Copy of Ch09 and 10 Columns

8/16/2019 Copy of Ch09 and 10 Columns

1/22

Square Column Capacity

1160 kips4000 psi

60000 psi

trial % 2 %

492.2

b = 22.19 in.

select b = 22 in.

10.34

No. of bars Bar sie

select bars ! " 11 12.#0 bars selecte$ %a

Bar $ia. 0.02#!2

1.410

23#2.9 kips

1223.# kips '((( )C* 31!(200! Co$e +q. 10(1

(

P u

=

f c ' =

f y =

Ag = in2

Ast = in2

)st , in2

ρ

,

P o= (0.85f

c 'A

n + A

sf

y) =

φP o =


2/22

e sufficient area


3/22

Square Column Capacity1000 kips

3#00 psi

60000 psi

trial % 4 %

29!.4

dia = 19.49 in.

select = 20 in.

11.12

No. of bar Bar sie

select bars 9 " 10 11.39 bars selecte$ %a

Bar $ia. 0.02!4!

1.2-0

1#!4.4 kips

1010.0 kips '((( )C* 31!(200! Co$e +q. 10(1

(

P u =

f c ' =

f y =

Ag = in2

Ast = in2

)st , in2

ρ

,

P o= (0.85f

c 'A

n + A

sf

y) =

φP o =


4/22

e sufficient area


5/22

ectan/ular Column Capacity

420 k160 ft(k , 1920 k(in e , 4.#-143 in.

b = 16 in.

! = 1# in.

0.6

4000 psi

60000 psi

9.00

9.00

240.0

0.03-#

0.!#0.0020-

29000 "si

-.10 in. (

4.# in.

(

132#.4 kips

-32.3 kips '((( )C* 31!(200! Co$e +q. 10(1

P u =#

u =

γ =

f c ' =

f y =

As$

= in2

As2

= in2

Ast = in2

Ag = in2

ρ

t=

$ =

y=

s =

c bal

=

c .005

=

P o= (0.85f

c 'A

n + A

sf y) =

φP o =

cb

d1

d2

d3

b

h

h


6/22


7/22

623 1482 5043 4.#0 in. 521 0 560

#.2# 2.2# in.

-.# 0 in.

9.-# 2.2# in.

12 4.#0 in.

d $ = y

$ =

d 2 = y

2 =

d & = y

& =

d = y

=

d 5 = y

5 =

Note %is sprea$s%eet isbase$ on an assumption t%att%ere are interior layers ofbars. %e &alue of )

s1entere$

is $i&i$e$ into 2 equal partsan$ )

s2 is $i&i$e$ into t%e

t%ree interior layers s%on.Calculations are base$ on bar

locations s%on on t%e$rain/. *f t%e actual numberof layers of interior bars is$ifferent from 3 sli/%t errorsill resultc 005

d4

d5


8/22

0.00 0.00 0.00 0.00 0.00 0.00

-270.00 -270.00 -270.00 -270.00 -270.00 -270.00

277.44 208.08 208.08 138.72 69.36 34.68

0.729 0.900 0.900 0.900 0.900 0.900 0.900

187.9 53.3 53.3 -131.3 -470.6 -505.3 -540.0

137 48 48 -118 -424 -455 -486

812.03 518.40 518.40 0.00 -1215.00 -1215.00

0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00

1215.00 1215.00 1215.00 1215.00 1215.00 1215.00

1373.33 1162.65 1162.65 863.53 475.98 249.05

3400 2896 2896 2079 476 249 0

2480 2606 2606 1871 428 224 0

18.10 54.36 54.36 -15.83 -1.01 -0.49


9/22

0 -360297 0


10/22


11/22

0 500 1000 1500 2000 2500 3000 3500 4000

-1000

-500

0

500

1000

1500

Pn s MnPmax

Pu s Mu

a!!l"e# forces Pu an# Mu

balance# case

s$ra"n of .005

Momen$ Ca!ac"$%& '"!-"n

( x " a l ) o a # & '

" ! s


12/22

Non($imensionalie$ ectan/ular *) 120 k

103.# ft(k , 1242

b = 14 in.

! = 1# in.

0.6

4000 psi

60000 psi

3.60

3.60

210.0

0.01-1

0.!#

0.0020-

29000 "si

-.10 in. (

4.# in.

