Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
ANALISIS KEKUATAN KOLOM BETON BERTULANG DENGAN DIAGRAM INTERAKSI [C]2010 : M. Noer Ilham
KODE KOLOM
K10
INPUT DATA KOLOM Kuat tekan beton,
f c' =
Tegangan leleh baja,
f y = 390 b = 1000 h = 1000 ds = 75 n = 46 D = 25
Lebar kolom, Tinggi kolom, Tebal brutto selimut beton, Jumlah tulangan, Diameter tulangan,
20
MPa MPa mm mm mm buah mm
PERHITUNGAN DIAGRAM INTERAKSI Es =
Modulus elastis baja, β1 = 0.85
untuk f c' 30 MPa
β1 = 0.85 - 0.008 (fc' - 30)
untuk f c' > 30 MPa
2.E+05 MPa
β1 =
Luas baja tulangan total,
0.85 2 2 As = n * p / 4 * D = 22580 mm
Jarak antara tulangan,
x = ( h - 2*d s ) / 9 = 94.44 mm
Faktor distribusi tegangan,
r = As / Ag =
Rasio tulangan, Faktor reduksi kekuatan, f = 0.65 untuk Pn ≥ 0.1 * fc' * b * h f=
0.80
untuk Pn = 0
Untuk : 0
≤
Pn ≤ 0.1 * f c' * b * h
f = 0.65 + 0.15 * ( P no - Pn ) / Pno
2.26%
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
15000 14000 13000 12000 11000 10000 9000 ) N k ( n P . f
8000 7000 6000 5000 4000 3000 2000 1000 0 0
400
800
1200
1600
2000
2400
2800
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
3200
3600
4000
b= h= 46 f c' =
1000 1000 D
mm mm 25
20
MPa
f y =
390
MPa
Pu
Mu
(kN)
(kNm)
32 75 75.28
4 72 72.09
37 51 51.28
5 83 83.01
34 94 94.17
1 32 32.86
24 80 80.36 31 56 56.58
5 97 97.16 7 47 47.88
32 60 60.96
7 74 74.83
29 30 30.99
4 11 11.36
2284 22 84.4 .43 3
1483 14 83.0 .04 4
1457 14 57.0 .01 1
1066 10 66.9 .96 6
1782 17 82.0 .02 2
1665 16 65.5 .51 1
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
15000 14000 13000 12000 11000 10000 9000 ) N k ( n P . f
8000 7000 6000 5000 4000 3000 2000 1000 0 0
400
800
1200
1600
2000
2400
2800
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
3200
3600
4000
b= h= 46 f c' =
1000 1000 D
mm mm 25
20
MPa
f y =
390
MPa
Pu
Mu
(kN)
(kNm)
3275.28
472.09
3751.28
583.01
3494.17
132.86
2480.36 3156.58
597.16 747.88
3260.96
774.83
2930.99
411.36
228 4. 4.43
1 48 483 .0 .04
145 7. 7.01
1 06 066 .9 .96
178 2. 2.02
1 66 665 .5 .51
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
No
Luas masing-masing tu tulangan
Pada kondisi tekan aksial sentris (Mno = 0) :
Jarak tu tulangan mm
d1 = 9*x + d s =
925
mm
1
As1 = 10/36 * As =
2
As2 = 2/36 * As =
1254
mm
d2 = 8*x + d s =
831
mm
3
As3 = 2/36 * As =
1254
mm
d3 = 7*x + d s =
736
mm
4
As4 = 2/36 * As =
1254
mm
d4 = 6*x + d s =
642
mm
5
As5 = 2/36 * As =
1254
mm
d5 = 5*x + d s =
547
mm
6272
-
Pno = 0.80*[ 0.85*f c' *b*h + As*(f y - 0.85*f c')]*10 = 20338 kN -
0.1 * f c' * b * h *10 =
Pada Pada kondis kondisii grs netral netral terlet terletak ak pada pada jarak jarak c dari dari sisi sisi beton beton tekan tekan terlua terluarr :
6
As6 = 2/36 * As =
1254
mm
d6 = 4*x + d s =
453
mm
Rega Regang ngan an pada pada masi masing ng-m -mas asin ing g baja baja tula tulang ngan an :
7
As7 = 2/36 * As =
1254
mm
d7 = 3*x + d s =
358
mm
εsi = 0.003 * ( c - d i ) / c
8
As8 = 2/36 * As =
1254
mm
d8 = 2*x + d s =
264
mm
Tega Tegang ngan an pada pada masin masingg-ma masi sing ng baja baja tula tulang ngan an :
9
As9 = 2/36 * As =
1254
mm
d9 = x + d s =
169
mm
Untuk
| εsi | < f y / Es
maka : f si = esi* Es
As10 = 10/36 * As =
6272
mm
d10 = ds =
75
mm
Untuk
| εsi | f y / Es
maka : f si =| εsi | / esi* f y
As =
22580
mm
10
2000 kN
c = cb = 600 / (600 + f y) * d1 = 560.6 mm
Pada kondisi balance :
Jumlah interval jarak grs netral =
URAIAN PERHITUNGAN
PERSAMAAN
Gaya-gaya internal pada masing-masing baja tulangan :
Fsi = Asi * f si * 10
112
→
Dc =
8.93
UNIT -3
kN
-3
Resultan gaya internal baja tulangan :
Cs = [ S Fsi ]*10
Momen akibat gaya internal masing-masing baja tulangan :
Msi = Fsi*(h/2 - di)
kNmm
Momen total akibat gaya internal baja t ulangan :
Ms = S Msi
kNmm
Tinggi blok tegangan tekan beton,
a = β1 * c
Gaya internal pada beton tekan :
Cc = 0.85 * f c' * b * a * 10
kN
mm -
Momen akibat gaya internal tekan beton :
Mc = Cc * (h - a) / 2
kN kNmm
Gaya aksial nominal :
Pn = Cs + Cc
Momen nominal :
Mn = (Mc + Ms)*10
Gaya aksial rencana :
Pu = f * Pn
kN
Momen rencana :
Mu = f * Mn
kNm
kN -
kNm
mm
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
15000 14000 13000 12000 11000 10000 9000 ) N k ( n P . f
8000 7000 6000 5000 4000 3000 2000 1000 0 0
400
800
1200
1600
2000
2400
2800
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
3200
3600
4000
b= h= 46 f c' =
1000 1000 D 20
mm mm 25 MPa
f y =
390
MPa
Pu
Mu
(kN)
(kNm)
32 75.28
472 .09
37 51.28
583 .01
34 94.17
132 .86
24 80.36
597 .16
31 56.58
747 .88
32 60.96
774 .83
29 30.99
411 .36
2284.43
1483.04
1457.01
1066.96
1782.02
1665.51
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
15000 14000 13000 12000 11000 10000 9000 ) N k ( n P . f
8000 7000 6000 5000 4000 3000 2000 1000 0 0
400
800
1200
1600
2000
2400
2800
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
3200
3600
4000
b= h= 46 f c' =
1000 1000 D 20
mm mm 25 MPa
f y =
390
MPa
Pu
Mu
(kN)
(kNm)
3275.28
472.09
3751.28
583.01
3494.17
132.86
2480.36
597.16
3156.58
747.88
3260.96
774.83
2930.99
411.36
2284 .4 3
1 483 .04
1457 .0 1
1 066 .96
1782 .0 2
1 665 .51
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
εs6
εs7
εs8
εs9
εs10
mm
f s1
f s2
f s3
f s4
f s5
f s6
f s7
f s8
f s9
f s10
MPa
MPa
MPa
MPa
MPa
MPa
MPa
MPa
MPa
MPa
KONDISI TEKAN AKSIAL SENTRIS 1100
0.00048
0.00073
0.00099
1.37500
0.00151
0.00177
0.00202
0.00228
0.00254 0.00280
95.45
146.97
198.48
390.00
301.52
353.03
390.00
390.00
390.00
390.00
1091
0.00046
0.00072
0.00098
1.34821
0.00150
0.00176
0.00201
0.00227
0.00253 0.00279
91.33
143.26
195.20
390.00
299.07
351.01
390.00
390.00
390.00
390.00
1082
0.00044
0.00070
0.00096
1.32143
0.00148
0.00174
0.00201
0.00227
0.00253 0.00279
87.13
139.49
191.86
390.00
296.59
348.95
390.00
390.00
390.00
390.00
1073
0.00041
0.00068
0.00094
1.29464
0.00147
0.00173
0.00200
0.00226
0.00253 0.00279
82.86
135.66
188.46
390.00
294.07
346.87
390.00
390.00
390.00
390.00
1064
0.00039
0.00066
0.00093
1.26786
0.00146
0.00172
0.00199
0.00226
0.00252 0.00279
78.52
131.77
185.01
390.00
291.50
344.74
390.00
390.00
390.00
390.00
1055
0.00037
0.00064
0.00091
1.24107
0.00144
0.00171
0.00198
0.00225
0.00252 0.00279
74.11
127.81
181.50
390.00
288.89
342.58
390.00
390.00
390.00
390.00
1046
0.00035
0.00062
0.00089
1.21429
0.00143
0.00170
0.00197
0.00224
0.00251 0.00278
69.62
123.78
177.93
390.00
286.23
340.39
390.00
390.00
390.00
390.00
1038
0.00033
0.00060
0.00087
1.18750
0.00142
0.00169
0.00196
0.00224
0.00251 0.00278
65.06
119.68
174.30
390.00
283.53
338.15
390.00
390.00
390.00
390.00
1029
0.00030
0.00058
0.00085
1.16071
0.00140
0.00168
0.00195
0.00223
0.00251 0.00278
60.42
115.51
170.60
390.00
280.79
335.88
390.00
390.00
390.00
390.00
1020
0.00028
0.00056
0.00083
1.13393
0.00139
0.00167
0.00195
0.00222
0.00250 0.00278
55.69
111.27
166.84
390.00
277.99
333.57
389.14
390.00
390.00
390.00
1011
0.00025
0.00053
0.00082
1.10714
0.00138
0.00166
0.00194
0.00222
0.00250 0.00278
50.88
106.95
163.02
390.00
275.15
331.21
387.28
390.00
390.00
390.00
1002
0.00023
0.00051
0.00080
1.08036
0.00136
0.00164
0.00193
0.00221
0.00249 0.00278
45.99
102.55
159.12
390.00
272.25
328.82
385.38
390.00
390.00
390.00
993
0.00021
0.00049
0.00078
1.05357
0.00135
0.00163
0.00192
0.00220
0.00249 0.00277
41.01
98.08
155.16
390.00
269.30
326.38
383.45
390.00
390.00
390.00
984
0.00018
0.00047
0.00076
1.02679
0.00133
0.00162
0.00191
0.00220
0.00248 0.00277
35.93
93.53
151.12
390.00
266.30
323.90
381.49
390.00
390.00
390.00
975
0.00015
0.00044
0.00074
1.00000
0.00132
0.00161
0.00190
0.00219
0.00248 0.00277
30.77
88.89
147.01
390.00
263.25
321.37
379.49
390.00
390.00
390.00
966
0.00013
0.00042
0.00071
0.97321
0.00130
0.00159
0.00189
0.00218
0.00247 0.00277
25.51
84.17
142.82
390.00
260.14
318.79
377.45
390.00
390.00
390.00
957
0.00010
0.00040
0.00069
0.94643
0.00128
0.00158
0.00188
0.00217
0.00247 0.00276
20.15
79.35
138.56
390.00
256.97
316.17
375.37
390.00
390.00
390.00
948
0.00007
0.00037
0.00067
0.91964
0.00127
0.00157
0.00187
0.00217
0.00246 0.00276
14.69
74.45
134.21
390.00
253.74
313.50
373.26
390.00
390.00
390.00
939
0.00005
0.00035
0.00065
0.89286
0.00125
0.00155
0.00186
0.00216
0.00246 0.00276
9.13
69.46
129.78
390.00
250.44
310.77
371.10
390.00
390.00
390.00
930
0.00002
0.00032
0.00063
0.86607
0.00124
0.00154
0.00184
0.00215
0.00245 0.00276
3.45
64.36
125.27
390.00
247.09
308.00
368.91
390.00
390.00
390.00
921
-0.00001
0.00030
0.00060
0.83929
0.00122
0.00153
0.00183
0.00214
0.00245 0.00276
-2.33
59.17
120.67
390.00
243.67
305.17
366.67
390.00
390.00
390.00
913
-0.00004
0.00027
0.00058
0.81250
0.00120
0.00151
0.00182
0.00213
0.00244 0.00275
-8.22
53.88
115.98
390.00
240.18
302.28
364.38
390.00
390.00
390.00
904 -0.00007
0.00024
0.00056
0.78571
0.00118
0.00150
0.00181
0.00212
0.00244 0.00275
-14.23
48.48
111.20
390.00
236.63
299.34
362.06
390.00
390.00
390.00
895 -0.00010
0.00021
0.00053
0.75893
0.00117
0.00148
0.00180
0.00212
0.00243 0.00275
-20.36
42.98
106.32
390.00
233.00
296.34
359.68
390.00
390.00
390.00
886 -0.00013
0.00019
0.00051
0.73214
0.00115
0.00147
0.00179
0.00211
0.00243 0.00275
-26.61
37.37
101.34
390.00
229.30
293.28
357.26
390.00
390.00
390.00
877
-0.00016
0.00016
0.00048
0.70536
0.00113
0.00145
0.00177
0.00210
0.00242 0.00274
-32.99
31.64
96.27
390.00
225.53
290.16
354.79
390.00
390.00
390.00
868
-0.00020
0.00013
0.00046
0.67857
0.00111
0.00143
0.00176
0.00209
0.00241 0.00274
-39.51
25.79
91.08
390.00
221.67
286.97
352.26
390.00
390.00
390.00
859
-0.00023
0.00010
0.00043
0.65179
0.00109
0.00142
0.00175
0.00208
0.00241 0.00274
-46.15
19.82
85.79
390.00
217.74
283.71
349.69
390.00
390.00
390.00
850
-0.00026
0.00007
0.00040
0.62500
0.00107
0.00140
0.00174
0.00207
0.00240 0.00274
-52.94
13.73
80.39
390.00
213.73
280.39
347.06
390.00
390.00
390.00
841 -0.00030
0.00004
0.00037
0.59821
0.00105
0.00138
0.00172
0.00206
0.00240 0.00273
-59.87
7.50
74.88
390.00
209.62
277.00
344.37
390.00
390.00
390.00
832 -0.00033
0.00001
0.00035
0.57143
0.00103
0.00137
0.00171
0.00205
0.00239 0.00273
-66.95
1.14
69.24
390.00
205.44
273.53
341.63
390.00
390.00
390.00
-0.00037 -0.00003
0.00032
0.54464
0.00101
0.00135
0.00169
0.00204
0.00238 0.00273
-74.19
-5.35
63.49
390.00
201.16
269.99
338.83
390.00
390.00
390.00
814 -0.00041 -0.00006
0.00029
0.51786
0.00098
0.00133
0.00168
0.00203
0.00238 0.00272
-81.58
-11.99
57.60
390.00
196.78
266.37
335.96
390.00
390.00
390.00
805 -0.00045 -0.00009
0.00026
0.49107
0.00096
0.00131
0.00167
0.00202
0.00237 0.00272
-89.14
-18.77
51.59
390.00
192.31
262.68
333.04
390.00
390.00
390.00
796 -0.00048 -0.00013
0.00023
0.46429
0.00094
0.00129
0.00165
0.00201
0.00236 0.00272
-96.86
-25.71
45.44
390.00
187.74
258.89
330.04
390.00
390.00
390.00
788
-0.00052 -0.00016
0.00020
0.43750
0.00092
0.00128
0.00163
0.00199
0.00235 0.00271
-104.76
-32.80
39.15
390.00
183.07
255.03
326.98
390.00
390.00
390.00
779
-0.00056 -0.00020
0.00016
0.41071
0.00089
0.00126
0.00162
0.00198
0.00235 0.00271
-112.84
-40.06
32.72
390.00
178.29
251.07
323.85
390.00
390.00
390.00
770
-0.00061 -0.00024
0.00013
0.38393
0.00087
0.00124
0.00160
0.00197
0.00234 0.00271
-121.11
-47.49
26.14
390.00
173.40
247.02
320.65
390.00
390.00
390.00
823
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Fs1
Fs2
Fs3
Fs4
Fs5
Fs6
Fs7
Fs8
Fs9
Fs10
Cs
Ms1
Ms2
Ms3
Ms4
Ms5
Ms6
kN
kN
kN
kN
kN
kN
kN
kN
kN
kN
kN
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
598.72
184.37
248.99
489.24
378.24
442.86
489.24
489.24
489.24
2446.19
6256.31
-254454.87
-60943.51
-58789.40
-69308.66
-17861.21
20912.87
572.82
179.72
244.87
489.24
375.17
440.33
489.24
489.24
489.24
2446.19
6216.04
-243448.53
-59406.22
-57816.20
-69308.66
-17716.51
20793.15
546.50
174.99
240.68
489.24
372.06
437.75
489.24
489.24
489.24
2446.19
6175.11
-232260.55
-57843.57
-56826.94
-69308.66
-17569.43
20671.45
519.73
170.18
236.42
489.24
368.89
435.13
489.24
489.24
489.24
2446.19
6133.49
-220886.43
-56254.91
-55821.22
-69308.66
-17419.90
20547.73
492.52
165.30
232.09
489.24
365.67
432.46
489.24
489.24
489.24
2446.19
6091.18
-209321.46
-54639.59
-54798.62
-69308.66
-17267.86
20421.93
464.85
160.33
227.68
489.24
362.40
429.76
489.24
489.24
489.24
2446.19
6048.15
-197560.81
-52996.95
-53758.72
-69308.66
-17113.25
20294.00
436.70
155.27
223.20
489.24
359.07
427.00
489.24
489.24
489.24
2446.19
6004.39
-185599.46
-51326.27
-52701.08
-69308.66
-16956.00
20163.89
408.08
150.13
218.65
489.24
355.68
424.20
489.24
489.24
489.24
2446.19
5959.87
-173432.24
-49626.84
-51625.23
-69308.66
-16796.04
20031.54
378.95
144.90
214.01
489.24
352.23
421.35
489.24
489.24
489.24
2446.19
5914.58
-161053.78
-47897.90
-50530.71
-69308.66
-16633.31
19896.90
349.31
139.58
209.30
489.24
348.73
418.44
488.16
489.24
489.24
2446.19
5867.42
-148458.54
-46138.69
-49417.02
-69308.66
-16467.73
19759.89
319.15
134.16
204.50
489.24
345.16
415.49
485.82
489.24
489.24
2446.19
5818.19
-135640.76
-44348.39
-48283.65
-69308.66
-16299.22
19620.46
288.46
128.65
199.61
489.24
341.53
412.49
483.45
489.24
489.24
2446.19
5768.08
-122594.50
-42526.18
-47130.07
-69308.66
-16127.71
19478.55
257.21
123.04
194.64
489.24
337.83
409.43
481.02
489.24
489.24
2446.19
5717.07
-109313.60
-40671.20
-45955.75
-69308.66
-15953.11
19334.09
225.39
117.33
189.57
489.24
334.07
406.31
478.56
489.24
489.24
2446.19
5665.13
-95791.67
-38782.55
-44760.12
-69308.66
-15775.34
19187.00
192.99
111.51
184.42
489.24
330.23
403.14
476.05
489.24
489.24
2446.19
5612.24
-82022.08
-36859.31
-43542.59
-69308.66
-15594.32
19037.22
160.00
105.58
179.16
489.24
326.33
399.91
473.49
489.24
489.24
2446.19
5558.37
-67997.98
-34900.52
-42302.55
-69308.66
-15409.95
18884.68
126.38
99.55
173.81
489.24
322.35
396.62
470.89
489.24
489.24
2446.19
5503.50
-53712.22
-32905.18
-41039.38
-69308.66
-15222.15
18729.28
92.14
93.40
168.36
489.24
318.30
393.27
468.24
489.24
489.24
2446.19
5447.60
-39157.44
-30872.27
-39752.42
-69308.66
-15030.80
18570.96
57.24
87.13
162.81
489.24
314.17
389.85
465.53
489.24
489.24
2446.19
5390.63
-24325.94
-28800.71
-38440.99
-69308.66
-14835.82
18409.63
21.67
80.74
157.15
489.24
309.96
386.37
462.78
489.24
489.24
2446.19
5332.57
-9209.77
-26689.39
-37104.40
-69308.66
-14637.10
18245.21
-14.59
74.23
151.38
489.24
305.67
382.82
459.97
489.24
489.24
2446.19
5273.38
6199.34
-24537.15
-35741.89
-69308.66
-14434.52
18077.59
-51.55
67.59
145.49
489.24
301.30
379.20
457.10
489.24
489.24
2446.19
5213.04
21910.01
-22342.80
-34352.73
-69308.66
-14227.98
17906.70
-89.25
60.82
139.49
489.24
296.84
375.51
454.18
489.24
489.24
2446.19
5151.50
37931.16
-20105.08
-32936.11
-69308.66
-14017.36
17732.43
-127.70
53.92
133.37
489.24
292.29
371.75
451.20
489.24
489.24
2446.19
5088.73
54272.10
-17822.69
-31491.22
-69308.66
-13802.53
17554.68
-166.92
46.87
127.13
489.24
287.65
367.91
448.16
489.24
489.24
2446.19
5024.70
70942.49
-15494.29
-30017.19
-69308.66
-13583.38
17373.35
-206.95
39.69
120.76
489.24
282.91
363.99
445.06
489.24
489.24
2446.19
4959.37
87952.40
-13118.46
-28513.15
-69308.66
-13359.76
17188.32
-247.79
32.35
114.26
489.24
278.08
359.99
441.90
489.24
489.24
2446.19
4892.69
105312.31
-10693.75
-26978.15
-69308.66
-13131.53
16999.49
-289.49
24.86
107.62
489.24
273.15
355.91
438.67
489.24
489.24
2446.19
4824.62
123033.13
-8218.63
-25411.25
-69308.66
-12898.57
16806.73
-332.06
17.22
100.85
489.24
268.11
351.74
435.37
489.24
489.24
2446.19
4755.12
141126.23
-5691.51
-23811.42
-69308.66
-12660.71
16609.92
-375.54
9.41
93.93
489.24
262.97
347.48
432.00
489.24
489.24
2446.19
4684.15
159603.48
-3110.74
-22177.63
-69308.66
-12417.80
16408.93
-419.95
1.44
86.86
489.24
257.71
343.14
428.56
489.24
489.24
2446.19
4611.66
178477.24
-474.58
-20508.78
-69308.66
-12169.67
16203.63
-465.32
-6.71
79.64
489.24
252.34
338.69
425.05
489.24
489.24
2446.19
4537.59
197760.40
2218.75
-18803.73
-69308.66
-11916.17
15993.88
-511.69
-15.04
72.26
489.24
246.86
334.15
421.45
489.24
489.24
2446.19
4461.90
217466.45
4971.16
-17061.29
-69308.66
-11657.10
15779.52
-559.08
-23.55
64.72
489.24
241.25
329.51
417.78
489.24
489.24
2446.19
4384.53
237609.43
7784.59
-15280.21
-69308.66
-11392.29
15560.42
-607.54
-32.25
57.00
489.24
235.52
324.77
414.03
489.24
489.24
2446.19
4305.43
258204.05
10661.10
-13459.20
-69308.66
-11121.55
15336.40
-657.10
-41.15
49.12
489.24
229.65
319.92
410.19
489.24
489.24
2446.19
4224.53
279265.67
13602.84
-11596.89
-69308.66
-10844.66
15107.30
-707.79
-50.25
41.05
489.24
223.65
314.96
406.26
489.24
489.24
2446.19
4141.77
300810.35
16612.05
-9691.87
-69308.66
-10561.42
14872.95
-759.66
-59.57
32.79
489.24
217.52
309.88
402.24
489.24
489.24
2446.19
4057.10
322854.91
19691.08
-7742.65
-69308.66
-10271.61
14633.16
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Ms7
Ms8
Ms9
Ms10
Ms
a
Cc
Mc
Pn
Mn
kNmm
kNmm
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
kNm
20337.93 69308.66
115514.43
Ф 0.00
0.650
Ф.Pn
Ф.Mn
kN
kNm
13219.66
161720.21
1039629.91
945728.44
935.00
15895.00
516587.50
20337.93
1462.32
0.65
13219.66
0.00 950.51
69308.66
115514.43
161720.21
1039629.91
959270.25
927.41
15765.98
572220.69
20337.93
1531.49
0.65
13219.66
995.47
69308.66
115514.43
161720.21
1039629.91
973035.52
919.82
15636.96
626874.73
20337.93
1599.91
0.65
13219.66
1039.94
69308.66
115514.43
161720.21
1039629.91
987029.83
912.23
15507.95
680549.61
20337.93
1667.58
0.65
13219.66
1083.93
69308.66
115514.43
1 61720.21
1039629.91
1001258.95
904.64
15378.93
733245.34
20337.93
1734.50
0.65
13219.66
1127.43
69308.66
115514.43
1 61720.21
1039629.91
1015728.83
897.05
15249.91
784961.92
20337.93
1800.69
0.65
13219.66
1170.45
69308.66
115514.43
1 61720.21
1039629.91
1030445.64
889.46
15120.89
835699.35
20337.93
1866.14
0.65
13219.66
1212.99
69308.66
115514.43
1 61720.21
1039629.91
1045415.75
881.88
14991.88
885457.62
20337.93
1930.87
0.65
13219.66
1255.07
69308.66
115514.43
1 61720.21
1039629.91
1060645.75
874.29
14862.86
934236.73
20337.93
1994.88
0.65
13219.66
1296.67
69156.16
115514.43
1 61720.21
1039629.91
1075989.98
866.70
14733.84
982036.70
20337.93
2058.03
0.65
13219.66
1337.72
68825.13
115514.43
161720.21
1039629.91
1091429.47
859.11
14604.82
1028857.51
20337.93
2120.29
0.65
13219.66
1378.19
68488.20
115514.43
161720.21
1039629.91
1107144.18
851.52
14475.80
1074699.17
20243.88
2181.84
0.65
13158.52
1418.20
68145.21
115514.43
161720.21
1039629.91
1123141.53
843.93
14346.79
1119561.67
20063.85
2242.70
0.65
13041.50
1457.76
67795.99
115514.43
161720.21
1039629.91
1139429.21
836.34
14217.77
1163445.02
19882.90
2302.87
0.65
12923.88
1496.87
67440.38
115514.43
161720.21
1039629.91
1156015.20
828.75
14088.75
1206349.22
19700.99
2362.36
0.65
12805.64
1535.54
67078.20
115514.43
161720.21
1039629.91
1172907.77
821.16
13959.73
1248274.26
19518.11
2421.18
0.65
12686.77
1573.77
66709.25
115514.43
161720.21
1039629.91
1190115.50
813.57
13830.71
1289220.15
19334.22
2479.34
0.65
12567.24
1611.57
66333.37
115514.43
161720.21
1039629.91
1207647.29
805.98
13701.70
1329186.89
19149.29
2536.83
0.65
12447.04
1648.94
65950.33
115514.43
161720.21
1039629.91
1225512.39
798.39
13572.68
1368174.47
18963.31
2593.69
0.65
12326.15
1685.90
65559.94
115514.43
161720.21
1039629.91
1243720.38
790.80
13443.66
1406182.90
18776.23
2649.90
0.65
12204.55
1722.44
65161.99
115514.43
161720.21
1039629.91
1262281.25
783.21
13314.64
1443212.18
18588.02
2705.49
0.65
12082.22
1758.57
64756.25
115514.43
161720.21
1039629.91
1281205.34
775.63
13185.63
1479262.30
18398.66
2760.47
0.65
11959.13
1794.30
64342.49
115514.43
161720.21
1039629.91
1300503.43
768.04
13056.61
1514333.27
18208.11
2814.84
0.65
11835.27
1829.64
63920.47
115514.43
161720.21
1039629.91
1320186.70
760.45
12927.59
1548425.09
18016.32
2868.61
0.65
11710.61
1864.60
63489.94
115514.43
161720.21
1039629.91
1340266.82
752.86
12798.57
1581537.76
17823.27
2921.80
0.65
11585.13
1899.17
63050.65
115514.43
161720.21
1039629.91
1360755.90
745.27
12669.55
1613671.27
17628.92
2974.43
0.65
11458.80
1933.38
62602.31
115514.43
161720.21
1039629.91
1381666.57
737.68
12540.54
1644825.62
17433.22
3026.49
0.65
11331.59
1967.22
62144.66
115514.43
161720.21
1039629.91
1403011.96
730.09
12411.52
1675000.83
17236.14
3078.01
0.65
11203.49
2000.71
61677.39
115514.43
161720.21
1039629.91
1424805.80
722.50
12282.50
1704196.88
17037.62
3129.00
0.65
11074.46
2033.85
61200.20
115514.43
161720.21
1039629.91
1447062.34
714.91
12153.48
1732413.77
16837.63
3179.48
0.65
10944.46
2066.66
60712.77
115514.43
161720.21
1039629.91
1469796.50
707.32
12024.46
1759651.51
16636.12
3229.45
0.65
10813.48
2099.14
60214.77
115514.43
161720.21
1039629.91
1493023.80
699.73
11895.45
1785910.10
16433.04
3278.93
0.65
10681.47
2131.31
59705.84
115514.43
161720.21
1039629.91
1516760.48
692.14
11766.43
1811189.54
16228.33
3327.95
0.65
10548.41
2163.17
59185.63
115514.43
161720.21
1039629.91
1541023.46
684.55
11637.41
1835489.82
16021.94
3376.51
0.65
10414.26
2194.73
58653.76
115514.43
161720.21
1039629.91
1565830.46
676.96
11508.39
1858810.95
15813.82
3424.64
0.65
10278.98
2226.02
58109.83
115514.43
161720.21
1039629.91
1591199.98
669.38
11379.38
1881152.93
15603.90
3472.35
0.65
10142.54
2257.03
57553.42
115514.43
161720.21
1039629.91
1617151.36
661.79
11250.36
1902515.75
15392.13
3519.67
0.65
10004.89
2287.78
56984.10
115514.43
1 61720.21
1039629.91
1643704.87
654.20
11121.34
1922899.42
15178.44
3566.60
0.65
9865.99
2318.29
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
εs6
εs7
εs8
εs9
εs10
mm
f s1 MPa
f s2
f s3
f s4
f s5
f s6
f s7
f s8
f s9
f s10
MPa
MPa
MPa
MPa
MPa
MPa
MPa
MPa
MPa
761
-0.00065 -0.00028
0.00010
0.35714
0.00084
0.00121
0.00159
0.00196
0.00233 0.00270
-129.58
-55.09
19.41
390.00
168.39
242.88
317.37
390.00
390.00
390.00
752
-0.00069 -0.00031
0.00006
0.33036
0.00082
0.00119
0.00157
0.00195
0.00232 0.00270
-138.24
-62.87
12.51
390.00
163.26
238.64
314.01
389.39
390.00
390.00
743 -0.00074 -0.00035
0.00003
0.30357
0.00079
0.00117
0.00155
0.00193
0.00232 0.00270
-147.12
-70.83
5.45
390.00
158.01
234.29
310.58
386.86
390.00
390.00
734
-0.00078 -0.00039 -0.00001
0.27679
0.00076
0.00115
0.00154
0.00192
0.00231 0.00269
-156.20
-78.99
-1.78
390.00
152.64
229.85
307.06
384.27
390.00
390.00
725
-0.00083 -0.00044 -0.00005
0.25000
0.00074
0.00113
0.00152
0.00191
0.00230 0.00269
-165.52
-87.36
-9.20
390.00
147.13
225.29
303.45
381.61
390.00
390.00
716
-0.00088 -0.00048 -0.00008
0.22321
0.00071
0.00110
0.00150
0.00189
0.00229 0.00269
-175.06
-95.93
-16.79
390.00
141.48
220.62
299.75
378.89
390.00
390.00
707
-0.00092 -0.00052 -0.00012
0.19643
0.00068
0.00108
0.00148
0.00188
0.00228 0.00268
-184.85
-104.71
-24.58
390.00
135.69
215.82
295.96
376.09
390.00
390.00
698
-0.00097 -0.00057 -0.00016
0.16964
0.00065
0.00105
0.00146
0.00187
0.00227 0.00268
-194.88
-113.73
-32.57
390.00
129.75
210.91
292.07
373.23
390.00
390.00
689
-0.00103 -0.00061 -0.00020
0.14286
0.00062
0.00103
0.00144
0.00185
0.00226 0.00267
-205.18
-122.97
-40.76
390.00
123.66
205.87
288.08
370.29
390.00
390.00
680
-0.00108 -0.00066 -0.00025
0.11607
0.00059
0.00100
0.00142
0.00184
0.00225 0.00267
-215.75
-132.46
-49.17
390.00
117.41
200.70
283.99
367.28
390.00
390.00
671
-0.00113 -0.00071 -0.00029
0.08929
0.00055
0.00098
0.00140
0.00182
0.00224 0.00266
-226.60
-142.20
-57.80
390.00
110.99
195.39
279.79
364.18
390.00
390.00
663
-0.00119 -0.00076 -0.00033
0.06250
0.00052
0.00095
0.00138
0.00181
0.00223 0.00266
-237.74
-152.20
-66.67
390.00
104.40
189.94
275.47
361.01
390.00
390.00
654
-0.00125 -0.00081 -0.00038
0.03571
0.00049
0.00092
0.00136
0.00179
0.00222 0.00266
-249.18
-162.48
-75.77
390.00
97.63
184.34
271.04
357.74
390.00
390.00
645
-0.00130 -0.00087 -0.00043
0.00893
0.00045
0.00089
0.00133
0.00177
0.00221 0.00265
-260.94
-173.04
-85.13
390.00
90.67
178.58
266.48
354.39
390.00
390.00
636
-0.00137 -0.00092 -0.00047 -0.01786
0.00042
0.00086
0.00131
0.00175
0.00220 0.00265
-273.03
-183.90
-94.76
-390.00
83.52
172.66
261.80
350.94
390.00
390.00
627
-0.00143 -0.00098 -0.00052 -0.04464
0.00038
0.00083
0.00128
0.00174
0.00219 0.00264
-285.47
-195.06
-104.65
-390.00
76.16
166.57
256.98
347.39
390.00
390.00
618
-0.00149 -0.00103 -0.00057 -0.07143
0.00034
0.00080
0.00126
0.00172
0.00218 0.00264
-298.27
-206.55
-114.84
-390.00
68.59
160.31
252.02
343.74
390.00
390.00
609
-0.00156 -0.00109 -0.00063 -0.09821
0.00030
0.00077
0.00123
0.00170
0.00217 0.00263
-311.44
-218.38
-125.32
-390.00
60.80
153.86
246.92
339.98
390.00
390.00
600
-0.00163 -0.00115 -0.00068 -0.12500
0.00026
0.00074
0.00121
0.00168
0.00215 0.00263
-325.00
-230.56
-136.11
-390.00
52.78
147.22
241.67
336.11
390.00
390.00
591
-0.00169 -0.00122 -0.00074 -0.15179
0.00022
0.00070
0.00118
0.00166
0.00214 0.00262
-338.97
-243.10
-147.23
-390.00
44.51
140.38
236.25
332.12
390.00
390.00
582
-0.00177 -0.00128 -0.00079 -0.17857
0.00018
0.00067
0.00115
0.00164
0.00213 0.00261
-353.37
-256.03
-158.69
-390.00
35.99
133.33
230.67
328.02
390.00
390.00
573
-0.00184 -0.00135 -0.00085 -0.20536
0.00014
0.00063
0.00112
0.00162
0.00211 0.00261
-368.22
-269.37
-170.51
-390.00
27.21
126.06
224.92
323.78
390.00
390.00
564
-0.00192 -0.00142 -0.00091 -0.23214
0.00009
0.00059
0.00109
0.00160
0.00210 0.00260
-383.54
-283.12
-182.70
-390.00
18.14
118.57
218.99
319.41
390.00
390.00
555
-0.00200 -0.00149 -0.00098 -0.25893
0.00004
0.00055
0.00106
0.00157
0.00208 0.00259
-390.00
-297.32
-195.28
-390.00
8.79
110.83
212.86
314.90
390.00
390.00
546
-0.00208 -0.00156 -0.00104 -0.28571
0.00000
0.00051
0.00103
0.00155
0.00207 0.00259
-390.00
-311.98
-208.28
-390.00
-0.87
102.83
206.54
310.24
390.00
390.00
538
-0.00216 -0.00164 -0.00111 -0.31250 -0.00005
0.00047
0.00100
0.00153
0.00205 0.00258
-390.00
-327.13
-221.71
-390.00
-10.85
94.57
200.00
305.43
390.00
390.00
529
-0.00225 -0.00171 -0.00118 -0.33929 -0.00011
0.00043
0.00097
0.00150
0.00204 0.00257
-390.00
-342.79
-235.59
-390.00
-21.17
86.04
193.24
300.45
390.00
390.00
520
-0.00234 -0.00179 -0.00125 -0.36607 -0.00016
0.00039
0.00093
0.00148
0.00202 0.00257
-390.00
-358.99
-249.94
-390.00
-31.84
77.21
186.25
295.30
390.00
390.00
511
-0.00243 -0.00188 -0.00132 -0.39286 -0.00021
0.00034
0.00090
0.00145
0.00200 0.00256
-390.00
-375.76
-264.80
-390.00
-42.89
68.07
179.02
289.98
390.00
390.00
502
-0.00253 -0.00197 -0.00140 -0.41964 -0.00027
0.00029
0.00086
0.00142
0.00199 0.00255
-390.00
-390.00
-280.19
-390.00
-54.33
58.60
171.53
284.46
390.00
390.00
493
-0.00263 -0.00206 -0.00148 -0.44643 -0.00033
0.00024
0.00082
0.00139
0.00197 0.00254
-390.00
-390.00
-296.14
-390.00
-66.18
48.79
163.77
278.74
390.00
390.00
484
-0.00273 -0.00215 -0.00156 -0.47321 -0.00039
0.00019
0.00078
0.00136
0.00195 0.00254
-390.00
-390.00
-312.67
-390.00
-78.47
38.62
155.72
272.82
389.91
390.00
475
-0.00284 -0.00225 -0.00165 -0.50000 -0.00046
0.00014
0.00074
0.00133
0.00193 0.00253
-390.00
-390.00
-329.82
-390.00
-91.23
28.07
147.37
266.67
385.96
390.00
466
-0.00295 -0.00235 -0.00174 -0.52679 -0.00052
0.00009
0.00069
0.00130
0.00191 0.00252
-390.00
-390.00
-347.64
-390.00
-104.47
17.11
138.70
260.28
381.86
390.00
457
-0.00307 -0.00245 -0.00183 -0.55357 -0.00059
0.00003
0.00065
0.00127
0.00189 0.00251
-390.00
-390.00
-366.15
-390.00
-118.23
5.73
129.69
253.65
377.60
390.00
448
