Ch09 and 10 Columns
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Transcript of Ch09 and 10 Columns
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7/29/2019 Ch09 and 10 Columns
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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
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e sufficient area
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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
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e sufficient area
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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.
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Po = (0.85fc'A n + A sfy) = 1325.4 kipsPo = 732.3 kips
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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
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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
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-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
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1482 504 0 -3600 560 297 0
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-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
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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.
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Po = (0.85fc'An + Asfy) =
917.8 kipsPo = 507.1 kips
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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
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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
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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
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6 0.18
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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
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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
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Pbal = 0 465.1
Mbal = 0 5005
P.005 = 0 -34.7
M.005 = 0 4278
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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
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-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
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-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