Ch09 and 10 Columns

7/29/2019 Ch09 and 10 Columns

1/21

Square Column CapacityP

u= 1160 kips

fc' = 4000 psi

fy = 60000 psi

trial % 2 %

A g = 492.2 in2

b = 22.19 in.

select b = 22 in.

A st = 10.34 in2

No. of bars

select bars 8 # 11 Ast = 12.50 in bars selected hav

z = 0.0258

Po = (0.85fc'A n + A sfy) = 2352.9 kips

Po = 1223.5 kips


2/21

e sufficient area


3/21

Square Column CapacityP

u

= 1000 kips

fc' = 3500 psi

fy = 60000 psi

trial % 4 %

A g = 298.4 in2

dia = 19.49 in.

select D = 20 in.

A st = 11.12 in2

No. of bar

select bars 9 # 10 Ast = 11.39 in bars selected hav

z = 0.0285

Po = (0.85fc'A n + A sfy) = 1584.4 kips

Po = 1010.0 kips


4/21

e sufficient area


5/21

Rectangular Column Capacity

Pu = 420 kMu = 160 ft-k = 1920 k-in e = 4.5714 in.

b = 16 in.

h = 15 in.

= 0.6

fc' = 4000 psi

fy = 60000 psi

A s1 = 9.00 in2

A s2 = in2

A st= 9.00 in2

A g = 240.0 in2

t = 0.0375

1 = 0.85

y = 0.0021

Es = 29000 ksi

cbal = 7.10 in.

c.005 = 4.5 in.

-

Po = (0.85fc'A n + A sfy) = 1325.4 kipsPo = 732.3 kips


6/21

C or T5 109.98 63.00 43.50 0.00 -55.93 -130.50 -270.00

Cc = 816.00 693.60 624.24 554.88 485.52 416.16 328.40

f = 0.650 0.650 0.650 0.650 0.650 0.650 0.650Pn = 1325.4 1180.7 1011.3 922.4 809.6 684.3 531.4 269.2

Pu = 861.5 767 657 600 526 445 345 175

M1 1146.15 1146.15 1146.15 1146.15 1146.15 1105.65 948.71

M2 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M3 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M4 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M5 -494.91 -283.50 -195.75 0.00 251.68 587.25 1215.00Mc = 0.00 780.30 1100.22 1331.71 1474.77 1529.39 1471.76

Mn = 0 651 1643 2051 2478 2873 3222 3635

Mu = 0 423 1068 1333 1611 1867 2094 2363

e = 0.55 1.62 2.22 3.06 4.20 6.06 13.50

Pmax 732.3 732.3 302.9561

0 1068

54.3

Pbal = 0 269.2

Mbal = 0 3635

P.005 = 0 53.3

M.005 = 0 2896


7/21

623d1 = 3 y1 = 4.50 in. 521

d2 = 5.25 y2 = 2.25 in.

d3 = 7.5 y3 = 0 in.

d4 = 9.75 y4 = 2.25 in.

d5 = 12 y5 = 4.50 in.

c.005

6 75 6 4 5 4 5 3 1 5 0 75

based on an assumption that

there are interior layers of

bars. The value of As1 entered

is divided into 2 equal parts

and As2 is divided into the

three interior layers shown.

Calculations are based on bar

locations shown on the

drawing. If the actual number

of layers of interior bars isdifferent from 3, slight errors

will result.

d1

d2

d4

d3

d5


8/21

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

312.12 277.44 208.08 208.08 138.72 69.36 34.68

0.673 0.729 0.900 0.900 0.900 0.900 0.900 0.900244.3 187.9 53.3 53.3 -131.3 -470.6 -505.3 -540.0

164 137 48 48 -118 -424 -455 -486

909.90 812.03 518.40 518.40 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 0.00 0.00 0.00

1215.00 1215.00 1215.00 1215.00 1215.00 1215.00 1215.001445.51 1373.33 1162.65 1162.65 863.53 475.98 249.05

3570 3400 2896 2896 2079 476 249 0

2401 2480 2606 2606 1871 428 224 0

14.61 18.10 54.36 54.36 -15.83 -1.01 -0.49


9/21

1482 504 0 -3600 560 297 0


10/21

-1000

-500

0

500

1000

1500

0 500 1000 1500 2000 2500 3000 3500 4000

AxialLoad,

kips

Moment Capacity, kip-in

Pn vs Mn

Pmax

Pu vs Mu

applied forces Pu and Mu

balanced case

strain of .005


11/21

Non-dimensionalized Rectangular I/A Pu = 120 k

Mu = 103.5 ft-k =

b = 14 in.

h = 15 in.