-0.00319 -0.00256 -0.00193 -0.58036 -0.00066 -0.00003
0.00060
0.00123
0.00187 0.00250
-390.00
-390.00
-385.39
-390.00
-132.54
-6.11
120.32
246.75
373.17
390.00
439
-0.00332 -0.00267 -0.00203 -0.60714 -0.00074 -0.00009
0.00055
0.00120
0.00184 0.00249
-390.00
-390.00
-390.00
-390.00
-147.43
-18.43
110.57
239.57
368.56
390.00
430
-0.00345 -0.00279 -0.00213 -0.63393 -0.00081 -0.00016
0.00050
0.00116
0.00182 0.00248
-390.00
-390.00
-390.00
-390.00
-162.93
-31.26
100.41
232.09
363.76
390.00
421
-0.00358 -0.00291 -0.00224 -0.66071 -0.00090 -0.00022
0.00045
0.00112
0.00179 0.00247
-390.00
-390.00
-390.00
-390.00
-179.10
-44.63
89.83
224.29
358.76
390.00
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Fs1 kN
Fs2
Fs3
kN
kN
Fs4 kN
Fs5 kN
Fs6 kN
Fs7 kN
Fs8 kN
Fs9 kN
Fs10 kN
Cs kN
Ms1 kNmm
Ms2
Ms3
Ms4
Ms5
kNmm
Ms6
kNmm
kNmm
kNmm
kNmm
-812.75
-69.10
24.34
489.24
211.24
304.68
398.13
489.24
489.24
2446.19
3970.44
345416.94
22842.39
-5747.68
-69308.66
-9975.00
14387.74
-867.09
-78.86
15.69
489.24
204.80
299.36
393.92
488.47
489.24
2446.19
3880.96
368514.90
26068.55
-3705.32
-69308.66
-9671.35
14136.49
-922.75
-88.86
6.84
489.24
198.22
293.91
389.60
485.30
489.24
2446.19
3786.93
392168.09
29372.26
-1613.86
-69308.66
-9360.39
13879.20
-979.76
-99.09
-2.24
489.24
191.47
288.33
385.19
482.04
489.24
2446.19
3690.61
416396.78
32756.35
528.48
-69308.66
-9041.87
13615.65
-1038.17
-109.58
-11.54
489.24
184.56
282.61
380.66
478.71
489.24
2446.19
3591.92
441222.24
36223.80
2723.59
-69308.66
-8715.50
13345.61
-1098.04
-120.34
-21.06
489.24
177.48
276.75
376.02
475.30
489.24
2446.19
3490.78
466666.79
39777.72
4973.45
-69308.66
-8380.99
13068.84
-1159.42
-131.36
-30.83
489.24
170.22
270.74
371.27
471.79
489.24
2446.19
3387.07
492753.88
43421.38
7280.11
-69308.66
-8038.04
12785.07
-1222.37
-142.66
-40.85
489.24
162.77
264.58
366.39
468.20
489.24
2446.19
3280.72
519508.16
47158.23
9645.77
-69308.66
-7686.32
12494.05
-1286.95
-154.26
-51.13
489.24
155.13
258.26
361.39
464.52
489.24
2446.19
3171.61
546955.55
50991.89
12072.72
-69308.66
-7325.48
12195.49
-1353.23
-166.16
-61.68
489.24
147.29
251.77
356.25
460.74
489.24
2446.19
3059.63
575123.35
54926.17
14563.37
-69308.66
-6955.17
11889.10
-1421.27
-178.38
-72.51
489.24
139.24
245.11
350.98
456.85
489.24
2446.19
2944.68
604040.29
58965.09
17120.25
-69308.66
-6575.02
11574.55
-1491.15
-190.93
-83.63
489.24
130.97
238.27
345.57
452.87
489.24
2446.19
2826.63
633736.67
63112.87
19746.06
-69308.66
-6184.61
11251.53
-1562.93
-203.82
-95.06
489.24
122.48
231.24
340.01
448.77
489.24
2446.19
2705.35
664244.42
67373.98
22443.61
-69308.66
-5783.54
10919.68
-1636.70
-217.07
-106.80
489.24
113.75
224.02
334.29
444.56
489.24
2446.19
2580.71
695597.26
71753.12
25215.88
-69308.66
-5371.37
10578.64
-1712.54
-230.69
-118.87
-489.24
104.77
216.59
328.41
440.23
489.24
2446.19
1474.10
727830.79
76255.28
28066.03
69308.66
-4947.61
10228.01
-1790.55
-244.70
-131.28
-489.24
95.54
208.96
322.37
435.78
489.24
2446.19
1342.31
760982.67
80885.70
30997.37
69308.66
-4511.78
9867.40
-1870.81
-259.11
-144.06
-489.24
86.05
201.10
316.15
431.20
489.24
2446.19
1206.72
795092.69
85649.95
34013.44
69308.66
-4063.35
9496.37
-1953.42
-273.94
-157.21
-489.24
76.27
193.01
309.75
426.49
489.24
2446.19
1067.15
830203.00
90553.91
37117.96
69308.66
-3601.77
9114.46
-2038.49
-289.22
-170.75
-489.24
66.21
184.68
303.16
421.64
489.24
2446.19
923.42
866358.26
95603.83
40314.87
69308.66
-3126.46
8721.18
-2126.13
-304.96
-184.69
-489.24
55.84
176.10
296.37
416.64
489.24
2446.19
775.35
903605.83
100806.31
43608.36
69308.66
-2636.78
8316.01
-2216.46
-321.18
-199.07
-489.24
45.15
167.26
289.37
411.48
489.24
2446.19
622.74
941995.96
106168.37
47002.88
69308.66
-2132.09
7898.42
-2309.60
-337.91
-213.90
-489.24
34.13
158.14
282.15
406.17
489.24
2446.19
465.37
981582.04
111697.48
50503.16
69308.66
-1611.67
7467.82
-2405.70
-355.16
-229.19
-489.24
22.76
148.74
274.71
400.68
489.24
2446.19
303.03
1022420.85
117401.56
54114.19
69308.66
-1074.79
7023.60
-2446.19
-372.98
-244.98
-489.24
11.03
139.03
267.03
395.03
489.24
2446.19
194.15
1039629.91
123289.05
57841.34
69308.66
-520.64
6565.09
-2446.19
- 391.37
-261.28
- 489.24
-1.09
129.00
259.09
389.18
489.24
2446.19
123.53
1039629.91
129368.94
61690.30
69308.66
51.62
6091.59
-2446.19
-410.37
-278.12
-489.24
-13.61
118.64
250.89
383.14
489.24
2446.19
50.57
1039629.91
135650.82
65667.12
69308.66
642.89
5602.37
-2446.19
-430.02
-295.53
-489.24
-26.56
107.93
242.42
376.90
489.24
2446.19
-24.86
1039629.91
142144.93
69778.30
69308.66
1254.14
5096.62
-2446.19
-450.34
-313.54
-489.24
-39.95
96.85
233.65
370.45
489.24
2446.19
-102.89
1039629.91
148862.20
74030.75
69308.66
1886.39
4573.49
-2446.19
-471.37
-332.18
-489.24
-53.80
85.38
224.57
363.76
489.24
2446.19
-183.64
1039629.91
155814.34
78431.89
69308.66
2540.75
4032.06
-2446.19
-489.24
-351.49
-489.24
-68.15
73.51
215.18
356.84
489.24
2446.19
-263.35
1039629.91
161720.21
82989.66
69308.66
3218.40
3471.37
-2446.19
-489.24
-371.49
-489.24
-83.02
61.21
205.44
349.67
489.24
2446.19
-327.43
1039629.91
161720.21
87712.56
69308.66
3920.59
2890.36
-2446.19
-489.24
-392.23
-489.24
-98.44
48.45
195.34
342.24
489.13
2446.19
-393.99
1039629.91
161720.21
92609.74
69308.66
4648.70
2287.92
-2446.19
-489.24
-413.75
-489.24
-114.44
35.21
184.87
334.52
484.18
2446.19
-467.89
1039629.91
161720.21
97691.02
69308.66
5404.18
1662.83
-2446.19
-489.24
-436.10
-489.24
-131.05
21.47
173.99
326.51
479.03
2446.19
-544.62
1039629.91
161720.21
102966.99
69308.66
6188.61
1013.78
-2446.19
-489.24
-459.31
-489.24
-148.31
7.19
162.69
318.19
473.69
2446.19
-624.35
1039629.91
161720.21
108449.05
69308.66
7003.68
339.39
-2446.19
-489.24
-483.46
-489.24
-166.26
-7.66
150.93
309.53
468.13
2446.19
-707.26
1 039629.91
161720.21
114149.52
69308.66
7851.22
-361.88
-2446.19
-489.24
-489.24
-489.24
-184.94
-23.12
138.70
300.53
462.35
2446.19
-774.19
1039629.91
161720.21
115514.43
69308.66
8733.22
-1091.65
-2446.19
-489.24
-489.24
-489.24
-204.39
-39.21
125.97
291.14
456.32
2446.19
-837.88
1039629.91
161720.21
115514.43
69308.66
9651.81
-1851.70
-2446.19
-489.24
-489.24
-489.24
-224.67
-55.99
112.69
281.37
450.04
2446.19
-904.27
1039629.91
161720.21
115514.43
69308.66
10609.32
-2643.96
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Ms7
Ms8
Ms9
Ms10
Ms
a
Cc
Mc
Pn
Mn
kNmm
kNmm
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
kNm
Ф
Ф.Pn
Ф.Mn
kN
kNm
56401.41
115514.43
1 61720.21
1039629.91
1670881.70
646.61
10992.32
1942303.94
14962.76
3613.19
0.65
9725.79
2348.57
55804.89
115333.86
1 61720.21
1039629.91
1698523.48
639.02
10863.30
1960729.30
14744.26
3659.25
0.65
9583.77
2378.51
55194.03
114584.09
1 61720.21
1039629.91
1726264.88
631.43
10734.29
1978175.51
14521.21
3704.44
0.65
9438.79
2407.89
54568.30
113816.08
1 61720.21
1039629.91
1754681.25
623.84
10605.27
1994642.57
14295.88
3749.32
0.65
9292.32
2437.06
53927.16
113029.16
1 61720.21
1039629.91
1783797.53
616.25
10476.25
2010130.47
14068.17
3793.93
0.65
9144.31
2466.05
53270.04
112222.60
1 61720.21
1039629.91
1813639.90
608.66
10347.23
2024639.22
13838.01
3838.28
0.65
8994.70
2494.88
52596.32
111395.69
1 61720.21
1039629.91
1844235.87
601.07
10218.21
2038168.81
13605.29
3882.40
0.65
8843.44
2523.56
51905.36
110547.62
1 61720.21
1039629.91
1875614.34
593.48
10089.20
2050719.26
13369.91
3926.33
0.65
8690.44
2552.12
51196.51
109677.58
161720.21
1039629.91
1907805.73
585.89
9960.18
2062290.55
13131.78
3970.10
0.65
8535.66
2580.56
50469.06
108784.71
161720.21
1039629.91
1940842.04
578.30
9831.16
2072882.68
12890.79
4013.72
0.65
8379.01
2608.92
49722.25
107868.09
161720.21
1039629.91
1974756.97
570.71
9702.14
2082495.66
12646.82
4057.25
0.65
8220.43
2637.21
48955.32
106926.76
161720.21
1039629.91
2009586.05
563.13
9573.13
2091129.49
12399.75
4100.72
0.65
8059.84
2665.47
48167.43
105959.72
161720.21
1039629.91
2045366.74
555.54
9444.11
2098784.17
12149.46
4144.15
0.65
7897.15
2693.70
47357.72
104965.88
161720.21
1039629.91
2082138.59
547.95
9315.09
2105459.69
11895.80
4187.60
0.65
7732.27
2721.94
46525.26
103944.13
161720.21
1039629.91
2258560.68
540.36
9186.07
2111156.06
10660.17
4369.72
0.65
6929.11
2840.32
45669.09
102893.27
161720.21
1039629.91
2297442.51
532.77
9057.05
2115873.27
10399.37
4413.32
0.65
6759.59
2868.66
44788.17
101812.04
161720.21
1039629.91
2337448.08
525.18
8928.04
2119611.34
10134.75
4457.06
0.65
6587.59
2897.09
43881.41
100699.10
161720.21
1039629.91
2378626.85
517.59
8799.02
2122370.24
9866.16
4501.00
0.65
6413.01
2925.65
42947.67
99553.04
161720.21
1039629.91
2421031.17
510.00
8670.00
2124150.00
9593.42
4545.18
0.65
6235.72
2954.37
41985.73
98372.35
161720.21
1039629.91
2464716.58
502.41
8540.98
2124950.60
9316.33
4589.67
0.65
6055.62
2983.28
40994.27
97155.45
161720.21
1039629.91
2509742.04
494.82
8411.96
2124772.05
9034.70
4634.51
0.65
5872.56
3012.43
39971.93
95900.63
161720.21
1039629.91
2556170.17
487.23
8282.95
2123614.35
8748.32
4679.78
0.65
5686.41
3041.86
38917.23
94606.11
161720.21
1039629.91
2604067.53
479.64
8153.93
2121477.49
8456.96
4725.55
0.65
5497.02
3071.60
37828.62
93269.96
161720.21
1039629.91
2628562.12
472.05
8024.91
2118361.48
8219.06
4746.92
0.65
5342.39
3085.50
36704.44
91890.15
161720.21
1039629.91
2636085.73
464.46
7895.89
2114266.31
8019.43
4750.35
0.65
5212.63
3087.73
35542.90
90464.49
161720.21
1039629.91
2643859.30
456.88
7766.88
2109191.99
7817.44
4753.05
0.65
5081.34
3089.48
34342.13
88990.68
161720.21
1039629.91
2651895.48
449.29
7637.86
2103138.52
7612.99
4755.03
0.65
4948.45
3090.77
33100.09
87466.21
161720.21
1039629.91
2660207.83
441.70
7508.84
2096105.90
7405.95
4756.31
0.65
4813.87
3091.60
31814.63
85888.44
161720.21
1039629.91
2668810.81
434.11
7379.82
2088094.12
7196.19
4756.90
0.65
4677.52
3091.99
30483.42
84254.53
161720.21
1039629.91
2676426.27
426.52
7250.80
2079103.18
6987.46
4755.53
0.65
4541.85
3091.09
29103.97
82561.41
161720.21
1039629.91
2678197.81
418.93
7121.79
2069133.10
6794.35
4747.33
0.65
4416.33
3085.77
27673.63
80805.82
161684.51
1039629.91
2679999.01
411.34
6992.77
2058183.86
6598.78
4738.18
0.65
4289.21
3079.82
26189.51
78984.23
160046.99
1039629.91
2680267.45
403.75
6863.75
2046255.47
6395.86
4726.52
0.65
4157.31
3072.24
24648.53
77092.84
158346.73
1039629.91
2680546.18
396.16
6734.73
2033347.92
6190.11
4713.89
0.65
4023.57
3064.03
23047.35
75127.58
156580.06
1039629.91
2680835.80
388.57
6605.71
2019461.22
5981.36
4700.30
0.65
3887.88
3055.19
21382.38
73084.01
154743.01
1039629.91
2681136.96
380.98
6476.70
2004595.37
5769.44
4685.73
0.65
3750.13
3045.73
19649.73
70957.38
152831.27
1039629.91
2676883.08
373.39
6347.68
1988750.37
5573.49
4665.63
0.65
3622.77
3032.66
17845.19
68742.50
150840.21
1039629.91
2671031.13
365.80
6218.66
1971926.21
5380.78
4642.96
0.65
3497.51
3017.92
15964.19
66433.77
148764.79
1039629.91
2664931.23
358.21
6089.64
1954122.90
5185.37
4619.05
0.65
3370.49
3002.39
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
εs6
εs7
εs8
εs9
εs10
mm
f s1
f s2
f s3
f s4
f s5
f s6
f s7
f s8
f s9
f s10
MPa
MPa
MPa
MPa
MPa
MPa
MPa
MPa
MPa
MPa
413
-0.00373 -0.00304 -0.00235 -0.68750 -0.00098 -0.00029
0.00039
0.00108
0.00177 0.00245
-390.00
-390.00
-390.00
-390.00
-195.96
-58.59
78.79
216.16
353.54
390.00
404
-0.00388 -0.00317 -0.00247 -0.71429 -0.00107 -0.00037
0.00034
0.00104
0.00174 0.00244
-390.00
-390.00
-390.00
-390.00
-213.57
-73.16
67.26
207.67
348.08
390.00
395
-0.00403 -0.00331 -0.00260 -0.74107 -0.00116 -0.00044
0.00028
0.00099
0.00171 0.00243
-390.00
-390.00
-390.00
-390.00
-231.98
-88.39
55.20
198.79
342.38
390.00
386
-0.00419 -0.00346 -0.00273 -0.76786 -0.00126
-0.00052
0.00021
0.00095
0.00168 0.00242
-390.00
-390.00
-390.00
-390.00
-251.23
-104.32
42.59
189.51
336.42
390.00
377
-0.00436 -0.00361 -0.00286 -0.79464 -0.00136
-0.00061
0.00015
0.00090
0.00165 0.00240
-390.00
-390.00
-390.00
-390.00
-271.41
-121.01
29.38
179.78
330.17
390.00
368
-0.00454 -0.00377 -0.00300 -0.82143 -0.00146
-0.00069
0.00008
0.00085
0.00162 0.00239
-390.00
-390.00
-390.00
-390.00
-292.56
-138.51
15.53
169.58
323.62
390.00
359
-0.00473 -0.00394 -0.00315 -0.84821 -0.00157 -0.00078
0.00000
0.00079
0.00158 0.00237
-390.00
-390.00
-390.00
-390.00
-314.76
-156.88
1.00
158.87
316.75
390.00
350
-0.00493 -0.00412 -0.00331 -0.87500 -0.00169 -0.00088 -0.00007
0.00074
0.00155 0.00236
-390.00
-390.00
-390.00
-390.00
-338.10
-176.19
-14.29
147.62
309.52
390.00
341
-0.00514 -0.00431 -0.00347 -0.90179 -0.00181 -0.00098 -0.00015
0.00068
0.00151 0.00234
-390.00
-390.00
-390.00
-390.00
-362.65
-196.51
-30.37
135.78
301.92
390.00
332
-0.00535 -0.00450 -0.00365 -0.92857 -0.00194 -0.00109 -0.00024
0.00062
0.00147 0.00232
-390.00
-390.00
-390.00
-390.00
-388.53
-217.92
-47.31
123.30
293.91
390.00
323
-0.00559 -0.00471 -0.00383 -0.95536 -0.00208 -0.00120 -0.00033
0.00055
0.00143 0.00230
-390.00
-390.00
-390.00
-390.00
-390.00
-240.52
-65.19
110.13
285.45
390.00
314
-0.00583 -0.00493 -0.00403 -0.98214 -0.00222
-0.00132 -0.00042
0.00048
0.00138 0.00228
-390.00
-390.00
-390.00
-390.00
-390.00
-264.39
-84.09
96.21
276.52
390.00
305
-0.00609 -0.00516 -0.00423 -1.00893 -0.00238 -0.00145 -0.00052
0.00041
0.00134 0.00226
-390.00
-390.00
-390.00
-390.00
-390.00
-289.67
-104.09
81.48
267.06
390.00
296
-0.00636 -0.00541 -0.00445 -1.03571 -0.00254 -0.00158 -0.00063
0.00033
0.00129 0.00224
-390.00
-390.00
-390.00
-390.00
-390.00
-316.47
-125.30
65.86
257.03
390.00
287
-0.00665 -0.00567 -0.00468 -1.06250 -0.00271 -0.00172 -0.00074
0.00025
0.00123 0.00222
-390.00
-390.00
-390.00
-390.00
-390.00
-344.93
-147.83
49.28
246.38
390.00
279
-0.00696 -0.00594 -0.00493 -1.08929 -0.00289 -0.00188 -0.00086
0.00016
0.00118 0.00219
-390.00
-390.00
-390.00
-390.00
-390.00
-375.21
-171.79
31.62
235.04
390.00
270
-0.00729 -0.00624 -0.00519 -1.11607 -0.00309 -0.00204 -0.00099
0.00006
0.00111 0.00217
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-197.35
12.80
222.96
390.00
261
-0.00764 -0.00656 -0.00547 -1.14286 -0.00330 -0.00221 -0.00112 -0.00004
0.00105 0.00214
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-224.66
-7.31
210.05
390.00
252
-0.00802 -0.00690 -0.00577 -1.16964 -0.00352 -0.00239 -0.00127 -0.00014
0.00098 0.00211
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-253.90
-28.84
196.22
390.00
243
-0.00843 -0.00726 -0.00609 -1.19643 -0.00376 -0.00259 -0.00143 -0.00026
0.00091 0.00207
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-285.29
-51.96
181.37
390.00
234
-0.00886 -0.00765 -0.00644 -1.22321 -0.00402 -0.00281 -0.00160 -0.00038
0.00083 0.00204
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-319.08
-76.84
165.39
390.00
225
-0.00933 -0.00807 -0.00681 -1.25000 -0.00430 -0.00304 -0.00178 -0.00052
0.00074 0.00200
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-355.56
-103.70
148.15
390.00
216
-0.00984 -0.00853 -0.00722 -1.27679 -0.00460 -0.00329 -0.00198 -0.00066
0.00065 0.00196
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-132.78
129.48
390.00
213
-0.01002 -0.00869 -0.00736 -1.28579 -0.00470 -0.00338 -0.00205 -0.00072
0.00061 0.00194
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-143.10
122.85
388.80
210
-0.01021 -0.00886 -0.00751 -1.29479 -0.00481 -0.00347 -0.00212 -0.00077
0.00058 0.00193
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-153.71
116.04
385.79
209.5
-0.01025 -0.00889 -0.00754 -1.29650 -0.00484 -0.00348 -0.00213 -0.00078
0.00057 0.00193
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-390.00
-155.77
114.72
385.20
0.00209 0.00260
-390.00
-288.92
-187.84
-390.00
14.32
115.41
216.49
317.57
390.00
390.00
KONDISI TEKAN AKSIAL KECIL : Pn = 0.1 * fc' * b * h
KONDISI BALANCE 561
-0.00195 -0.00144 -0.00094 -0.24318
0.00007
0.00058
0.00108
0.00159
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Fs1 kN
Fs2 kN
Fs3 kN
Fs4 kN
Fs5
Fs6
Fs7
kN
Fs8 kN
Fs9 kN
Fs10 kN
Cs kN
Ms1
Ms2
Ms3
Ms4 kNmm
Ms5
Ms6
kNmm
kNmm
kN
kN
kNmm
kNmm
kNmm
-2446.19
-489.24
-489.24
-489.24
-245.82
-73.49
98.84
271.17
443.49
2446.19
-973.53
1039629.91
161720.21
115514.43
69308.66
11608.29
-3470.52
-2446.19
-489.24
-489.24
-489.24
-267.91
-91.77
84.37
260.51
436.65
2446.19
-1045.86
1039629.91
161720.21
115514.43
69308.66
12651.46
-4333.65
-2446.19
-489.24
-489.24
-489.24
-291.00
-110.88
69.25
249.38
429.50
2446.19
-1121.46
1039629.91
161720.21
115514.43
69308.66
13741.83
-5235.83
-2446.19
-489.24
-489.24
-489.24
-315.16
-130.87
53.43
237.73
422.02
2446.19
-1200.56
1039629.91
161720.21
115514.43
69308.66
14882.68
-6179.78
-2446.19
-489.24
-489.24
-489.24
-340.47
-151.80
36.86
225.52
414.19
2446.19
-1283.41
1039629.91
161720.21
115514.43
69308.66
16077.60
-7168.47
-2446.19
-489.24
-489.24
-489.24
-367.00
-173.76
19.49
212.73
405.97
2446.19
-1370.28
1039629.91
161720.21
115514.43
69308.66
17330.52
-8205.16
-2446.19
-489.24
-489.24
-489.24
-394.85
-196.80
1.25
199.30
397.35
2446.19
-1461.47
1039629.91
161720.21
115514.43
69308.66
18645.78
-9293.42
-2446.19
-489.24
-489.24
-489.24
-424.13
-221.02
-17.92
185.18
388.28
2446.19
-1557.32
1039629.91
161720.21
115514.43
69308.66
20028.14
-10437.20
-2446.19
-489.24
-489.24
-489.24
-454.93
-246.51
-38.09
170.33
378.74
2446.19
-1658.18
1039629.91
161720.21
115514.43
69308.66
21482.88
-11640.87
-2446.19
-489.24
-489.24
-489.24
-487.39
-273.37
-59.35
154.67
368.69
2446.19
-1764.47
1039629.91
161720.21
115514.43
69308.66
23015.83
-12909.25
-2446.19
-489.24
-489.24
-489.24
-489.24
-301.72
-81.78
138.15
358.09
2446.19
-1844.21
1039629.91
161720.21
115514.43
69308.66
23102.89
-14247.71
-2446.19
-489.24
-489.24
-489.24
-489.24
-331.67
-105.49
120.69
346.88
2446.19
-1926.54
1039629.91
161720.21
115514.43
69308.66
23102.89
-15662.21
-2446.19
-489.24
-489.24
-489.24
-489.24
-363.38
-130.58
102.21
335.01
2446.19
-2013.68
1039629.91
161720.21
115514.43
69308.66
23102.89
-17159.44
-2446.19
-489.24
-489.24
-489.24
-489.24
-396.99
-157.18
82.62
322.43
2446.19
-2106.07
1039629.91
161720.21
115514.43
69308.66
23102.89
-18746.86
-2446.19
-489.24
-489.24
-489.24
-489.24
-432.70
-185.44
61.81
309.07
2446.19
-2204.21
1039629.91
161720.21
115514.43
69308.66
23102.89
-20432.88
-2446.19
-489.24
-489.24
-489.24
-489.24
-470.69
-215.51
39.67
294.85
2446.19
-2308.63
1039629.91
161720.21
115514.43
69308.66
23102.89
-22226.97
-2446.19
-489.24
-489.24
-489.24
-489.24
-489.24
-247.57
16.06
279.69
2446.19
-2398.00
1039629.91
161720.21
115514.43
69308.66
23102.89
-23102.89
-2446.19
-489.24
-489.24
-489.24
-489.24
-489.24
-281.82
-9.16
263.49
2446.19
-2473.68
1039629.91
161720.21
115514.43
69308.66
23102.89
-23102.89
-2446.19
-489.24
-489.24
-489.24
-489.24
-489.24
-318.51
-36.18
246.15
2446.19
-2554.73
1039629.91
161720.21
115514.43
69308.66
23102.89
-23102.89
-2446.19
-489.24
-489.24
-489.24
-489.24
-489.24
-357.89
-65.18
227.52
2446.19
-2641.74
1039629.91
161720.21
115514.43
69308.66
23102.89
-23102.89
-2446.19
-489.24
-489.24
-489.24
-489.24
-489.24
-400.28
-96.40
207.48
2446.19
-2735.38
1039629.91
161720.21
115514.43
69308.66
23102.89
-23102.89
-2446.19
-489.24
-489.24
-489.24
-489.24
-489.24
-446.03
-130.09
185.85
2446.19
-2836.46
1039629.91
161720.21
115514.43
69308.66
23102.89
-23102.89
-2446.19
-489.24
-489.24
-489.24
-489.24
-489.24
-489.24
-166.57
162.42
2446.19
-2939.57
1039629.91
161720.21
115514.43
69308.66
23102.89
-23102.89
-2446.19
-489.24
-489.24
-489.24
-489.24
-489.24
-489.24
-179.51
154.11
2438.68
-2968.33
1039629.91
161720.21
115514.43
69308.66
23102.89
-23102.89
-2446.19
-489.24
-489.24
-489.24
-489.24
-489.24
-489.24
-192.82
145.56
2419.76
-3009.11
1039629.91
161720.21
115514.43
69308.66
23102.89
-23102.89
-2446.19
-489.24
-489.24
-489.24
-489.24
-489.24
-489.24
-195.40
143.91
2416.10
-3017.01
1039629.91
161720.21
115514.43
69308.66
23102.89
-23102.89
-2446.19
-362.44
-235.63
-489.24
17.97
144.77
271.57
398.37
489.24
2446.19
234.62
1039629.91
119805.20
55635.85
69308.66
-848.55
6836.41
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Ms7
Ms8
Ms9
Ms10
Ms
a
Cc
Mc
kNmm
kNmm
kNmm
kNmm
kNmm
mm
kN
kNmm
14001.75
64025.09
146599.52
1039629.91
2658567.26
350.63
5960.63
1935340.43
4987.09
4593.91
0.65
3241.61
11952.48
61509.84
144338.44
1039629.91
2651921.70
343.04
5831.61
1915578.81
4785.75
4567.50
0.65
3110.74
2968.88
9810.48
58880.78
141975.04
1039629.91
2644975.43
335.45
5702.59
1894838.04
4581.13
4539.81
0.65
2977.73
2950.88
7569.32
56130.00
139502.24
1039629.91
2637707.58
327.86
5573.57
1873118.11
4373.01
4510.83
0.65
2842.46
2932.04
5221.94
53248.85
136912.24
1039629.91
2630095.28
320.27
5444.55
1850419.03
4161.14
4480.51
0.65
2704.74
2912.33
2760.61
50227.83
134196.51
1039629.91
2622113.45
312.68
5315.54
1826740.80
3945.26
4448.85
0.65
2564.42
2891.76
176.83
47056.52
131345.66
1039629.91
2613734.51
305.09
5186.52
1802083.41
3725.05
4415.82
0.65
2421.28
2870.28
-2538.78
43723.41
128349.37
1039629.91
2604928.08
297.50
5057.50
1776446.88
3500.18
4381.37
0.65
2275.12
2847.89
-5396.57
40215.79
125196.21
1039629.91
2595660.57
289.91
4928.48
1749831.18
3270.30
4345.49
0.65
2125.70
2824.57
-8408.00
36519.59
121873.51
1039629.91
2585894.82
282.32
4799.46
1722236.34
3035.00
4308.13
0.65
1972.75
2800.29
-11585.81
32619.18
118367.25
1039629.91
2574058.93
274.73
4670.45
1693662.34
2826.24
4267.72
0.65
1837.05
2774.02
-14944.18
28497.15
114661.76
1039629.91
2561458.54
267.14
4541.43
1664109.18
2614.89
4225.57
0.65
1699.68
2746.62
-18498.94
24134.07
110739.58
1039629.91
2548121.29
259.55
4412.41
1633576.88
2398.73
4181.70
0.65
1559.17
2718.10
-22267.84
19508.15
106581.13
1039629.91
2533980.60
251.96
4283.39
1602065.42
2177.32
4136.05
0.65
1415.26
2688.43
-26270.84
14594.91
102164.38
1039629.91
2518961.59
244.38
4154.37
1569574.80
1950.17
4088.54
0.65
1274.90
2672.83
-30530.44
9366.72
97464.51
1039629.91
2502979.83
236.79
4025.36
1536105.04
1716.73
4039.08
0.67
1152.35
2711.22
Pn
Mn
kN
Ф.Pn
Ф
kNm
Ф.Mn
kN
kNm 2986.04
-35072.14
3792.29
92453.39
1039629.91
2486976.68
229.20
3896.34
1501656.12
1498.34
3988.63
0.69
1030.29
2742.68
-39924.90
-2163.95
87099.05
1039629.91
2470813.32
221.61
3767.32
1466228.05
1293.64
3937.04
0.70
909.40
2767.65
-45121.84
-8542.62
81364.96
1039629.91
2453503.63
214.02
3638.30
1429820.82
1083.57
3883.32
0.72
778.80
2791.07
-50700.91
-15390.31
75209.25
1039629.91
2434921.16
206.43
3509.29
1392434.44
867.55
3827.36
0.73
637.59
2812.85
-56705.85
-22760.72
68583.63
1039629.91
2414920.19
198.84
3380.27
1354068.91
644.88
3768.99
0.75
484.72
2832.90
-63187.38
-30716.09
61432.18
1039629.91
2393331.84
191.25
3251.25
1314724.22
414.79
3708.06
0.77
318.93
2851.09
-69308.66
-39328.92
53689.69
1039629.91
2370855.24
183.66
3122.23
1274400.38
182.66
3645.26
0.79
143.63
2866.27
-69308.66
-42384.85
50942.58
1036439.63
2361861.91
181.11
3078.88
1260631.80
110.55
3622.49
0.79
87.52
2867.96
-69308.66
-45528.06
48117.00
1028399.64
2347853.13
178.56
3035.53
1246752.68
26.42
3594.61
0.80
21.08
2868.56
-69308.66
-46136.97
47569.62
1026842.10
2345139.31
178.08
3027.28
1244096.50
10.26
3589.24
0.80
8.20
2868.63
38472.79
94060.61
161720.21
1039629.91
2624251.00
476.52
8100.76
2120311.93
8335.37
4744.56
0.65
1300.00
0.00
1300.00
30000.00
0.00
0.00
5417.99
3083.97
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
ANALISIS KEKUATAN KOLOM BETON BERTULANG DENGAN DIAGRAM INTERAKSI [C]2010 : M. Noer Ilham
KODE KOLOM
K8
INPUT DATA KOLOM
f c' = 20 MPa f y = 390 MPa
Kuat tekan beton, Tegangan leleh baja,
b = 600 mm h = 600 mm ds = 50 mm n = 28 buah D = 22 mm
Lebar kolom, Tinggi kolom, Tebal brutto selimut beton, Jumlah tulangan, Diameter tulangan,
PERHITUNGAN DIAGRAM INTERAKSI Es =
Modulus elastis baja,
2.E+05
MPa
β1 = 0.85
untuk f c' 30 MPa
β1 = 0.85 - 0.008 (f c' - 30)
untuk f c ' > 30 MPa
Faktor distribusi tegangan,
β1 = 0.85
Luas tulangan total,
2
2 As = n * p / 4 * D = 10644 mm
Jarak tulangan,
x = ( h - 2*d s ) /7 = 71.43 mm
Rasio tulangan,
r = As / Ag = 2.96%
Faktor reduksi kekuatan, f = 0.65 untuk P n ≥ 0.1 * f c' * b * h f = 0.80
untuk P n = 0
Untuk : 0
≤
Pn ≤ 0.1 * f c' * b * h
f = 0.65 + 0.15 * ( Pno - Pn ) / Pno
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
6000
5500
5000
4500
4000
3500 ) N k ( n P .
3000
f
2500
2000
1500
b=
600
mm
h=
600
mm
28 f c' =
D
22
20
MPa
f y =
390
MPa
Pu
Mu
(kN)
(kNm)
1091.8
47.2
1250.4
58.3
1164.7
13.3
826.8
59.7
1052.2
74.8
1087.0
77.5
977.0
41.1
761.5
148.3
485.7
106.7
594.0
166.6
1000
500
0 0
50
100
150
200
250
300
350
400
450
500
550
600
650
700
750
800
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
850
900
950
1 000
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
No
Luas masing-masing tulangan 1
As1 = 8/28 * A s = 3041
mm
2
As2 = 2/28 * A s =
mm
760
2 2
3
As3 = 2/28 * A s =
760
mm
4
As4 = 2/28 * A s =
760
mm
5 6 7 8
As5 = 2/28 * A s = As6 = 2/28 * A s = As7 = 2/28 * A s =
760 760 760
As8 = 8/28 * A s = 3041 As = 10644
Pada kondisi tekan aksial sentris (M no = 0) :
Jarak tulangan thd. sisi beton 2
2 2
mm
2
mm
2
mm
2
mm
-3
d1 = 7*x + d s =
550 mm
Pno = 0.80*[ 0.85*f c' *b*h + As*(f y - 0.85*f c')]*10
d2 = 6*x + d s =
479 mm
Pno = 8072 kN
d3 = 5*x + d s =
407 mm
0.1 * f c' * b * h *10 = 720 kN
d4 = 4*x + d s =
336 mm
Pada kondisi balance :
d5 = 3*x + d s =
264 mm
c = cb = 600 / (600 + f y) * d1 =
d6 = 2*x + d s =
193 mm
Regangan pada masing-masing baja tulangan :
d7 =
x + ds =
121 mm
εsi = 0.003 * ( c - d i ) / c
d8 =
ds =
50 mm
-3
333.3 mm
2
mm
Tegangan pada masing-masing baja tulangan : Untuk Untuk
| εsi | < f y / Es | εsi | f y / Es
maka : f si = esi* Es
Gaya-gaya internal pada masing-masing baja tulangan : Resultan gaya internal baja tulangan : Momen akibat gaya internal masing-masing baja tulangan : Momen total akibat gaya internal baja tulangan : Tinggi blok tegangan tekan beton, Gaya internal pada beton tekan : Momen akibat gaya internal tekan beton : Momen nominal : Gaya aksial rencana : Momen rencana :
105
→
Dc = 5.7143
maka : f si =| εsi | / esi* f y
URAIAN PERHITUNGAN
Gaya aksial nominal :
Jumlah interval jarak garis netral =
PERSAMAAN
UNIT -3
Fsi = Asi * f si * 10 -3 Cs = [ S Fsi ]*10 Msi = Fsi*(h/2 - di) Ms = S Msi a = β1 * c -3 Cc = 0.85 * f c' * b * a * 10 Mc = Cc * (h - a) / 2 Pn = Cs + Cc -3 Mn = (Mc + Ms)*10 Pu = f * Pn Mu = f * Mn
kN kN kNmm kNmm mm kN kNmm kN kNm kN kNm
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
6000
5500
5000
4500
4000
3500 ) N k ( n P .
3000
f
2500
2000
1500
1000
500
0 0
50
100
150
200
250
300
350
400
450
500
550
600
650
700
750
800
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
850
900
950
1 000
b=
600
mm
h=
600
mm
28 f c' =
D
22
20
MPa
f y =
390
MPa
Pu
Mu
(kN)
(kNm)
1091.8
47.2
1250.4
58.3
1164.7
13.3
826.8
59.7
1052.2
74.8
1087.0
77.5
977.0
41.1
761.5
148.3
485.7
106.7
594.0
166.6
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
εs6
εs7
εs8
mm KONDISI TEKAN AKSIAL SENTRIS
f s1
f s2
f s3
f s4
f s5
f s6
f s7
f s8
Fs1
Fs2
Fs3
Fs4
Fs5
MPa
MPa
MPa
MPa
MPa
MPa
MPa
MPa
kN
kN
kN
kN
kN
720.0
0.0007
0.0010
0.0013
0.0016
0.0019
0.0022
0.0025
0.0028
141.67
201.19
2 60.71
320.24
379.76
390.00
390.00
390.00
430.8
153.0
198.2
243.5
288.
714.3
0.0007
0.0010
0.0013
0.0016
0.0019
0.0022
0.0025
0.0028
138.00
198.00
2 58.00
318.00
378.00
390.00
390.00
390.00
419.7
150.5
196.1
241.8
287.
