502 22 6 12 6.13

S 6.13 147 439 347

2ND ESTIMATE





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.005 60 0 9 0

2 1.27 2.64 0.005 60 71 9 56

3 2.54 2.64 0.005 60 143 9 111

4 2.54 2.64 0.005 60 143 9 111

5 2.54 7.32 0.008 60 143 5 56

6 2.54 12.00 0.011 60 143 0 0

7 2.54 16.69 0.015 60 143 -5 -56

8 1.90 21.37 0.018 60 107 -9 -83

9 1.27 21.37 0.018 60 71 -9 -56

10 1.27 21.37 0.018 60 71 -9 -56

11 1.27 21.37 0.018 60 71 -9 -56

12 0.64 21.37 0.018 60 36 -9 -28

CONC 65277 78315

S 66418 78315

Ec = 3824 ksi eo = 0.0020

b to end b conc sec thick to end b control DA ec fc force arm moment to end

6.00 2.40 6722.62 1 -0.43 -0.43 -1198.51 0.00 256.495 0.00285 3.825 981 12 999 0.00

e 2 case 3 cas

e 2 case 3 cas


25/38

12.00 4.80 13445.24 2 -0.43 -0.86 -2397.02 0.01 769.486 0.00255 3.825 2943 13 3102 0.00

18.00 7.20 20167.86 3 -0.43 -1.28 -3595.52 24.00 1282.48 0.00225 3.825 4905 13 5345 0.01

24.00 9.60 26890.47 4 -0.43 -1.71 -4794.03 24.01 1795.47 0.00195 3.82254 6863 14 7723 0.01

24.00 12.00 33613.09 5 -0.43 -2.14 -5992.54 2564.95 0.00165 3.70748 9510 14 11039 6.01

24.00 14.41 40335.71 6 -0.43 -2.57 -7191.05 3077.95 0.00135 3.4204 10528 14 12597 12.00

24.00 16.81 47058.33 7 -0.43 -3.00 -8389.56 3590.94 0.00105 2.96132 10634 15 13103 18.00

24.00 19.21 53780.95 8 -0.43 -3.42 -9588.06 4103.93 0.00075 2.33024 9563 15 12125 24.00

24.00 21.61 60503.57 9 -0.43 -3.85 ####### 4360.42 0.00045 1.52715 6659 16 8680 9.86

24.00 24.01 67226.19 10 -0.43 -4.28 ####### 4873.41 0.00015 0.55205 2690 16 3603 -4.28

S -4.28 26676 65277 78315

4TH ITERATION





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 60 143 5 56

6 2.54 12.00 0.002 48 112 0 0

7 2.54 16.69 0.001 33 73 -5 -28

8 1.90 21.37 0.001 17 26 -9 -20

9 1.27 21.37 0.001 17 17 -9 -13

10 1.27 21.37 0.001 17 17 -9 -13

11 1.27 21.37 0.001 17 17 -9 -13

12 0.64 21.37 0.001 17 9 -9 -7

CONC 1881 209

S 2650 448

Ec = 3824 ksi eo = 0.0020


6.00 2.53 7076.50 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 5.05 14153.00 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 7.58 21229.50 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.01

24.00 10.11 28306.00 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 12.64 35382.50 5 6.00 6.01 24.00 143.949 0.00266 3.825 551 9 413 6.01

24.00 15.16 42459.00 6 6.00 12.00 24.00 143.949 0.00199 3.8248 551 3 138 12.00

24.00 17.69 49535.50 7 6.00 18.00 24.00 143.949 0.00131 3.3705 485 -3 -121 18.00

24.00 20.22 56612.00 8 6.00 24.00 24.00 143.949 0.00064 2.04489 294 -9 -221 24.00