(

91-.! kips

#0-.1 kips '((( )C* 31!(200! Co$e +q. 10(1

P u =

# u =

γ =

f c ' =

f y =

As$ = in2

As2

= in2

Ast = in2

Ag = in2

ρ

t=

$=

y=

s =

c bal

=

c .005

=

5o, 0.!#f

c7)

n 8 )

sf y ,

5o ,

cb

d1

d2

d3

h

b

h

0

0

0

0

0

1

1


13/22

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

43.99 25.20 17.40 0.00 -22.37 -52.20 -108.00 -108.00

714.00 606.90 546.21 485.52 424.83 364.14 287.35 273.110.650 0.650 0.650 0.650 0.650 0.650 0.650 0.673

917.8 859.9 734.0 665.5 587.4 504.3 410.2 263.7 246.0

596.5 559 477 433 382 328 267 171 165

458.46 458.46 458.46 458.46 458.46 442.26 379.49 363.96

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-197.96 -113.40 -78.30 0.00 100.67 234.90 486.00 486.00

0.00 682.76 962.70 1165.25 1290.42 1338.21 1287.79 1264.82

0 260 1028 1343 1624 1850 2015 2153 2115

0 169 668 873 1055 1202 1310 1400 1422

e = 0.30 1.40 2.02 2.76 3.67 4.91 8.17 8.60

507.1 507.1 179.43960 668

21.7

*n = 0.0000 0.0207 0.0816 0.1066 0.1289 0.1468 0.1600 0.1709 0.1678

,n = 1.0926 1.0237 0.8738 0.7923 0.6993 0.6004 0.4884 0.3139 0.2928

*n = 0.0000 0.0207 0.0816 0.1066 0.1289 0.1468 0.1600 0.1709 0.1678

C or T4

C or T5

Cc =

φ =

Pn =

Pu=

M1

M2

M3

M4

M5

Mc =

Mn =

Mu =

Pmax


14/22

k(in3 4.#0 in.

#.2# 2.2# in.

-.# 0 in.

9.-# 2.2# in.

12 4.#0 in.

d $ = y

$ =

d 2 = y

2 =

d & = y

& =

d = y

=

d 5 = y

5 =

Note %is sprea$s%eet isbase$ on an assumption t%att%ere are interior layers ofbars. %e &alue of )

s1entere$

is $i&i$e$ into 2 equal partsan$ )s2 is $i&i$e$ into t%et%ree interior layers s%on.Calculations are base$ on barlocations s%on on t%e

$rain/. *f t%e actual numberof layers of interior bars is$ifferent from 3 sli/%t errorsill result.c.005

d4

d5

0.0000 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200 0.1400 0.1600 0.1800.0000

.2000

.4000

.6000

.8000

.0000

.2000

*o+ 59


15/22

0.00 0.00 0.00 0.00 0.00 0.00

-108.00 -108.00 -108.00 -108.00 -108.00 -108.00

242.76 182.07 182.07 121.38 60.69 30.350.729 0.900 0.900 0.900 0.900 0.900 0.900

206.9 120.2 120.2 13.4 -155.3 -185.7 -216.0

151 108 108 12 -140 -167 -194

324.81 207.36 207.36 0.00 -486.00 -486.00

0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00

486.00 486.00 486.00 486.00 486.00 486.00

1201.66 1017.32 1017.32 755.59 416.49 217.92

2012 1711 1711 1242 416 218 0

1468 1540 1540 1117 375 196 0

9.72 14.24 14.24 92.79 -2.68 -1.17

0.1597 0.1358 0.1358 0.0985 0.0331 0.0173 0.0000

0.2464 0.1430 0.1430 0.0159 -0.1849 -0.2210 -0.2571

0.1597 0.1358 0.1358 0.0985 0.0331 0.0173 0.0000


16/22

Circular Column Capacity

400 k

300 ft(k , 3600 k(in! = 20 in.

0.-#

4000 psi

60000 psi

12.#0

314.2

0.039-9

0.!#0.002069

29000 "si

10.36 in.

6.#62# in.