708.6
0.0007
0.0010
0.0013
0.0016
0.0019
0.0022
0.0025
0.0028
134.27
194.76
2 55.24
315.73
376.21
390.00
390.00
390.00
408.3
148.1
194.1
240.0
286.
702.9
0.0007
0.0010
0.0013
0.0016
0.0019
0.0022
0.0025
0.0028
130.49
191.46
2 52.44
313.41
374.39
390.00
390.00
390.00
396.8
145.6
191.9
238.3
284.
697.1
0.0006
0.0009
0.0012
0.0016
0.0019
0.0022
0.0025
0.0028
126.64
188.11
2 49.59
311.07
372.54
390.00
390.00
390.00
385.1
143.0
189.8
236.5
283.
691.4
0.0006
0.0009
0.0012
0.0015
0.0019
0.0022
0.0025
0.0028
122.73
184.71
2 46.69
308.68
370.66
390.00
390.00
390.00
373.2
140.4
187.6
234.7
281.
685.7
0.0006
0.0009
0.0012
0.0015
0.0018
0.0022
0.0025
0.0028
118.75
181.25
2 43.75
306.25
368.75
390.00
390.00
390.00
361.1
137.8
185.3
232.8
280.
680.0
0.0006
0.0009
0.0012
0.0015
0.0018
0.0021
0.0025
0.0028
114.71
177.73
2 40.76
303.78
366.81
390.00
390.00
390.00
348.8
135.1
183.0
231.0
278.
674.3
0.0006
0.0009
0.0012
0.0015
0.0018
0.0021
0.0025
0.0028
110.59
174.15
2 37.71
301.27
364.83
390.00
390.00
390.00
336.3
132.4
180.7
229.0
277.
668.6
0.0005
0.0009
0.0012
0.0015
0.0018
0.0021
0.0025
0.0028
106.41
170.51
2 34.62
298.72
362.82
390.00
390.00
390.00
323.6
129.6
178.4
227.1
275.
662.9
0.0005
0.0008
0.0012
0.0015
0.0018
0.0021
0.0025
0.0028
102.16
166.81
2 31.47
296.12
360.78
390.00
390.00
390.00
310.7
126.8
176.0
225.1
274.
657.1
0.0005
0.0008
0.0011
0.0015
0.0018
0.0021
0.0024
0.0028
97.83
163.04
228.26
293.48
358.70
390.00
390.00
390.00
297.5
124.0
173.5
223.1
272.
651.4
0.0005
0.0008
0.0011
0.0015
0.0018
0.0021
0.0024
0.0028
93.42
159.21
225.00
290.79
356.58
390.00
390.00
390.00
284.1
121.0
171.1
221.1
271.
645.7
0.0004
0.0008
0.0011
0.0014
0.0018
0.0021
0.0024
0.0028
88.94
155.31
221.68
288.05
354.42
390.00
390.00
390.00
270.5
118.1
168.5
219.0
269.
640.0
0.0004
0.0008
0.0011
0.0014
0.0018
0.0021
0.0024
0.0028
84.38
151.34
218.30
285.27
352.23
390.00
390.00
390.00
256.6
115.1
166.0
216.9
267.
634.3
0.0004
0.0007
0.0011
0.0014
0.0018
0.0021
0.0024
0.0028
79.73
147.30
214.86
282.43
350.00
390.00
390.00
390.00
242.5
112.0
163.4
214.7
266.
628.6
0.0004
0.0007
0.0011
0.0014
0.0017
0.0021
0.0024
0.0028
75.00
143.18
211.36
279.55
347.73
390.00
390.00
390.00
228.1
108.9
160.7
212.5
264.
622.9
0.0004
0.0007
0.0010
0.0014
0.0017
0.0021
0.0024
0.0028
70.18
138.99
207.80
276.61
345.41
390.00
390.00
390.00
213.4
105.7
158.0
210.3
262.
617.1
0.0003
0.0007
0.0010
0.0014
0.0017
0.0021
0.0024
0.0028
65.28
134.72
204.17
273.61
343.06
390.00
390.00
390.00
198.5
102.4
155.2
208.0
260.
611.4
0.0003
0.0007
0.0010
0.0014
0.0017
0.0021
0.0024
0.0028
60.28
130.37
200.47
270.56
340.65
3 90.00
3 90.00
390.00
183.3
99.1
152.4
205.7
259.
605.7
0.0003
0.0006
0.0010
0.0013
0.0017
0.0020
0.0024
0.0028
55.19
125.94
196.70
267.45
338.21
3 90.00
3 90.00
390.00
167.8
95.8
149.5
203.3
257.
600.0
0.0003
0.0006
0.0010
0.0013
0.0017
0.0020
0.0024
0.0028
50.00
121.43
192.86
264.29
335.71
3 90.00
3 90.00
390.00
152.1
92.3
146.6
200.9
255.
594.3
0.0002
0.0006
0.0009
0.0013
0.0017
0.0020
0.0024
0.0027
44.71
116.83
188.94
261.06
333.17
3 90.00
3 90.00
390.00
136.0
88.8
143.6
198.5
253.
588.6
0.0002
0.0006
0.0009
0.0013
0.0017
0.0020
0.0024
0.0027
39.32
112.14
184.95
257.77
330.58
3 90.00
3 90.00
390.00
119.6
85.3
140.6
196.0
251.
582.9
0.0002
0.0005
0.0009
0.0013
0.0016
0.0020
0.0024
0.0027
33.82
107.35
180.88
254.41
327.94
3 90.00
3 90.00
390.00
102.9
81.6
137.5
193.4
249.
577.1
0.0001
0.0005
0.0009
0.0013
0.0016
0.0020
0.0024
0.0027
28.22
102.48
176.73
250.99
325.25
390.00
390.00
390.00
85.8
77.9
134.4
190.8
247.
571.4
0.0001
0.0005
0.0009
0.0012
0.0016
0.0020
0.0024
0.0027
22.50
97.50
172.50
247.50
322.50
390.00
390.00
390.00
68.4
74.1
131.1
188.2
245.
565.7
0.0001
0.0005
0.0008
0.0012
0.0016
0.0020
0.0024
0.0027
16.67
92.42
168.18
243.94
319.70
390.00
390.00
390.00
50.7
70.3
127.9
185.5
243.
560.0
0.0001
0.0004
0.0008
0.0012
0.0016
0.0020
0.0023
0.0027
10.71
87.24
163.78
240.31
316.84
390.00
390.00
390.00
32.6
66.3
124.5
182.7
240.
554.3
0.0000
0.0004
0.0008
0.0012
0.0016
0.0020
0.0023
0.0027
4.64
81.96
159.28
236.60
313.92
390.00
390.00
390.00
14.1
62.3
121.1
179.9
238.
548.6
0.0000
0.0004
0.0008
0.0012
0.0016
0.0019
0.0023
0.0027
-1.56
76.56
154.69
2 32.81
3 10.94
389.06
390.00
390.00
-4.8
58.2
117.6
177.0
236.
542.9
0.0000
0.0004
0.0008
0.0011
0.0015
0.0019
0.0023
0.0027
-7.89
71.05
150.00
228.95
307.89
386.84
390.00
390.00
-24.0
54.0
114.0
174.1
234.
537.1
-0.0001
0.0003
0.0007
0.0011
0.0015
0.0019
0.0023
0.0027
-14.36
65.43
145.21
225.00
304.79
3 84.57
3 90.00
390.00
-43.7
49.7
110.4
171.1
231.
531.4
-0.0001
0.0003
0.0007
0.0011
0.0015
0.0019
0.0023
0.0027
-20.97
59.68
140.32
220.97
301.61
3 82.26
3 90.00
390.00
-63.8
45.4
106.7
168.0
229.
525.7
-0.0001
0.0003
0.0007
0.0011
0.0015
0.0019
0.0023
0.0027
-27.72
53.80
135.33
216.85
298.37
3 79.89
3 90.00
390.00
-84.3
40.9
102.9
164.9
226.
520.0
-0.0002
0.0002
0.0007
0.0011
0.0015
0.0019
0.0023
0.0027
-34.62
47.80
130.22
212.64
295.05
3 77.47
3 90.00
390.00
-105.3
36.3
99.0
161.7
224.
514.3
-0.0002
0.0002
0.0006
0.0010
0.0015
0.0019
0.0023
0.0027
-41.67
41.67
125.00
208.33
291.67
3 75.00
3 90.00
390.00
-126.7
31.7
95.0
158.4
221.
508.6
-0.0002
0.0002
0.0006
0.0010
0.0014
0.0019
0.0023
0.0027
-48.88
35.39
119.66
203.93
288.20
3 72.47
3 90.00
390.00
-148.6
26.9
91.0
155.0
219.
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Fs6
Fs7
Fs8
Cs
Ms1
Ms2
Ms3
Ms4
Ms5
Ms6
Ms7
Ms8
Ms
a
Cc
Mc
kN
kN
kN
kN
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
mm
kN
kNmm
Pn kN 8072.08
Mn
Ф
kNm 0.00
Ф.Pn kN
0.65
5246.86
Ф.Mn kNm 0.0
296.5
296.5 1186.0
3093.2 -107704.3
-27314.0 -21237.0
-8695.2
10311.4
31768.2
52947.1 296503.5
226579.8 612.00
6242.4
-37454.4
8072.08
189.13
0.65
5246.86
122.9
296.5
296.5 1186.0
3074.5 -104916.6
-26880.8 -21015.9
-8634.4
10263.6
31768.2
52947.1 296503.5
230034.6 607.14
6192.9
-22117.3
8072.08
207.92
0.65
5246.86
135.1
296.5
296.5 1186.0
3055.5 -102084.0
-26440.7 -20791.2
-8572.7
10215.0
31768.2
52947.1 296503.5
233545.1 602.29
6143.3
-7020.9
8072.08
226.52
0.65
5246.86
147.2
296.5
296.5 1186.0
3036.2 -99205.4 -25993.4 -20562.9
-8509.9
10165.6
31768.2
52947.1 296503.5
237112.7 597.43
6093.8
7834.8
8072.08
244.95
0.65
5246.86
159.2
296.5
296.5 1186.0
3016.6 -96279.5
-25538.8 -20330.9
-8446.2
10115.4
31768.2
52947.1 296503.5
240738.8 592.57
6044.2
22450.0
8072.08
263.19
0.65
5246.86
171.0
296.5
296.5 1186.0
2996.7 -93305.3
-25076.6 -20095.0
-8381.3
10064.3
31768.2
52947.1 296503.5
244424.9 587.71
5994.7
36824.5
8072.08
281.25
0.65
5246.86
182.81
296.5
296.5 1186.0
2976.4 -90281.5
-24606.8 -19855.1
-8315.4
10012.4
31768.2
52947.1 296503.5
248172.4 582.86
5945.1
50958.4
8072.08
299.13
0.65
5246.86
194.4
296.5
296.5 1186.0
2955.8 -87206.9 -24129.1 -19611.3
-8248.4
9959.7
31768.2
52947.1 296503.5
251982.8 578.00
5895.6
64851.6
8072.08
316.83
0.65
5246.86
205.9
296.5
296.5 1186.0
2934.9 -84080.2 -23643.2 -19363.3
-8180.2
9906.0
31768.2
52947.1 296503.5
255857.8 573.14
5846.1
78504.2
8072.08
334.36
0.65
5246.86
217.3
296.5
296.5 1186.0
2913.6 -80900.0 -23149.1 -19111.1
-8110.9
9851.4
31768.2
52947.1 296503.5
259799.1 568.29
5796.5
91916.2
8072.08
351.72
0.65
5246.86
228.61
296.5
296.5 1186.0
2891.9 -77665.0
-22646.5 -18854.5
-8040.4
9795.9
31768.2
52947.1 296503.5
263808.4 563.43
5747.0
105087.5
8072.08
368.90
0.65
5246.86
239.7
296.5
296.5 1186.0
2869.8 -74373.8
-22135.1 -18593.4
-7968.6
9739.4
31768.2
52947.1 296503.5
267887.3 558.57
5697.4
118018.2
8072.08
385.91
0.65
5246.86
250.8
296.5
296.5 1186.0
2847.4 -71024.8
-21614.7 -18327.8
-7895.6
9682.0
31768.2
52947.1 296503.5
272037.8 553.71
5647.9
130708.2
8072.08
402.75
0.65
5246.86
261.7
296.5
296.5 1186.0
2824.6 -67616.5
-21085.1 -18057.5
-7821.3
9623.5
31768.2
52947.1 296503.5
276261.8 548.86
5598.3
143157.6
8072.08
419.42
0.65
5246.86
272.6
296.5
296.5 1186.0
2801.3 -64147.4
-20546.1 -17782.4
-7745.7
9563.9
31768.2
52947.1 296503.5
280561.2 544.00
5548.8
155366.4
8072.08
435.93
0.65
5246.86
283.3
296.5
296.5 1186.0
2777.6 -60615.8
-19997.3 -17502.2
-7668.7
9503.3
31768.2
52947.1 296503.5
284938.1 539.14
5499.3
167334.5
8072.08
452.27
0.65
5246.86
293.9
296.5
296.5 1186.0
2753.5 -57019.9
-19438.6 -17217.0
-7590.3
9441.6
31768.2
52947.1 296503.5
289394.5 534.29
5449.7
179062.0
8072.08
468.46
0.65
5246.86
304.5
296.5
296.5 1186.0
2729.0 -53358.1
-18869.6 -16926.6
-7510.5
9378.8
31768.2
52947.1 296503.5
293932.8 529.43
5400.2
190548.9
8072.08
484.48
0.65
5246.86
314.91
296.5
296.5 1186.0
2704.0 -49628.4
-18290.1 -16630.8
-7429.2
9314.8
31768.2
52947.1 296503.5
298555.0 524.57
5350.6
201795.1
8054.64
500.35
0.65
5235.52
325.2
296.5
296.5 1186.0
2678.6 -45829.1
-17699.8 -16329.5
-7346.4
9249.6
31768.2
52947.1 296503.5
303263.7 519.71
5301.1
212800.7
7979.64
516.06
0.65
5186.76
335.4
296.5
296.5 1186.0
2652.6 -41958.0
-17098.3 -16022.4
-7262.0
9183.1
31768.2
52947.1 296503.5
308061.2 514.86
5251.5
223565.7
7904.15
531.63
0.65
5137.70
345.5
296.5
296.5 1186.0
2626.2 -38013.3
-16485.3 -15709.6
-7176.0
9115.4
31768.2
52947.1 296503.5
312950.1 510.00
5202.0
234090.0
7828.17
547.04
0.65
5088.31
355.5
296.5
296.5 1186.0
2599.2 -33992.6
-15860.6 -15390.7
-7088.3
9046.4
31768.2
52947.1 296503.5
317933.0 505.14
5152.5
244373.7
7751.69
562.31
0.65
5038.60
365.5
296.5
296.5 1186.0
2571.8 -29893.9
-15223.8 -15065.6
-6999.0
8976.1
31768.2
52947.1 296503.5
323012.6 500.29
5102.9
254416.7
7674.68
577.43
0.65
4988.54
375.3
296.5
296.5 1186.0
2543.8 -25714.9
-14574.4 -14734.1
-6907.9
8904.4
31768.2
52947.1 296503.5
328191.9 495.43
5053.4
264219.1
7597.13
592.41
0.65
4938.13
385.0
296.5
296.5 1186.0
2515.2 -21453.0
-13912.2 -14396.1
-6815.0
8831.2
31768.2
52947.1 296503.5
333473.7 490.57
5003.8
273780.9
7519.03
607.25
0.65
4887.37
394.7
296.5
296.5 1186.0
2486.1 -17106.0
-13236.8 -14051.3
-6720.2
8756.6
31768.2
52947.1 296503.5
338861.2 485.71
4954.3
283102.0
7440.35
621.96
0.65
4836.23
404.2
296.5
296.5 1186.0
2456.3 -12671.1
-12547.7 -13699.6
-6623.5
8680.5
31768.2
52947.1 296503.5
344357.5 480.86
4904.7
292182.5
7361.09
636.54
0.65
4784.71
413.7
296.5
296.5 1186.0
2426.0
-8145.7
-11844.5 -13340.7
-6524.9
8602.9
31768.2
52947.1 296503.5
349965.9 476.00
4855.2
301022.4
7281.22
650.99
0.65
4732.79
423.1
296.5
296.5 1186.0
2395.1
-3527.0
-11126.9 -12974.3
-6424.2
8523.6
31768.2
52947.1 296503.5
355690.0 471.14
4805.7
309621.6
7200.73
665.31
0.65
4680.47
432.4
295.8
296.5 1186.0
2362.8
1187.9
-10394.3 -12600.4
-6321.4
8442.7
31691.9
52947.1 296503.5 361457.0 466.29
4756.1
317980.2
7118.88
679.44
0.65
4627.27
441.6
294.1
296.5 1186.0
2328.8
6002.1
-9646.2 -12218.6
-6216.5
8360.1
31511.0
52947.1 296503.5 367242.5 461.43
4706.6
326098.2
7035.38
693.34
0.65
4573.00
450.6
292.4
296.5 1186.0
2294.1
10918.7
-8882.3
-11828.6
-6109.3
8275.7
31326.3
52947.1 296503.5
373151.1 456.57
4657.0
333975.5
6951.17
707.13
0.65
4518.26
459.6
290.6
296.5 1186.0
2258.7
15941.0
-8101.9
-11430.3
-5999.8
8189.5
31137.6
52947.1 296503.5
379186.8 451.71
4607.5
341612.2
6866.21
720.80
0.65
4463.04
468.5
288.8
296.5 1186.0
2222.5
21072.6
-7304.6
-11023.3
-5887.9
8101.4
30944.8
52947.1 296503.5
385353.6 446.86
4557.9
349008.2
6780.48
734.36
0.65
4407.31
477.3
287.0
296.5 1186.0
2185.6
26316.9
-6489.7
-10607.3
-5773.6
8011.4
30747.8
52947.1 296503.5
391656.0 442.00
4508.4
356163.6
6693.95
747.82
0.65
4351.07
486.0
285.1
296.5 1186.0
2147.7
31677.7
-5656.7
-10182.1
-5656.7
7919.4
30546.4
52947.1 296503.5
398098.5 437.14
4458.9
363078.4
6606.61
761.18
0.65
4294.29
494.7
283.2
296.5 1186.0
2109.1
37159.0
-4805.0
-9747.4
-5537.2
7825.4
30340.4
52947.1 296503.5 404685.7 432.29
4409.3
369752.5
6518.41
774.44
0.65
4236.97
503.3
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
εs6
εs7
εs8
mm
f s1
f s2
f s3
f s4
f s5
f s6
f s7
f s8
Fs1
Fs2
Fs3
kN
kN
Fs4
Fs5
MPa
MPa
MPa
MPa
MPa
MPa
MPa
MPa
kN
kN
kN
502.9
-0.0003
0.0001
0.0006
0.0010
0.0014
0.0018
0.0023
0.0027
-56.25
28.98
114.20
199.43
284.66
3 69.89
3 90.00
390.00
-171.1
22.0
86.8
151.6
216.
497.1
-0.0003
0.0001
0.0005
0.0010
0.0014
0.0018
0.0023
0.0027
-63.79
22.41
108.62
194.83
281.03
3 67.24
3 90.00
390.00
-194.0
17.0
82.6
148.1
213.
491.4
-0.0004
0.0001
0.0005
0.0010
0.0014
0.0018
0.0023
0.0027
-71.51
15.70
102.91
190.12
277.33
3 64.53
3 90.00
390.00
-217.5
11.9
78.2
144.5
210.
485.7
-0.0004
0.0000
0.0005
0.0009
0.0014
0.0018
0.0023
0.0027
-79.41
8.82
97.06
185.29
273.53
361.76
390.00
390.00
-241.5
6.7
73.8
140.9
208.
480.0
-0.0004
0.0000
0.0005
0.0009
0.0013
0.0018
0.0022
0.0027
-87.50
1.79
91.07
180.36
269.64
358.93
390.00
390.00
-266.1
1.4
69.2
137.1
205.
474.3
-0.0005
0.0000
0.0004
0.0009
0.0013
0.0018
0.0022
0.0027
-95.78
-5.42
84.94
175.30
265.66
356.02
390.00
390.00
-291.3
-4.1
64.6
133.3
202.
468.6
-0.0005
-0.0001
0.0004
0.0009
0.0013
0.0018
0.0022
0.0027 -104.27
-12.80
78.66
170.12
261.59
353.05
390.00
390.00
-317.1
-9.7
59.8
129.3
198.
462.9
-0.0006
-0.0001
0.0004
0.0008
0.0013
0.0018
0.0022
0.0027 -112.96
-20.37
72.22
164.81
257.41
350.00
390.00
390.00
-343.5
-15.5
54.9
125.3
195.
457.1
-0.0006
-0.0001
0.0003
0.0008
0.0013
0.0017
0.0022
0.0027 -121.87
-28.12
65.63
159.38
253.13
346.88
390.00
390.00
-370.6
-21.4
49.9
121.2
192.
451.4
-0.0007
-0.0002
0.0003
0.0008
0.0012
0.0017
0.0022
0.0027 -131.01
-36.08
58.86
153.80
248.73
343.67
390.00
390.00
-398.4
-27.4
44.7
116.9
189.
445.7
-0.0007
-0.0002
0.0003
0.0007
0.0012
0.0017
0.0022
0.0027 -140.38
-44.23
51.92
148.08
244.23
340.38
390.00
390.00
-426.9
-33.6
39.5
112.6
185.
440.0
-0.0007
-0.0003
0.0002
0.0007
0.0012
0.0017
0.0022
0.0027 -150.00
-52.60
44.81
142.21
239.61
337.01
390.00
390.00
-456.2
-40.0
34.1
108.1
182.
434.3
-0.0008
-0.0003
0.0002
0.0007
0.0012
0.0017
0.0022
0.0027 -159.87
-61.18
37.50
136.18
234.87
333.55
390.00
390.00
-486.2
-46.5
28.5
103.5
178.
428.6
-0.0008
-0.0003
0.0002
0.0007
0.0012
0.0017
0.0022
0.0027 -170.00
-70.00
30.00
130.00
230.00
330.00
390.00
390.00
-517.0
-53.2
22.8
98.8
174.
422.9
-0.0009
-0.0004
0.0001
0.0006
0.0011
0.0016
0.0021
0.0026 -180.41
-79.05
22.30
123.65
225.00
326.35
390.00
390.00
-548.6
-60.1
17.0
94.0
171.
417.1
-0.0010
-0.0004
0.0001
0.0006
0.0011
0.0016
0.0021
0.0026 -191.10
-88.36
14.38
117.12
219.86
322.60
390.00
390.00
-581.1
-67.2
10.9
89.0
167.
411.4
-0.0010
-0.0005
0.0000
0.0006
0.0011
0.0016
0.0021
0.0026 -202.08
-97.92
6.25
110.42
214.58
318.75
390.00
390.00
-614.5
-74.4
4.8
83.9
163.
405.7
-0.0011
-0.0005
0.0000
0.0005
0.0010
0.0016
0.0021
0.0026 -213.38
-107.75
-2.11
103.52
209.15
314.79
390.00
390.00
-648.9
-81.9
-1.6
78.7
159.
400.0
-0.0011
-0.0006
-0.0001
0.0005
0.0010
0.0016
0.0021
0.0026 -225.00
-117.86
-10.71
96.43
203.57
310.71
390.00
390.00
-684.2
-89.6
-8.1
73.3
154.
394.3
-0.0012
-0.0006
-0.0001
0.0004
0.0010
0.0015
0.0021
0.0026 -236.96
-128.26
-19.57
89.13
197.83
3 06.52
3 90.00
390.00
-720.6
-97.5
-14.9
67.8
150.
388.6
-0.0012
-0.0007
-0.0001
0.0004
0.0010
0.0015
0.0021
0.0026 -249.26
-138.97
-28.68
81.62
191.91
302.21
390.00
390.00
-758.0
-105.7
-21.8
62.1
145.
382.9
-0.0013
-0.0007
-0.0002
0.0004
0.0009
0.0015
0.0020
0.0026 -261.94
-150.00
-38.06
73.88
185.82
297.76
390.00
390.00
-796.6
-114.0
-28.9
56.2
141.
377.1
-0.0014
-0.0008
-0.0002
0.0003
0.0009
0.0015
0.0020
0.0026 -275.00
-161.36
-47.73
65.91
179.55
293.18
390.00
390.00
-836.3
-122.7
-36.3
50.1
136.
371.4
-0.0014
-0.0009
-0.0003
0.0003
0.0009
0.0014
0.0020
0.0026 -288.46
-173.08
-57.69
57.69
173.08
288.46
390.00
390.00
-877.2
-131.6
-43.9
43.9
131.
365.7
-0.0015
-0.0009
-0.0003
0.0002
0.0008
0.0014
0.0020
0.0026 -302.34
-185.16
-67.97
49.22
166.41
283.59
390.00
390.00
-919.4
-140.8
-51.7
37.4
126.
360.0
-0.0016
-0.0010
-0.0004
0.0002
0.0008
0.0014
0.0020
0.0026 -316.67
-197.62
-78.57
40.48
159.52
278.57
390.00
390.00
-963.0
-150.2
-59.7
30.8
121.
354.3
-0.0017
- 0.0011
-0.0004
0.0002
0.0008
0.0014
0.0020
0.0026
-331.45
- 210.48
-89.52
31.45
152.42
273.39
390.00
390.00
-1008.0
-160.0
-68.1
23.9
115.
348.6
-0.0017
- 0.0011
-0.0005
0.0001
0.0007
0.0013
0.0020
0.0026
-346.72
- 223.77 -100.82
22.13
145.08
268.03
390.00
390.00
-1054.4
-170.1
-76.6
16.8
110.
342.9
-0.0018
- 0.0012
-0.0006
0.0001
0.0007
0.0013
0.0019
0.0026
-362.50
- 237.50 -112.50
12.50
137.50
262.50
387.50
390.00
-1102.4
-180.6
-85.5
9.5
104.
337.1
-0.0019
-0.0013
-0.0006
0.0000
0.0006
0.0013
0.0019
0.0026 -378.81
-251.69 -124.58
2.54
129.66
2 56.78
3 83.90
390.00 -1152.0
-191.4
-94.7
1.9
98.
331.4
-0.0020
- 0.0013
-0.0007
0.0000
0.0006
0.0013
0.0019
0.0025
-390.00
- 266.38 -137.07
-7.76
121.55
250.86
380.17
390.00
-1186.0
-202.5
-104.2
-5.9
92.
325.7
-0.0021
-0.0014
-0.0007
-0.0001
0.0006
0.0012
0.0019
0.0025
-390.00
-281.58 -150.00
-18.42
113.16
244.74
376.32
390.00 -1186.0
-214.1
-114.0
-14.0
86.
320.0
-0.0022
-0.0015
-0.0008
-0.0001
0.0005
0.0012
0.0019
0.0025
-390.00
-297.32 -163.39
-29.46
104.46
238.39
372.32
390.00 -1186.0
-226.0
-124.2
-22.4
79.
314.3
-0.0022
- 0.0016
-0.0009
-0.0002
0.0005
0.0012
0.0018
0.0025
-390.00
- 313.64 -177.27
-40.91
95.45
231.82
368.18
390.00
-1186.0
-238.4
-134.8
-31.1
72.
308.6
-0.0023
- 0.0017
-0.0010
-0.0003
0.0004
0.0011
0.0018
0.0025
-390.00
- 330.56 -191.67
-52.78
86.11
225.00
363.89
390.00
-1186.0
-251.3
-145.7
-40.1
65.
302.9
-0.0024
- 0.0017
-0.0010
-0.0003
0.0004
0.0011
0.0018
0.0025
-390.00
- 348.11 -206.60
-65.09
76.42
217.92
359.43
390.00
-1186.0
-264.7
-157.1
-49.5
58.
297.1
-0.0026
- 0.0018
-0.0011
-0.0004
0.0003
0.0011
0.0018
0.0025
-390.00
- 366.35 -222.12
-77.88
66.35
210.58
354.81
390.00
-1186.0
-278.5
-168.9
-59.2
50.
291.4
-0.0027
- 0.0019
-0.0012
-0.0005
0.0003
0.0010
0.0018
0.0025
-390.00
- 385.29 -238.24
-91.18
55.88
202.94
350.00
390.00
-1186.0
-292.9
-181.1
-69.3
42.
285.7
-0.0028
-0.0020
-0.0013
-0.0005
0.0002
0.0010
0.0017
0.0025
-390.00
-390.00 -255.00 -105.00
45.00
195.00
345.00
390.00 -1186.0
-296.5
-193.9
-79.8
34.
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Fs6
Fs7
Fs8
Cs
Ms1
Ms2
Ms3
Ms4
Ms5
kN
kN
kN
281.2
296.5 1186.0
2069.6
Ms7
Ms8
Ms
a
kNmm
kNmm
kNmm
kNmm
kNmm
42764.9
-3934.0
-9302.8
-5415.0
7729.2
kNmm
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
30129.8
52947.1 296503.5 411422.7 427.43
4359.8
376186.0
6429.33
787.61
0.65
4179.07
511.9
279.2
296.5 1186.0
2029.1
277.1
296.5 1186.0
1987.7
48499.7
-3042.9
-8847.9
-5290.0
7630.7
54367.8
-2131.1
-8382.5
-5162.1
7530.0
29914.4
52947.1 296503.5 418314.5 422.57
4310.2
382378.8
6339.35
800.69
0.65
4120.58
520.4
29693.9
52947.1 296503.5 425366.6 417.71
4260.7
388331.1
6248.43
813.70
0.65
4061.48
275.0
296.5 1186.0
1945.4
60374.0
-1197.9
-7906.1
-5031.2
528.9
7427.0
29468.3
52947.1 296503.5 432584.6 412.86
4211.1
394042.7
6156.53
826.63
0.65
4001.74
272.9
296.5 1186.0
1902.0
66523.2
-242.4
-7418.4
537.31
-4897.1
7321.4
29237.2
52947.1 296503.5 439974.5 408.00
4161.6
399513.6
6063.62
839.49
0.65
3941.35
270.7
296.5 1186.0
1857.6
72820.6
736.1
545.6
-6918.9
-4759.8
7213.4
29000.7
52947.1 296503.5
447542.5 403.14
4112.1
404743.9
5969.67
852.29
0.65
3880.29
553.9
268.4
296.5 1186.0
1812.1
79271.6
266.1
296.5 1186.0
1765.5
85881.8
1738.4
-6407.3
-4619.2
7102.7
28758.3
52947.1 296503.5 455295.0 398.29
4062.5
409733.6
5874.63
865.03
0.65
3818.51
562.2
2765.5
-5883.0
-4475.1
6989.2
28510.0
52947.1 296503.5 463239.0 393.43
4013.0
414482.6
5778.48
877.72
0.65
3756.01
263.7
296.5 1186.0
1717.7
570.5
92657.3
3818.3
-5345.6
-4327.4
6872.9
28255.4
52947.1 296503.5 471381.5 388.57
3963.4
418991.0
5681.15
890.37
0.65
3692.75
261.3
296.5 1186.0
1668.7
578.7
99604.4
4897.7
-4794.6
-4176.0
6753.7
27994.4
52947.1 296503.5 479730.2 383.71
3913.9
423258.8
5582.62
902.99
0.65
3628.70
258.8
586.9
296.5 1186.0
1618.5 106729.6
6004.8
-4229.5
-4020.6
6631.4
27726.7
52947.1 296503.5 488293.0 378.86
3864.3
427285.9
5482.83
915.58
0.65
3563.84
595.1
256.2
296.5 1186.0
1566.9 114039.8
7140.7
-3649.7
-3861.3
6506.0
27452.1
52947.1 296503.5 497078.2 374.00
3814.8
431072.4
5381.74
928.15
0.65
3498.13
603.3
253.6
296.5 1186.0
1514.0 121542.4
8306.5
-3054.6
-3697.7
6377.2
27170.2
52947.1 296503.5 506094.5 369.14
3765.3
434618.3
5279.29
940.71
0.65
3431.54
611.4
250.9
296.5 1186.0
1459.7 129245.1
9503.3
-2443.7
-3529.8
6245.0
26880.8
52947.1 296503.5 515351.3 364.29
3715.7
437923.5
5175.42
953.27
0.65
3364.03
619.6
248.1
296.5 1186.0
1403.9 137156.0
10732.5
-1816.3
-3357.3
6109.3
26583.6
52947.1 296503.5
524858.3 359.43
3666.2
440988.0
5070.09
965.85
0.65
3295.56
627.8
245.3
296.5 1186.0
1346.6 145283.6
11995.4
-1171.6
-3180.2
5969.8
26278.3
52947.1 296503.5
534625.8 354.57
3616.6
443812.0
4963.24
978.44
0.65
3226.10
635.9
242.3
296.5 1186.0
1287.7 153637.0
13293.3
-509.1
-2998.1
5826.4
25964.4
52947.1 296503.5 544664.6 349.71
3567.1
446395.3
4854.79
991.06
0.65
3155.61
644.1
239.3
296.5 1186.0
1227.1 162225.6
14627.8
172.1
-2810.8
5679.0
25641.7
52947.1 296503.5 554986.1 344.86
3517.5
448738.0
4744.68
1003.72
0.65
3084.04
652.4
236.2
296.5 1186.0
1164.8 171059.7
16000.5
872.8
-2618.3
5527.4
25309.9
52947.1 296503.5 565602.6 340.00
3468.0
450840.0
4632.84
1016.44
0.65
3011.34
660.6
233.0
296.5 1186.0
1100.7 180149.9
17412.9
1593.7
-2420.1
5371.4
24968.3
52947.1 296503.5
576526.7 335.14
3418.5
452701.4
4519.19
1029.23
0.65
2937.47
669.0
229.8
296.5 1186.0
1034.7 189507.3
18866.9
2335.9
-2216.1
5210.9
24616.8
52947.1 296503.5
587772.2 330.29
3368.9
454322.2
4403.66
1042.09
0.65
2862.38
677.3
226.4
296.5 1186.0
966.8 199144.2
20364.3
3100.2
-2006.0
5045.5
24254.7
52947.1 296503.5 599353.4 325.43
3319.4
455702.3
4286.16
1055.06
0.65
2786.00
685.7
222.9
296.5 1186.0
896.8 209073.0
21907.0
3887.7
-1789.6
4875.1
23881.7
52947.1 296503.5 611285.5 320.57
3269.8
456841.8
4166.60
1068.13
0.65
2708.29
694.2
219.3
296.5 1186.0
824.6 219307.3
23497.2
4699.4
-1566.5
4699.4
23497.2
52947.1 296503.5 623584.7 315.71
3220.3
457740.6
4044.88
1081.33
0.65
2629.17
702.8
215.6
296.5 1186.0
750.2 229861.5
25137.1
5536.5
-1336.4
4518.3
23100.7
52947.1 296503.5 636268.3 310.86
3170.7
458398.8
3920.91
1094.67
0.65
2548.59
711.5
211.8
296.5 1186.0
673.4 240750.7
26829.1
6400.2
-1099.0
4331.4
22691.6
52947.1 296503.5 649354.6 306.00
3121.2
458816.4
3794.58
1108.17
0.65
2466.48
720.31
207.8
296.5 1186.0
594.1 251991.2
28575.6
7291.7
-854.0
4138.5
22269.3
52947.1 296503.5 662863.0 301.14
3071.7
458993.3
3665.77
1121.86
0.65
2382.75
729.21
203.8
296.5 1186.0
512.2 263600.2
30379.5
8212.5
-600.9
3939.3
21833.1
52947.1 296503.5 676814.3 296.29
3022.1
458929.6
3534.36
1135.74
0.65
2297.33
738.2
199.6
294.6 1186.0
425.7 275596.2
32243.4
9163.9
-339.4
3733.4
21382.5
52607.7 296503.5 690891.2 291.43
2972.6
458625.3
3398.32
1149.52
0.65
2208.91
747.1
195.2
291.9 1186.0
335.5 287998.9
34170.5
10147.6
-69.0
3520.6
20916.5
52118.7 296503.5 705307.3 286.57
2923.0
458080.3
3258.58
1163.39
0.65
2118.07
756.2
190.7
289.0 1186.0
259.5 296503.5
36164.1
11165.2
210.7
3300.4
20434.5
51612.8 296503.5 715894.8 281.71
2873.5
457294.7
3133.02
1173.19
0.65
2036.47
762.5
186.1
286.1 1186.0
216.1 296503.5
38227.6
12218.6
500.2
3072.5
19935.5
51089.3 296503.5 718050.7 276.86
2823.9
456268.5
3040.02
1174.32
0.65
1976.01
763.31
181.2
283.1 1186.0
171.1 296503.5
40364.9
13309.5
800.0
2836.4
19418.8
50547.0 296503.5 720283.6 272.00
2774.4
455001.6
2945.46
1175.29
0.65
1914.55
763.9
176.2
279.9 1186.0
124.4 296503.5
42579.8
14440.1
1110.8
2591.8
18883.2
49985.0 296503.5
722597.7 267.14
2724.9
453494.1
2849.26
1176.09
0.65
1852.02
764.4
171.1
276.7 1186.0
76.0 296503.5
44876.8
15612.6
1433.0
2338.1
18327.8
49402.2 296503.5 724997.6 262.29
2675.3
451745.9
2751.34
1176.74
0.65
1788.37
764.8
165.7
273.3 1186.0
25.8 296503.5
47260.4
16829.3
1767.5
2074.8
17751.5
48797.4 296503.5 727487.9 257.43
2625.8
449757.1
2651.59
1177.25
0.65
1723.53
765.21
160.1
269.7 1186.0
-26.3 296503.5
49735.8
18092.9
2114.7
1801.5
17153.0
48169.3 296503.5 730074.1 252.57
2576.2
447527.7
2549.91
1177.60
0.65
1657.44
765.4
154.3
266.1 1186.0
-80.5 296503.5
52308.2
19405.9
2475.7
1517.3
16531.0
47516.6 296503.5 732761.7 247.71
2526.7
445057.6
2446.19
1177.82
0.65
1590.02
765.5
148.3
262.3 1186.0
-125.4 296503.5
52947.1
20771.5
2851.0
1221.9
15884.1
46837.8 296503.5
2477.1
442346.9
2351.70
1175.87
0.65
1528.60
764.31
kN
Ms6
733520.4 242.86
Cc
Mc
Pn
Mn
Ф
kNm
Ф.Pn kN
Ф.Mn kNm
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
εs6
εs7
εs8
mm
f s1 MPa
f s2
f s3
MPa
MPa
f s4
f s5
MPa
MPa
f s6
f s7
f s8
Fs1
Fs2
Fs3
Fs4
Fs5
kN
kN
MPa
MPa
MPa
kN
kN
kN
280.0
-0.0029
-0.0021
-0.0014
-0.0006
0.0002
0.0009
0.0017
0.0025
-390.00
-390.00 -272.45
-119.39
33.67
186.73
339.80
390.00
-1186.0
-296.5
-207.1
-90.8
25.