24.00 22.75 63688.50 9 0.00 24.00 12.00 0.07714 0.0003 1.05457 0 -12 0 24.00

24.00 25.27 70765.00 10 0.00 24.01 0.00 0.02571 0.0003 1.053 0 -12 0 24.01

S 24.01 576 1881 209

6TH ITERATION





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.002 60 143 5 56

6 2.54 12.00 0.002 48 112 0 0

7 2.54 16.69 0.001 33 74 -5 -29

8 1.90 21.37 0.001 18 27 -9 -21

9 1.27 21.37 0.001 18 18 -9 -14

10 1.27 21.37 0.001 18 18 -9 -14

e 2 case 3 cas


26/38

11 1.27 21.37 0.001 18 18 -9 -14

12 0.64 21.37 0.001 18 9 -9 -7

CONC 1890 203

S 2665 439

Ec = 3824 ksi eo = 0.0020


6.00 -1.30 -3640.60 1 0.00 0.00 6.00 0.00 0.00643 0.003 3.825 0 12 0 0.00

12.00 -2.60 -7281.19 2 0.00 0.00 12.00 0.01 0.01929 0.003 3.825 0 12 0 0.00

18.00 -3.90 -10921.79 3 0.00 0.01 18.00 24.00 0.03214 0.003 3.825 0 12 0 0.0124.00 -5.20 -14562.39 4 0.00 0.01 24.00 24.01 0.045 0.003 3.825 0 12 0 0.01

24.00 -6.50 -18202.98 5 6.00 6.01 24.00 143.949 0.00266 3.825 551 9 413 6.01

24.00 -7.80 -21843.58 6 6.00 12.00 24.00 143.949 0.00199 3.82496 551 3 138 12.00

24.00 -9.10 -25484.18 7 6.00 18.00 24.00 143.949 0.00132 3.38721 488 -3 -122 18.00

24.00 -10.40 -29124.78 8 6.00 24.00 24.00 143.949 0.00065 2.09131 301 -9 -226 24.00

24.00 -11.70 -32765.37 9 0.00 24.00 12.00 0.07714 0.00032 1.1208 0 -12 0 24.00

24.00 -13.00 -36405.97 10 0.00 24.01 0.00 0.02571 0.00032 1.11926 0 -12 0 24.01

S 24.01 576 1890 203

8TH ITERATION





E = 29000 ksi d = 21 in

fy = 60 ksi D = 24 in

fc' = 5 ksi q = 0.02


to end

1 0.00 2.64 0.003 60 0 9 0

2 1.27 2.64 0.003 60 71 9 56

3 2.54 2.64 0.003 60 143 9 111

4 2.54 2.64 0.003 60 143 9 111

5 2.54 7.32 0.004 60 143 5 56

6 2.54 12.00 0.005 60 143 0 0

7 2.54 16.69 0.006 60 143 -5 -56

8 1.90 21.37 0.006 60 107 -9 -83

9 1.27 21.37 0.006 60 71 -9 -56

10 1.27 21.37 0.006 60 71 -9 -56

11 1.27 21.37 0.006 60 71 -9 -56

12 0.64 21.37 0.006 60 36 -9 -28

CONC 1211583 ######

S 1212724 ######

Ec = 3824 ksi eo = 0.0020


6.00 2.71 7576.53 1 -1.84 -1.84 -5163.42 0.00 4760.73 0.00285 3.825 18210 13 19615 0.00

12.00 5.41 15153.06 2 -1.84 -3.69 ####### 0.01 14282.2 0.00255 3.825 54629 15 67241 0.00

18.00 8.12 22729.60 3 -1.84 -5.53 ####### 24.00 23803.6 0.00225 3.825 91049 17 126060 0.01

24.00 10.82 30306.13 4 -1.84 -7.38 ####### 24.01 33325.1 0.00195 3.82254 127387 18 195946 0.01

24.00 13.53 37882.66 5 -1.84 -9.22 ####### 47607.3 0.00165 3.70748 176503 20 298619 6.01

24.00 16.23 45459.19 6 -1.84 -11.06 ####### 57128.7 0.00135 3.4204 195403 22 360623 12.00

24.00 18.94 53035.73 7 -1.84 -12.91 ####### 66650.2 0.00105 2.96132 197373 24 394588 18.00

24.00 21.65 60612.26 8 -1.84 -14.75 ####### 76171.6 0.00075 2.33024 177498 26 382130 24.00

24.00 24.35 68188.79 9 -1.84 -16.60 ####### 80932.4 0.00045 1.52715 123596 28 285078 2.78

24.00 27.06 75765.32 10 -1.84 -18.44 ####### 90453.8 0.00015 0.55205 49935 30 122851 -18.44