(

(

1--#.6 kips

1132.0 kips '((( )C* 31!(200! Co$e +q. 10(1

c = 23.53 20 18 16 14 13 12 11 10.36 10.00 9

a = 20.0000 17.0000 15.3000 13.6000 11.9000 11.0500 10.2000 9.3500 8.8036 8.5000 7.6500

0.002681 0.002625 0.002583 0.002531 0.002464 0.002423 0.002375 0.002318 0.002276 0.002250 0.002167

0.002401 0.002295 0.002217 0.002119 0.001994 0.001916 0.001826 0.001719 0.001640 0.001591 0.001434

0.001725 0.001500 0.001333 0.001125 0.000857 0.000692 0.000500 0.000273 0.000103 0.000000 -0.000333

0.001049 0.000705 0.000449 0.000131 -0.000279 -0.000532 -0.000826 -0.001174 -0.001433 -0.001591 -0.002101

P u =

# u

=

γ = Note %is sprea$base$ on an assut%at t%ere are ! bacolumn. %e &alu

entere$ is $i&i$e$equal bars an$calculations are bbar locations s%o

$rain/. *f t%e actnumber of bars isfrom ! sli/%t erroresult.

f c ' =

f y =

Ast = in2

Ag = in2

ρ

t=

$ =

y=

s =

c bal

=

c .005

=

5o, 0.!#f

c7)

n 8 )

sf

y ,

5o ,

cb

εs1

=

εs2

=

εs3

=

εs4

=

h

d1 d

2

d

4

h

d3

d5


17/22

0.000769 0.000375 0.000083 -0.000281 -0.000750 -0.001038 -0.001375 -0.001773 -0.002069 -0.002250 -0.002833

60000 60000 60000 60000 60000 60000 60000 60000 60000 60000 60000

60000 60000 60000 60000 57813 55568 52949 49853 47548 46139 41599

50025 43500 38667 32625 24857 20077 14500 7909 3000 0 -9667

30416 20431 13034 3788 -8099 -15414 -23949 -34035 -41548 -46139 -60000

22294 10875 2417 -8156 -21750 -30115 -39875 -51409 -60000 -60000 -60000

88.44 88.44 88.44 88.44 88.44 88.44 88.44 88.44 88.44 88.44 88.44

176.88 176.88 176.88 176.88 170.04 163.03 154.84 145.17 137.96 133.56 119.37

145.70 125.31 110.21 91.33 67.05 52.12 34.69 24.72 9.37 0.00 -30.21

84.43 53.22 40.73 11.84 -25.31 -48.17 -74.84 -106.36 -129.84 -144.18 -187.50

29.52 16.99 3.78 -12.74 -33.98 -47.06 -62.30 -80.33 -93.75 -93.75 -93.75

6.2832 4.6924 4.2588 3.8781 3.5239 3.3520 3.1816 3.0115 2.9017 2.8405 2.6672

semen$= 314.159 284.609 257.884 227.493 194.850 178.041 161.079 144.089 133.208 127.193 110.5161068.14 967.67 876.80 773.48 662.49 605.34 547.67 489.90 452.91 432.45 375.75

0.750 0.750 0.750 0.750 0.750 0.750 0.750 0.750 0.750 0.759 0.789

1775.6 1593.1 1428.5 1296.8 1129.2 928.7 813.7 688.5 561.5 465.1 416.5 272.1

1331.7 1195 1071 973 847 697 610 516 421 349 316 215

0.00000 0.85 1.58 2.38 3.24 3.68 4.14 4.60 4.90 5.07 5.54

663.28 663.28 663.28 663.28 663.28 663.28 663.28 663.28 663.28 663.28 663.28

938.02 938.02 938.02 938.02 901.79 864.58 821.17 769.87 731.65 708.30 633.06

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-447.73 -282.25 -216.01 -62.78 134.23 255.46 396.90 564.06 688.57 764.65 994.37

-221.41 -127.44 -28.32 95.58 254.88 352.91 467.29 602.45 703.13 703.13 703.13

0.00 825.55 1382.20 1840.63 2145.04 2229.29 2265.31 2252.32 2218.17 2190.60 2081.52

0 932 2017 2739 3475 4099 4366 4614 4852 5005 5030 5075

0 699 1513 2054 2606 3074 3274 3460 3639 3754 3819 4005

e = 0.59 1.41 2.11 3.08 4.41 5.37 6.70 8.64 10.76 12.08 18.65

1132.0 1132.0

0 1513

εs5

=

f s1

=

f s2

=

f s3

=

f s4

=

f s5

=

C or T1

C or T2

C or T3

C or T4

C or T5

θ =

Cc =

φ =

Pn =

Pu=

%c =

M1

M2

M3

M4

M5

Mc =

Mn =

Mu =

Pmax


18/22

0 465.1

0 5005

0 -34.7

0 4278

Pbal

=

Mbal

=

P.005

=

M.005

=


19/22

2.# -.#0 in.