274.3
-0.0030
-0.0022
-0.0015
-0.0007
0.0001
0.0009
0.0017
0.0025
-390.00
-390.00 -290.62
-134.37
21.88
178.13
334.38
390.00
-1186.0
-296.5
-221.0
-102.2
16.
268.6
-0.0031
-0.0023
-0.0015
-0.0007
0.0000
0.0008
0.0016
0.0024
-390.00
- 390.00 -309.57
-150.00
9.57
169.15
328.72
390.00
-1186.0
-296.5
-235.4
-114.0
7.
262.9
-0.0033
-0.0025
-0.0016
-0.0008
0.0000
0.0008
0.0016
0.0024
-390.00
-390.00 -329.35
-166.30
-3.26
159.78
322.83
390.00
-1186.0
-296.5
-250.4
-126.4
-2.
257.1
-0.0034
-0.0026
-0.0017
-0.0009
-0.0001
0.0008
0.0016
0.0024 -390.00 -390.00 -350.00 -183.33
-16.67
150.00
316.67
390.00 -1186.0
-296.5
-266.1
-139.4
-12.
251.4
-0.0036
-0.0027
-0.0019
-0.0010
-0.0002
0.0007
0.0016
0.0024 -390.00 -390.00 -371.59 -201.14
-30.68
139.77
310.23
390.00 -1186.0
-296.5
-282.5
-152.9
-23.
245.7
-0.0037
-0.0028
-0.0020
-0.0011
-0.0002
0.0006
0.0015
0.0024 -390.00 -390.00 -390.00 -219.77
-45.35
129.07
303.49
390.00 -1186.0
-296.5
-296.5
-167.1
-34.
240.0
-0.0039
-0.0030
-0.0021
-0.0012
-0.0003
0.0006
0.0015
0.0024 -390.00 -390.00 -390.00 -239.29
-60.71
117.86
296.43
390.00 -1186.0
-296.5
-296.5
-181.9
-46.
234.3
-0.0040
-0.0031
-0.0022
-0.0013
-0.0004
0.0005
0.0014
0.0024 -390.00 -390.00 -390.00 -259.76
-76.83
106.10
289.02
390.00 -1186.0
-296.5
-296.5
-197.5
-58.
228.6
-0.0042
-0.0033
-0.0023
-0.0014
-0.0005
0.0005
0.0014
0.0023
-93.75
93.75
281.25
390.00
-1186.0
-296.5
-296.5
-213.8
-71.
222.9
-0.0044
-0.0034
-0.0025
-0.0015
-0.0006
0.0004
0.0014
0.0023 -390.00 -390.00 -390.00 -303.85 -111.54
80.77
273.08
390.00 -1186.0
-296.5
-296.5
-231.0
-84.
217.1
-0.0046
-0.0036
-0.0026
-0.0016
-0.0007
0.0003
0.0013
0.0023 -390.00 -390.00 -390.00 -327.63 -130.26
67.11
264.47
390.00 -1186.0
-296.5
-296.5
-249.1
-99.
211.4
-0.0048
-0.0038
-0.0028
-0.0018
-0.0007
0.0003
0.0013
0.0023 -390.00 -390.00 -390.00 -352.70 -150.00
52.70
255.41
390.00 -1186.0
-296.5
-296.5
-268.1
-114.
205.7
-0.0050
-0.0040
-0.0029
-0.0019
-0.0009
0.0002
0.0012
0.0023 -390.00 -390.00 -390.00 -379.17 -170.83
37.50
245.83
390.00 -1186.0
-296.5
-296.5
-288.3
-129.
200.0
-0.0052
-0.0042
-0.0031
-0.0020
-0.0010
0.0001
0.0012
0.0023 -390.00 -390.00 -390.00 -390.00 -192.86
21.43
235.71
390.00 -1186.0
-296.5
-296.5
-296.5
-146.
194.3
-0.0055
-0.0044
-0.0033
-0.0022
-0.0011
0.0000
0.0011
0.0022 -390.00 -390.00 -390.00 -390.00 -216.18
4.41
225.00
390.00 -1186.0
-296.5
-296.5
-296.5
-164.
188.6
-0.0057
-0.0046
-0.0035
-0.0023
-0.0012
-0.0001
0.0011
0.0022 -390.00
-390.00 -390.00
-390.00
-240.91
-13.64
213.64
390.00
-1186.0
-296.5
-296.5
-296.5
-183.
182.9
-0.0060
-0.0049
-0.0037
-0.0025
-0.0013
-0.0002
0.0010
0.0022 -390.00
-390.00 -390.00
-390.00
-267.19
-32.81
201.56
390.00
-1186.0
-296.5
-296.5
-296.5
-203.
177.1
-0.0063
-0.0051
-0.0039
-0.0027
-0.0015
-0.0003
0.0009
0.0022 -390.00
-390.00 -390.00
-390.00
-295.16
-53.23
188.71
390.00
-1186.0
-296.5
-296.5
-296.5
-224.
171.4
-0.0066
-0.0054
-0.0041
-0.0029
-0.0016
-0.0004
0.0009
0.0021 -390.00
-390.00 -390.00
-390.00
-325.00
-75.00
175.00
390.00
-1186.0
-296.5
-296.5
-296.5
-247.
165.7
-0.0070
-0.0057
-0.0044
-0.0031
-0.0018
-0.0005
0.0008
0.0021 -390.00
-390.00 -390.00
-390.00
-356.90
-98.28
160.34
390.00
-1186.0
-296.5
-296.5
-296.5
-271.
160.0
-0.0073
-0.0060
-0.0046
-0.0033
-0.0020
-0.0006
0.0007
0.0021 -390.00 -390.00 -390.00 -390.00 -390.00 -123.21
144.64
390.00 -1186.0
-296.5
-296.5
-296.5
-296.
159.0
-0.0074
-0.0060
-0.0047
-0.0033
-0.0020
-0.0006
0.0007
0.0021 -390.00 -390.00 -390.00 -390.00 -390.00 -127.76
141.78
390.00 -1186.0
-296.5
-296.5
-296.5
-296.
158.0
-0.0074
-0.0061
-0.0047
-0.0034
-0.0020
-0.0007
0.0007
0.0021 -390.00 -390.00 -390.00 -390.00 -390.00 -132.37
138.88
390.00 -1186.0
-296.5
-296.5
-296.5
-296.
157.0
-0.0075
-0.0061
-0.0048
-0.0034
-0.0021
-0.0007
0.0007
0.0020 -390.00 -390.00 -390.00 -390.00 -390.00 -137.03
135.94
390.00 -1186.0
-296.5
-296.5
-296.5
-296.
156.0
-0.0076
-0.0062
-0.0048
-0.0035
-0.0021
-0.0007
0.0007
0.0020 -390.00 -390.00 -390.00 -390.00 -390.00 -141.76
132.97
390.00 -1186.0
-296.5
-296.5
-296.5
-296.
146.0
-0.0083
-0.0068
-0.0054
-0.0039
-0.0024
-0.0010
0.0005
0.0020 -390.00 -390.00 -390.00 -390.00 -390.00 -192.56
100.98
390.00 -1186.0
-296.5
-296.5
-296.5
-296.
0.0013
0.0019
0.0026
381.43
390.00
-198.8
-101.0
-3.3
94.
-390.00
-390.00 -390.00
-281.25
KONDISI TEKAN AKSIAL KECIL : Pn = 0.1 * fc' * b * h KONDISI BALANCE 333.3
-0.0020
- 0.0013
-0.0007
0.0000
0.0006
-390.00
-261.43 -132.86
-4.29
124.29
252.86
-1186.0
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Fs6
Fs7
Fs8
Cs
Ms1
kN
kN
kN
142.0
258.3 1186.0
-168.5 296503.5
kN
kNmm
135.4
254.2 1186.0
-213.3 296503.5
128.6
249.9 1186.0
-260.1 296503.5
121.5
245.4 1186.0
114.0
Ms2
Ms3
Ms4
Ms5
kNmm
kNmm
k Nmm
kNmm
52947.1
22192.9
3241.7
914.3
52947.1
23673.4
3648.6
594.0
52947.1
25217.0
4072.9
260.0
-308.9 296503.5
52947.1
26827.7
4515.6
240.8 1186.0
-359.9 296503.5
52947.1
28510.0
4977.9
106.3
235.9 1186.0
-413.1 296503.5
52947.1
30268.7
98.1
230.7 1186.0
-465.7 296503.5
52947.1
31768.2
89.6
225.4 1186.0
-506.1 296503.5
52947.1
80.7
219.7 1186.0
-548.5 296503.5
71.3
213.8 1186.0
61.4
Ms6
Ms7
Ms8
Ms
a
kNmm
mm
Cc
Mc
kNmm
kNmm
kNmm
kN
kNmm
kN
kNm
15210.8
46131.3 296503.5
733645.0 238.00
2427.6
439395.6
2259.10
14509.5
45395.3 296503.5
733774.9 233.14
2378.1
436203.6
13778.4
44628.0 296503.5
733910.3 228.29
2328.5
432771.0
-88.5
13015.4
43827.4 296503.5
734051.6 223.43
2279.0
-452.5
12218.6
42991.2 296503.5 734199.2 218.57
5461.3
-833.1
11385.5
5967.2
-1231.3
10513.6
31768.2
6497.2
-1648.5
52947.1
31768.2
7053.0
-593.0 296503.5
52947.1
31768.2
207.6 1186.0
-639.8 296503.5
52947.1
51.0
201.1 1186.0
-689.0 296503.5
40.1
194.2 1186.0
28.5
Pn
Mn
Ф
Ф.Pn
1173.04
0.65
1468.42
762.4
2164.71
1169.98
0.65
1407.06
760.4
2068.41
1166.68
0.65
1344.46
758.3
429097.8
1970.07
1163.15
0.65
1280.55
756.0
2229.4
425183.9
1869.57
1159.38
0.65
1215.22
753.6
42117.0 296503.5 734353.5 213.71
2179.9
421029.4
1766.75
1155.38
0.65
1148.39
751.0
41202.1 296503.5
734173.9 208.86
2130.3
416634.2
1664.64
1150.81
0.65
1082.01
748.0
9600.3
40243.6 296503.5 732414.9 204.00
2080.8
411998.4
1574.68
1144.41
0.65
1023.54
743.8
-2086.1
8642.4
39238.4 296503.5
730570.0 199.14
2031.3
407122.0
1482.75
1137.69
0.65
963.79
739.5
7636.6
-2545.5
7636.6
38183.0 296503.5
728633.0 194.29
1981.7
402004.9
1388.71
1130.64
0.65
902.66
734.91
31768.2
8250.1
-3028.5
6579.2
37073.4 296503.5
726596.5 189.43
1932.2
396647.2
1292.38
1123.24
0.65
840.05
730.11
52947.1
31768.2
8896.0
-3536.9
5466.2
35905.4 296503.5
724452.9 184.57
1882.6
391048.8
1193.59
1115.50
0.65
775.83
725.0
-741.0 296503.5
52947.1
31768.2
9576.7
-4072.9
4293.0
34674.3 296503.5
722193.4 179.71
1833.1
385209.9
1092.14
1107.40
0.65
709.89
719.81
186.9 1186.0
-795.7 296503.5
52947.1
31768.2
10295.3
-4638.5
3054.6
33374.7 296503.5
719808.4 174.86
1783.5
379130.3
987.80
1098.94
0.65
642.07
714.31
16.3
179.2 1186.0
-840.6 296503.5
52947.1
31768.2
10589.4
-5236.5
1745.5
32001.0 296503.5
716821.7 170.00
1734.0
372810.0
893.36
1089.63
0.65
580.69
708.2
3.4
171.1 1186.0
-879.4 296503.5
52947.1
31768.2
10589.4
-5869.7
359.4
30546.4 296503.5
713347.8 165.14
1684.5
366249.1
805.01
1079.60
0.65
523.26
701.7
-10.4
162.4 1186.0
-920.6 296503.5
52947.1
31768.2
10589.4
-6541.2
-1110.8
29003.6 296503.5
709663.3 160.29
1634.9
359447.6
714.30
1069.11
0.65
465.14
696.1
-24.9
153.2 1186.0
-964.3 296503.5
52947.1
31768.2
10589.4
-7254.8
-2672.8
27364.5 296503.5
705748.6 155.43
1585.4
352405.4
621.02
1058.15
0.67
416.47
709.6
-40.5
143.5 1186.0 -1010.9 296503.5
52947.1
31768.2
10589.4
-8014.3
-4335.6
25619.5 296503.5
701581.3 150.57
1535.8
345122.6
524.92
1046.70
0.69
362.53
722.9
-57.0
133.0 1186.0 -1060.6 296503.5
52947.1
31768.2
10589.4
-8824.5
-6109.3
23758.3 296503.5
697136.2 145.71
1486.3
337599.2
425.72
1034.74
0.71
302.82
736.0
-74.7
121.9 1186.0 -1113.7 296503.5
52947.1
31768.2
10589.4
-9690.6
-8005.3
21768.7 296503.5
692384.6 140.86
1436.7
329835.1
323.09
1022.22
0.73
236.72
748.9
-93.7
110.0 1186.0 -1169.7 296503.5
52947.1
31768.2
10589.4 -10589.4 -10036.7
19637.0 296503.5
687322.6 136.00
1387.2
321830.4
217.48
1009.15
0.75
164.13
761.6
kN
Ф.Mn kNm
-97.1
107.8 1186.0 -1175.4 296503.5
52947.1
31768.2
10589.4 -10589.4 -10407.2
19248.2 296503.5
686563.3 135.15
1378.5
320404.8
203.17
1006.97
0.76
153.94
762.9
-100.6
105.6 1186.0 -1181.1 296503.5
52947.1
31768.2
10589.4 -10589.4 -10782.4
18854.4 296503.5
685794.4 134.30
1369.9
318971.9
188.80
1004.77
0.76
143.61
764.2
-104.2
103.4 1186.0 -1186.8 296503.5
52947.1
31768.2
10589.4 -10589.4 -11162.4
18455.7 296503.5
685015.6 133.45
1361.2
317531.6
174.35
1002.55
0.76
133.14
765.6
-107.8
101.1 1186.0 -1192.7 296503.5
52947.1
31768.2
10589.4 -10589.4 -11547.2
18051.8 296503.5
684226.9 132.60
1352.5
316083.9
159.82
1000.31
0.77
122.54
766.9
-146.4
76.8 1186.0 -1255.6 296503.5
52947.1
31768.2
10589.4 -10589.4 -15685.7
13709.0 296503.5
675745.7 124.10
1265.8
301201.9
10.18
976.95
0.80
8.12
779.4
468.00
0.0
468.00
1000.0
0.00 192.2
290.0 1186.0
273.7 296503.5
35492.0
10822.1
116.4
3374.6
20597.0
51783.4 296503.5
715192.5 283.33
2890.0
457583.3
3163.70
1172.78
0.65
2056.40
0.0 762.3
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
ANALISIS KEKUATAN KOLOM BETON BERTULANG DENGAN DIAGRAM INTERAKSI [C]2010 : M. Noer Ilham
KODE KOLOM
K7
INPUT DATA KOLOM
f c' = f y =
Kuat tekan beton, Tegangan leleh baja, Lebar kolom, Tinggi kolom, Tebal brutto selimut beton, Jumlah tulangan, Diameter tulangan,
b= h= ds = n= D=
20
MPa
390
MPa
600
mm
600
mm
50
mm
24
buah
22
mm
2.E+05
MPa
PERHITUNGAN DIAGRAM INTERAKSI Es =
Modulus elastis baja, β1 = 0.85
untuk f c' 30 MPa
β1 = 0.85 - 0.008 (f c' - 30)
untuk f c ' > 30 MPa
Faktor distribusi tegangan,
β1 =
0.85
2
2
Luas tulangan total,
As = n * p / 4 * D = 9123 mm
Jarak tulangan,
x = ( h - 2*d s ) / 6 = 83.33 mm
Rasio tulangan,
r = As / Ag = 2.53%
Faktor reduksi kekuatan, f = 0.65 untuk P n ≥ 0.1 * f c' * b * h f = 0.80
untuk P n = 0
Untuk : 0
≤
Pn ≤ 0.1 * f c' * b * h
f = 0.65 + 0.15 * ( Pno - Pn ) / Pno
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
6000
5500
b
5000
h
4500
4000
) N k ( n P .
3500
3000
f
2500
2000
1500
1000
500
0 0
50
100
150
200
250
300
350
400
450
500
550
f.Mn (kNm)
600
650
700
750
800
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
850
900
950
1000
b=
600
mm
h=
600
mm
24 f c' =
D
22
20
MPa
f y =
390
MPa
Pu
Mu
(kN)
(kNm)
1091.76
47.21
1250.43
58.30
1164.72
13.29
826.79
59.72
1052.19
74.79
1086.99
77.48
977.00
41.14
761.48
148.30
485.67
106.70
594.01
166.55
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
No
Luas masing-masing tulangan
Jarak tulangan thd. sisi beton 2
1
As1 = 7/24 * A s = 2661
mm
2
As2 = 2/24 * A s =
mm
3 4 5 6 7
As3 = 2/24 * A s = As4 = 2/24 * A s = As5 = 2/24 * A s = As6 = 2/24 * A s =
760 760 760 760 760
As7 = 7/24 * A s = 2661 As = 9123
2 2
mm
2
mm
2
mm
2
mm
2
mm
Pada kondisi tekan aksial sentris (M no = 0) : -3
d1 = 6*x + d s =
550 mm
Pno = 0.80*[ 0.85*f c' *b*h + A s*(f y - 0.85*f c')]*10
d2 = 5*x + d s =
467 mm
Pno = 7618 kN
d3 = 4*x + d s =
383 mm
d4 = 3*x + d s =
300 mm
Pada kondisi balance :
d5 = 2*x + d s =
217 mm
c = cb = 600 / (600 + f y) * d1 =
d6 =
x + ds =
133 mm
d7 =
ds =
50 mm
-3
0.1 * f c' * b * h *10 =
720
kN
333.33 mm
2
mm
Regangan pada masing-masing baja tulangan :
εsi = 0.003 * ( c - di ) / c
Tegangan pada masing-masing baja tulangan : Untuk Untuk
| εsi | < f y / Es | εsi | f y / Es
maka : f si = esi* Es
Gaya-gaya internal pada masing-masing baja tulangan : Resultan gaya internal baja tulangan : Momen akibat gaya internal masing-masing baja tulangan : Momen total akibat gaya internal baja tulangan : Tinggi blok tegangan tekan beton, Gaya internal pada beton tekan : Momen akibat gaya internal tekan beton : Momen nominal : Gaya aksial rencana : Momen rencana :
105
→
Dc = 5.7143
maka : f si =| εsi | / esi* f y
URAIAN PERHITUNGAN
Gaya aksial nominal :
Jumlah interval jarak garis netral =
PERSAMAAN
UNIT -3
Fsi = Asi * f si * 10 -3 Cs = [ S Fsi ]*10 Msi = Fsi*(h/2 - di) Ms = S Msi a = β1 * c -3 Cc = 0.85 * f c' * b * a * 10 Mc = Cc * (h - a) / 2 Pn = Cs + Cc -3 Mn = (Mc + Ms)*10 Pu = f * Pn Mu = f * Mn
kN kN kNmm kNmm mm kN kNmm kN kNm kN kNm
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
6000
5500
b
5000
4500
h
4000
b=
600
mm
h=
600
mm
24 f c' =
D
22
20
MPa
f y =
390
MPa
3500 ) N k ( n P .
3000
f
2500
2000
1500
1000
500
0 0
50
100
150
200
250
300
350
400
450
500
550
600
650
700
750
800
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
850
900
950
1000
Pu
Mu
(kN)
(kNm)
1091.76
47.21
1250.43
58.30
1164.72
13.29
826.79
59.72
1052.19
74.79
1086.99
77.48
977.00
41.14
761.48
148.30
485.67
106.70
594.01
166.55
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
εs6
εs7
mm KONDISI TEKAN AKSIAL SENTRIS
f s1
f s2
f s3
f s4
f s5
f s6
f s7
Fs1
Fs2
Fs3
Fs4
Fs5
MPa
MPa
MPa
MPa
MPa
MPa
MPa
kN
kN
kN
kN
kN
720.0
0.00071
0.00106
0.00140
0.00175
0.00210
0.00244 0.00279
141.67
211.11
280.56
350.00
390.00
390.00
390.00
376.96
160.50
213.30
266.09
296.50
714.3
0.00069
0.00104
0.00139
0.00174
0.00209
0.00244 0.00279
138.00
208.00
278.00
348.00
390.00
390.00
390.00
367.21
158.14
211.35
264.57
296.50
708.6
0.00067
0.00102
0.00138
0.00173
0.00208
0.00244 0.00279
134.27
204.84
275.40
345.97
390.00
390.00
390.00
357.29
155.73
209.38
263.03
296.50
702.9
0.00065
0.00101
0.00136
0.00172
0.00208
0.00243 0.00279
130.49
201.63
272.76
343.90
390.00
390.00
390.00
347.22
153.29
207.37
261.46
296.50
697.1
0.00063
0.00099
0.00135
0.00171
0.00207
0.00243 0.00278
126.64
198.36
270.08
341.80
390.00
390.00
390.00
336.98
150.81
205.33
259.86
296.50
691.4
0.00061
0.00098
0.00134
0.00170
0.00206
0.00242 0.00278
122.73
195.04
267.36
339.67
390.00
390.00
390.00
326.57
148.28
203.26
258.24
296.50
685.7
0.00059
0.00096
0.00132
0.00169
0.00205
0.00242 0.00278
118.75
191.67
264.58
337.50
390.00
390.00
390.00
315.99
145.72
201.15
256.59
296.50
680.0
0.00057
0.00094
0.00131
0.00168
0.00204
0.00241 0.00278
114.71
188.24
261.76
335.29
390.00
390.00
390.00
305.22
143.11
199.01
254.91
296.50
674.3
0.00055
0.00092
0.00129
0.00167
0.00204
0.00241 0.00278
110.59
184.75
258.90
333.05
390.00
390.00
390.00
294.28
140.46
196.83
253.21
296.50
668.6
0.00053
0.00091
0.00128
0.00165
0.00203
0.00240 0.00278
106.41
181.20
255.98
330.77
390.00
390.00
390.00
283.15
137.76
194.61
251.47
296.50
662.9
0.00051
0.00089
0.00127
0.00164
0.00202
0.00240 0.00277
102.16
177.59
253.02
328.45
390.00
390.00
390.00
271.83
135.01
192.36
249.71
296.50
657.1
0.00049
0.00087
0.00125
0.00163
0.00201
0.00239
0 .00277
97.83
173.91
250.00
326.09
390.00
390.00
390.00
260.31
132.22
190.07
247.91
296.50
651.4
0.00047
0.00085
0.00123
0.00162
0.00200
0.00239
0 .00277
93.42
170.18
246.93
323.68
390.00
390.00
390.00
248.59
129.38
187.73
246.09
296.50
645.7
0.00044
0.00083
0.00122
0.00161
0.00199
0.00238
0 .00277
88.94
166.37
243.81
321.24
390.00
390.00
390.00
236.66
126.49
185.36
244.23
296.50
640.0
0.00042
0.00081
0.00120
0.00159
0.00198
0.00238
0 .00277
84.38
162.50
240.63
318.75
390.00
390.00
390.00
224.52
123.54
182.94
242.33
296.50
634.3
0.00040
0.00079
0.00119
0.00158
0.00198
0.00237
0 .00276
79.73
158.56
237.39
316.22
390.00
390.00
390.00
212.16
120.55
180.48
240.41
296.50
628.6
0.00038
0.00077
0.00117
0.00157
0.00197
0.00236
0 .00276
75.00
154.55
234.09
313.64
390.00
390.00
390.00
199.57
117.50
177.97
238.45
296.50
622.9
0.00035
0.00075
0.00115
0.00156
0.00196
0.00236
0 .00276
70.18
150.46
230.73
311.01
390.00
390.00
390.00
186.75
114.39
175.42
236.45
296.50
617.1
0.00033
0.00073
0.00114
0.00154
0.00195
0.00235
0 .00276
65.28
146.30
227.31
308.33
389.35
390.00
390.00
173.70
111.22
172.82
234.42
296.01
611.4
0.00030
0.00071
0.00112
0.00153
0.00194
0.00235
0 .00275
60.28
142.06
223.83
305.61
387.38
390.00
390.00
160.40
108.00
170.17
232.34
294.51
605.7
0.00028
0.00069
0.00110
0.00151
0.00193
0.00234
0 .00275
55.19
137.74
220.28
302.83
385.38
390.00
390.00
146.85
104.72
167.47
230.23
292.99
600.0
0.00025
0.00067
0.00108
0.00150
0.00192
0.00233
0 .00275
50.00
133.33
216.67
300.00
383.33
390.00
390.00
133.05
101.37
164.72
228.08
291.44
594.3
0.00022
0.00064
0.00106
0.00149
0.00191
0.00233
0.00275
44.71
128.85
212.98
297.12
381.25
390.00
390.00
118.97
97.96
161.92
225.89
289.85
588.6
0.00020
0.00062
0.00105
0.00147
0.00190
0.00232
0.00275
39.32
124.27
209.22
294.17
379.13
390.00
390.00
104.63
94.48
159.07
223.65
288.24
582.9
0.00017
0.00060
0 .00103
0 .00146
0 .00188
0.00231
0.00274
33.82
119.61
205.39
291.18
376.96
390.00
390.00
90.00
90.93
156.15
221.37
286.59
577.1
0.00014
0.00057
0 .00101
0 .00144
0 .00187
0.00231
0.00274
28.22
114.85
201.49
288.12
374.75
390.00
390.00
75.09
87.32
153.18
219.05
284.91
571.4
0.00011
0.00055
0 .00099
0 .00143
0 .00186
0.00230
0.00274
22.50
110.00
197.50
285.00
372.50
390.00
390.00
59.87
83.63
150.15
216.68
283.20
565.7
0.00008
0.00053
0 .00097
0 .00141
0 .00185
0.00229
0.00273
16.67
105.05
193.43
281.82
370.20
390.00
390.00
44.35
79.87
147.06
214.26
281.45
560.0
0.00005
0.00050
0 .00095
0 .00139
0 .00184
0.00229
0.00273
10.71
100.00
189.29
278.57
367.86
390.00
390.00
28.51
76.03
143.91
211.79
279.67
554.3
0.00002
0.00047
0.00093
0.00138
0.00183
0.00228
0.00273
4.64
94.85
185.05
275.26
365.46
390.00
390.00
12.34
72.11
140.69
209.27
277.85
548.6
-0.00001
0.00045
0 .00090
0.00136
0 .00182
0.00227
0.00273
-1.56
89.58
180.73
271.88
363.02
390.00
390.00
-4.16
68.11
137.40
206.70
275.99
542.9
-0.00004
0.00042
0 .00088
0 .00134
0 .00180
0.00226
0.00272
-7.89
84.21
176.32
268.42
360.53
390.00
390.00
-21.01
64.02
134.05
204.07
274.10
537.1
-0.00007
0.00039
0 .00086
0 .00132
0 .00179
0.00226
0.00272
-14.36
78.72
171.81
264.89
357.98
390.00
390.00
-38.22
59.85
130.62
201.39
272.16
531.4
-0.00010
0.00037
0 .00084
0 .00131
0 .00178
0.00225
0.00272
-20.97
73.12
167.20
261.29
355.38
390.00
390.00
-55.79
55.59
127.12
198.65
270.18
525.7
-0.00014
0.00034
0 .00081
0 .00129
0 .00176
0.00224
0.00271
-27.72
67.39
162.50
257.61
352.72
390.00
390.00
-73.75
51.24
123.54
195.85
268.16
520.0
-0.00017
0.00031
0 .00079
0 .00127
0 .00175
0.00223
0.00271
-34.62
61.54
157.69
253.85
350.00
390.00
390.00
-92.11
46.79
119.89
192.99
266.09
514.3
-0.00021
0.00028
0.00076
0.00125
0.00174
0.00222
0 .00271
-41.67
55.56
152.78
250.00
347.22
390.00
390.00
-110.87
42.24
116.15
190.07
263.98
508.6
-0.00024
0.00025
0.00074
0.00123
0.00172
0.00221
0 .00271
-48.88
49.44
147.75
246.07
344.38
390.00
390.00
-130.06
37.59
112.33
187.08
261.82
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Fs6
Fs7
Cs
Ms1
Ms2
Ms3
Ms4
Ms5
Ms6
Ms7
Ms
a
Cc
Mc
kN
kN
kN
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
mm
kN
kNmm
Pn kN 7618.36
Mn
Ф
kNm 0.00
Ф.Pn kN
0.65
4951.93
Ф.Mn kNm 0.0
296.50
1037.76
2647.62
-94241.23 -26750.08 -17774.72
0.00
24708.63
49417.25 259440.58 194800.42
612.00
6242.40 -37454.40
7618.36
157.35
0.65
4951.93
102.2
296.50
1037.76
2632.04
-91802.05 -26355.87 -17612.82
0.00
24708.63
49417.25 259440.58 197795.72
607.14
6192.86 -22117.35
7618.36
175.68
0.65
4951.93
114.1
296.50
1037.76
2616.20
-89323.52
-25955.30 -17448.30
0.00
24708.63
49417.25 259440.58 200839.34
602.29
6143.31
-7020.93
7618.36
193.82
0.65
4951.93
125.9
296.50
1037.76
2600.11
-86804.70
-25548.21 -17281.10
0.00
24708.63
49417.25 259440.58 203932.44
597.43
6093.77
7834.85
7618.36
211.77
0.65
4951.93
137.6
296.50
1037.76
2583.75
-84244.58
-25134.46 -17111.17
0.00
24708.63
49417.25 259440.58 207076.26
592.57
6044.23
22449.99
7618.36
229.53
0.65
4951.93
149.1
296.50
1037.76
2567.12
-81642.14
-24713.86 -16938.42
0.00
24708.63
49417.25 259440.58 210272.03
587.71
5994.69
36824.50
7618.36
247.10
0.65
4951.93
160.61
296.50
1037.76
2550.22
-78996.33
-24286.26 -16762.80
0.00
24708.63
49417.25 259440.58 213521.07
582.86
5945.14
50958.37
7618.36
264.48
0.65
4951.93
171.91
296.50
1037.76
2533.03
-76306.05
-23851.46 -16584.22
0.00
24708.63
49417.25 259440.58 216824.72
578.00
5895.60
64851.60
7618.36
281.68
0.65
4951.93
183.0
296.50
1037.76
2515.54
-73570.18
-23409.30 -16402.62
0.00
24708.63
49417.25 259440.58 220184.36
573.14
5846.06
78504.20
7618.36
298.69
0.65
4951.93
194.1
296.50
1037.76
2497.76
-70787.53
-22959.58 -16217.91
0.00
24708.63
49417.25 259440.58 223601.43
568.29
5796.51
91916.16
7618.36
315.52
0.65
4951.93
205.0
296.50
1037.76
2479.68
-67956.91 -22502.11 -16030.02
0.00
24708.63
49417.25 259440.58 227077.41
563.43
5746.97 105087.48
7618.36
332.16
0.65
4951.93
215.91
296.50
1037.76
2461.28
-65077.07 -22036.68 -15838.86
0.00
24708.63
49417.25 259440.58 230613.84
558.57
5697.43 118018.16
7618.36
348.63
0.65
4951.93
226.61
296.50
1037.76
2442.55
-62146.70
-21563.08 -15644.35
0.00
24708.63
49417.25 259440.58 234212.32
553.71
5647.89 130708.21
7618.36
364.92
0.65
4951.93
237.2
296.50
1037.76
2423.50
-59164.46
-21081.11 -15446.40
0.00
24708.63
49417.25 259440.58 237874.49
548.86
5598.34 143157.62
7618.36
381.03
0.65
4951.93
247.6
296.50
1037.76
2404.10
-56128.97
-20590.52 -15244.91
0.00
24708.63
49417.25 259440.58 241602.06
544.00
5548.80 155366.40
7618.36
396.97
0.65
4951.93
258.0
296.50
1037.76
2384.36
-53038.79
-20091.10 -15039.79
0.00
24708.63
49417.25 259440.58 245396.78
539.14
5499.26 167334.54
7618.36
412.73
0.65
4951.93
268.2
296.50
1037.76
2364.25
-49892.42 -19582.59 -14830.94
0.00
24708.63
49417.25 259440.58 249260.51
534.29
5449.71 179062.04
7618.36
428.32
0.65
4951.93
278.41
296.50
1037.76
2343.78
-46688.32
-19064.76 -14618.25
0.00
24708.63
49417.25 259440.58 253195.12
529.43
5400.17 190548.91
7618.36
443.74
0.65
4951.93
288.4
296.50
1037.76
2322.43
-43424.88
-18537.34 -14401.63
0.00
24667.56
49417.25 259440.58 257161.54
524.57
5350.63 201795.13
7618.36
458.96
0.65
4951.93
298.3
296.50
1037.76
2299.70
-40100.45
-18000.05 -14180.96
0.00
24542.84
49417.25 259440.58 261119.20
519.71
5301.09 212800.73
7600.78
473.92
0.65
4940.51
308.0
296.50
1037.76
2276.53
-36713.29
-17452.63 -13956.13
0.00
24415.76
49417.25 259440.58 265151.53
514.86
5251.54 223565.68
7528.07
488.72
0.65
4893.25
317.6
296.50
1037.76
2252.92
-33261.61
-16894.79 -13727.01
0.00
24286.26
49417.25 259440.58 269260.67
510.00
5202.00 234090.00
7454.92
503.35
0.65
4845.70
327.1
296.50
1037.76
2228.86
-29743.56
-16326.21 -13493.49
0.00
24154.27
49417.25 259440.58 273448.83
505.14
5152.46 244373.68
7381.31
517.82
0.65
4797.85
336.5
296.50
1037.76
2204.33
-26157.19
-15746.60 -13255.44
0.00
24019.71
49417.25 259440.58 277718.32
500.29
5102.91 254416.73
7307.24
532.14
0.65
4749.71
345.8
296.50
1037.76
2179.32
-22500.50
-15155.62 -13012.71
0.00
23882.52
49417.25 259440.58 282071.52
495.43
5053.37 264219.13
7232.69
546.29
0.65
4701.25
355.0
296.50
1037.76
2153.81
-18771.40
-14552.94 -12765.18
0.00
23742.61
49417.25 259440.58 286510.92
490.57
5003.83 273780.91
7157.64
560.29
0.65
4652.46
364.1
296.50
1037.76
2127.79
-14967.73
-13938.20 -12512.70
0.00
23599.91
49417.25 259440.58 291039.11
485.71
4954.29 283102.04
7082.08
574.14
0.65
4603.35
373.1
296.50
1037.76
2101.25
-11087.20
-13311.04 -12255.12
0.00
23454.32
49417.25 259440.58 295658.78
480.86
4904.74 292182.54
7005.99
587.84
0.65
4553.90
382.1
296.50
1037.76
2074.17
-7127.49
-12671.09 -11992.28
0.00
23305.76
49417.25 259440.58 300372.72
476.00
4855.20 301022.40
6929.37
601.40
0.65
4504.09
390.91
296.50
1037.76
2046.52
-3086.13
-12017.94 -11724.02
0.00
23154.13
49417.25 259440.58 305183.86
471.14
4805.66 309621.62
6852.18
614.81
0.65
4453.92
399.6
296.50
1037.76
2018.31
1039.43
-11351.19 -11450.18
0.00
22999.35
49417.25 259440.58 310095.24
466.29
4756.11 317980.21
6774.42
628.08
0.65
4403.37
408.2
296.50
1037.76
1989.49
5251.83
-10670.39 -11170.57
0.00
22841.31
49417.25 259440.58 315110.01
461.43
4706.57 326098.16
6696.07
641.21
0.65
4352.44
416.7
296.50
1037.76
1960.07
9553.87
-9975.11 -10885.01
0.00
22679.90
49417.25 259440.58 320231.48
456.57
4657.03 333975.48
6617.10
654.21
0.65
4301.11
425.2
296.50
1037.76
1930.01
13948.42
-9264.88 -10593.30
0.00
22515.03
49417.25 259440.58 325463.09
451.71
4607.49 341612.16
6537.50
667.08
0.65
4249.37
433.6
296.50
1037.76
1899.30
18438.50
-8539.21 -10295.26
0.00
22346.57
49417.25 259440.58 330808.43
446.86
4557.94 349008.20
6457.24
679.82
0.65
4197.21
441.8
296.50
1037.76
1867.91
23027.27
-7797.59
-9990.67
0.00
22174.41
49417.25 259440.58 336271.24
442.00
4508.40 356163.60
6376.31
692.43
0.65
4144.60
450.0
296.50
1037.76
1835.83
27718.01
-7039.49
-9679.31
0.00
21998.42
49417.25 259440.58 341855.46
437.14
4458.86 363078.37
6294.69
704.93
0.65
4091.55
458.21
296.50
1037.76
1803.02
32514.16
-6264.36
-9360.95
0.00
21818.48
49417.25 259440.58 347565.16
432.29
4409.31 369752.50
6212.34
717.32
0.65
4038.02
466.2
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
εs6
εs7
mm
f s1
f s2
f s3
f s4
f s5
f s6
f s7
Fs1
Fs2
kN
Fs4 kN
Fs5
MPa
MPa
MPa
MPa
MPa
MPa
MPa
kN
502.9
-0.00028
0.00022
0.00071
0.00121
0.00171
0.00220
0.00270
-56.25
43.18
142.61
242.05
341.48
390.00
390.00
-149.68
32.83
108.42
184.02
259.61
497.1
-0.00032
0.00018
0.00069
0.00119
0.00169
0.00220
0.00270
-63.79
36.78
137.36
237.93
338.51
390.00
390.00
-169.75
27.96
104.43
180.89
257.35
491.4
-0.00036
0.00015
0.00066
0.00117
0.00168
0.00219
0.00269
-71.51
30.23
131.98
233.72
335.47
390.00
390.00
-190.29
22.98
100.34
177.69
255.04
485.7
-0.00040
0.00012
0 .00063
0 .00115
0 .00166
0.00218
0.00269
-79.41
23.53
126.47
229.41
332.35
390.00
390.00
-211.31
17.89
96.15
174.41
252.68
480.0
-0.00044
0.00008
0 .00060
0 .00113
0 .00165
0.00217
0.00269
-87.50
16.67
120.83
225.00
329.17
390.00
390.00
-232.83
12.67
91.87
171.06
250.25
474.3
-0.00048
0.00005
0.00058
0 .00110
0.00163
0.00216
0.00268
-95.78
9.64
115.06
220.48
325.90
390.00
390.00
-254.87
7.33
87.48
167.62
247.77
468.6
-0.00052
0.00001
0 .00055
0 .00108
0 .00161
0.00215
0.00268
-104.27
2.44
109.15
215.85
322.56
390.00
390.00
-277.45
1.85
82.98
164.11
245.23
462.9
-0.00056
-0.00002
0.00052
0.00106
0.00160
0.00214
0.00268
-112.96
-4.94
103.09
211.11
319.14
390.00
390.00
-300.59
-3.75
78.37
160.50
242.63
457.1
-0.00061
-0.00006
0.00048
0.00103
0.00158
0.00213
0.00267
-121.87
-12.50
96.88
206.25
315.63
390.00
390.00
-324.30
-9.50
73.65
156.80
239.96
451.4
-0.00066
-0.00010
0.00045
0.00101
0.00156
0.00211
0.00267
-131.01
-20.25
90.51
201.27
312.03
390.00
390.00
-348.62
-15.40
68.81
153.02
237.22
445.7
-0.00070
-0.00014
0.00042
0.00098
0.00154
0.00210
0.00266
-140.38
-28.21
83.97
196.15
308.33
390.00
390.00
-373.55
-21.44
63.84
149.13
234.42
440.0
-0.00075
-0.00018
0.00039
0.00095
0.00152
0.00209
0.00266
-150.00
-36.36
77.27
190.91
304.55
390.00
390.00
-399.14
-27.65
58.75
145.14
231.54
434.3
-0.00080
-0.00022
0.00035
0.00093
0.00150
0.00208
0.00265
-159.87
-44.74
70.39
185.53
300.66
390.00
390.00
-425.40
-34.01
53.52
141.05
228.58
428.6
-0.00085
-0.00027
0.00032
0.00090
0.00148
0.00207
0.00265
-170.00
-53.33
63.33
180.00
296.67
390.00
390.00
-452.36
-40.55
48.15
136.85
225.55
422.9
-0.00090
-0.00031
0.00028
0.00087
0.00146
0.00205
0.00265
-180.41
-62.16
56.08
174.32
292.57
390.00
390.00
-480.05
-47.26
42.64
132.53
222.43
417.1
-0.00096
-0.00036
0.00024
0.00084
0.00144
0.00204
0.00264
-191.10
-71.23
48.63
168.49
288.36
390.00
390.00
-508.49
-54.16
36.97
128.10
219.23
411.4
-0.00101
-0.00040
0.00020
0.00081
0.00142
0.00203
0.00264
-202.08
-80.56
40.97
162.50
284.03
390.00
390.00
-537.73
-61.24
31.15
123.54
215.94
405.7
-0.00107
-0.00045
0.00017
0.00078
0.00140
0.00201
0.00263
-213.38
-90.14
33.10
156.34
279.58
390.00
390.00
-567.79
-68.53
25.16
118.86
212.55
400.0
-0.00112
-0.00050
0.00013
0.00075
0.00138
0.00200
0.00263
-225.00
-100.00
25.00
150.00
275.00
390.00
390.00
-598.71
-76.03
19.01
114.04
209.07
394.3
-0.00118
-0.00055
0.00008
0.00072
0.00135
0.00199
0.00262
-236.96
-110.14
16.67
143.48
270.29
390.00
390.00
-630.52
-83.74
12.67
109.08
205.49
388.6
-0.00125
-0.00060
0.00004
0.00068
0.00133
0.00197
0.00261
-249.26
- 120.59
8.09
136.76
265.44
390.00
390.00
-663.28
-91.68
6.15
103.98
201.81
382.9
-0.00131
-0.00066
0.00000
0.00065
0.00130
0.00196
0.00261
-261.94
-131.34
-0.75
129.85
260.45
390.00
390.00
-697.00
-99.86
-0.57
98.72
198.01
377.1
-0.00137
-0.00071 -0.00005
0.00061
0.00128
0.00194
0.00260
-275.00
-142.42
-9.85
122.73
255.30
387.88
390.00
-731.76
-108.28
-7.49
93.31
194.10
371.4