S -18.44 495116 ###### ######

e 2 case 3 cas

e 2 case 3 cas


27/38


28/38

b to end b to end b

6.00 0.00 6.00 2.65 7413.69

12.00 0.00 12.00 5.30 14827.39

18.00 0.01 18.00 7.94 22241.08

24.00 0.01 24.00 10.59 29654.77

24.00 4.42 24.00 13.24 37068.46

24.00 8.83 24.00 15.89 44482.16

24.00 13.24 24.00 18.53 51895.8524.00 17.65 24.00 21.18 59309.54

12.00 22.07 24.00 23.83 66723.23

0.00 26.48 24.00 26.48 74136.93

case 2 case 3e 1


29/38

b to end b to end b

6.00 0.00 6.00 2.70 7563.26

12.00 0.00 12.00 5.40 15126.5218.00 0.01 18.00 8.10 22689.78

24.00 0.01 24.00 10.80 30253.04

24.00 4.51 24.00 13.51 37816.30

24.00 9.01 24.00 16.21 45379.56

24.00 13.51 24.00 18.91 52942.82

24.00 18.01 24.00 21.61 60506.08

12.00 22.51 24.00 24.31 68069.34

0.00 27.01 24.00 27.01 75632.60

b to end b to end b

6.00 0.00 6.00 2.70 7564.17

12.00 0.00 12.00 5.40 15128.34

18.00 0.01 18.00 8.10 22692.51

24.00 0.01 24.00 10.81 30256.68

24.00 4.51 24.00 13.51 37820.85

24.00 9.01 24.00 16.21 45385.03

24.00 13.51 24.00 18.91 52949.20

24.00 18.01 24.00 21.61 60513.37

12.00 22.51 24.00 24.31 68077.54

0.00 27.01 24.00 27.01 75641.71

case 2 case 3e 1

e 1 case 2 case 3


30/38

b to end b to end b

6.00 0.00 6.00 2.70 7564.17

12.00 0.00 12.00 5.40 15128.34

18.00 0.01 18.00 8.10 22692.51

24.00 0.01 24.00 10.81 30256.68

24.00 4.51 24.00 13.51 37820.85

24.00 9.01 24.00 16.21 45385.03

24.00 13.51 24.00 18.91 52949.20

24.00 18.01 24.00 21.61 60513.37

12.00 22.51 24.00 24.31 68077.54

0.00 27.01 24.00 27.01 75641.71

e 1 case 2 case 3


31/38

b to end b to end b

6.00 0.00 6.00 1.82 5104.45

12.00 0.00 12.00 3.65 10208.91

18.00 0.01 18.00 5.47 15313.36

24.00 0.01 24.00 7.29 20417.81

24.00 3.05 24.00 9.11 25522.27

24.00 6.08 24.00 10.94 30626.72

24.00 9.12 24.00 12.76 35731.17

24.00 12.16 24.00 14.58 40835.62

8102.83 15.19 24.00 16.41 45940.08

###### 18.23 24.00 18.23 51044.53

b to end b to end b

6.00 0.00 6.00 1.28 3590.72

12.00 0.00 12.00 2.56 7181.44

18.00 0.01 18.00 3.85 10772.16

24.00 0.01 24.00 5.13 14362.87

24.00 2.14 24.00 6.41 17953.59

24.00 4.28 24.00 7.69 21544.31

24.00 6.42 24.00 8.98 25135.03

24.00 8.55 24.00 10.26 28725.75

###### 10.69 24.00 11.54 32316.47

###### 12.82 24.00 12.82 35907.19

case 2 case 3

case 2 case 3e 1

e 1


32/38

b to end b to end b

6.00 0.00 6.00 0.80 2244.20

12.00 0.00 12.00 1.60 4488.40

18.00 0.01 18.00 2.40 6732.60

24.00 0.01 24.00 3.21 8976.80

24.00 1.34 24.00 4.01 11221.00

24.00 2.68 24.00 4.81 13465.19

24.00 4.01 24.00 5.61 15709.39

24.00 5.35 24.00 6.41 17953.59

###### 6.68 24.00 7.21 20197.79

###### 8.01 24.00 8.01 22441.99

b to end b to end b

6.00 0.00 6.00 0.37 1023.57

12.00 0.00 12.00 0.73 2047.13

18.00 0.01 18.00 1.10 3070.70

24.00 0.01 24.00 1.46 4094.26

24.00 0.62 24.00 1.83 5117.83

24.00 1.22 24.00 2.19 6141.40

24.00 1.83 24.00 2.56 7164.96

24.00 2.44 24.00 2.92 8188.53

###### 3.05 24.00 3.29 9212.09

###### 3.66 24.00 3.66 10235.66

e 1

e 1 case 2 case 3

case 2 case 3


33/38

b to e

Documents

Columna de Sotano