= 0.6

fc' = 4000 psi

fy = 60000 psi

A s1 = 3.60 in2

A s2 = in2

A st= 3.60 in2

A g = 210.0 in2

t = 0.0171

1 = 0.85

y = 0.0021

Es = 29000 ksi

cbal = 7.10 in.

c.005 = 4.5 in.

-

Po = (0.85fc'An + Asfy) =

917.8 kipsPo = 507.1 kips


12/21

Cc = 714.00 606.90 546.21 485.52 424.83 364.14 287.35

f = 0.650 0.650 0.650 0.650 0.650 0.650 0.650

Pn = 917.8 859.9 734.0 665.5 587.4 504.3 410.2 263.7Pu = 596.5 559 477 433 382 328 267 171

M1 458.46 458.46 458.46 458.46 458.46 442.26 379.49

M2 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M3 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M4 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M5 -197.96 -113.40 -78.30 0.00 100.67 234.90 486.00

Mc = 0.00 682.76 962.70 1165.25 1290.42 1338.21 1287.79Mn = 0 260 1028 1343 1624 1850 2015 2153

Mu = 0 169 668 873 1055 1202 1310 1400

e = 0.30 1.40 2.02 2.76 3.67 4.91 8.17

Pmax 507.1 507.1 179.4396

0 668

21.7

Rn = 0.0000 0.0207 0.0816 0.1066 0.1289 0.1468 0.1600 0.1709Kn = 1.0926 1.0237 0.8738 0.7923 0.6993 0.6004 0.4884 0.3139

Rn = 0.0000 0.0207 0.0816 0.1066 0.1289 0.1468 0.1600 0.1709


13/21

1242 k-ind1 = 3 y1 = 4.50 in.

d2 = 5.25 y2 = 2.25 in.

d3 = 7.5 y3 = 0 in.

d4 = 9.75 y4 = 2.25 in.

d5 = 12 y5 = 4.50 in.

c.005

6.75 6 4.5 4.5 3 1.5 0.75

based on an assumption that

there are interior layers ofbars. The value of As1 entered

is divided into 2 equal parts

and As2 is divided into the

three interior layers shown.

Calculations are based on bar

locations shown on the

drawing. If the actual number

of layers of interior bars isdifferent from 3, slight errors

will result.

d1

d2

d4

d3

d5

-0.2000

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.1

Series1


14/21

273.11 242.76 182.07 182.07 121.38 60.69 30.35

0.673 0.729 0.900 0.900 0.900 0.900 0.900 0.900

246.0 206.9 120.2 120.2 13.4 -155.3 -185.7 -216.0165 151 108 108 12 -140 -167 -194

363.96 324.81 207.36 207.36 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 0.00 0.00 0.00

486.00 486.00 486.00 486.00 486.00 486.00 486.00

1264.82 1201.66 1017.32 1017.32 755.59 416.49 217.922115 2012 1711 1711 1242 416 218 0

1422 1468 1540 1540 1117 375 196 0

8.60 9.72 14.24 14.24 92.79 -2.68 -1.17

0.1678 0.1597 0.1358 0.1358 0.0985 0.0331 0.0173 0.00000.2928 0.2464 0.1430 0.1430 0.0159 -0.1849 -0.2210 -0.2571

0.1678 0.1597 0.1358 0.1358 0.0985 0.0331 0.0173 0.0000


15/21

6 0.18


16/21

Circular Column Capacity

Pu = 400 k

Mu = 300ft-k = 3600 k-in

h = 20 in.