-0.00144 -0.00077 -0.00010 0.00058 0.00125
0.00192 0.00260
-288.46
-153.85
-19.23
115.38
250.00
384.62
390.00
-767.58
-116.96
-14.62
87.72
190.07
365.7
-0.00151 -0.00083 -0.00014 0.00054 0.00122
0.00191 0.00259
-302.34
-165.62
-28.91
107.81
244.53
381.25
390.00
-804.52
-125.92
-21.98
81.97
185.91
360.0
-0.00158 -0.00089 -0.00019 0.00050 0.00119
0.00189 0.00258
-316.67
-177.78
-38.89
100.00
238.89
377.78
390.00
-842.63
-135.16
-29.57
76.03
181.62
354.3
-0.00166
-0.00095 -0.00025
0.00046
0.00117
0.00187
0.00258
-331.45
-190.32
-49.19
91.94
233.06
374.19
390.00
-881.97
-144.70
-37.40
69.90
177.19
348.6
-0.00173
-0.00102 -0.00030
0.00042
0.00114
0.00185
0.00257
-346.72
-203.28
-59.84
83.61
227.05
370.49
390.00
-922.60
-154.55
-45.49
63.56
172.62
342.9
-0.00181
-0.00108 -0.00035
0.00038
0.00110
0.00183
0.00256
-362.50
-216.67
-70.83
75.00
220.83
366.67
390.00
-964.59
-164.72
-53.85
57.02
167.89
337.1
-0.00189 -0.00115 -0.00041 0.00033 0.00107
0.00181 0.00256
-378.81
-230.51
-82.20
66.10
214.41
362.71
390.00 -1008.00
-175.25
-62.50
50.25
163.01
331.4
-0.00198 -0.00122 -0.00047 0.00028 0.00104
0.00179 0.00255
-390.00
-244.83
-93.97
56.90
207.76
358.62
390.00 -1037.76
-186.13
-71.44
43.26
157.95
325.7
-0.00207 -0.00130 -0.00053
0.00100
0.00177
0.00254
-390.00
-259.65
-106.14
47.37
200.88
354.39
390.00 -1037.76
-197.40
-80.69
36.01
152.72
320.0
-0.00216 -0.00137 -0.00059
0.00019
0.00097
0.00175
0.00253
-390.00
-275.00
-118.75
37.50
193.75
350.00
390.00 -1037.76
-209.07
-90.28
28.51
147.30
314.3
-0.00225
-0.00145 -0.00066
0.00014
0.00093
0.00173
0.00252
-390.00
-290.91
-131.82
27.27
186.36
345.45
390.00 -1037.76
-221.17
-100.22
20.73
141.69
308.6
-0.00235
-0.00154 -0.00073
0.00008
0.00089
0.00170
0.00251
-390.00
-307.41
-145.37
16.67
178.70
340.74
390.00 -1037.76
-233.71
-110.52
12.67
135.86
302.9
-0.00245 -0.00162 -0.00080 0.00003 0.00085
0.00168 0.00250
-390.00
-324.53
-159.43
5.66
170.75
335.85
390.00 -1037.76
-246.73
-121.21
4.30
129.82
297.1
-0.00255
-0.00171 -0.00087 -0.00003
0.00081
0.00165
0.00250
-390.00
-342.31
-174.04
-5.77
162.50
330.77
390.00 -1037.76
-260.24
-132.32
-4.39
123.54
291.4
-0.00266 -0.00180 -0.00095 -0.00009
0.00077
0.00163
0.00249
-390.00
-360.78
-189.22
-17.65
153.92
325.49
390.00 -1037.76
-274.29
-143.85
-13.42
117.02
285.7
-0.00277 -0.00190 -0.00102 -0.00015
0.00073
0.00160
0.00248
-390.00
-380.00
-205.00
-30.00
145.00
320.00
390.00 -1037.76
-288.90
-155.85
-22.81
110.24
0.00024
kN
Fs3
kN
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Fs6 kN
Fs7 kN
Cs kN
Ms1
Ms2
Ms3
Ms4 kNmm
Ms5
Ms7
Ms
kNmm
kNmm
kNmm
a
Mc
kN
kNmm
Pn kN
Mn
Ф
kNm
Ф.Pn
Ф.Mn
kNmm
kNmm
kNmm
kN
kNm
1037.76
1769.47
37419.31
-5471.61
-9035.35
0.00
21634.45
49417.25 259440.58 353404.63
427.43
4359.77 376185.99
6129.25
729.59
0.65
3984.01
474.2
296.50
1037.76
1735.15
42437.23
-4660.63
-8702.27
0.00
21446.18
49417.25 259440.58 359378.34
422.57
4310.23 382378.85
6045.38
741.76
0.65
3929.50
482.1
296.50
1037.76
1700.03
47571.84
-3830.79
-8361.45
0.00
21253.54
49417.25 259440.58 365490.97
417.71
4260.69 388331.07
5960.72
753.82
0.65
3874.47
489.9
296.50
1037.76
1664.09
52827.27
-2981.43
-8012.60
0.00
21056.37
49417.25 259440.58 371747.43
412.86
4211.14 394042.65
5875.23
765.79
0.65
3818.90
497.7
296.50
1037.76
1627.28
58207.82
-2111.85
-7655.45
0.00
20854.50
49417.25 259440.58 378152.85
408.00
4161.60 399513.60
5788.88
777.67
0.65
3762.78
505.4
296.50
1037.76
1589.60
63718.03
-1221.31
-7289.69
0.00
20647.77
49417.25 259440.58 384712.62
403.14
4112.06 404743.91
5701.65
789.46
0.65
3706.07
513.1
296.50
1037.76
1550.99
69362.63
-309.05
-6915.02
0.00
20436.00
49417.25 259440.58 391432.39
398.29
4062.51 409733.58
5613.50
801.17
0.65
3648.78
520.7
296.50
1037.76
1511.43
75146.61
625.73
-6531.09
0.00
20218.99
49417.25 259440.58 398318.07
393.43
4012.97 414482.62
5524.40
812.80
0.65
3590.86
528.3
296.50
1037.76
1470.88
81075.18
1583.89
-6137.56
0.00
19996.56
49417.25 259440.58 405375.90
388.57
3963.43 418991.02
5434.30
824.37
0.65
3532.30
535.8
296.50
1037.76
1429.30
87153.84
2566.30
-5734.07
0.00
19768.50
49417.25 259440.58 412612.40
383.71
3913.89 423258.78
5343.18
835.87
0.65
3473.07
543.3
296.50
1037.76
1386.66
93388.37
3573.90
-5320.23
0.00
19534.60
49417.25 259440.58 420034.46
378.86
3864.34 427285.91
5251.00
847.32
0.65
3413.15
550.7
296.50
1037.76
1342.91
99784.84
4607.67
-4895.65
0.00
19294.61
49417.25 259440.58 427649.30
374.00
3814.80 431072.40
5157.71
858.72
0.65
3352.51
558.1
296.50
1037.76
1298.00 106349.63
5668.65
-4459.89
0.00
19048.32
49417.25 259440.58 435464.53
369.14
3765.26 434618.25
5063.26
870.08
0.65
3291.12
565.5
296.50
1037.76
1251.90 113089.48
6757.91
-4012.51
0.00
18795.45
49417.25 259440.58 443488.16
364.29
3715.71 437923.47
4967.62
881.41
0.65
3228.95
572.9
296.50
1037.76
1204.56 120011.49
7876.62
-3553.04
0.00
18535.75
49417.25 259440.58 451728.65
359.43
3666.17 440988.05
4870.73
892.72
0.65
3165.97
580.2
296.50
1037.76
1155.92 127123.15
9025.98
-3080.98
0.00
18268.94
49417.25 259440.58 460194.91
354.57
3616.63 443811.99
4772.54
904.01
0.65
3102.15
587.6
296.50
1037.76
1105.92
134432.35
10207.27
-2595.81
0.00
17994.71
49417.25 259440.58 468896.34
349.71
3567.09 446395.30
4673.01
915.29
0.65
3037.46
594.9
296.50
1037.76
1054.52
141947.44
11421.83
-2096.98
0.00
17712.76
49417.25 259440.58 477842.88
344.86
3517.54 448737.97
4572.06
926.58
0.65
2971.84
602.2
296.50
1037.76
1001.65
149677.25
12671.09
-1583.89
0.00
17422.75
49417.25 259440.58 487045.04
340.00
3468.00 450840.00
4469.65
937.89
0.65
2905.27
609.6
296.50
1037.76
947.25 157631.12
13956.56
-1055.92
0.00
17124.34
49417.25 259440.58 496513.92
335.14
3418.46 452701.40
4365.70
949.22
0.65
2837.71
616.9
296.50
1037.76
891.24 165818.92
15279.84
-512.43
0.00
16817.15
49417.25 259440.58 506261.30
330.29
3368.91 454322.16
4260.16
960.58
0.65
2769.10
624.3
296.50
1037.76
833.57 174251.13
16642.63
47.28
0.00
16500.79
49417.25 259440.58 516299.65
325.43
3319.37 455702.28
4152.94
972.00
0.65
2699.41
631.8
294.89
1037.76
772.53 182938.87
18046.70
623.96
0.00
16174.84
49148.47 259440.58 526373.41
320.57
3269.83 456841.76
4042.36
983.22
0.65
2627.54
639.0
292.41
1037.76
708.80 191893.92
19493.99
1218.37
0.00
15838.86
48734.96 259440.58 536620.68
315.71
3220.29 457740.61
3929.09
994.36
0.65
2553.91
646.3
289.85
1037.76
643.08 201128.81
20986.49
1831.37
0.00
15492.39
48308.53 259440.58 547188.17
310.86
3170.74 458398.82
3813.82
1005.59
0.65
2478.98
653.6
287.21
1037.76
575.27 210656.88
22526.38
2463.82
0.00
15134.91
47868.56 259440.58 558091.14
306.00
3121.20 458816.40
3696.47
1016.91
0.65
2402.70
660.9
284.49
1037.76
505.27 220492.30
24115.95
3116.68
0.00
14765.91
47414.40 259440.58 569345.81
301.14
3071.66 458993.34
3576.93
1028.34
0.65
2325.00
668.4
281.67
1037.76
432.98 230650.20
25757.63
3790.94
0.00
14384.80
46945.35 259440.58 580969.49
296.29
3022.11 458929.64
3455.09
1039.90
0.65
2245.81
675.9
278.76
1037.76
358.28 241146.69
27454.03
4487.68
0.00
13991.00
46460.66 259440.58 592980.63
291.43
2972.57 458625.31
3330.85
1051.61
0.65
2165.05
683.5
275.76
1037.76
281.04 251998.99
29207.94
5208.03
0.00
13583.84
45959.55 259440.58 605398.93
286.57
2923.03 458080.33
3204.07
1063.48
0.65
2082.64
691.2
272.65
1037.76
216.28 259440.58
31022.32
5953.23
0.00
13162.64
45441.15 259440.58 614460.50
281.71
2873.49 457294.73
3089.77
1071.76
0.65
2008.35
696.6
269.43
1037.76
180.06 259440.58
32900.37
6724.57
0.00
12726.67
44904.57 259440.58 616137.33
276.86
2823.94 456268.48
3004.01
1072.41
0.65
1952.60
697.0
266.09
1037.76
142.55 259440.58
34845.50
7523.46
0.00
12275.12
44348.82 259440.58 617874.04
272.00
2774.40 455001.60
2916.95
1072.88
0.65
1896.02
697.3
262.64
1037.76
103.67 259440.58
36861.35
8351.40
0.00
11807.15
43772.86 259440.58 619673.91
267.14
2724.86 453494.08
2828.53
1073.17
0.65
1838.54
697.5
259.05
1037.76
63.36 259440.58
38951.87
9210.01
0.00
11321.85
43175.57 259440.58 621540.45
262.29
2675.31 451745.93
2738.67
1073.29
0.65
1780.14
697.6
255.33
1037.76
21.52 259440.58
41121.27
10101.01
0.00
10818.24
42555.74 259440.58 623477.42
257.43
2625.77 449757.13
2647.29
1073.23
0.65
1720.74
697.6
251.47
1037.76
-21.93
259440.58
43374.12
11026.29
0.00
10295.26
41912.07 259440.58 625488.88
252.57
2576.23 447527.71
2554.30
1073.02
0.65
1660.29
697.4
247.46
1037.76
-67.08 259440.58
45715.31
11987.85
0.00
9751.77
41243.16 259440.58 627579.23
247.71
2526.69 445057.64
2459.60
1072.64
0.65
1598.74
697.21
243.28
1037.76
48150.14
12987.87
0.00
9186.54
40547.49 259440.58 629753.19
242.86
2477.14 442346.94
2363.10
1072.10
0.65
1536.02
696.8
259440.58
mm
Cc
296.50
-114.04
kNmm
Ms6
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
εs6
εs7
f s1 MPa
MPa
MPa
MPa
MPa
0.00246
-390.00
-390.00
-221.43
-42.86
135.71
mm 0.00157
f s3
f s4
f s5
f s6
f s7
Fs1
Fs2
Fs3
Fs4
MPa
MPa
kN
kN
kN
314.29
390.00 -1037.76
-296.50
-168.34
-32.58
103.18
kN
Fs5 kN
280.0
-0.00289 -0.00200 -0.00111 -0.00021
274.3
-0.00302 -0.00210 -0.00119 -0.00028 0.00063
0.00154 0.00245
-390.00
-390.00
-238.54
-56.25
126.04
308.33
390.00 -1037.76
-296.50
-181.35
-42.76
95.83
268.6
-0.00314 -0.00221 -0.00128 -0.00035 0.00058
0.00151 0.00244
-390.00
-390.00
-256.38
-70.21
115.96
302.13
390.00 -1037.76
-296.50
-194.92
-53.38
88.16
262.9
-0.00328 -0.00233 -0.00137 -0.00042 0.00053
0.00148 0.00243
-390.00
-390.00
-275.00
-84.78
105.43
295.65
390.00 -1037.76
-296.50
-209.07
-64.46
80.16
257.1
-0.00342 -0.00244 -0.00147 -0.00050 0.00047
0.00144 0.00242
-390.00
-390.00
-294.44
-100.00
94.44
288.89
390.00 -1037.76
-296.50
-223.86
-76.03
71.80
251.4
-0.00356 -0.00257 -0.00157 -0.00058 0.00041
0.00141 0.00240
-390.00
-390.00
-314.77
-115.91
82.95
281.82
390.00 -1037.76
-296.50
-239.31
-88.12
63.07
245.7
-0.00372 -0.00270 -0.00168 -0.00066
0.00035
0.00137
0.00239
-390.00
-390.00
-336.05
-132.56
70.93
274.42
390.00 -1037.76
-296.50
-255.48
-100.78
53.93
240.0
-0.00387 -0.00283 -0.00179 -0.00075
0.00029
0.00133
0.00238
-390.00
-390.00
-358.33
-150.00
58.33
266.67
390.00 -1037.76
-296.50
-272.43
-114.04
44.35
234.3
-0.00404 -0.00298 -0.00191 -0.00084
0.00023
0.00129
0.00236
-390.00
-390.00
-381.71
-168.29
45.12
258.54
390.00 -1037.76
-296.50
-290.20
-127.95
34.30
228.6
-0.00422 -0.00312 -0.00203 -0.00094
0.00016
0.00125
0.00234
-390.00
-390.00
-390.00
-187.50
31.25
250.00
390.00 -1037.76
-296.50
-296.50
-142.55
23.76
222.9
-0.00440 -0.00328 -0.00216 -0.00104
0.00008
0.00121
0.00233
-390.00
-390.00
-390.00
-207.69
16.67
241.03
390.00 -1037.76
-296.50
-296.50
-157.90
12.67
217.1
-0.00460
0.00001
0.00116
0.00231
-390.00
-390.00
-390.00
-228.95
1.32
231.58
390.00 -1037.76
-296.50
-296.50
-174.06
1.00
211.4
-0.00480 -0.00362 -0.00244 -0.00126 -0.00007
0.00111
0.00229
-390.00
-390.00
-390.00
-251.35
-14.86
221.62
390.00 -1037.76
-296.50
-296.50
-191.09
-11.30
205.7
-0.00502 -0.00381 -0.00259 -0.00137 -0.00016
0.00106
0.00227
-390.00
-390.00
-390.00
-275.00
-31.94
211.11
390.00 -1037.76
-296.50
-296.50
-209.07
-24.29
200.0
-0.00525 -0.00400 -0.00275 -0.00150 -0.00025
0.00100
0.00225
-390.00
-390.00
-390.00
-300.00
-50.00
200.00
390.00 -1037.76
-296.50
-296.50
-228.08
-38.01
194.3
-0.00549 -0.00421 -0.00292 -0.00163 -0.00035
0.00094
0.00223
-390.00
-390.00
-390.00
-326.47
-69.12
188.24
390.00 -1037.76
-296.50
-296.50
-248.20
-52.55
188.6
-0.00575 -0.00442 -0.00310 -0.00177 -0.00045
0.00088
0.00220
-390.00
-390.00
-390.00
-354.55
-89.39
175.76
390.00 -1037.76
-296.50
-296.50
-269.55
-67.96
182.9
-0.00602 -0.00466 -0.00329 -0.00192 -0.00055
0.00081
0.00218
-390.00
-390.00
-390.00
-384.37
-110.94
162.50
390.00 -1037.76
-296.50
-296.50
-292.23
-84.34
177.1
-0.00631 -0.00490 -0.00349 -0.00208 -0.00067
0.00074
0.00215
-390.00
-390.00
-390.00
-390.00
-133.87
148.39
390.00 -1037.76
-296.50
-296.50
-296.50
-101.78
171.4
-0.00662 -0.00517 -0.00371 -0.00225 -0.00079
0.00067
0.00213
-390.00
-390.00
-390.00
-390.00
-158.33
133.33
390.00 -1037.76
-296.50
-296.50
-296.50
-120.38
165.7
-0.00696 -0.00545 -0.00394 -0.00243 -0.00092
0.00059
0.00209
-390.00
-390.00
-390.00
-390.00
-184.48
117.24
390.00 -1037.76
-296.50
-296.50
-296.50
-140.26
160.0
-0.00731 -0.00575 -0.00419 -0.00262 -0.00106
0.00050
0.00206
-390.00
-390.00
-390.00
-390.00
-212.50
100.00
390.00 -1037.76
-296.50
-296.50
-296.50
-161.56
154.3
-0.00769 -0.00607 -0.00445 -0.00283 -0.00121
0.00041
0.00203
-390.00
-390.00
-390.00
-390.00
-242.59
81.48
390.00 -1037.76
-296.50
-296.50
-296.50
-184.43
148.6
-0.00811 -0.00642 -0.00474 -0.00306 -0.00137
0.00031
0.00199
-390.00
-390.00
-390.00
-390.00
-275.00
61.54
390.00 -1037.76
-296.50
-296.50
-296.50
-209.07
142.9
-0.00855 -0.00680 -0.00505 -0.00330 -0.00155
0.00020
0.00195
-390.00
-390.00
-390.00
-390.00
-310.00
40.00
390.00 -1037.76
-296.50
-296.50
-296.50
-235.68
137.1
-0.00903 -0.00721 -0.00539 -0.00356 -0.00174
0.00008
0.00191
-390.00
-390.00
-390.00
-390.00
-347.92
16.67
381.25 -1037.76
-296.50
-296.50
-296.50
-264.51
136.2
-0.00911 -0.00728 -0.00544 -0.00361 -0.00177
0.00006
0.00190
-390.00
-390.00
-390.00
-390.00
-354.48
12.63
379.74 -1037.76
-296.50
-296.50
-296.50
-269.50
0.00180 0.00255
-390.00
-240.00
-90.00
60.00
210.00
360.00
390.00 -1037.76
-182.46
-68.42
45.62
159.66
-0.00345 -0.00230 -0.00114
0.00068
f s2
KONDISI TEKAN AKSIAL KECIL : Pn = 0.1 * fc' * b * h KONDISI BALANCE 333.3
-0.00195 -0.00120 -0.00045 0.00030
0.00105
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Fs6 kN
Fs7 kN
Cs
Ms1
kN
kNmm
Ms2
Ms3
Ms4
Ms5
kNmm
kNmm
Ms6
Ms7
Ms
kNmm
kNmm
kNmm
a mm
Cc
Mc
kN
kNmm
Pn
Mn
Ф
Ф.Pn kN
Ф.Mn
kNmm
kNmm
kN
kNm
238.94
1037.76
-155.31 259440.58
49417.25
14028.71
0.00
8598.24
39823.43 259440.58 630748.78
238.00
2427.60 439395.60
2272.29
1070.14
0.65
1476.99
695.5
kNm
234.42
1037.76
-190.38 259440.58
49417.25
15112.92
0.00
7985.43
39069.20 259440.58 630465.94
233.14
2378.06 436203.62
2187.67
1066.67
0.65
1421.99
693.3
229.70
1037.76
-226.95 259440.58
49417.25
16243.26
0.00
7346.54
38282.87 259440.58 630171.07
228.29
2328.51 432771.01
2101.57
1062.94
0.65
1366.02
690.91
224.77
1037.76
-265.10 259440.58
49417.25
17422.75
0.00
6679.87
37462.35 259440.58 629863.37
223.43
2278.97 429097.76
2013.87
1058.96
0.65
1309.02
688.3
219.63
1037.76
-304.95 259440.58
49417.25
18654.66
0.00
5983.57
36605.37 259440.58 629542.01
218.57
2229.43 425183.88
1924.48
1054.73
0.65
1250.91
685.5
214.26
1037.76
-346.61 259440.58
49417.25
19942.57
0.00
5255.62
35709.44 259440.58 629206.03
213.71
2179.89 421029.36
1833.27
1050.24
0.65
1191.63
682.6
208.63
1037.76
-390.21 259440.58
49417.25
21290.38
0.00
4493.82
34771.83 259440.58 628854.43
208.86
2130.34 416634.20
1740.13
1045.49
0.65
1131.09
679.5
202.74
1037.76
-435.89 259440.58
49417.25
22702.37
0.00
3695.73
33789.57 259440.58 628486.08
204.00
2080.80 411998.40
1644.91
1040.48
0.65
1069.19
676.31
196.56
1037.76
-483.79 259440.58
49417.25
24183.24
0.00
2858.72
32759.40 259440.58 628099.77
199.14
2031.26 407121.97
1547.47
1035.22
0.65
1005.85
672.8
190.07
1037.76
-521.73 259440.58
49417.25
24708.63
0.00
1979.86
31677.73 259440.58 626664.61
194.29
1981.71 402004.90
1459.98
1028.67
0.65
948.99
668.6
183.24
1037.76
-554.99 259440.58
49417.25
24708.63
0.00
1055.92
30540.58 259440.58 624603.53
189.43
1932.17 396647.19
1377.18
1021.25
0.65
895.17
663.81
176.06
1037.76
-590.01 259440.58
49417.25
24708.63
0.00
83.36
29343.58 259440.58 622433.97
184.57
1882.63 391048.85
1292.62
1013.48
0.65
840.20
658.7
168.49
1037.76
-626.91 259440.58
49417.25
24708.63
0.00
-941.77
28081.88 259440.58 620147.14
179.71
1833.09 385209.87
1206.17
1005.36
0.65
784.01
653.4
160.50
1037.76
-665.87 259440.58
49417.25
24708.63
0.00
-2023.85
26750.08 259440.58 617733.25
174.86
1783.54 379130.25
1117.68
996.86
0.65
726.49
647.9
152.05
1037.76
-707.05 259440.58
49417.25
24708.63
0.00
-3167.77
25342.18 259440.58 615181.44
170.00
1734.00 372810.00
1026.95
987.99
0.65
667.52
642.1
143.11
1037.76
-750.65 259440.58
49417.25
24708.63
0.00
-4378.98
23851.46 259440.58 612479.51
165.14
1684.46 366249.11
933.81
978.73
0.65
606.97
636.1
133.62
1037.76
-796.90 259440.58
49417.25
24708.63
0.00
-5663.59
22270.40 259440.58 609613.84
160.29
1634.91 359447.58
838.02
969.06
0.65
544.71
629.8
123.54
1037.76
-846.03 259440.58
49417.25
24708.63
0.00
-7028.50
20590.52 259440.58 606569.06
155.43
1585.37 352405.42
739.34
958.97
0.65
480.57
623.3
112.81
1037.76
-878.47 259440.58
49417.25
24708.63
0.00
-8481.46
18802.26 259440.58 603327.84
150.57
1535.83 345122.62
657.35
948.45
0.66
435.86
628.8
101.37
1037.76
-908.52 259440.58
49417.25
24708.63
0.00 -10031.28
16894.79 259440.58 599870.54
145.71
1486.29 337599.18
577.77
937.47
0.68
392.67
637.1
89.13
1037.76
-940.63 259440.58
49417.25
24708.63
0.00 -11687.99
14855.76 259440.58 596174.80
140.86
1436.74 329835.11
496.11
926.01
0.70
345.61
645.1
76.03
1037.76
-975.04 259440.58
49417.25
24708.63
0.00 -13463.03
12671.09 259440.58 592215.09
136.00
1387.20 321830.40
412.16
914.05
0.71
294.34
652.7
61.95
1037.76
-1012.00 259440.58
49417.25
24708.63
0.00 -15369.56
10324.59 259440.58 587962.06
131.14
1337.66 313585.05
325.66
901.55
0.73
238.43
660.0
46.79
1037.76
-1051.80 259440.58
49417.25
24708.63
0.00 -17422.75
7797.59 259440.58 583381.87
126.29
1288.11 305099.07
236.32
888.48
0.75
177.42
667.0
30.41
1037.76
-1094.78 259440.58
49417.25
24708.63
0.00 -19640.19
5068.44 259440.58 578435.28
121.43
1238.57 296372.45
143.79
874.81
0.77
110.72
673.6
12.67
1014.48
-1164.63 259440.58
49417.25
24708.63
0.00 -22042.42
2111.85 253619.79 567255.68
116.57
1189.03 287405.19
24.40
854.66
0.79
19.39
679.3
9.60
1010.45
-1176.72 259440.58
49417.25
2 4708.63
0.00 -22458.16
1600.17 252612.42 565320.88
115.77
1180.85 285902.47
4.13
851.22
0.80
3.30
680.2
468.00
0.0
468.00
1000.0
0.00 273.70
1037.76
228.08 259440.58
30410.62
5701.99
0.00
13304.64
45615.93 259440.58 613914.33
283.33
2890.00 457583.33
3118.08
1071.50
0.65
2026.75
0.0 696.4
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
ANALISIS KEKUATAN KOLOM BETON BERTULANG DENGAN DIAGRAM INTERAKSI [C]2010 : M. Noer Ilham
KODE KOLOM
K6
INPUT DATA KOLOM
f c' = f y =
Kuat tekan beton, Tegangan leleh baja,
b= h= ds = n= D=
Lebar kolom, Tinggi kolom, Tebal brutto selimut beton, Jumlah tulangan, Diameter tulangan,
20
MPa
390
MPa
450
mm
450
mm
50
mm
20
buah
22
mm
PERHITUNGAN DIAGRAM INTERAKSI Es = 2.E+05 MPa Modulus elastis baja, β1 = β1 =
untuk f c' 30 MPa
0.85 0.85 - 0.008 (f c' - 30)
β1 =
Faktor distribusi tegangan, Luas tulangan total, Jarak antara tulangan,
untuk f c ' > 30 MPa 2
As = n * p / 4 * D = 7603 mm x = ( h - 2*d s )/5 = 70.00 mm
Rasio tulangan,
r = As / Ag = 3.75%
Faktor reduksi kekuatan, f = 0.65 untuk P n ≥ 0.1 * fc' * b * h f=
0.85
2
0.80 untuk P n = 0
Untuk : 0
≤
Pn ≤ 0.1 * f c' * b * h
f = 0.65 + 0.15 * ( Pno - Pn ) / Pno
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
3500
b 3000
h
2500
2000 ) N k ( n P . f
1500
1000
500
0 0
50
100
150
200
250
300
350
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
400
450
b=
450
mm
h=
450
mm
20
D
22
f c' =
20
MPa
f y =
390
MPa
Pu
Mu
(kN)
(kNm)
1091.76
47.21
1250.43
58.30
1164.72
13.29
826.79
59.72
1052.19
74.79
1086.99
77.48
977.00
41.14
761.48
148.30
485.67
106.70
594.01
166.55
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Pada kondisi tekan aksial sentris (M no = 0) : No Luas masing-masing tulangan Jarak tulangan thd. sisi beton 2 -3 As1 = 6/20 * A s = 2281 mm d1 = 5*x + d s = 400 mm Pno = 0.80*[ 0.85*f c' *b*h + A s*(f y - 0.85*f c')]*10 1 2 3 4 5 6
As2 = 2/20 * A s = As3 = 2/20 * A s = As4 = 2/20 * A s = As5 = 2/20 * A s =
760 760 760 760
As6 = 6/20 * A s = 2281 As = 7603
2
mm
2
mm
2
mm
2
mm
2
mm
d2 = 4*x + d s =
330
mm
Pno =
5023
kN
-3
405
kN
d3 = 3*x + d s =
260
mm
0.1 * f c' * b * h *10 =
d4 = 2*x + d s =
190
mm Pada kondisi balance :
d5 =
x + ds =
120
mm
d6 =
ds =
50
mm
c = cb = 600 / (600 + f y) * d1 = 242.42 mm
2
mm
Pada kondisi garis netral terletak pada jarak c dari sisi beton tekan terluar : Regangan pada masing-masing baja tulangan :
εsi = 0.003 * ( c - d i ) / c
Tegangan pada masing-masing baja tulangan : Untuk Untuk
| εsi | < f y / E maka : f si = esi* Es | εsi | f y / Es maka : f si =| εsi | / esi* f y
URAIAN PERHITUNGAN Gaya-gaya internal pada masing-masing baja tulangan : Resultan gaya internal baja tulangan : Momen akibat gaya internal masing-masing baja tulangan : Momen total akibat gaya internal baja tulangan : Tinggi blok tegangan tekan beton, Gaya internal pada beton tekan : Momen akibat gaya internal tekan beton : Gaya aksial nominal : Momen nominal : Gaya aksial rencana : Momen rencana :
Jumlah interval jarak grs netral =
125
PERSAMAAN
→
Dc =
3.6000
UNIT -3
Fsi = Asi * f si * 10 -3 Cs = [ S Fsi ]*10 Msi = Fsi*(h/2 - di) Ms = S Msi a = β1 * c -3 Cc = 0.85 * f c' * b * a * 10 Mc = Cc * (h - a) / 2 Pn = Cs + Cc -3 Mn = (Mc + Ms)*10 Pu = f * Pn Mu = f * Mn
kN kN kNmm kNmm mm kN kNmm kN kNm kN kNm
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
3500
b 3000
h
2500
2000 ) N k ( n P . f
1500
1000
500
b=
450
mm
h=
450
mm
20
D
22
f c' =
20
MPa
f y =
390
MPa
Pu
Mu
(kN)
(kNm)
1091.76
47.21
1250.43
58.30
1164.72
13.29
826.79
59.72
1052.19
74.79
1086.99
77.48
977.00
41.14
761.48
148.30
485.67
106.70
594.01
166.55
0 0
50
100
150
200
250
300
350
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
400
450
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
εs6
mm KONDISI TEKAN AKSIAL SENTRIS
f s1
f s2
f s3
f s4
f s5
f s6
Fs1
Fs2
Fs3
Fs4
Fs5
MPa
MPa
MPa
MPa
MPa
MPa
kN
kN
kN
kN
kN
495.000
0.00058
0.00100
0.00142
0.00185
0.00227
0.00270
115.152
200.000
284.848
369.697
390.000
390.000
262.637
152.053
216.560
281.068
296.504
491.400
0.00056
0.00099
0.00141
0.00184
0.00227
0.00269
111.600
197.070
282.540
368.010
390.000
390.000
254.536
149.825
214.805
279.785
296.504
487.800
0.00054
0.00097
0.00140
0.00183
0.00226
0.00269
107.995
194.096
280.197
366.298
390.000
390.000
246.315
147.564
213.024
278.483
296.504
484.200
0.00052
0.00096
0.00139
0.00182
0.00226
0.00269
104.337
191.078
277.819
364.560
390.000
390.000
237.972
145.270
211.216
277.162
296.504
480.600
0.00050
0.00094
0.00138
0.00181
0.00225
0.00269
100.624
188.015
275.406
362.797
390.000
390.000
229.503
142.941
209.381
275.822
296.504
477.000
0.00048
0.00092
0.00136
0.00181
0.00225
0.00269
96.855
184.906
272.956
361.006
390.000
390.000
220.907
140.577
207.519
274.461
296.504
473.400
0.00047
0.00091
0.00135
0.00180
0.00224
0.00268
93.029
181.749
270.469
359.189
390.000
390.000
212.181
138.178
205.628
273.079
296.504
469.800
0.00045
0.00089
0.00134
0.00179
0.00223
0.00268
89.144
178.544
267.944
357.344
390.000
390.000
203.320
135.741
203.708
271.676
296.504
466.200
0.00043
0.00088
0.00133
0.00178
0.00223
0.00268
85.199
175.290
265.380
355.470
390.000
390.000
194.323
133.267
201.759
270.251
296.504
462.600
0.00041
0.00086
0.00131
0.00177
0.00222
0.00268
81.193
171.984
262.776
353.567
390.000
390.000
185.185
130.754
199.779
268.805
296.504
459.000
0.00039
0.00084
0.00130
0.00176
0.00222
0.00267
77.124
168.627
260.131
351.634
390.000
390.000
175.905
128.202
197.768
267.335
296.504
455.400
0.00036
0.00083
0.00129
0.00175
0.00221
0.00267
72.991
165.217
257.444
349.671
390.000
390.000
166.477
125.609
195.726
265.842
296.504
451.800
0.00034
0.00081
0.00127
0.00174
0.00220
0.00267
68.792
161.753
254.714
347.676
390.000
390.000
156.899
122.975
193.651
264.326
296.504
448.200
0.00032
0.00079
0.00126
0.00173
0.00220
0.00267
64.525
158.233
251.941
345.649
390.000
390.000
147.168
120.299
191.542
262.785
296.504
444.600
0.00030
0.00077
0.00125
0.00172
0.00219
0.00266
60.189
154.656
249.123
343.590
390.000
390.000
137.279
117.580
189.399
261.219
296.504
441.000
0.00028
0.00076
0.00123
0.00171
0.00218
0.00266
55.782
151.020
246.259
341.497
390.000
390.000
127.228
114.816
187.222
259.628
296.504
437.400
0.00026
0.00074
0.00122
0.00170
0.00218
0.00266
51.303
147.325
243.347
339.369
390.000
390.000
117.012
112.006
185.008
258.011
296.504
433.800
0.00023
0.00072
0.00120
0.00169
0.00217
0.00265
46.750
143.568
240.387
337.206
390.000
390.000
106.626
109.150
182.758
256.366
296.504
430.200
0.00021
0.00070
0.00119
0.00168
0.00216
0.00265
42.120 139.749 237.378
335.007
390.000
390.000
96.067
106.246
180.470
254.694
296.504
426.600
0.00019
0.00068
0.00117
0.00166
0.00216
0.00265
37.412 135.865 234.318
332.771
390.000
390.000
85.329
103.293
178.144
252.994
296.504
423.000
0.00016
0.00066
0.00116
0.00165
0.00215
0.00265
32.624 131.915 231.206
330.496
390.000
390.000
74.409
100.290
175.778
251.265
296.504
419.400
0.00014
0.00064
0.00114
0.00164
0.00214
0.00264
27.754
127.897
228.040
328.183
390.000
390.000
63.301
97.236
173.371
249.506
296.504
415.800
0.00011
0.00062
0.00112
0.00163
0.00213
0.00264
22.799
123.810
224.820
325.830
390.000
390.000
52.001
94.128
170.923
247.717
296.504
412.200
0.00009
0.00060
0.00111
0.00162
0.00213
0.00264
17.758
119.651
221.543
323.435
390.000
390.000
40.503
90.966
168.431
245.897
296.504
408.600
0.00006
0.00058
0.00109
0.00160
0.00212
0.00263
12.628
115.419
218.209
320.999
390.000
390.000
28.803
87.749
165.896
244.044
296.504
405.000
0.00004
0.00056
0.00107
0.00159
0.00211
0.00263
7.407
111.111
214.815
318.519
390.000
390.000
16.895
84.474
163.316
242.159
296.504
401.400
0.00001
0.00053
0.00106
0.00158
0.00210
0.00263
2.093 106.726
211.360
315.994
390.000
390.000
4.773
81.140
160.690
240.239
296.504
397.800
-0.00002
0.00051
0.00104
0.00157
0.00210
0.00262
-3.318
102.262
207.843
313.424
390.000
390.000
-7.568
77.747
158.016
238.285
296.504
394.200
-0.00004
0.00049
0.00102
0.00155
0.00209
0.00262
-8.828
97.717
204.262
310.807
390.000
390.000
-20.135
74.291
155.293
236.296
296.504
390.600
-0.00007
0.00047
0.00100
0.00154
0.00208
0.00262
-14.439
93.088 200.614
308.141
390.000
390.000
-32.933
70.771
152.520
234.269
296.504
387.000
-0.00010
0.00044
0.00098
0.00153
0.00207
0.00261
-20.155
88.372 196.899
305.426
390.000
390.000
-45.970
67.186
149.696
232.205
296.504
383.400
-0.00013
0.00042
0.00097
0.00151
0.00206
0.00261
-25.978
83.568 193.114
302.660
390.000
390.000
-59.251
63.534
146.818
230.102
296.504
379.800
-0.00016
0.00039
0.00095
0.00150
0.00205
0.00261
-31.912
78.673 189.258
299.842
390.000
390.000
-72.784
59.812
143.886
227.960
296.504
376.200
-0.00019
0.00037
0.00093
0.00148
0.00204
0.00260
-37.959
73.684 185.327
296.970
390.000
390.000
-86.576
56.020
140.898
225.776
296.504
372.600
-0.00022
0.00034
0.00091
0.00147
0.00203
0.00260
-44.122
68.599
181.320
294.042
390.000
390.000 -100.634
52.153
137.852
223.550
296.504
369.000
-0.00025
0.00032
0.00089
0.00146
0.00202
0.00259
-50.407
63.415
177.236
291.057
390.000
390.000 -114.967
48.212
134.746
221.281
296.504
365.400
-0.00028
0.00029
0.00087
0.00144
0.00201
0.00259
-56.814
58.128
173.071
288.013
390.000
390.000 -129.582
44.193
131.580
218.966
296.504
361.800
-0.00032
0.00026
0.00084
0.00142
0.00200
0.00259
-63.350
52.736
168.823
284.909
390.000
390.000 -144.488
40.094
128.350
216.606
296.504
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Fs6
Cs
Ms1
Ms2
Ms3
Ms4
Ms5
Ms6
Ms
a
Cc
Mc
Pn
Mn
kN
kN
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
kNm
5022.63
0.00
Ф.Pn
Ф
kN 0.65
3264.71
Ф.Mn kNm 0.00
889.511
2098.333
-45961.50
-15965.57
-7579.62
9837.37
31132.87
155664.35 127127.90
420.75
3218.74
47074.04
5022.63
174.20
0.65
3264.71
113.23
889.511
2084.965
-44543.76
-15731.65
-7518.18
9792.48
31132.87
155664.35 128796.11
417.69
3195.33
51620.53
5022.63
180.42
0.65
3264.71
117.27
889.511
2071.401
-43105.09
-15494.27
-7455.84
9746.92
31132.87
155664.35 130488.95
414.63
3171.92
56095.40
5022.63
186.58
0.65
3264.71
121.28
889.511
2057.634
-41645.02
-15253.35
-7392.57
9700.69
31132.87
155664.35 132206.95
411.57
3148.51
60498.63
5022.63
192.71
0.65
3264.71
125.26
889.511
2043.662
-40163.09
-15008.84
-7328.35
9653.76
31132.87
155664.35 133950.70
408.51
3125.10
64830.23
5022.63
198.78
0.65
3264.71
129.21
889.511
2029.478
-38658.78
-14760.62
-7263.16
9606.12
31132.87
155664.35 135720.77
405.45
3101.69
69090.20
5022.63
204.81
0.65
3264.71
133.13
889.511
2015.079
-37131.59
-14508.64
-7196.99
9557.76
31132.87
155664.35 137517.75
402.39
3078.28
73278.54
5022.63
210.80
0.65
3264.71
137.02
889.511
2000.459
-35581.00
-14252.79
-7129.79
9508.66
31132.87
155664.35 139342.28
399.33
3054.87
77395.25