4.-0 #.30 in.

10 0 in.

1#.30 #.30 in.

1-.# -.#0 in.

,n = 0.424412

*n = 0.190985

8 7 6.5625 6 5 4 3 2 1.5 1

6.8000 5.9500 5.5781 5.1000 4.2500 3.4000 2.5500 1.7000 1.2750 0.8500

0.002063 0.001929 0.001857 0.001750 0.001500 0.001125 0.000500 -0.000750 -0.002000 -0.004500

0.001239 0.000987 0.000853 0.000652 0.000182 -0.000523 -0.001697 -0.004045 -0.006393 -0.011090

-0.000750 -0.001286 -0.001571 -0.002000 -0.003000 -0.004500 -0.007000 -0.012000 -0.017000 -0.027000

-0.002739 -0.003559 -0.003996 -0.004652 -0.006182 -0.008477 -0.012303 -0.019955 -0.027607 -0.042910

d $ = y

$ =

d 2 = y

2 =

%eet isption

rs in t%eof )

st

into !

se$ onn on t%e

ual$ifferentrs ill

d & = y

& =

d = y

=

d 5 = y

5 =

c.005


20/22

-0.003563 -0.004500 -0.005000 -0.005750 -0.007500 -0.010125 -0.014500 -0.023250 -0.032000 -0.049500

59813 55929 53857 50750 43500 32625 14500 -21750 -58000 -60000

35923 28627 24735 18898 5278 -15153 -49204 -60000 -60000 -60000

-21750 -37286 -45571 -58000 -60000 -60000 -60000 -60000 -60000 -60000

-60000 -60000 -60000 -60000 -60000 -60000 -60000 -60000 -60000 -60000

-60000 -60000 -60000 -60000 -60000 -60000 -60000 -60000 -60000 -60000

88.14 82.08 78.84 73.98 62.66 45.66 17.34 -33.98 -90.63 -93.75

101.64 78.83 66.67 48.43 16.49 -47.35 -153.76 -187.50 -187.50 -187.50

-67.97 -116.52 -142.41 -181.25 -187.50 -187.50 -187.50 -187.50 -187.50 -187.50

-187.50 -187.50 -187.50 -187.50 -187.50 -187.50 -187.50 -187.50 -187.50 -187.50

-93.75 -93.75 -93.75 -93.75 -93.75 -93.75 -93.75 -93.75 -93.75 -93.75

2.4901 2.3076 2.2255 2.1174 1.9164 1.7000 1.4605 1.1834 1.0210 0.8306

94.189 78.352 71.615 63.156 48.775 35.414 23.330 12.875 8.418 4.613320.24 266.40 243.49 214.73 165.84 120.41 79.32 43.77 28.62 15.68

0.826 0.874 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.9

160.8 29.5 -34.7 -125.4 -223.8 -350.0 -525.8 -646.5 -718.3 -734.3 -750.0

133 26 -31 -113 -201 -315 -473 -582 -646 -661 -675

6.02 6.50 6.72 6.99 7.49 7.98 8.48 8.99 9.24 9.49

661.08 615.57 591.29 554.88 469.92 342.48 130.08 -254.88 -679.69 -703.13

539.01 418.08 353.59 256.85 87.46 -251.13 -815.45 -994.37 -994.37 -994.37

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

994.37 994.37 994.37 994.37 994.37 994.37 994.37 994.37 994.37 994.37

703.13 703.13 703.13 703.13 703.13 703.13 703.13 703.13 703.13 703.13

1927.58 1732.52 1635.51 1501.49 1241.34 961.10 672.81 393.31 264.41 148.86

4825 4464 4278 4011 3496 2750 1685 842 288 149 0

3988 3903 3850 3610 3147 2475 1516 757 259 134 0

30.01 151.11 -123.44 -32.00 -15.62 -7.86 -3.20 -1.30 -0.40 -0.20


21/22


22/22

0 1000 2000 3000 4000 #000 6000

(600

(400

(200

0

200

400

600

!00

1000

1200

1400

1600

1!00

2000

C*rcular Column *nteraction :ia/ram

Pn s MnPu s Mu

Pmax

(!!l"e# Pu an#

Mu

balance# case

s$ra"n of .005

;oment Capacity kip(inc%es

)

< i a l

=

o

a $

C

a p

a c i

Date post:	05-Jul-2018
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