= 0.75

fc' = 4000 psi

fy = 60000 psi

A st = 12.50 in2

A g = 314.2 in2

t = 0.03979

1= 0.85

y = 0.00207

Es = 29000 ksi

cbal = 10.36 in.c.005 = 6.5625 in.

-Po = (0.85fc'An + Asfy) = 1775.6 kips

Po = 1132.0 kips


17/21

es5 = 0.000769 0.000375 0.000083 -0.000281 -0.000750 -0.001038 -0.001375 -0.001773 -0.002069 -0.002250 -0.002833

fs1 = 60000 60000 60000 60000 60000 60000 60000 60000 60000 60000 60000

fs2 = 60000 60000 60000 60000 57813 55568 52949 49853 47548 46139 41599

fs3 = 50025 43500 38667 32625 24857 20077 14500 7909 3000 0 -9667

fs4 = 30416 20431 13034 3788 -8099 -15414 -23949 -34035 -41548 -46139 -60000

fs5 = 22294 10875 2417 -8156 -21750 -30115 -39875 -51409 -60000 -60000 -60000

C or T1 88.44 88.44 88.44 88.44 88.44 88.44 88.44 88.44 88.44 88.44 88.44

C or T2 176.88 176.88 176.88 176.88 170.04 163.03 154.84 145.17 137.96 133.56 119.37

C or T3 145.70 125.31 110.21 91.33 67.05 52.12 34.69 24.72 9.37 0.00 -30.21

C or T4 84.43 53.22 40.73 11.84 -25.31 -48.17 -74.84 -106.36 -129.84 -144.18 -187.50

C or T5 29.52 16.99 3.78 -12.74 -33.98 -47.06 -62.30 -80.33 -93.75 -93.75 -93.75

q = 6.2832 4.6924 4.2588 3.8781 3.5239 3.3520 3.1816 3.0115 2.9017 2.8405 2.6672

segment= 314.159 284.609 257.884 227.493 194.850 178.041 161.079 144.089 133.208 127.193 110.516Cc = 1068.14 967.67 876.80 773.48 662.49 605.34 547.67 489.90 452.91 432.45 375.75

f = 0.750 0.750 0.750 0.750 0.750 0.750 0.750 0.750 0.750 0.759 0.789

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

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

yc = 0.00000 0.85 1.58 2.38 3.24 3.68 4.14 4.60 4.90 5.07 5.54

M1 663.28 663.28 663.28 663.28 663.28 663.28 663.28 663.28 663.28 663.28 663.28

M2 938.02 938.02 938.02 938.02 901.79 864.58 821.17 769.87 731.65 708.30 633.06

M3 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

M4 -447.73 -282.25 -216.01 -62.78 134.23 255.46 396.90 564.06 688.57 764.65 994.37M5 -221.41 -127.44 -28.32 95.58 254.88 352.91 467.29 602.45 703.13 703.13 703.13

Mc = 0.00 825.55 1382.20 1840.63 2145.04 2229.29 2265.31 2252.32 2218.17 2190.60 2081.52

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

Mu = 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

Pmax 1132.0 1132.0

0 1513


18/21

Pbal = 0 465.1

Mbal = 0 5005

P.005 = 0 -34.7

M.005 = 0 4278


19/21

d1 = 2.5 y1 = 7.50 in.

d2 = 4.70 y2 = 5.30 in.

d3 = 10 y3 = 0 in.

d4 = 15.30 y4 = 5.30 in.

d5 = 17.5 y5 = 7.50 in.

Kn = 0.424412

Rn = 0.190985

c.005

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

heet is

ption

rs in the

of Ast

into 8

sed on

n onactual

different

rs will


20/21

-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 4.613

320.24 266.40 243.49 214.73 165.84 120.41 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


21/21

-600

-400

-200

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 1000 2000 3000 4000 5000 6000

AxialLoad

Capacity,

kips

Moment Capacity, kip-inches

CIrcular Column Interaction Diagram

Pn vs Mn

Pu vs Mu

Pmax

Applied Pu and Mu

balanced case

strain of .005

Documents

Ch09 and 10 Columns