5022.63
216.74
0.65
3264.71
140.88
889.511
1985.614
-34006.47
-13992.99
-7061.56
9458.80
31132.87
155664.35 141194.99
396.27
3031.47
81440.32
5017.08
222.64
0.65
3261.10
144.71
889.511
1970.537
-32407.42
-13729.15
-6992.27
9408.16
31132.87
155664.35 143076.53
393.21
3008.06
85413.76
4978.59
228.49
0.65
3236.09
148.52
889.511
1955.224
-30783.30
-13461.17
-6921.89
9356.73
31132.87
155664.35 144987.59
390.15
2984.65
89315.58
4939.87
234.30
0.65
3210.92
152.30
889.511
1939.668
-29133.49
-13188.95
-6850.40
9304.49
31132.87
155664.35 146928.86
387.09
2961.24
93145.76
4900.91
240.07
0.65
3185.59
156.05
889.511
1923.865
-27457.39
-12912.40
-6777.77
9251.41
31132.87
155664.35 148901.06
384.03
2937.83
96904.31
4861.69
245.81
0.65
3160.10
159.77
889.511
1907.808
-25754.37
-12631.40
-6703.97
9197.48
31132.87 155664.35 150904.95
380.97
2914.42 100591.22
4822.23
251.50
0.65
3134.45
163.47
889.511
1891.491
-24023.77
-12345.85
-6628.98
9142.68
31132.87 155664.35 152941.29
377.91
2891.01 104206.51
4782.50
257.15
0.65
3108.63
167.15
889.511
1874.908
-22264.92
-12055.64
-6552.76
9086.98
31132.87 155664.35 155010.88
374.85
2867.60 107750.16
4742.51
262.76
0.65
3082.63
170.79
889.511
1858.051
-20477.11
-11760.65
-6475.29
9030.37
31132.87 155664.35 157114.53
371.79
2844.19 111222.19
4702.24
268.34
0.65
3056.46
174.42
889.511
1840.915
-18659.63
-11460.76
-6396.53
8972.81
31132.87 155664.35 159253.10
368.73
2820.78 114622.58
4661.70
273.88
0.65
3030.10
178.02
889.511
1823.492
-16811.73
-11155.86
-6316.46
8914.30
31132.87 155664.35 161427.46
365.67
2797.38 117951.34
4620.87
279.38
0.65
3003.56
181.60
889.511
1805.775
-14932.64
-10845.81
-6235.03
8854.79
31132.87 155664.35 163638.52
362.61
2773.97 121208.47
4579.74
284.85
0.65
2976.83
185.15
889.511
1787.756
-13021.57
-10530.48
-6152.22
8794.28
31132.87 155664.35 165887.22
359.55
2750.56 124393.96
4538.31
290.28
0.65
2949.90
188.68
889.511
1769.428
-11077.69
-10209.74
-6067.98
8732.72
31132.87 155664.35 168174.52
356.49
2727.15 127507.83
4496.58
295.68
0.65
2922.77
192.19
889.511
1750.783
-9100.15
-9883.45
-5982.29
8670.10
31132.87
155664.35 170501.42
353.43
2703.74 130550.06
4454.52
301.05
0.65
2895.44
195.68
889.511
1731.812
-7088.06
-9551.46
-5895.10
8606.38
31132.87
155664.35 172868.97
350.37
2680.33 133520.66
4412.14
306.39
0.65
2867.89
199.15
889.511
1712.506
-5040.53
-9213.61
-5806.37
8541.54
31132.87
155664.35 175278.24
347.31
2656.92 136419.63
4369.43
311.70
0.65
2840.13
202.60
889.511
1692.858
-2956.59
-8869.76
-5716.07
8475.55
31132.87
155664.35 177730.35
344.25
2633.51 139246.97
4326.37
316.98
0.65
2812.14
206.04
889.511
1672.857
-835.27
-8519.75
-5624.15
8408.38
31132.87
155664.35 180226.43
341.19
2610.10 142002.68
4282.96
322.23
0.65
2783.92
209.45
889.511
1652.494
1324.44
-8163.39
-5530.56
8339.99
31132.87
155664.35 182767.69
338.13
2586.69 144686.76
4239.19
327.45
0.65
2755.47
212.85
889.511
1631.759
3523.60
-7800.53
-5435.26
8270.35
31132.87
155664.35 185355.37
335.07
2563.29 147299.20
4195.04
332.65
0.65
2726.78
216.23
889.511
1610.642
5763.30
-7430.98
-5338.21
8199.42
31132.87
155664.35 187990.75
332.01
2539.88 149840.01
4150.52
337.83
0.65
2697.84
219.59
889.511
1589.132
8044.67
-7054.56
-5239.35
8127.18
31132.87
155664.35 190675.16
328.95
2516.47 152309.20
4105.60
342.98
0.65
2668.64
222.94
889.511
1567.218
10368.88
-6671.06
-5138.63
8053.58
31132.87
155664.35 193409.98
325.89
2493.06 154706.75
4060.28
348.12
0.65
2639.18
226.28
889.511
1544.888
12737.15
-6280.30
-5036.01
7978.58
31132.87
155664.35 196196.64
322.83
2469.65 157032.66
4014.54
353.23
0.65
2609.45
229.60
889.511
1522.131
15150.74
-5882.05
-4931.42
7902.15
31132.87
155664.35 199036.64
319.77
2446.24 159286.95
3968.37
358.32
0.65
2579.44
232.91
889.511
1498.935
17610.98
-5476.11
-4824.81
7824.25
31132.87
155664.35 201931.52
316.71
2422.83 161469.61
3921.77
363.40
0.65
2549.15
236.21
889.511
1475.286
20119.22
-5062.26
-4716.12
7744.82
31132.87
155664.35 204882.88
313.65
2399.42 163580.63
3874.71
368.46
0.65
2518.56
239.50
889.511
1451.171
22676.88
-4640.24
-4605.29
7663.83
31132.87
155664.35 207892.40
310.59
2376.01 165620.02
3827.18
373.51
0.65
2487.67
242.78
889.511
1426.576
25285.44
-4209.83
-4492.25
7581.22
31132.87
155664.35 210961.80
307.53
2352.60 167587.78
3779.18
378.55
0.65
2456.47
246.06
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
εs6
mm
f s1 MPa
f s2
f s4
f s5
f s6
Fs1
MPa
kN
Fs2
kN
Fs4 kN
Fs5
MPa
MPa
MPa
-0.00035
0.00024
0.00082
0.00141
0.00199
0.00258
-70.017
47.236
164.489
281.742
390.000
390.000 -159.694
35.912
125.055
214.199
296.504
354.600
-0.00038
0.00021
0.00080
0.00139
0.00198
0.00258
-76.819
41.624
160.068
278.511
390.000
390.000 -175.208
31.646
121.694
211.742
296.504
351.000
-0.00042
0.00018
0.00078
0.00138
0.00197
0.00257
-83.761
35.897
155.556
275.214
390.000
390.000 -191.041
27.292
118.264
209.235
296.504
347.400
-0.00045
0.00015
0.00075
0.00136
0.00196
0.00257
-90.846
30.052
150.950
271.848
390.000
390.000 -207.202
22.847
114.762
206.677
296.504
343.800
-0.00049
0.00012
0.00073
0.00134
0.00195
0.00256
-98.080
24.084
146.248
268.412
390.000
390.000 -223.701
18.310
111.187
204.064
296.504
340.200
-0.00053
0.00009
0.00071
0.00132
0.00194
0.00256
-105.467
17.989
141.446
264.903
388.360
390.000 -240.550
13.677
107.537
201.397
295.257
336.600
-0.00057
0.00006
0.00068
0.00131
0.00193
0.00255 -113.012
11.765
136.542
261.319
386.096
390.000 -257.758
8.944
103.808
198.672
293.536
333.000
-0.00060
0.00003
0.00066
0.00129
0.00192
0.00255 -120.721
5.405
131.532
257.658
383.784
390.000 -275.339
4.110
99.999
195.888
291.778
329.400
-0.00064
-0.00001
0.00063
0.00127
0.00191
0.00254 -128.597
-1.093
126.412
253.916
381.421
390.000 -293.305
-0.831
96.106
193.044
289.981
325.800
-0.00068
-0.00004
0.00061
0.00125
0.00190
0.00254 -136.648
-7.735
121.179
250.092
379.006
390.000 -311.667
-5.881
92.128
190.136
288.145
322.200
-0.00072 -0.00007
0.00058
0.00123
0.00188
0.00253 -144.879
-14.525
115.829
246.182
376.536
390.000 -330.439
-11.043
88.061
187.164
286.268
318.600
-0.00077 -0.00011
0.00055
0.00121
0.00187
0.00253 -153.296
-21.469
110.358
242.185
374.011
390.000 -349.636
-16.322
83.901
184.125
284.348
315.000
-0.00081 -0.00014
0.00052
0.00119
0.00186
0.00252 -161.905
-28.571
104.762
238.095
371.429
390.000 -369.272
-21.722
79.647
181.016
282.384
311.400
-0.00085
-0.00018
0.00050
0.00117
0.00184
0.00252 -170.713
-35.838
99.037
233.911
368.786
390.000 -389.361
-27.247
75.294
177.835
280.375
307.800
-0.00090
-0.00022
0.00047
0.00115
0.00183
0.00251 -179.727
-43.275
93.177
229.630
366.082
390.000 -409.921
-32.900
70.840
174.579
278.319
304.200
-0.00094
-0.00025
0.00044
0.00113
0.00182
0.00251 -188.955
-50.888
87.179
225.247
363.314
390.000 -430.967
-38.688
66.280
171.247
276.215
300.600
-0.00099
-0.00029
0.00041
0.00110
0.00180
0.00250 -198.403
-58.683
81.038
220.758
360.479
390.000 -452.517
-44.614
61.610
167.835
274.060
297.000
-0.00104
-0.00033
0.00037
0.00108
0.00179
0.00249 -208.081
-66.667
74.747
216.162
357.576
390.000 -474.590
-50.684
56.828
164.340
271.852
293.400
-0.00109
-0.00037
0.00034
0.00106
0.00177
0.00249 -217.996
-74.847
68.303
211.452
354.601
390.000 -497.204
-56.903
51.928
160.760
269.591
289.800
-0.00114
-0.00042
0.00031
0.00103
0.00176
0.00248 -228.157
-83.230
61.698
206.625
351.553
390.000 -520.380
-63.277
46.907
157.090
267.273
286.200
-0.00119
-0.00046
0.00027
0.00101
0.00174
0.00248 -238.574
-91.824
54.927
201.677
348.428
390.000 -544.140
-69.811
41.759
153.328
264.898
282.600
-0.00125 -0.00050
0.00024
0.00098
0.00173
0.00247 -249.257 -100.637
47.983
196.603
345.223
390.000 -568.504
-76.511
36.480
149.470
262.461
279.000
-0.00130 -0.00055
0.00020
0.00096
0.00171
0.00246 -260.215 -109.677
40.860
191.398
341.935
390.000 -593.498
-83.384
31.065
145.513
259.962
275.400
-0.00136 -0.00059
0.00017
0.00093
0.00169
0.00246 -271.460 -118.954
33.551
186.057
338.562
390.000 -619.144
-90.437
25.508
141.452
257.397
271.800
-0.00142 -0.00064
0.00013
0.00090
0.00168
0.00245 -283.002 -128.477
26.049
180.574
335.099
390.000 -645.470
-97.676
19.804
137.284
254.764
268.200
-0.00147 -0.00069
0.00009
0.00087
0.00166
0.00244 -294.855 -138.255
18.345
174.944
331.544
390.000 -672.503
-105.111
13.947
133.004
252.061
264.600
-0.00154 -0.00074
0.00005
0.00085
0.00164
0.00243 -307.029 -148.299
10.431
169.161
327.891
390.000 -700.272 -112.747
7.930
128.607
249.284
261.000
-0.00160
0.00001
0.00082
0.00162
0.00243 -319.540 -158.621
2.299
163.218
324.138
390.000 -728.806
-120.594
1.748
124.089
246.431
257.400
-0.00166 -0.00085 -0.00003
0.00079
0.00160
0.00242 -332.401 -169.231
-6.061
157.110
320.280
390.000 -758.139
-128.660
-4.608
119.445
243.498
253.800
-0.00173 -0.00090 -0.00007
0.00075
0.00158
0.00241 -345.626 -180.142
-14.657
150.827
316.312
390.000 -788.304
-136.956
-11.143
114.669
240.481
250.200
-0.00180 -0.00096 -0.00012
0.00072
0.00156
0.00240 -359.233 -191.367
-23.501
144.365
312.230
390.000 -819.336
-145.490
-17.867
109.755
237.378
246.600
-0.00187 -0.00101 -0.00016
0.00069
0.00154
0.00239 -373.236 -202.920
-32.603
137.713
308.029
390.000 -851.275
-154.273
-24.787
104.698
234.184
243.000
-0.00194 -0.00107
-0.00021
0.00065
0.00152
0.00238 -387.654 -214.815
-41.975
130.864
303.704
390.000 -884.161
-163.316
-31.912
99.492
230.895
239.400
-0.00201 -0.00114
-0.00026
0.00062
0.00150
0.00237 -390.000 -227.068
-51.629
123.810
299.248
390.000 -889.511
-172.632
-39.252
94.128
227.508
235.800
-0.00209 -0.00120
-0.00031
0.00058
0.00147
0.00236 -390.000 -239.695
-61.578
116.539
294.656
390.000 -889.511
-182.232
-46.815
88.601
224.017
232.200
-0.00217 -0.00126
-0.00036
0.00055
0.00145
0.00235 -390.000 -252.713
-71.835
109.044
289.922
390.000 -889.511
-192.129
-54.613
82.902
220.418
228.600
-0.00225 -0.00133
-0.00041
0.00051
0.00143
0.00234 -390.000 -266.142
-82.415
101.312
285.039
390.000 -889.511
-202.338
-62.657
77.024
216.706
225.000
-0.00233 -0.00140 -0.00047
0.00047
0.00140
0.00233 -390.000 -280.000
-93.333
93.333
280.000
390.000 -889.511
-212.874
-70.958
70.958
212.874
221.400
-0.00242 -0.00147
0.00043
0.00137
0.00232 -390.000 -294.309 -104.607
85.095
274.797
390.000 -889.511
-223.753
-79.529
64.695
208.918
-0.00052
kN
Fs3
358.200
-0.00079
MPa
f s3
kN
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Fs6
Cs
Ms1
Ms2
Ms3
Ms4
Ms5
Ms6
Ms
a
Cc
Mc
Pn
Mn
kN
kN
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
kNm
Ф
Ф.Pn kN
Ф.Mn kNm
889.511
1401.486
27946.44
-3770.76
-4376.94
7496.96
31132.87
155664.35 214092.91
304.47
2329.20 169483.91
3730.68
383.58
0.65
2424.94
249.32
889.511
1375.887
30661.47
-3322.78
-4259.29
7410.98
31132.87
155664.35 217287.59
301.41
2305.79 171308.41
3681.67
388.60
0.65
2393.09
252.59
889.511
1349.764
33432.18
-2865.62
-4139.22
7323.24
31132.87
155664.35 220547.80
298.35
2282.38 173061.27
3632.14
393.61
0.65
2360.89
255.85
889.511
1323.098
36260.33
-2398.97
-4016.67
7233.68
31132.87
155664.35 223875.58
295.29
2258.97 174742.51
3582.07
398.62
0.65
2328.34
259.10
889.511
1295.874
39147.70
-1922.56
-3891.55
7142.25
31132.87
155664.35 227273.06
292.23
2235.56 176352.11
3531.43
403.63
0.65
2295.43
262.36
889.511
1266.827
42096.18
-1436.06
-3763.78
7048.88
31001.93
155664.35 230611.50
289.17
2212.15 177890.08
3478.98
408.50
0.65
2261.34
265.53
889.511
1236.712
45107.73
-939.15
-3633.28
6953.51
30821.24
155664.35 233974.39
286.11
2188.74 179356.42
3425.45
413.33
0.65
2226.54
268.67
889.511
1205.945
48184.39
-431.50
-3499.96
6856.09
30636.64
155664.35 237410.00
283.05
2165.33 180751.13
3371.28
418.16
0.65
2191.33
271.80
889.511
1174.506
51328.30
87.24
-3363.72
6756.53
30448.01
155664.35 240920.70
279.99
2141.92 182074.21
3316.43
422.99
0.65
2155.68
274.95
889.511
1142.372
54541.69
617.45
-3224.48
6654.77
30255.20
155664.35 244508.99
276.93
2118.51 183325.65
3260.89
427.83
0.65
2119.58
278.09
889.511
1109.520
57826.89
1159.51
-3082.12
6550.74
30058.09
155664.35 248177.46
273.87
2095.11 184505.47
3204.63
432.68
0.65
2083.01
281.24
889.511
1075.926
61186.33
1713.82
-2936.54
6444.36
29856.53
155664.35 251928.84
270.81
2071.70 185613.65
3147.62
437.54
0.65
2045.95
284.40
889.511
1041.564
64622.56
2280.80
-2787.64
6335.55
29650.35
155664.35 255765.96
267.75
2048.29 186650.20
3089.85
442.42
0.65
2008.40
287.57
889.511
1006.407
68138.24
2860.88
-2635.29
6224.22
29439.41
155664.35 259691.80
264.69
2024.88 187615.12
3031.29
447.31
0.65
1970.34
290.75
889.511
970.428
71736.16
3454.54
-2479.38
6110.28
29223.54
155664.35 263709.47
261.63
2001.47 188508.40
2971.90
452.22
0.65
1931.73
293.94
889.511
933.597
75419.23
4062.25
-2319.78
5993.65
29002.55
155664.35 267822.24
258.57
1978.06 189330.06
2911.66
457.15
0.65
1892.58
297.15
889.511
895.884
79190.52
4684.51
-2156.36
5874.23
28776.27
155664.35 272033.51
255.51
1954.65 190080.09
2850.54
462.11
0.65
1852.85
300.37
889.511
857.257
83053.24
5321.86
-1988.98
5751.91
28544.51
155664.35 276346.88
252.45
1931.24 190758.48
2788.50
467.11
0.65
1812.52
303.62
889.511
817.682
87010.75
5974.85
-1817.49
5626.59
28307.06
155664.35 280766.10
249.39
1907.83 191365.24
2725.52
472.13
0.65
1771.58
306.89
889.511
777.123
91066.58
6644.06
-1641.73
5498.15
28063.71
155664.35 285295.11
246.33
1884.42 191900.37
2661.55
477.20
0.65
1730.01
310.18
889.511
735.545
95224.44
7330.11
-1461.56
5366.49
27814.24
155664.35 289938.06
243.27
1861.02 192363.87
2596.56
482.30
0.65
1687.76
313.50
889.511
692.907
99488.24
8033.63
-1276.79
5231.47
27558.41
155664.35 294699.30
240.21
1837.61 192755.73
2530.51
487.46
0.65
1644.83
316.85
889.511
649.169 103862.07
8755.31
-1087.26
5092.96
27295.98
155664.35 299583.41
237.15
1814.20 193075.97
2463.37
492.66
0.65
1601.19
320.23
889.511
604.287 108350.25
9495.86
-892.77
4950.84
27026.69
155664.35 304595.21
234.09
1790.79 193324.57
2395.08
497.92
0.65
1556.80
323.65
889.511
558.216 112957.32
10256.03
-693.13
4804.94
26750.27
155664.35 309739.77
231.03
1767.38 193501.54
2325.60
503.24
0.65
1511.64
327.11
889.511
510.909 117688.07
11036.60
-488.13
4655.14
26466.42
155664.35 315022.44
227.97
1743.97 193606.89
2254.88
508.63
0.65
1465.67
330.61
889.511
462.314 122547.55
11838.42
-277.56
4501.25
26174.85
155664.35 320448.86
224.91
1720.56 193640.59
2182.88
514.09
0.65
1418.87
334.16
889.511
412.378 127541.08
12662.35
-61.17
4343.13
25875.24
155664.35 326024.97
221.85
1697.15 193602.67
2109.53
519.63
0.65
1371.20
337.76
889.511
361.046 132674.29
13509.33
161.27
4180.57
25567.25
155664.35 331757.06
218.79
1673.74 193493.12
2034.79
525.25
0.65
1322.61
341.41
889.511
308.258 137953.13
14380.34
390.02
4013.41
25250.52
155664.35 337651.76
215.73
1650.33 193311.93
1958.59
530.96
0.65
1273.09
345.13
889.511
253.951 143383.87
15276.41
625.35
3841.44
24924.67
155664.35 343716.09
212.67
1626.93 193059.11
1880.88
536.78
0.65
1222.57
348.90
889.511
198.057 148973.18
16198.65
867.55
3664.44
24589.31
155664.35 349957.48
209.61
1603.52 192734.67
1801.57
542.69
0.65
1171.02
352.75
889.511
140.508 154728.09
17148.21
1116.93
3482.20
24244.02
155664.35 356383.80
206.55
1580.11 192338.59
1720.62
548.72
0.65
1118.40
356.67
889.511
109.753 155664.35
18126.33
1373.81
3294.48
23888.34
155664.35 358011.65
203.49
1556.70 191870.87
1666.45
549.88
0.65
1083.19
357.42
889.511
83.571 155664.35
19134.31
1638.54
3101.03
23521.80
155664.35 358724.37
200.43
1533.29 191331.53
1616.86
550.06
0.65
1050.96
357.54
889.511
56.578 155664.35
20173.55
1911.47
2901.58
23143.89
155664.35 359459.19
197.37
1509.88 190720.56
1566.46
550.18
0.65
1018.20
357.62
889.511
28.734 155664.35
21245.53
2193.00
2695.85
22754.09
155664.35 360217.15
194.31
1486.47 190037.95
1515.21
550.26
0.65
984.88
357.67
889.511
0.000 155664.35
22351.80
2483.53
2483.53
22351.80
155664.35 360999.36
191.25
1463.06 189283.71
1463.06
550.28
0.65
950.99
357.68
889.511
-29.669 155664.35
23494.06
2783.52
2264.31
21936.44
155664.35 361807.02
188.19
1439.65 188457.84
1409.98
550.26
0.65
916.49
357.67
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
mm
εs6
f s1
f s2
f s3
MPa
MPa
MPa
f s4 MPa
f s5 MPa
f s6
Fs1
MPa
kN
Fs2 kN
Fs3
Fs4
kN
kN
-88.383
58.224
Fs5 kN
217.800
-0.00251 -0.00155 -0.00058
0.00038
0.00135
0.00231 -390.000 -309.091 -116.253
76.584
269.421
390.000 -889.511
-234.991
204.832
214.200
-0.00260 -0.00162 -0.00064
0.00034
0.00132
0.00230 -390.000 -324.370 -128.291
67.787
263.866
390.000 -889.511
-246.607
-97.535
51.536
200.608
210.600
-0.00270 -0.00170
-0.00070
0.00029
0.00129
0.00229 -390.000 -340.171 -140.741
58.689
258.120
390.000 -889.511
-258.620
-107.000
44.620
196.239
207.000
-0.00280 -0.00178
-0.00077
0.00025
0.00126
0.00228 -390.000 -356.522 -153.623
49.275
252.174
390.000 -889.511
-271.051
-116.794
37.462
191.719
203.400
-0.00290 -0.00187
-0.00083
0.00020
0.00123
0.00226 -390.000 -373.451 -166.962
39.528
246.018
390.000 -889.511
-283.922
-126.935
30.052
187.039
199.800
-0.00301 -0.00195
-0.00090
0.00015
0.00120
0.00225 -390.000 -390.000 -180.781
29.429
239.640
390.000 -889.511
-296.504
-137.441
22.374
182.190
196.200
-0.00312 -0.00205
-0.00098
0.00009
0.00117
0.00224 -390.000 -390.000 -195.107
18.960
233.028
390.000 -889.511
-296.504
-148.333
14.415
177.163
192.600
-0.00323 -0.00214 -0.00105
0.00004
0.00113
0.00222 -390.000 -390.000 -209.969
8.100
226.168
390.000 -889.511
-296.504
-159.632
6.158
171.948
189.000
-0.00335 -0.00224
-0.00113
-0.00002
0.00110
0.00221 -390.000 -390.000 -225.397
-3.175
219.048
390.000 -889.511
-296.504
-171.361
-2.414
166.534
185.400
-0.00347 -0.00234
-0.00121
-0.00007
0.00106
0.00219 -390.000 -390.000 -241.424
-14.887
211.650
390.000 -889.511
-296.504
-183.546
-11.318
160.911
181.800
-0.00360 -0.00245
-0.00129
-0.00014
0.00102
0.00217 -390.000 -390.000 -258.086
-27.063
203.960
390.000 -889.511
-296.504
-196.214
-20.575
155.064
178.200
-0.00373 -0.00256
-0.00138
-0.00020
0.00098
0.00216 -390.000 -390.000 -275.421
-39.731
195.960
390.000 -889.511
-296.504
-209.393
-30.206
148.981
174.600
-0.00387 -0.00267
-0.00147
-0.00026
0.00094
0.00214 -390.000 -390.000 -293.471
-52.921
187.629
390.000 -889.511
-296.504
-223.116
-40.234
142.648
171.000
-0.00402 -0.00279
-0.00156
-0.00033
0.00089
0.00212 -390.000 -390.000 -312.281
-66.667
178.947
390.000 -889.511
-296.504
-237.416
-50.684
136.047
167.400
-0.00417 -0.00291
-0.00166
-0.00041
0.00085
0.00210 -390.000 -390.000 -331.900
-81.004
169.892
390.000 -889.511
-296.504
-252.332
-61.584
129.163
163.800
-0.00433 -0.00304
-0.00176
-0.00048
0.00080
0.00208 -390.000 -390.000 -352.381
-95.971
160.440
390.000 -889.511
-296.504
-267.903
-72.963
121.977
160.200
-0.00449 -0.00318 -0.00187
-0.00056
0.00075
0.00206 -390.000 -390.000 -373.783 -111.610
150.562
390.000 -889.511
-296.504
-284.174
-84.854
114.467
156.600
-0.00466 -0.00332 -0.00198
-0.00064
0.00070
0.00204 -390.000 -390.000 -390.000 -127.969
140.230
390.000 -889.511
-296.504
-296.504
-97.291
106.612
153.000
-0.00484 -0.00347 -0.00210
-0.00073
0.00065
0.00202 -390.000 -390.000 -390.000 -145.098
129.412
390.000 -889.511
-296.504
-296.504
-110.313
98.387
149.400
-0.00503 -0.00363 -0.00222
-0.00082
0.00059
0.00200 -390.000 -390.000 -390.000 -163.052
118.072
390.000 -889.511
-296.504
-296.504
-123.963
89.766
145.800
-0.00523 -0.00379 -0.00235
-0.00091
0.00053
0.00197 -390.000 -390.000 -390.000 -181.893
106.173
390.000 -889.511
-296.504
-296.504
-138.287
80.720
142.200
-0.00544 -0.00396
-0.00249
-0.00101
0.00047
0.00195 -390.000 -390.000 -390.000 -201.688
93.671
389.030 -889.511
-296.504
-296.504
-153.336
71.215
138.600
-0.00566 -0.00414
-0.00263
-0.00111
0.00040
0.00192 -390.000 -390.000 -390.000 -222.511
80.519
383.550 -889.511
-296.504
-296.504
-169.167
61.216
135.000
-0.00589 -0.00433
-0.00278
-0.00122
0.00033
0.00189 -390.000 -390.000 -390.000 -244.444
66.667
377.778 -889.511
-296.504
-296.504
-185.843
50.684
133.000
-0.00602 -0.00444
-0.00286
-0.00129
0.00029
0.00187 -390.000 -390.000 -390.000 -257.143
58.647
374.436 -889.511
-296.504
-296.504
-195.497
44.587
131.000
-0.00616 -0.00456
-0.00295
-0.00135
0.00025
0.00185 -390.000 -390.000 -390.000 -270.229
50.382
370.992 -889.511
-296.504
-296.504
-205.446
38.303
130.000
-0.00623 -0.00462
-0.00300
-0.00138
0.00023
0.00185 -390.000 -390.000 -390.000 -276.923
46.154
369.231 -889.511
-296.504
-296.504
-210.535
35.089
0.00152
0.00238 -390.000 -216.750
303.000
390.000 -889.511
-164.788
-33.072
98.644
230.360
KONDISI TEKAN AKSIAL KECIL : Pn = 0.1 * fc' * b * h KONDISI BALANCE 242
-0.00195 -0.00108 -0.00022
0.00065
-43.500
129.750
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Fs6
Cs
Ms1
Ms2
Ms3
Ms4
Ms5
Ms6
Ms
a
Cc
Mc
Pn
Mn
kN
kN
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
kNm
Ф
Ф.Pn
Ф.Mn
kN
kNm 357.63
889.511
-60.319 155664.35
24674.07
3093.42
2037.85
21507.34
155664.35 362641.37
185.13
1416.24 187560.34
1355.93
550.20
0.65
881.35
889.511
-91.999 155664.35
25893.75
3413.74
1803.77
21063.82
155664.35 363503.77
182.07
1392.84 186591.21
1300.84
550.09
0.65
845.54
357.56
889.511
-124.762 155664.35
27155.12
3745.01
1561.68
20605.14
155664.35 364395.65
179.01
1369.43 185550.44
1244.66
549.95
0.65
809.03
357.46
889.511
-158.664 155664.35
28460.37
4087.80
1311.18
20130.51
155664.35 365318.55
175.95
1346.02 184438.05
1187.35
549.76
0.65
771.78
357.34
889.511
-193.767 155664.35
29811.82
4442.73
1051.81
19639.07
155664.35 366274.13
172.89
1322.61 183254.02
1128.84
549.53
0.65
733.75
357.19
889.511
-229.381 155664.35
31132.87
4810.45
783.10
19129.92
155664.35 367185.03
169.83
1299.20 181998.36
1069.82
549.18
0.65
695.38
356.97
889.511
-253.259 155664.35
31132.87
5191.66
504.52
18602.09
155664.35 366759.83
166.77
1275.79 180671.07
1022.53
547.43
0.65
664.65
355.83
889.511
-278.030 155664.35
31132.87
5587.12
215.53
18054.53
155664.35 366318.74
163.71
1252.38 179272.15
974.35
545.59
0.65
633.33
354.63
889.511
-303.744 155664.35
31132.87
5997.65
-84.47
17486.10
155664.35 365860.84
160.65
1228.97 177801.60
925.23
543.66
0.65
601.40
353.38
889.511
-330.457 155664.35
31132.87
6424.12
-396.13
16895.61
155664.35 365385.16
157.59
1205.56 176259.41
875.11
541.64
0.65
568.82
352.07
889.511
-358.228 155664.35
31132.87
6867.48
-720.12
16281.72
155664.35 364890.64
154.53
1182.15 174645.60
823.93
539.54
0.65
535.55
350.70
889.511
-387.121 155664.35
31132.87
7328.75
-1057.20
15643.04
155664.35 364376.15
151.47
1158.75 172960.15
771.62
537.34
0.65
501.56
349.27
889.511
-417.205 155664.35
31132.87
7809.05
-1408.19
14978.01
155664.35 363840.43
148.41
1135.34 171203.07
718.13
535.04
0.65
466.79
347.78
889.511
-448.557 155664.35
31132.87
8309.57
-1773.95
14284.99
155664.35 363282.16
145.35
1111.93 169374.36
663.37
532.66
0.65
431.19
346.23
889.511
-481.256 155664.35
31132.87
8831.61
-2155.45
13562.15
155664.35 362699.88
142.29
1088.52 167474.01
607.26
530.17
0.65
394.72
344.61
889.511
-515.393 155664.35
31132.87
9376.61
-2553.71
12807.55
155664.35 362092.00
139.23
1065.11 165502.04
549.72
527.59
0.65
357.32
342.94
889.511
-551.064 155664.35
31132.87
9946.09
-2969.88
12019.03
155664.35 361456.81
136.17
1041.70 163458.43
490.64
524.92
0.65
318.91
341.19
889.511
-583.686 155664.35
31132.87
10377.62
-3405.17
11194.25
155664.35 360628.26
133.11
1018.29 161343.20
434.61
521.97
0.65
282.49
339.28
889.511
-604.933 155664.35
31132.87
10377.62
-3860.96
10330.67
155664.35 359308.89
130.05
994.88 159156.33
389.95
518.47
0.66
255.64
339.89
889.511
-627.204 155664.35
31132.87
10377.62
-4338.70
9425.46
155664.35 357925.94
126.99
971.47 156897.83
344.27
514.82
0.67
231.52
346.22
889.511
-650.574 155664.35
31132.87
10377.62
-4840.04
8475.55
155664.35 356474.69
123.93
948.06 154567.70
297.49
511.04
0.69
205.21
352.53
887.297
-677.342 155664.35
31132.87
10377.62
-5366.77
7477.55
155276.99 354562.61
120.87
924.66 152165.93
247.31
506.73
0.71
175.20
358.97
874.799
-715.670 155664.35
31132.87
10377.62
-5920.85
6427.70
153089.81 350771.49
117.81
901.25 149692.54
185.58
500.46
0.73
135.71
365.97
861.634
-756.042 155664.35
31132.87
10377.62
-6504.49
5321.86
150785.98 346778.18
114.75
877.84 147147.51
121.80
493.93
0.75
91.94
372.86
854.012
-779.415 155664.35
31132.87
10377.62
-6842.39
4681.63
149452.18 344466.26
113.05
864.83 145702.66
85.42
490.17
0.77
65.63
376.63
846.158
-803.502 155664.35
31132.87
10377.62
-7190.60
4021.86
148077.65 342083.75
111.35
851.83 144235.69
48.33
486.32
0.78
37.80
380.35
842.140
-815.823 155664.35
31132.87
10377.62
-7368.73
3684.36
147374.53 340865.00
110.50
845.32 143493.92
29.50
484.36
0.79
23.28
382.19
263.25
0.00
263.25
450.00
0.00 889.511
131.146 155664.35
17302.69
1157.50
3452.56
24187.84
155664.35 357429.28
206.06
1576.36 192268.60
1707.51
549.70
0.65
1109.88
0.00 357.30
Analisis Kekuatan Kolo Beton Bertulang Dengan Diagram Interaksi
ANALISIS KEKUATAN KOLOM BETON BERTULANG DENGAN DIAGRAM INTERAKSI [C]2010 : M. Noer Ilham
KODE KOLOM
K5
INPUT DATA KOLOM
f c' = f y =
Kuat tekan beton, Tegangan leleh baja,
b= h= ds = n= D=
Lebar kolom, Tinggi kolom, Tebal brutto selimut beton, Jumlah tulangan, Diameter tulangan,
20
MPa
390
MPa
400
mm
400
mm
50
mm
16
buah
16
mm
PERHITUNGAN DIAGRAM INTERAKSI Es =
Modulus elastis baja,
2.E+05 MPa
β1 = 0.85
untuk f c' 30 MPa
β1 = 0.85 - 0.008 (f c' - 30)
untuk f c ' > 30 MPa
Faktor distribusi tegangan,
β1 =
0.85
2
3217
2
mm
Luas tulangan total,
As = n * p / 4 * D =
Jarak antara tulangan,
x = ( h - 2*d s ) / 4 = 75.000 mm
Rasio tulangan,
r = As / Ag =
Faktor reduksi kekuatan, f = 0.65 untuk P n ≥ 0.1 * fc' * b * h f=
0.80 untuk P n = 0
2.01%
Untuk : 0
≤
Pn ≤ 0.1 * f c' * b * h
f = 0.65 + 0.15 * ( Pno - Pn ) / Pno
Analisis Kekuatan Kolo Beton Bertulang Dengan Diagram Interaksi
2500 2400 2300
b
2200 2100 2000 1900
h
1800 1700
b=
400
mm
h=
400
mm
16 f c' =
D
16
20
MPa
f y =
390
MPa
1600 1500 ) N k ( n P . f
1400 1300 1200 1100 1000 900 800
Pu
Mu
(kN)
(kNm)
700
272.940
47.209
600
562.606
58.301
466.181
13.286
300
206.697
59.716
200
263.048
74.788
271.746
77.483
319.249
41.136
190.370
118.304
121.417
116.696
148.502
106.551
500 400
100 0 0
10
20
30
40
50
60
70
80
90
100 110 120 130 140 150 160 170 180 190 200
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
Analisis Kekuatan Kolo Beton Bertulang Dengan Diagram Interaksi
No
Luas masing-masing tulangan
Jarak tulangan thd. sisi beton 2
1
As1 = 5/16 * A s = 1005
mm
2
As2 = 2/16 * A s =
mm
3 4 5
As3 = 2/16 * A s = As4 = 2/16 * A s =
402 402 402
As5 = 5/16 * A s = 1005 As = 3217
2 2
mm
2
mm
2
mm
Pada kondisi tekan aksial sentris (M no = 0) : -3
d1 = 4*x + d s =
350
mm
Pno = 0.80*[ 0.85*f c' *b*h + A s*(f y - 0.85*f c')]*10
d2 = 3*x + d s =
275
mm
Pno =
3136
kN
-3
320
kN
d3 = 2*x + d s =
200
mm
0.1 * f c' * b * h *10 =
d4 =
x + ds =
125
mm
Pada kondisi balance :
d5 =
ds =
50
mm
c = cb = 600 / (600 + f y) * d1 =
212.12 mm
2
mm
Pada kondisi garis netral terletak pada jarak c dari sisi beton tekan terluar : Regangan pada masing-masing baja tulangan :
εsi = 0.003 * ( c - di ) / c
Tegangan pada masing-masing baja tulangan : Untuk | εsi | < f y / Es maka : f si = esi* Es Untuk
| εsi | f y / Es maka : f si =| εsi | / esi* f y Jumlah interval jarak grs netral =
URAIAN PERHITUNGAN Gaya-gaya internal pada masing-masing baja tulangan : Resultan gaya internal baja tulangan : Momen akibat gaya internal masing-masing baja tulangan : Tinggi blok tegangan tekan beton, Gaya internal pada beton tekan : Momen akibat gaya internal tekan beton : Gaya aksial nominal : Momen nominal : Gaya aksial rencana : Momen rencana :
125
PERSAMAAN
→
Dc =
3.2000
UNIT -3
Fsi = Asi * f si * 10 -3 Cs = [ S Fsi ]*10 Msi = Fsi*(h/2 - di) Ms = S Msi a = β1 * c -3 Cc = 0.85 * f c' * b * a * 10 Mc = Cc * (h - a) / 2 Pn = Cs + Cc -3 Mn = (Mc + Ms)*10 Pu = f * Pn Mu = f * Mn
kN kN kNmm kNmm mm kN kNmm kN kNm kN kNm
Analisis Kekuatan Kolo Beton Bertulang Dengan Diagram Interaksi
2500 2400 2300
b
2200 2100 2000 1900
h
1800 1700
b=
400
mm
1500
h=
400
mm
1400
16
D
16
1300
f c' =
20
MPa
f y =
390
MPa
1600
) N k ( n P . f
1200 1100 1000 900
Pu
Mu
(kN)
(kNm)
800 700
272.940
47.209
600
562.606
58.301
466.181
13.286
300
206.697
59.716
200
263.048
74.788
271.746
77.483
319.249
41.136
190.370
118.304
121.417
116.696
148.502
106.551
500 400
100 0 0
10
20
30
40
50
60
70
80
90
100 110 120 130 140 150 160 170 180 190 200
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
Analisis Kekuatan Kolo Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
mm
f s1
f s2
f s3
f s4
f s5
Fs1
Fs2
Fs3
Fs4
Fs5
MPa
MPa
MPa
MPa
MPa
kN
kN
kN
kN
kN
KONDISI TEKAN AKSIAL SENTRIS 420.00
0.00050
0.00104
0.00157
0.00211
0.00264
100.000
207.143
314.286
390.000
390.000
100.531
83.297
126.382
156.828
392.071
416.80
0.00048
0.00102
0.00156
0.00210
0.00264
96.161
204.127
312.092
390.000
390.000
96.672
82.084
125.500
156.828
392.071
413.60
0.00046
0.00101
0.00155
0.00209
0.00264
92.263
201.064
309.865
390.000
390.000
92.753
80.853
124.604
156.828
392.071
410.40
0.00044
0.00099
0.00154
0.00209
0.00263
88.304
197.953
307.602
390.000
390.000
88.773
79.602
123.694
156.828
392.071
407.20
0.00042
0.00097
0.00153
0.00208
0.00263
84.283
194.794
305.305
390.000
390.000
84.730
78.331
122.770
156.828
392.071
404.00
0.00040
0.00096
0.00151
0.00207
0.00263
80.198
191.584
302.970
390.000
390.000
80.624
77.041
121.832
156.828
392.071
400.80
0.00038
0.00094
0.00150
0.00206
0.00263
76.048
188.323
300.599
390.000
390.000
76.452
75.729
120.878
156.828
392.071
397.60
0.00036
0.00093
0.00149
0.00206
0.00262
71.831
185.010
298.189
390.000
390.000
72.212
74.397
119.909
156.828
392.071
394.40
0.00034
0.00091
0.00148
0.00205
0.00262
67.546
181.643
295.740
390.000
390.000
67.904
73.043
118.924
156.828
392.071
391.20
0.00032
0.00089
0.00147
0.00204
0.00262
63.190
178.221
293.252
390.000
390.000
63.526
71.667
117.923
156.828
392.071
388.00
0.00029
0.00087
0.00145
0.00203
0.00261
58.763
174.742
290.722
390.000
390.000
59.075
70.268
116.906
156.828
392.071
384.80
0.00027
0.00086
0.00144
0.00203
0.00261
54.262
171.206
288.150
390.000
390.000
54.550
68.846
115.872
156.828
392.071
381.60
0.00025
0.00084
0.00143
0.00202
0.00261
49.686
167.610
285.535
390.000
390.000
49.949
67.400
114.820
156.828
392.071
378.40
0.00023
0.00082
0.00141
0.00201
0.00260
45.032
163.953
282.875
390.000
390.000
45.271
65.930
113.751
156.828
392.071
375.20
0.00020
0.00080
0.00140
0.00200
0.00260
40.299
160.235
280.171
390.000
390.000
40.512
64.434
112.663
156.828
392.071
372.00
0.00018
0.00078
0.00139
0.00199
0.00260
35.484
156.452
277.419
390.000
390.000
35.672
62.913
111.557
156.828
392.071
368.80
0.00015
0.00076
0.00137
0.00198
0.00259
30.586
152.603
274.620
390.000
390.000
30.748
61.365
110.431
156.828
392.071
365.60
0.00013
0.00074
0.00136
0.00197
0.00259
25.602
148.687
271.772
390.000
390.000
25.738
59.791
109.286
156.828
392.071
362.40
0.00010
0.00072
0.00134
0.00197
0.00259
20.530
144.702
268.874
390.000
390.000
20.639
58.188
108.121
156.828
392.071
359.20
0.00008
0.00070
0.00133
0.00196
0.00258
15.367
140.646
265.924
390.000
390.000
15.449
56.557
106.934
156.828
392.071
356.00
0.00005
0.00068
0.00131
0.00195
0.00258
10.112
136.517
262.921
389.326
390.000
10.166
54.897
105.727
156.557
392.071
352.80
0.00002
0.00066
0.00130
0.00194
0.00257
4.762
132.313
259.864
387.415
390.000
4.787
53.206
104.497
155.789
392.071
349.60
0.00000
0.00064
0.00128
0.00193
0.00257
-0.686
128.032
256.751
385.469
390.000
-0.690
51.485
103.246
155.006
392.071
346.40
-0.00003
0.00062
0.00127
0.00192
0.00257
-6.236
123.672
253.580
383.487
390.000
-6.269
49.731
101.970
154.209
392.071
343.20
-0.00006
0.00060
0.00125
0.00191
0.00256
-11.888
119.231
250.350
381.469
390.000
-11.951
47.946
100.672
153.398
392.071
340.00
-0.00009
0.00057
0.00124
0.00190
0.00256
-17.647
114.706
247.059
379.412
390.000
-17.741
46.126
99.348
152.571
392.071
336.80
-0.00012
0.00055
0.00122
0.00189
0.00255
-23.515
110.095
243.705
377.316
390.000
-23.640
44.272
98.000
151.728
392.071
333.60
-0.00015
0.00053
0.00120
0.00188
0.00255
-29.496
105.396
240.288
375.180
390.000
-29.653
42.382
96.625
150.869
392.071
330.40
-0.00018
0.00050
0.00118
0.00187
0.00255
-35.593
100.605
236.804
373.002
390.000
-35.782
40.456
95.224
149.993
392.071
327.20
-0.00021
0.00048
0.00117
0.00185
0.00254
-41.809
95.721
233.252
370.782
390.000
-42.031
38.492
93.796
149.100
392.071
324.00
-0.00024
0.00045
0.00115
0.00184
0.00254
-48.148
90.741
229.630
368.519
390.000
-48.404
36.489
92.340
148.190
392.071
320.80
-0.00027
0.00043
0.00113
0.00183
0.00253
-54.613
85.661
225.935
366.209
390.000
-54.903
34.446
90.854
147.262
392.071
317.60
-0.00031
0.00040
0.00111
0.00182
0.00253
-61.209
80.479
222.166
363.854
390.000
-61.534
32.362
89.338
146.314
392.071
314.40
-0.00034
0.00038
0.00109
0.00181
0.00252
-67.939
75.191
218.321
361.450
390.000
-68.300
30.236
87.792
145.348
392.071
311.20
-0.00037
0.00035
0.00107
0.00179
0.00252
-74.807
69.794
214.396
358.997
390.000
-75.204
28.066
86.214
144.361
392.071
308.00
-0.00041
0.00032
0.00105
0.00178
0.00251
-81.818
64.286
210.390
356.494
390.000
-82.253
25.851
84.603
143.355
392.071
304.80
-0.00044
0.00029
0.00103
0.00177
0.00251
-88.976
58.661
206.299
353.937
390.000
-89.449
23.589
82.958
142.327
392.071
301.60
-0.00048
0.00026
0.00101
0.00176
0.00250
-96.286
52.918
202.122
351.326
390.000
-96.798
21.279
81.278
141.277
392.071
Analisis Kekuatan Kolo Beton Bertulang Dengan Diagram Interaksi
Cs
Ms1
Ms2
Ms3
Ms4
Ms5
Ms
a
Cc
Mc
Pn
Mn
kN
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
kNm
3135.95
0.00
Ф.Pn
Ф
kN 0.65
2038.37
Ф.Mn kNm 0.00
859.109
-15079.64
-6247.28
0.00
11762.12
58810.61
49245.81
357.00
2427.60
52193.40
3135.95
101.44
0.65
2038.37
65.94
853.155
-14500.77
-6156.32
0.00
11762.12
58810.61
49915.65
354.28
2409.10
55072.12
3135.95
104.99
0.65
2038.37
68.24
847.109
-13912.94
-6063.94
0.00
11762.12
58810.61
50595.85
351.56
2390.61
57900.53
3135.95
108.50
0.65
2038.37
70.52
840.968
-13315.94
-5970.13
0.00
11762.12
58810.61
51286.67
348.84
2372.11
60678.62
3135.95
111.97
0.65
2038.37
72.78
834.731
-12709.56
-5874.84
0.00
11762.12
58810.61
51988.33
346.12
2353.62
63406.42
3135.95
115.39
0.65
2038.37
75.01
828.395
-12093.58
-5778.04
0.00
11762.12
58810.61
52701.12
343.40
2335.12
66083.90
3135.95
118.79
0.65
2038.37
77.21
821.958
-11467.75
-5679.70
0.00
11762.12
58810.61
53425.29
340.68
2316.62
68711.07
3135.95
122.14
0.65
2038.37
79.39
815.417
-10831.86
-5579.77
0.00
11762.12
58810.61
54161.11
337.96
2298.13
71287.93
3113.55
125.45
0.65
2023.80
81.54
808.771
-10185.64
-5478.22
0.00
11762.12
58810.61
54908.87
335.24
2279.63
73814.48
3088.40
128.72
0.65
2007.46
83.67
802.015
-9528.86
-5375.01
0.00
11762.12
58810.61
55668.87
332.52
2261.14
76290.73
3063.15
131.96
0.65
1991.05
85.77
795.148
-8861.23
-5270.10
0.00
11762.12
58810.61
56441.40
329.80
2242.64
78716.66
3037.79
135.16
0.65
1974.56
87.85
788.167
-8182.51
-5163.45
0.00
11762.12
58810.61
57226.78
327.08
2224.14
81092.29
3012.31
138.32
0.65
1958.00
89.91
781.069
-7492.40
-5055.00
0.00
11762.12
58810.61
58025.33
324.36
2205.65
83417.61
2986.72
141.44
0.65
1941.37
91.94
773.850
-6790.62
-4944.72
0.00
11762.12
58810.61
58837.39
321.64
2187.15
85692.62
2961.00
144.53
0.65
1924.65
93.94
766.509
-6076.87
-4832.56
0.00
11762.12
58810.61
59663.31
318.92
2168.66
87917.31
2935.16
147.58
0.65
1907.86
95.93
759.041
-5350.84
-4718.47
0.00
11762.12
58810.61
60503.43
316.20
2150.16
90091.70
2909.20
150.60
0.65
1890.98
97.89
751.444
-4612.21
-4602.40
0.00
11762.12
58810.61
61358.13
313.48
2131.66
92215.78
2883.11
153.57
0.65
1874.02
99.82
743.714
-3860.65
-4484.30
0.00
11762.12
58810.61
62227.79
310.76
2113.17
94289.56
2856.88
156.52
0.65
1856.97
101.74
735.847
-3095.82
-4364.11
0.00
11762.12
58810.61
63112.81
308.04
2094.67
96313.02
2830.52
159.43
0.65
1839.84
103.63
727.840
-2317.36
-4241.78
0.00
11762.12
58810.61
64013.60
305.32
2076.18
98286.17
2804.02
162.30
0.65
1822.61
105.49
719.418
-1524.91
-4117.25
0.00
11741.79
58810.61
64910.25
302.60
2057.68
100209.02
2777.10
165.12
0.65
1805.11
107.33
710.350
-718.08
-3990.46
0.00
11684.16
58810.61
65786.23
299.88
2039.18
102081.55
2749.53
167.87
0.65
1787.20
109.11
701.117
103.52
-3861.36
0.00
11625.47
58810.61
66678.26
297.16
2020.69
103903.78
2721.81
170.58
0.65
1769.17
110.88
691.713
940.30
-3729.86
0.00
11565.70
58810.61
67586.76
294.44
2002.19
105675.69
2693.91
173.26
0.65
1751.04
112.62
682.134
1792.69
-3595.92
0.00
11504.82
58810.61
68512.20
291.72
1983.70
107397.30
2665.83
175.91
0.65
1732.79
114.34
672.375
2661.11
-3459.45
0.00
11442.79
58810.61
69455.07
289.00
1965.20
109068.60
2637.57
178.52
0.65
1714.42
116.04
662.430
3546.04
-3320.39
0.00
11379.58
58810.61
70415.85
286.28
1946.70
110689.59
2609.13
181.11
0.65
1695.94
117.72
652.294
4447.95
-3178.66
0.00
11315.16
58810.61
71395.07
283.56
1928.21
112260.27
2580.50
183.66
0.65
1677.33
119.38
641.962
5367.33
-3034.19
0.00
11249.49
58810.61
72393.25
280.84
1909.71
113780.64
2551.67
186.17
0.65
1658.59
121.01
631.428
6304.69
-2886.89
0.00
11182.53
58810.61
73410.96
278.12
1891.22
115250.70
2522.64
188.66
0.65
1639.72
122.63
620.686
7260.57
-2736.68
0.00
11114.26
58810.61
74448.76
275.40
1872.72
116670.46
2493.41
191.12
0.65
1620.71
124.23
609.729
8235.52
-2583.47
0.00
11044.62
58810.61
75507.28
272.68
1854.22
118039.90
2463.95
193.55
0.65
1601.57
125.81
598.552
9230.11
-2427.18
0.00
10973.58
58810.61
76587.12
269.96
1835.73
119359.03
2434.28
195.95
0.65
1582.28
127.37
587.147
10244.95
-2267.70
0.00
10901.09
58810.61
77688.95
267.24
1817.23
120627.86
2404.38
198.32
0.65
1562.85
128.91
575.507
11280.66
-2104.95
0.00
10827.11
58810.61
78813.43
264.52
1798.74
121846.38
2374.24
200.66
0.65
1543.26
130.43
563.626
12337.89
-1938.81
0.00
10751.59
58810.61
79961.29
261.80
1780.24
123014.58
2343.87
202.98
0.65
1523.51
131.93
551.495
13417.32
-1769.19
0.00
10674.49
58810.61
81133.24
259.08
1761.74
124132.48
2313.24
205.27
0.65
1503.61
133.42
539.107
14519.66
-1595.96
0.00
10595.75
58810.61
82330.06
256.36
1743.25
125200.07
2282.36
207.53
0.65
1483.53
134.89
Analisis Kekuatan Kolo Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
mm
f s1
f s2
MPa
MPa
f s3
f s4
f s5
Fs1 kN
Fs2
Fs3
Fs4 kN
Fs5
MPa
MPa
MPa
kN
kN
298.40
-0.00052
0.00024
0.00099
0.00174
0.00250
-103.753
47.051
197.855
348.660
390.000
-104.304
18.920
79.562
140.204
392.071
kN
295.20
-0.00056
0.00021
0.00097
0.00173
0.00249
-111.382
41.057
193.496
345.935
390.000
-111.974
16.510
77.809
139.109
392.071
292.00
-0.00060
0.00017
0.00095
0.00172
0.00249
-119.178
34.932
189.041
343.151
390.000
-119.811
14.047
76.018
137.989
392.071
288.80
-0.00064
0.00014
0.00092
0.00170
0.00248
-127.147
28.670
184.488
340.305
390.000
-127.822
11.529
74.187
136.845
392.071
285.60
-0.00068
0.00011
0.00090
0.00169
0.00247
-135.294
22.269
179.832
337.395
390.000
-136.012
8.955
72.315
135.675
392.071
282.40
-0.00072
0.00008
0.00088
0.00167
0.00247
-143.626
15.722
175.071
334.419
390.000
-144.389
6.322
70.400
134.478
392.071
279.20
-0.00076
0.00005
0.00085
0.00166
0.00246
-152.149
9.026
170.201
331.375
390.000
-152.957
3.629
68.442
133.254
392.071
276.00
-0.00080
0.00001
0.00083
0.00164
0.00246
-160.870
2.174
165.217
328.261
390.000
-161.724
0.874
66.438
132.002
392.071
272.80
-0.00085
- 0.00002
0.00080
0.00163
0.00245
-169.795
-4.839
160.117
325.073
390.000
-170.696
-1.946
64.387
130.720
392.071
269.60
- 0.00089
- 0.00006
0.00077
0.00161
0.00244
-178.932
-12.018
154.896
321.810
390.000
- 179.882
-4.833
62.287
129.408
392.071
266.40
- 0.00094
- 0.00010
0.00075
0.00159
0.00244
-188.288
-19.369
149.550
318.468
390.000
- 189.288
-7.789
60.137
128.064
392.071
263.20
-0.00099
-0.00013
0.00072
0.00158
0.00243
-197.872
-26.900
144.073
315.046
390.000
-198.923
-10.817
57.935
126.687
392.071
260.00
-0.00104
-0.00017
0.00069
0.00156
0.00242
-207.692
-34.615
138.462
311.538
390.000
-208.795
-13.920
55.679
125.277
392.071
256.80
-0.00109
-0.00021
0.00066
0.00154
0.00242
-217.757
-42.523
132.710
307.944
390.000
-218.913
-17.100
53.366
123.832
392.071
253.60
-0.00114
-0.00025
0.00063
0.00152
0.00241
-228.076
-50.631
126.814
304.259
390.000
-229.287
-20.360
50.995
122.350
392.071
250.40
-0.00119
-0.00029
0.00060
0.00150
0.00240
-238.658
-58.946
120.767
300.479
390.000
-239.925
-23.703
48.563
120.830
392.071
247.20
-0.00125
-0.00034
0.00057
0.00148
0.00239
-249.515
-67.476
114.563
296.602
390.000
-250.839
-27.134
46.069
119.271
392.071
244.00
-0.00130
-0.00038
0.00054
0.00146
0.00239
-260.656
-76.230
108.197
292.623
390.000
-262.040
-30.654
43.508
117.671
392.071
240.80
-0.00136
-0.00043
0.00051
0.00144
0.00238
-272.093
-85.216
101.661
288.538
390.000
-273.538
-34.267
40.880
116.028
392.071
237.60
- 0.00142
- 0.00047
0.00047
0.00142
0.00237
-283.838
-94.444
94.949
284.343
390.000
- 285.345
-37.978
38.181
114.341
392.071
234.40
-0.00148
-0.00052
0.00044
0.00140
0.00236
-295.904
-103.925
88.055
280.034
390.000
-297.476
-41.791
35.409
112.608
392.071
231.20
-0.00154
-0.00057
0.00040
0.00138
0.00235
-308.304
-113.668
80.969
275.606
390.000
-309.941
-45.709
32.560
110.828
392.071
228.00
-0.00161
-0.00062
0.00037
0.00136
0.00234
-321.053
-123.684
73.684
271.053
390.000
-322.757
-49.736
29.630
108.997
392.071
224.80
-0.00167
-0.00067
0.00033
0.00133
0.00233
-334.164
-133.986
66.192
266.370
390.000
-335.938
-53.879
26.617
107.114
392.071
221.60
-0.00174
-0.00072
0.00029
0.00131
0.00232
-347.653
-144.585
58.484
261.552
390.000
-349.499
-58.141
23.518
105.176
392.071
218.40
-0.00181
-0.00078
0.00025
0.00128
0.00231
-361.538
-155.495
50.549
256.593
390.000
-363.458
-62.528
20.327
103.182
392.071
215.20
-0.00188
-0.00083
0.00021
0.00126
0.00230
-375.836
-166.729
42.379
251.487
390.000
-377.832
-67.046
17.042
101.129
392.071
212.00
- 0.00195
- 0.00089
0.00017
0.00123
0.00229
-390.000
-178.302
33.962
246.226
390.000
- 392.071
-71.699
13.657
99.014
392.071
208.80
- 0.00203
- 0.00095
0.00013
0.00120
0.00228
-390.000
-190.230
25.287
240.805
390.000
- 392.071
-76.496
10.169
96.833
392.071
205.60
-0.00211
- 0.00101
0.00008
0.00118
0.00227
-390.000
-202.529
16.342
235.214
390.000
-392.071
-81.442
6.572
94.585
392.071
202.40
-0.00219
-0.00108
0.00004
0.00115
0.00226
-390.000
-215.217
7.115
229.447
390.000
-392.071
-86.544
2.861
92.266
392.071
199.20
- 0.00227
- 0.00114
- 0.00001
0.00112
0.00225
-390.000
-228.313
-2.410
223.494
390.000
- 392.071
-91.810
-0.969
89.872
392.071
196.00
-0.00236
-0.00121
-0.00006
0.00109
0.00223
-390.000
-241.837
-12.245
217.347
390.000
-392.071
-97.248
-4.924
87.400
392.071
192.80
-0.00245
-0.00128
-0.00011
0.00105
0.00222
-390.000
-255.809
-22.407
210.996
390.000
-392.071
-102.867
-9.010
84.846
392.071
189.60
-0.00254
-0.00135
-0.00016
0.00102
0.00221
-390.000
-270.253
-32.911
204.430
390.000
- 392.071
-108.675
-13.234
82.206
392.071
186.40
-0.00263
-0.00143
-0.00022
0.00099
0.00220
-390.000
-285.193
-43.777
197.639
390.000
- 392.071
-114.683
-17.604
79.476
392.071
183.20
-0.00273
-0.00150
-0.00028
0.00095
0.00218
-390.000
-300.655
-55.022
190.611
390.000
- 392.071
-120.901
-22.126
76.649
392.071
180.00
-0.00283
-0.00158
-0.00033
0.00092
0.00217
-390.000
-316.667
-66.667
183.333
390.000
- 392.071
-127.339
-26.808
73.723
392.071
176.80
-0.00294
-0.00167
-0.00039
0.00088
0.00215
-390.000
-333.258
-78.733
175.792
390.000
- 392.071
-134.011
-31.660
70.690
392.071
Analisis Kekuatan Kolo Beton Bertulang Dengan Diagram Interaksi
Cs
Ms1
Ms2
Ms3
Ms4
Ms5
Ms
a
Cc
Mc
Pn
Mn
kN
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
kNm
526.453
15645.64
-1419.02
0.00
10515.32
58810.61
83552.55
253.64
1724.75
126217.35
2251.21
209.77
0.65
1463.28
136.35
513.525
16796.03
-1238.25
0.00
10433.15
58810.61
84801.55
250.92
1706.26
127184.32
2219.78
211.99
0.65
1442.86
137.79
500.314
17971.63
-1053.51
0.00
10349.18
58810.61
86077.92
248.20
1687.76
128100.98
2188.07
214.18
0.65
1422.25
139.22
486.809
19173.29
-864.68
0.00
10263.35
58810.61
87382.57
245.48
1669.26
128967.34
2156.07
216.35
0.65
1401.45
140.63
473.002
20401.87
-671.61
0.00
10175.59
58810.61
88716.46
242.76
1650.77
129783.38
2123.77
218.50
0.65
1380.45
142.02
458.883
21658.30
-474.18
0.00
10085.85
58810.61
90080.59
240.04
1632.27
130549.11
2091.15
220.63
0.65
1359.25
143.41
444.439
22943.53
-272.21
0.00
9994.05
58810.61
91475.98
237.32
1613.78
131264.54
2058.22
222.74
0.65
1337.84
144.78
429.661
24258.56
-65.56
0.00
9900.11
58810.61
92903.72
234.60
1595.28
131929.66
2024.94
224.83
0.65
1316.21
146.14
414.535
25604.44
145.93
0.00
9803.98
58810.61
94364.97
231.88
1576.78
132544.46
1991.32
226.91
0.65
1294.36
147.49
399.051
26982.27
362.45
0.00
9705.56
58810.61
95860.90
229.16
1558.29
133108.96
1957.34
228.97
0.65
1272.27
148.83
383.195
28393.20
584.17
0.00
9604.78
58810.61
97392.77
226.44
1539.79
133623.15
1922.99
231.02
0.65
1249.94
150.16
366.953
29838.45
811.28
0.00
9501.55
58810.61
98961.89
223.72
1521.30
134087.03
1888.25
233.05
0.65
1227.36
151.48
350.312
31319.26
1043.98
0.00
9395.78
58810.61
100569.63
221.00
1502.80
134500.60
1853.11
235.07
0.65
1204.52
152.80
333.255
32836.98
1282.47
0.00
9287.37
58810.61
102217.44
218.28
1484.30
134863.86
1817.56
237.08
0.65
1181.41
154.10
315.769
34393.01
1526.99
0.00
9176.23
58810.61
103906.84
215.56
1465.81
135176.81
1781.58
239.08
0.65
1158.02
155.40
297.835
35988.80
1777.76
0.00
9062.24
58810.61
105639.42
212.84
1447.31
135439.46
1745.15
241.08
0.65
1134.35
156.70
279.437
37625.91
2035.02
0.00
8945.30
58810.61
107416.85
210.12
1428.82
135651.79
1708.25
243.07
0.65
1110.36
157.99
260.556
39305.96
2299.03
0.00
8825.30
58810.61
109240.90
207.40
1410.32
135813.82
1670.88
245.05
0.65
1086.07
159.29
241.174
41030.66
2570.05
0.00
8702.11
58810.61
111113.44
204.68
1391.82
135925.53
1633.00
247.04
0.65
1061.45
160.58
221.270
42801.82
2848.38
0.00
8575.60
58810.61
113036.41
201.96
1373.33
135986.94
1594.60
249.02
0.65
1036.49
161.87
200.822
44621.34
3134.30
0.00
8445.63
58810.61
115011.88
199.24
1354.83
135998.04
1555.65
251.01
0.65
1011.17
163.16
179.808
46491.22
3428.14
0.00
8312.07
58810.61
117042.05
196.52
1336.34
135958.82
1516.14
253.00
0.65
985.49
164.45
158.204
48413.60
3730.23
0.00
8174.75
58810.61
119129.19
193.80
1317.84
135869.30
1476.04
255.00
0.65
959.43
165.75
135.985
50390.70
4040.92
0.00
8033.53
58810.61
121275.76
191.08
1299.34
135729.47
1435.33
257.01
0.65
932.96
167.05
113.125
52424.90
4360.58
0.00
7888.23
58810.61
123484.33
188.36
1280.85
135539.34
1393.97
259.02
0.65
906.08
168.37
89.594
54518.72
4689.60
0.00
7738.67
58810.61
125757.61
185.64
1262.35
135298.89
1351.95
261.06
0.65
878.76
169.69
65.364
56674.80
5028.42
0.00
7584.67
58810.61
128098.50
182.92
1243.86
135008.13
1309.22
263.11
0.65
850.99
171.02
40.971
58810.61
5377.46
0.00
7426.01
58810.61
130424.70
180.20
1225.36
134667.06
1266.33
265.09
0.65
823.12
172.31
30.506
58810.61
5737.20
0.00
7262.50
58810.61
130620.92
177.48
1206.86
134275.69
1237.37
264.90
0.65
804.29
172.18
19.715
58810.61
6108.14
0.00
7093.89
58810.61
130823.25
174.76
1188.37
133834.00
1208.08
264.66
0.65
785.25
172.03
8.583
58810.61
6490.80
0.00
6919.95
58810.61
131031.98
172.04
1169.87
133342.01
1178.45
264.37
0.65
766.00
171.84
-2.907
58810.61
6885.77
0.00
6740.42
58810.61
131247.41
169.32
1151.38
132799.71
1148.47
264.05
0.65
746.50
171.63
-14.772
58810.61
7293.62
0.00
6555.03
58810.61
131469.88
166.60
1132.88
132207.10
1118.11
263.68
0.65
726.77
171.39
-27.031
58810.61
7715.02
0.00
6363.48
58810.61
131699.74
163.88
1114.38
131564.18
1087.35
263.26
0.65
706.78
171.12
-39.703
58810.61
8150.64
0.00
6165.48
58810.61
131937.35
161.16
1095.89
130870.94
1056.18
262.81
0.65
686.52
170.83
-52.811
58810.61
8601.22
0.00
5960.67
58810.61
132183.12
158.44
1077.39
130127.41
1024.58
262.31
0.65
665.98
170.50
-66.377
58810.61
9067.54
0.00
5748.70
58810.61
132437.47
155.72
1058.90
129333.56
992.52
261.77
0.65
645.14
170.15
-80.425
58810.61
9550.44
0.00
5529.20
58810.61
132700.87
153.00
1040.40
128489.40
959.98
261.19
0.65
623.98
169.77
-94.981
58810.61
10050.82
0.00
5301.76
58810.61
132973.81
150.28
1021.90
127594.93
926.92
260.57
0.65
602.50
169.37
Ф
Ф.Pn
Ф.Mn
kN
kNm
Analisis Kekuatan Kolo Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
εs5
mm
f s1 MPa
f s2
f s3
MPa
f s4
f s5
Fs1 kN
Fs2 kN
Fs3 kN
Fs4 kN
Fs5
MPa
MPa
MPa
173.60
-0.00305
-0.00175
-0.00046
0.00084
0.00214
-390.000
-350.461
-91.244
167.972
390.000
- 392.071
-140.929
-36.691
67.546
392.071
kN
170.40
-0.00316
-0.00184
-0.00052
0.00080
0.00212
-390.000
-368.310
-104.225
159.859
390.000
-392.071
-148.106
-41.912
64.283
392.071
167.20
-0.00328
-0.00193
-0.00059
0.00076
0.00210
-390.000
-386.842
-117.703
151.435
390.000
-392.071
-155.558
-47.331
60.896
392.071
164.00
-0.00340
-0.00203
-0.00066
0.00071
0.00209
-390.000
-390.000
-131.707
142.683
390.000
-392.071
-156.828
-52.963
57.376
392.071
160.80
-0.00353
-0.00213
-0.00073
0.00067
0.00207
-390.000
-390.000
-146.269
133.582
390.000
-392.071
-156.828
-58.818
53.717
392.071
157.60
-0.00366
-0.00223
-0.00081
0.00062
0.00205
-390.000
-390.000
-161.421
124.112
390.000
-392.071
-156.828
-64.911
49.908
392.071
154.40
-0.00380
-0.00234
-0.00089
0.00057
0.00203
-390.000
-390.000
-177.202
114.249
390.000
-392.071
-156.828
-71.257
45.942
392.071
151.20
-0.00394
-0.00246
-0.00097
0.00052
0.00201
-390.000
-390.000
-193.651
103.968
390.000
-392.071
-156.828
-77.872
41.808
392.071
148.00
-0.00409
-0.00257
-0.00105
0.00047
0.00199
-390.000
-390.000
-210.811
93.243
390.000
- 392.071
-156.828
-84.772
37.495
392.071
144.80
-0.00425
-0.00270
-0.00114
0.00041
0.00196
-390.000
-390.000
-228.729
82.044
390.000
- 392.071
-156.828
-91.978
32.992
392.071
141.60
-0.00442
-0.00283
-0.00124
0.00035
0.00194
-390.000
-390.000
-247.458
70.339
388.136
- 392.071
-156.828
-99.509
28.285
390.196
138.40
-0.00459
-0.00296
-0.00134
0.00029
0.00192
-390.000
-390.000
-267.052
58.092
383.237
-392.071
-156.828
-107.388
23.360
385.272
135.20
-0.00477
-0.00310
-0.00144
0.00023
0.00189
-390.000
-390.000
-287.574
45.266
378.107
-392.071
-156.828
-115.640
18.203
380.114
132.00
-0.00495
-0.00325
-0.00155
0.00016
0.00186
-390.000
-390.000
-309.091
31.818
372.727
-392.071
-156.828
-124.293
12.795
374.706
128.80
-0.00515
-0.00341
-0.00166
0.00009
0.00184
-390.000
-390.000
-331.677
17.702
367.081
- 392.071
-156.828
-133.375
7.118
369.030
125.60
- 0.00536
- 0.00357
- 0.00178
0.00001
0.00181
-390.000
-390.000
-355.414
2.866
361.146
- 392.071
-156.828
-142.920
1.153
363.064
122.40
-0.00558
-0.00374
-0.00190
-0.00006
0.00177
-390.000
-390.000
-380.392
-12.745
354.902
-392.071
-156.828
-152.965
-5.125
356.786
119.20
-0.00581
-0.00392
-0.00203
-0.00015
0.00174
-390.000
-390.000
-390.000
-29.195
348.322
-392.071
-156.828
-156.828
-11.740
350.172
116.00
-0.00605
-0.00411
-0.00217
-0.00023
0.00171
-390.000
-390.000
-390.000
-46.552
341.379
-392.071
-156.828
-156.828
-18.720
343.192
112.80
-0.00631
-0.00431
-0.00232
-0.00032
0.00167
-390.000
-390.000
-390.000
-64.894
334.043
-392.071
-156.828
-156.828
-26.095
335.816
109.60
-0.00658
-0.00453
-0.00247
-0.00042
0.00163
-390.000
-390.000
-390.000
-84.307
326.277
-392.071
-156.828
-156.828
-33.902
328.010
106.40
-0.00687
-0.00475
-0.00264
-0.00052
0.00159
-390.000
-390.000
-390.000
-104.887
318.045
-392.071
-156.828
-156.828
-42.178
319.734
103.20
-0.00717
-0.00499
-0.00281
-0.00063
0.00155
-390.000
-390.000
-390.000
-126.744
309.302
-392.071
-156.828
-156.828
-50.967
310.945
100.00
-0.00750
-0.00525
-0.00300
-0.00075
0.00150
-390.000
-390.000
-390.000
-150.000
300.000
-392.071
-156.828
-156.828
-60.319
301.593
96.80
-0.00785
-0.00552
-0.00320
-0.00087
0.00145
-390.000
-390.000
-390.000
-174.793
290.083
-392.071
-156.828
-156.828
-70.289
291.623
93.60
-0.00822
-0.00581
-0.00341
-0.00101
0.00140
-390.000
-390.000
-390.000
-201.282
279.487
-392.071
-156.828
-156.828
-80.940
280.971
91.00
-0.00854
-0.00607
-0.00359
-0.00112
0.00135
-390.000
-390.000
-390.000
-224.176
270.330
-392.071
-156.828
-156.828
-90.146
271.765
0.00229
-390.000
-177.857
34.286
246.429
390.000
- 392.071
-71.521
13.787
99.095
392.071
KONDISI TEKAN AKSIAL KECIL : Pn = 0.1 * fc' * b * h KONDISI BALANCE 212.12
- 0.00195
- 0.00089
0.00017
0.00123
Analisis Kekuatan Kolo Beton Bertulang Dengan Diagram Interaksi
Cs
Ms1
Ms2
Ms3
Ms4
Ms5
Ms
a
Cc
Mc
kN
kNmm
kNmm
kNmm
kNmm
kNmm
kNmm
mm
kN
kNmm
-110.074
58810.61
10569.65
0.00
5065.93
58810.61
133256.81
147.56
1003.41
126650.16
893.33
259.91
0.65
580.67
168.94
-125.735
58810.61
11107.96
0.00
4821.24
58810.61
133550.43
144.84
984.91
125655.07
859.18
259.21
0.65
558.47
168.48
-141.994
58810.61
11666.88
0.00
4567.18
58810.61
133855.30
142.12
966.42
124609.68
824.42
258.46
0.65
535.87
168.00
-152.415
58810.61
11762.12
0.00
4303.22
58810.61
133686.57
139.40
947.92
123513.98
795.51
257.20
0.65
517.08
167.18
-161.930
58810.61
11762.12
0.00
4028.74
58810.61
133412.09
136.68
929.42
122367.96
767.49
255.78
0.65
498.87
166.26
-171.831
58810.61
11762.12
0.00
3743.12
58810.61
133126.47
133.96
910.93
121171.64
739.10
254.30
0.65
480.41
165.29
-182.143
58810.61
11762.12
0.00
3445.66
58810.61
132829.01
131.24
892.43
119925.01
710.29
252.75
0.65
461.69
164.29
-192.892
58810.61
11762.12
0.00
3135.61
58810.61
132518.96
128.52
873.94
118628.07
681.04
251.15
0.65
442.68
163.25
-204.105
58810.61
11762.12
0.00
2812.15
58810.61
132195.50
125.80
855.44
117280.82
651.33
249.48
0.65
423.37
162.16
-215.814
58810.61
11762.12
0.00
2474.39
58810.61
131857.75
123.08
836.94
115883.27
621.13
247.74
0.65
403.73
161.03
-229.926
58810.61
11762.12
0.00
2121.37
58529.47
131223.58
120.36
818.45
114435.40
588.52
245.66
0.65
382.54
159.68
-247.655
58810.61
11762.12
0.00
1752.03
57790.78
130115.54
117.64
799.95
112937.22
552.30
243.05
0.65
358.99
157.98
-266.223
58810.61
11762.12
0.00
1365.20
57017.12
128955.05
114.92
781.46
111388.74
515.23
240.34
0.65
334.90
156.22
-285.691
58810.61
11762.12
0.00
959.61
56205.95
127738.30
112.20
762.96
109789.94
477.27
237.53
0.65
310.23
154.39
-306.126
58810.61
11762.12
0.00
533.88
55354.47
126461.09
109.48
744.46
108140.84
438.34
234.60
0.65
284.92
152.49
-327.603
58810.61
11762.12
0.00
86.44
54459.61
125118.79
106.76
725.97
106441.43
398.37
231.56
0.65
258.94
150.51
-350.203
58810.61
11762.12
0.00
-384.38
53517.95
123706.31
104.04
707.47
104691.71
357.27
228.40
0.65
232.23
148.46
-367.296
58810.61
11762.12
0.00
-880.49
52525.74
122217.99
101.32
688.98
102891.68
321.68
225.11
0.65
209.09
146.32
-381.255
58810.61
11762.12
0.00
-1403.97
51478.79
120647.56
98.60
670.48
101041.34
289.22
221.69
0.66
192.17
147.30
-396.006
58810.61
11762.12
0.00
-1957.15
50372.43
118988.02
95.88
651.98
99140.69
255.98
218.13
0.68
174.07
148.33
-411.619
58810.61
11762.12
0.00
-2542.63
49201.47
117231.58
93.16
633.49
97189.73
221.87
214.42
0.70
154.42
149.24
-428.171
58810.61
11762.12
0.00
-3163.32
47960.07
115369.49
90.44
614.99
95188.46
186.82
210.56
0.71
133.10
150.01
-445.750
58810.61
11762.12
0.00
-3822.51
46641.69
113391.91
87.72
596.50
93136.89
150.75
206.53
0.73
109.95
150.63
-464.453
58810.61
11762.12
0.00
-4523.89
45238.93
111287.78
85.00
578.00
91035.00
113.55
202.32
0.75
84.79
151.09
-484.393
58810.61
11762.12
0.00
-5271.64
43743.43
109044.53
82.28
559.50
88882.81
75.11
197.93
0.76
57.44
151.37
-505.697
58810.61
11762.12
0.00
-6070.52
42145.67
106647.89
79.56
541.01
86680.30
35.31
193.33
0.78
27.66
151.46
-524.109
58810.61
11762.12
0.00
-6760.98
40764.75
104576.51
77.35
525.98
84853.72
1.87
189.43
0.80
1.50
151.38
41.361
58810.61
5364.05
0.00
7432.11
58810.61
130417.38
180.30
1226.06
134680.90
Pn kN
Mn
Ф.Pn
Ф
kNm
1267.42
265.10
kN
0.65
Ф.Mn kNm
208.00
0.00
208.00
200.00
0.00
0.00
823.82
172.31
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
ANALISIS KEKUATAN KOLOM BETON BERTULANG DENGAN DIAGRAM INTERAKSI [C]2010 : M. Noer Ilham
KODE KOLOM
K4
INPUT DATA KOLOM
f c' = f y =
Kuat tekan beton, Tegangan leleh baja,
b= h= ds = n= D=
Lebar kolom, Tinggi kolom, Tebal brutto selimut beton, Jumlah tulangan, Diameter tulangan,
20
MPa
390
MPa
300
mm
300
mm
50
mm
12
buah
16
mm
PERHITUNGAN DIAGRAM INTERAKSI Es =
Modulus elastis baja, β1 = β1 =
2.E+05 MPa
untuk f c' 30 MPa
0.85 0.85 - 0.008 (f c' - 30)
untuk f c ' > 30 MPa
Faktor distribusi tegangan,
β1 =
0.85
2
2413
2
mm
Luas tulangan total,
As = n * p / 4 * D =
Jarak antara tulangan,
x = ( h - 2*d s ) / 3 = 66.667 mm
Rasio tulangan,
r = As / Ag =
Faktor reduksi kekuatan, f = 0.65 untuk P n ≥ 0.1 * fc' * b * h f=
0.80 untuk P n = 0
2.68%
Untuk : 0
≤
Pn ≤ 0.1 * f c' * b * h
f = 0.65 + 0.15 * ( Pno - Pn ) / Pno
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
1300
1200
b 1100
1000
h 900
800 ) N k (
f
300
mm
h=
300
mm
12
D
16
f c' =
20
MPa
f y =
390
MPa
700
n
P .
b=
600
500
400
300
Pu
Mu
(kN)
(kNm)
109.176
18.884
225.043
23.320
186.472
5.314
82.679
23.886
105.219
29.915
108.699
30.993
127.700
16.454
76.148
47.322
48.567
16.678
59.401
22.620
200
100
0
0
10
20
30
40
50
60
70
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
80
90
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
No
Luas masing-masing tulangan
Jarak tulangan thd. sisi beton 2
1
As1 = 4/12 * A s =
804
mm
2
As2 = 2/12 * A s =
402
mm
3 4
As3 = 2/12 * A s = As4 = 4/12 * A s =
402 804
2
Pada kondisi tekan aksial sentris (M no = 0) : -3
d1 = 3*x + d s =
250
mm
d2 = 2*x + d s =
183
mm
Pno =
1944
kN
-3
180
kN
2
mm
d3 = x + ds =
117
mm
d4 = ds =
50
mm
2
mm
Pno = 0.80*[ 0.85*f c' *b*h + A s*(f y - 0.85*f c')]*10 0.1 * f c' * b * h *10 = Pada kondisi balance : c = cb = 600 / (600 + f y) * d1 =
As = 2413
151.52 mm
2
mm
Pada kondisi garis netral terletak pada jarak c dari sisi beton tekan terluar : Regangan pada masing-masing baja tulangan :
εsi = 0.003 * ( c - di ) / c
Tegangan pada masing-masing baja tulangan : Untuk | εsi | < f y / Es maka : f si = esi* Es Untuk
| εsi | f y / Es maka : f si =| εsi | / esi* f y Jumlah interval jarak grs netral =
URAIAN PERHITUNGAN Gaya-gaya internal pada masing-masing baja tulangan : Resultan gaya internal baja tulangan : Momen akibat gaya internal masing-masing baja tulangan : Tinggi blok tegangan tekan beton, Gaya internal pada beton tekan : Momen akibat gaya internal tekan beton : Gaya aksial nominal : Momen nominal : Gaya aksial rencana : Momen rencana :
134
PERSAMAAN
→
Dc =
2.2388
UNIT -3
Fsi = Asi * f si * 10 -3 Cs = [ S Fsi ]*10 Msi = Fsi*(h/2 - di) Ms = S Msi a = β1 * c -3 Cc = 0.85 * f c' * b * a * 10 Mc = Cc * (h - a) / 2 Pn = Cs + Cc -3 Mn = (Mc + Ms)*10 Pu = f * Pn Mu = f * Mn
kN kN kNmm kNmm mm kN kNmm kN kNm kN kNm
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
1300
1200
b
1100
1000
h 900
800 ) N k (
f
300
mm
h=
300
mm
12
D
16
f c' =
20
MPa
f y =
390
MPa
700
n
P .
b=
600
500
400
300
200
100
Pu
Mu
(kN)
(kNm)
109.176
18.884
225.043
23.320
186.472
5.314
82.679
23.886
105.219
29.915
108.699
30.993
127.700
16.454
76.148
47.322
48.567
16.678
59.401
22.620
0 0
10
20
30
40
50
60
70
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
80
90
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
mm
f s1
f s2
f s3
f s4
Fs1
Fs2
Fs3
Fs4
Cs
Ms1
Ms2
MPa
MPa
MPa
MPa
kN
kN
kN
kN
kN
kNmm
kNmm
KONDISI TEKAN AKSIAL SENTRIS 315.00
0.00062
0.00125
0.00189
0.00252
123.810
250.794
377.778
390.000
99.574
100.850
151.913
313.657
665.994
-9957.35
-3361.67
312.76
0.00060
0.00124
0.00188
0.00252
120.401
248.294
376.187
390.000
96.832
99.845
151.274
313.657
661.607
-9683.21
-3328.16
310.52
0.00058
0.00123
0.00187
0.00252
116.943
245.758
374.573
390.000
94.051
98.825
150.625
313.657
657.158
-9405.12
-3294.17
308.28
0.00057
0.00122
0.00186
0.00251
113.435
243.186
372.936
390.000
91.230
97.791
149.967
313.657
652.644
-9122.98
-3259.69
306.04
0.00055
0.00120
0.00186
0.00251
109.876
240.575
371.275
390.000
88.367
96.741
149.299
313.657
648.064
-8836.72
-3224.70
303.81
0.00053
0.00119
0.00185
0.00251
106.264
237.927
369.590
390.000
85.462
95.676
148.621
313.657
643.416
-8546.24
-3189.20
301.57
0.00051
0.00118
0.00184
0.00250
102.598
235.239
367.879
390.000
82.515
94.595
147.933
313.657
638.699
-8251.45
-3153.17
299.33
0.00049
0.00116
0.00183
0.00250
98.878
232.511
366.143
390.000
79.522
93.498
147.235
313.657
633.912
-7952.25
-3116.60
297.09
0.00048
0.00115
0.00182
0.00250
95.102
229.741
364.381
390.000
76.485
92.384
146.526
313.657
629.053
-7648.54
-3079.48
294.85
0.00046
0.00113
0.00181
0.00249
91.268
226.930
362.592
390.000
73.402
91.254
145.807
313.657
624.119
-7340.21
-3041.80
292.61
0.00044
0.00112
0.00180
0.00249
87.376
224.075
360.775
390.000
70.272
90.106
145.076
313.657
619.111
-7027.17
-3003.54
290.37
0.00042
0.00111
0.00179
0.00248
83.423
221.177
358.931
390.000
67.093
88.941
144.335
313.657
614.025
-6709.30
-2964.69
288.13
0.00040
0.00109
0.00179
0.00248
79.409
218.234
357.058
390.000
63.865
87.757
143.581
313.657
608.860
-6386.49
-2925.23
285.90
0.00038
0.00108
0.00178
0.00248
75.333
215.244
355.155
390.000
60.586
86.555
142.816
313.657
603.614
-6058.62
-2885.16
283.66
0.00036
0.00106
0.00177
0.00247
71.192
212.207
353.223
390.000
57.256
85.334
142.039
313.657
598.285
-5725.58
-2844.45
281.42
0.00033
0.00105
0.00176
0.00247
66.985
209.122
351.260
390.000
53.872
84.093
141.250
313.657
592.872
-5387.24
-2803.10
279.18
0.00031
0.00103
0.00175
0.00246
62.711
205.988
349.265
390.000
50.435
82.833
140.448
313.657
587.372
-5043.48
-2761.09
276.94
0.00029
0.00101
0.00174
0.00246
58.367
202.802
347.238
390.000
46.942
81.552
139.633
313.657
581.783
-4694.15
-2718.39
274.70
0.00027
0.00100
0.00173
0.00245
53.953
199.565
345.178
390.000
43.391
80.250
138.804
313.657
576.102
-4339.14
-2675.00
272.46
0.00025
0.00098
0.00172
0.00245
49.466
196.275
343.084
390.000
39.783
78.927
137.962
313.657
570.329
-3978.28
-2630.90
270.22
0.00022
0.00096
0.00170
0.00244
44.905
192.930
340.956
390.000
36.115
77.582
137.106
313.657
564.459
-3611.45
-2586.06
267.99
0.00020
0.00095
0.00169
0.00244
40.267
189.529
338.791
390.000
32.385
76.214
136.236
313.657
558.492
-3238.49
-2540.48
265.75
0.00018
0.00093
0.00168
0.00244
35.552
186.071
336.591
390.000
28.592
74.824
135.351
313.657
552.424
-2859.25
-2494.12
263.51
0.00015
0.00091
0.00167
0.00243
30.756
182.555
334.353
390.000
24.736
73.410
134.451
313.657
546.253
-2473.56
-2446.98
261.27
0.00013
0.00089
0.00166
0.00243
25.878
178.977
332.077
390.000
20.813
71.971
133.536
313.657
539.976
-2081.26
-2399.04
259.03
0.00010
0.00088
0.00165
0.00242
20.916
175.339
329.761
390.000
16.822
70.508
132.605
313.657
533.591
-1682.18
-2350.26
256.79
0.00008
0.00086
0.00164
0.00242
15.867
171.636
327.405
390.000
12.761
69.019
131.657
313.657
527.094
-1276.14
-2300.63
254.55
0.00005
0.00084
0.00163
0.00241
10.730
167.869
325.007
390.000
8.630
67.504
130.693
313.657
520.483
-862.96
-2250.13
252.31
0.00003
0.00082
0.00161
0.00241
5.501
164.034
322.567
390.000
4.424
65.962
129.712
313.657
513.755
-442.44
-2198.74
250.07
0.00000
0.00080
0.00160
0.00240
0.179
160.131
320.084
390.000
0.144
64.393
128.713
313.657
506.906
-14.40
-2146.42
247.84
-0.00003
0.00078
0.00159
0.00239
-5.239
156.158
317.555
390.000
-4.214
62.795
127.696
313.657
499.934
421.38
-2093.16
245.60
- 0.00005
0.00076
0.00157
0.00239
-10.757
152.112
314.980
390.000
-8.651
61.168
126.661
313.657
492.834
865.10
-2038.93
243.36
- 0.00008
0.00074
0.00156
0.00238
-16.375
147.991
312.358
390.000
-13.170
59.511
125.607
313.657
485.604
1316.98
-1983.70
241.12
- 0.00011
0.00072
0.00155
0.00238
-22.098
143.794
309.687
390.000
-17.773
57.823
124.533
313.657
478.240
1777.26
-1927.44
238.88
- 0.00014
0.00070
0.00153
0.00237
-27.929
139.519
306.967
390.000
-22.462
56.104
123.439
313.657
470.737
2246.17
-1870.13
236.64
- 0.00017
0.00068
0.00152
0.00237
-33.869
135.162
304.194
390.000
-27.239
54.352
122.324
313.657
463.093
2723.94
-1811.73
234.40
- 0.00020
0.00065
0.00151
0.00236
-39.924
130.723
301.369
390.000
-32.108
52.567
121.188
313.657
455.303
3210.85
-1752.22
232.16
- 0.00023
0.00063
0.00149
0.00235
-46.095
126.197
298.489
390.000
-37.071
50.747
120.030
313.657
447.362
3707.14
-1691.57
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Ms3
Ms4
Ms
a
Cc
Mc
Pn
Mn
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
kNm
Ф.Pn
Ф
kN
Ф.Mn kNm
1943.96
0.00
0.65
1263.58
0.00
5063.78
31365.66
23110.42
267.75
1365.53
22019.09
1943.96
45.13
0.65
1263.58
29.33
5042.46
31365.66
23396.75
265.85
1355.82
23152.65
1943.96
46.55
0.65
1263.58
30.26
5020.83
31365.66
23687.20
263.94
1346.11
24267.73
1943.96
47.95
0.65
1263.58
31.17
4998.89
31365.66
23981.87
262.04
1336.41
25364.35
1943.96
49.35
0.65
1263.58
32.08
4976.62
31365.66
24280.86
260.14
1326.70
26442.50
1943.96
50.72
0.65
1263.58
32.97
4954.03
31365.66
24584.25
258.24
1317.00
27502.18
1943.96
52.09
0.65
1263.58
33.86
4931.10
31365.66
24892.14
256.33
1307.29
28543.39
1943.96
53.44
0.65
1263.58
34.73
4907.83
31365.66
25204.64
254.43
1297.59
29566.13
1931.50
54.77
0.65
1255.48
35.60
4884.21
31365.66
25521.85
252.53
1287.88
30570.41
1916.94
56.09
0.65
1246.01
36.46
4860.23
31365.66
25843.88
250.62
1278.18
31556.21
1902.30
57.40
0.65
1236.49
37.31
4835.88
31365.66
26170.83
248.72
1268.47
32523.55
1887.58
58.69
0.65
1226.93
38.15
4811.16
31365.66
26502.83
246.82
1258.77
33472.41
1872.79
59.98
0.65
1217.32
38.98
4786.05
31365.66
26839.99
244.91
1249.06
34402.81
1857.92
61.24
0.65
1207.65
39.81
4760.55
31365.66
27182.43
243.01
1239.36
35314.74
1842.97
62.50
0.65
1197.93
40.62
4734.64
31365.66
27530.27
241.11
1229.65
36208.20
1827.94
63.74
0.65
1188.16
41.43
4708.33
31365.66
27883.64
239.21
1219.95
37083.19
1812.82
64.97
0.65
1178.33
42.23
4681.59
31365.66
28242.69
237.30
1210.24
37939.71
1797.61
66.18
0.65
1168.45
43.02
4654.42
31365.66
28607.54
235.40
1200.54
38777.77
1782.32
67.39
0.65
1158.51
43.80
4626.81
31365.66
28978.34
233.50
1190.83
39597.35
1766.93
68.58
0.65
1148.51
44.57
4598.74
31365.66
29355.23
231.59
1181.13
40398.47
1751.45
69.75
0.65
1138.45
45.34
4570.21
31365.66
29738.36
229.69
1171.42
41181.11
1735.88
70.92
0.65
1128.32
46.10
4541.20
31365.66
30127.90
227.79
1161.72
41945.29
1720.21
72.07
0.65
1118.13
46.85
4511.71
31365.66
30524.00
225.88
1152.01
42691.00
1704.43
73.21
0.65
1107.88
47.59
4481.71
31365.66
30926.83
223.98
1142.30
43418.24
1688.56
74.35
0.65
1097.56
48.32
4451.20
31365.66
31336.56
222.08
1132.60
44127.01
1672.58
75.46
0.65
1087.17
49.05
4420.16
31365.66
31753.38
220.18
1122.89
44817.31
1656.49
76.57
0.65
1076.72
49.77
4388.58
31365.66
32177.47
218.27
1113.19
45489.15
1640.28
77.67
0.65
1066.18
50.48
4356.44
31365.66
32609.01
216.37
1103.48
46142.51
1623.97
78.75
0.65
1055.58
51.19
4323.73
31365.66
33048.21
214.47
1093.78
46777.41
1607.53
79.83
0.65
1044.90
51.89
4290.44
31365.66
33495.28
212.56
1084.07
47393.83
1590.98
80.89
0.65
1034.14
52.58
4256.55
31365.66
33950.43
210.66
1074.37
47991.79
1574.30
81.94
0.65
1023.30
53.26
4222.04
31365.66
34413.87
208.76
1064.66
48571.28
1557.50
82.99
0.65
1012.37
53.94
4186.89
31365.66
34885.84
206.85
1054.96
49132.30
1540.56
84.02
0.65
1001.37
54.61
4151.09
31365.66
35366.57
204.95
1045.25
49674.85
1523.49
85.04
0.65
990.27
55.28
4114.62
31365.66
35856.32
203.05
1035.55
50198.93
1506.28
86.06
0.65
979.09
55.94
4077.46
31365.66
36355.33
201.15
1025.84
50704.55
1488.94
87.06
0.65
967.81
56.59
4039.59
31365.66
36863.87
199.24
1016.14
51191.69
1471.44
88.06
0.65
956.44
57.24
4000.99
31365.66
37382.22
197.34
1006.43
51660.37
1453.79
89.04
0.65
944.97
57.88
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
mm
f s1
f s2
f s3
f s4
Fs1
Fs2
Fs3 kN
Fs4 kN
Cs
Ms1
kN
Ms2
MPa
MPa
MPa
MPa
kN
kN
kNmm
kNmm
229.93
- 0.00026
0.00061
0.00148
0.00235
-52.386
121.584
295.553
390.000
-42.131
48.892
118.849
313.657
439.266
4213.10
-1629.73
227.69
- 0.00029
0.00058
0.00146
0.00234
-58.800
116.880
292.560
390.000
-47.290
47.000
117.645
313.657
431.012
4729.01
-1566.67
225.45
- 0.00033
0.00056
0.00145
0.00233
-65.343
112.082
289.507
390.000
-52.552
45.071
116.418
313.657
422.593
5255.16
-1502.36
223.21
- 0.00036
0.00054
0.00143
0.00233
-72.016
107.188
286.393
390.000
-57.919
43.103
115.165
313.657
414.006
5791.87
-1436.76
220.97
- 0.00039
0.00051
0.00142
0.00232
-78.825
102.195
283.215
390.000
-63.395
41.095
113.888
313.657
405.245
6339.46
-1369.84
218.73
-0.00043
0.00049
0.00140
0.00231
-85.773
97.100
279.973
390.000
-68.983
39.046
112.584
313.657
396.304
6898.26
-1301.54
216.49
-0.00046
0.00046
0.00138
0.00231
-92.865
91.899
276.663
390.000
-74.686
36.955
111.253
313.657
387.178
7468.61
-1231.83
214.25
- 0.00050
0.00043
0.00137
0.00230
- 100.104
86.590
273.285
390.000
-80.509
34.820
109.894
313.657
377.862
8050.88
-1160.66
212.01
- 0.00054
0.00041
0.00135
0.00229
- 107.497
81.169
269.835
390.000
-86.455
32.640
108.507
313.657
368.349
8645.45
-1087.99
209.78
- 0.00058
0.00038
0.00133
0.00228
- 115.048
75.631
266.311
390.000
-92.527
30.413
107.090
313.657
358.633
9252.71
-1013.77
207.54
-0.00061
0.00035
0.00131
0.00228
-122.762
69.975
262.711
390.000
-98.731
28.139
105.642
313.657
348.707
9873.07
-937.95
205.30
-0.00065
0.00032
0.00130
0.00227
-130.643
64.195
259.033
390.000
-105.070
25.814
104.163
313.657
338.565
10506.97
-860.48
203.06
-0.00069
0.00029
0.00128
0.00226
-138.699
58.287
255.274
390.000
-111.548
23.439
102.652
313.657
328.199
11154.84
-781.29
200.82
-0.00073
0.00026
0.00126
0.00225
-146.934
52.248
251.431
390.000
-118.172
21.010
101.106
313.657
317.602
11817.15
-700.34
198.58
- 0.00078
0.00023
0.00124
0.00224
- 155.355
46.073
247.501
390.000
-124.944
18.527
99.526
313.657
306.766
12494.40
-617.57
196.34
- 0.00082
0.00020
0.00122
0.00224
- 163.968
39.757
243.482
390.000
-131.871
15.987
97.910
313.657
295.683
13187.09
-532.90
194.10
- 0.00086
0.00017
0.00120
0.00223
- 172.780
33.295
239.369
390.000
-138.958
13.389
96.256
313.657
284.344
13895.77
-446.29
191.87
- 0.00091
0.00013
0.00118
0.00222
- 181.797
26.682
235.161
390.000
-146.210
10.730
94.564
313.657
272.740
14620.98
-357.65
189.63
-0.00096
0.00010
0.00115
0.00221
-191.027
19.913
230.854
390.000
-153.633
8.008
92.832
313.657
260.863
15363.32
-266.92
187.39
-0.00100
0.00006
0.00113
0.00220
-200.478
12.983
226.444
390.000
-161.234
5.221
91.058
313.657
248.702
16123.39
-174.02
185.15
-0.00105
0.00003
0.00111
0.00219
-210.157
5.885
221.927
390.000
-169.018
2.366
89.242
313.657
236.247
16901.84
-78.88
182.91
-0.00110
-0.00001
0.00109
0.00218
-220.073
-1.387
217.299
390.000
-176.994
-0.558
87.381
313.657
223.486
17699.36
18.59
180.67
-0.00115
- 0.00004
0.00106
0.00217
- 230.235
-8.839
212.557
390.000
-185.166
-3.555
85.474
313.657
210.410
18516.63
118.48
178.43
- 0.00120
- 0.00008
0.00104
0.00216
- 240.652
-16.478
207.696
390.000
-193.544
-6.626
83.519
313.657
197.005
19354.42
220.88
176.19
- 0.00126
- 0.00012
0.00101
0.00215
- 251.334
-24.312
202.711
390.000
-202.135
-9.776
81.515
313.657
183.260
20213.49
325.88
173.96
-0.00131
-0.00016
0.00099
0.00214
-262.291
-32.347
197.598
390.000
-210.947
-13.007
79.459
313.657
169.161
21094.68
433.58
171.72
-0.00137
-0.00020
0.00096
0.00213
-273.533
-40.591
192.351
390.000
-219.988
-16.323
77.349
313.657
154.694
21998.85
544.09
169.48
-0.00143
-0.00025
0.00093
0.00211
-285.073
-49.053
186.966
390.000
-229.269
-19.725
75.184
313.657
139.846
22926.90
657.52
167.24
-0.00148
-0.00029
0.00091
0.00210
-296.921
-57.742
181.437
390.000
-238.798
-23.219
72.960
313.657
124.599
23879.81
773.98
165.00
-0.00155
-0.00033
0.00088
0.00209
-309.091
-66.667
175.758
390.000
-248.586
-26.808
70.676
313.657
108.939
24858.57
893.61
162.76
-0.00161
-0.00038
0.00085
0.00208
-321.596
-75.837
169.922
390.000
-258.643
-30.496
68.330
313.657
92.848
25864.25
1016.53
160.52
-0.00167
-0.00043
0.00082
0.00207
-334.449
-85.263
163.924
390.000
-268.980
-34.286
65.918
313.657
76.308
26897.99
1142.87
158.28
-0.00174
-0.00047
0.00079
0.00205
-347.666
-94.955
157.756
390.000
-279.610
-38.184
63.437
313.657
59.300
27960.97
1272.79
156.04
-0.00181
-0.00052
0.00076
0.00204
-361.263
-104.926
151.411
390.000
-290.545
-42.193
60.886
313.657
41.805
29054.46
1406.44
153.81
-0.00188
-0.00058
0.00072
0.00202
-375.255
-115.187
144.881
390.000
-301.798
-46.319
58.260
313.657
23.800
30179.78
1543.98
151.57
-0.00195
-0.00063
0.00069
0.00201
-389.660
-125.751
138.159
390.000
-313.383
-50.567
55.557
313.657
5.263
31338.34
1685.58
149.33
-0.00202
-0.00068
0.00066
0.00200
-390.000
-136.632
131.234
390.000
-313.657
-54.943
52.772
313.657
-2.170
31365.66
1831.43
147.09
-0.00210
-0.00074
0.00062
0.00198
-390.000
-147.844
124.099
390.000
-313.657
-59.451
49.903
313.657
-9.548
31365.66
1981.72
144.85
- 0.00218
- 0.00080
0.00058
0.00196
- 390.000
-159.402
116.744
390.000
-313.657
-64.099
46.946
313.657
-17.154
31365.66
2136.65
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Ms3
Ms4
Ms
a
Cc
Mc
Pn
Mn
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
kNm
3961.64
31365.66
37910.67
195.44
996.73
52110.57
1435.99
90.02
0.65
933.40
58.51
3921.51
31365.66
38449.51
193.53
987.02
52542.31
1418.03
90.99
0.65
921.72
59.14
3880.59
31365.66
38999.05
191.63
977.32
52955.58
1399.91
91.95
0.65
909.94
59.77
3838.84
31365.66
39559.61
189.73
967.61
53350.38
1381.62
92.91
0.65
898.05
60.39
3796.25
31365.66
40131.54
187.82
957.91
53726.71
1363.15
93.86
0.65
886.05
61.01
3752.79
31365.66
40715.17
185.92
948.20
54084.57
1344.50
94.80
0.65
873.93
61.62
3708.43
31365.66
41310.87
184.02
938.50
54423.96
1325.67
95.73
0.65
861.69
62.23
3663.14
31365.66
41919.02
182.12
928.79
54744.89
1306.65
96.66
0.65
849.32
62.83
3616.90
31365.66
42540.01
180.21
919.08
55047.34
1287.43
97.59
0.65
836.83
63.43
3569.67
31365.66
43174.26
178.31
909.38
55331.33
1268.01
98.51
0.65
824.21
64.03
3521.42
31365.66
43822.20
176.41
899.67
55596.85
1248.38
99.42
0.65
811.45
64.62
3472.11
31365.66
44484.26
174.50
889.97
55843.90
1228.53
100.33
0.65
798.55
65.21
3421.72
31365.66
45160.93
172.60
880.26
56072.48
1208.46
101.23
0.65
785.50
65.80
3370.21
31365.66
45852.68
170.70
870.56
56282.59
1188.16
102.14
0.65
772.30
66.39
3317.53
31365.66
46560.03
168.79
860.85
56474.23
1167.62
103.03
0.65
758.95
66.97
3263.66
31365.66
47283.51
166.89
851.15
56647.40
1146.83
103.93
0.65
745.44
67.56
3208.54
31365.66
48023.68
164.99
841.44
56802.11
1125.79
104.83
0.65
731.76
68.14
3152.13
31365.66
48781.12
163.09
831.74
56938.34
1104.48
105.72
0.65
717.91
68.72
3094.40
31365.66
49556.45
161.18
822.03
57056.11
1082.90
106.61
0.65
703.88
69.30
3035.28
31365.66
50350.31
159.28
812.33
57155.41
1061.03
107.51
0.65
689.67
69.88
2974.73
31365.66
51163.36
157.38
802.62
57236.23
1038.87
108.40
0.65
675.26
70.46
2912.70
31365.66
51996.32
155.47
792.92
57298.59
1016.40
109.29
0.65
660.66
71.04
2849.14
31365.66
52849.92
153.57
783.21
57342.48
993.62
110.19
0.65
645.85
71.63
2783.98
31365.66
53724.94
151.67
773.51
57367.91
970.51
111.09
0.65
630.83
72.21
2717.16
31365.66
54622.19
149.76
763.80
57374.86
947.06
112.00
0.65
615.59
72.80
2648.62
31365.66
55542.55
147.86
754.10
57363.34
923.26
112.91
0.65
600.12
73.39
2578.30
31365.66
56486.90
145.96
744.39
57333.36
899.09
113.82
0.65
584.41
73.98
2506.12
31365.66
57456.20
144.06
734.69
57284.90
874.53
114.74
0.65
568.45
74.58
2432.00
31365.66
58451.45
142.15
724.98
57217.98
849.58
115.67
0.65
552.23
75.19
2355.88
31365.66
59473.71
140.25
715.27
57132.59
824.21
116.61
0.65
535.74
75.79
2277.66
31365.66
60524.10
138.35
705.57
57028.73
798.42
117.55
0.65
518.97
76.41
2197.26
31365.66
61603.78
136.44
695.86
56906.40
772.17
118.51
0.65
501.91
77.03
2114.58
31365.66
62714.01
134.54
686.16
56765.60
745.46
119.48
0.65
484.55
77.66
2029.53
31365.66
63856.09
132.64
676.45
56606.34
718.26
120.46
0.65
466.87
78.30
1942.01
31365.66
65031.42
130.74
666.75
56428.60
690.55
121.46
0.65
448.86
78.95
1851.89
31365.66
66241.47
128.83
657.04
56232.39
662.31
122.47
0.65
430.50
79.61
1759.08
31365.66
66321.83
126.93
647.34
56017.72
645.17
122.34
0.65
419.36
79.52
1663.44
31365.66
66376.48
125.03
637.63
55784.58
628.09
122.16
0.65
408.26
79.40
1564.85
31365.66
66432.82
123.12
627.93
55532.97
610.77
121.97
0.65
397.00
79.28
Ф.Pn
Ф
kN
Ф.Mn kNm
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
εs4
mm
f s1 MPa
f s2 MPa
f s3
f s4
Fs1 kN
Fs2 kN
Fs3 kN
Fs4 kN
Cs kN
Ms1
Ms2
kNmm
kNmm
MPa
MPa
142.61
- 0.00226
- 0.00086
0.00055
0.00195
- 390.000
-171.324
109.158
389.639
-313.657
-68.893
43.895
313.366
-25.289
31365.66
2296.45
140.37
- 0.00234
- 0.00092
0.00051
0.00193
- 390.000
-183.626
101.329
386.284
-313.657
-73.840
40.747
310.668
-36.082
31365.66
2461.34
138.13
-0.00243
-0.00098
0.00047
0.00191
-390.000
-196.326
93.247
382.820
-313.657
-78.947
37.497
307.882
-47.225
31365.66
2631.58
135.90
-0.00252
-0.00105
0.00042
0.00190
-390.000
-209.445
84.898
379.242
-313.657
-84.223
34.140
305.005
-58.735
31365.66
2807.43
133.66
-0.00261
-0.00112
0.00038
0.00188
-390.000
-223.004
76.270
375.544
-313.657
-89.675
30.670
302.031
-70.631
31365.66
2989.17
131.42
-0.00271
-0.00119
0.00034
0.00186
-390.000
-237.024
67.348
371.721
-313.657
-95.313
27.082
298.955
-82.932
31365.66
3177.11
129.18
- 0.00281
- 0.00126
0.00029
0.00184
- 390.000
-251.531
58.117
367.764
-313.657
-101.147
23.370
295.774
-95.659
31365.66
3371.55
126.94
-0.00291
-0.00133
0.00024
0.00182
-390.000
-266.549
48.560
363.668
-313.657
-107.186
19.527
292.480
-108.836
31365.66
3572.86
124.70
-0.00301
-0.00141
0.00019
0.00180
-390.000
-282.107
38.659
359.425
-313.657
-113.442
15.546
289.067
-122.485
31365.66
3781.39
122.46
-0.00312
-0.00149
0.00014
0.00178
-390.000
-298.233
28.397
355.027
-313.657
-119.927
11.419
285.530
-136.634
31365.66
3997.55
120.22
- 0.00324
- 0.00157
0.00009
0.00175
- 390.000
-314.960
17.753
350.466
-313.657
-126.653
7.139
281.861
-151.309
31365.66
4221.76
117.99
-0.00336
-0.00166
0.00003
0.00173
-390.000
-332.321
6.705
345.731
-313.657
-133.634
2.696
278.053
-166.542
31365.66
4454.48
115.75
-0.00348
-0.00175
-0.00002
0.00170
-390.000
-350.355
-4.771
340.812
-313.657
-140.886
-1.919
274.098
-182.364
31365.66
4696.20
113.51
-0.00361
-0.00185
-0.00008
0.00168
-390.000
-369.099
-16.700
335.700
-313.657
-148.424
-6.715
269.986
-198.809
31365.66
4947.45
111.27
-0.00374
-0.00194
-0.00015
0.00165
-390.000
-388.598
-29.108
330.382
-313.657
-156.265
-11.705
265.709
-215.917
31365.66
5208.82
109.03
-0.00388
-0.00204
-0.00021
0.00162
-390.000
-390.000
-42.026
324.846
-313.657
-156.828
-16.900
261.257
-226.128
31365.66
5227.61
106.79
-0.00402
-0.00215
-0.00028
0.00160
-390.000
-390.000
-55.486
319.078
-313.657
-156.828
-22.312
256.617
-236.180
31365.66
5227.61
104.55
-0.00417
-0.00226
-0.00035
0.00157
-390.000
-390.000
-69.522
313.062
-313.657
-156.828
-27.956
251.779
-246.662
31365.66
5227.61
102.31
-0.00433
-0.00238
-0.00042
0.00153
-390.000
-390.000
-84.172
306.783
-313.657
-156.828
-33.848
246.730
-257.603
31365.66
5227.61
100.07
-0.00449
-0.00250
-0.00050
0.00150
-390.000
-390.000
-99.478
300.224
-313.657
-156.828
-40.002
241.454
-269.033
31365.66
5227.61
97.84
-0.00467
-0.00262
-0.00058
0.00147
-390.000
-390.000
-115.484
293.364
-313.657
-156.828
-46.439
235.937
-280.987
31365.66
5227.61
95.60
-0.00485
-0.00275
-0.00066
0.00143
-390.000
-390.000
-132.240
286.183
-313.657
-156.828
-53.177
230.162
-293.500
31365.66
5227.61
93.36
-0.00503
-0.00289
-0.00075
0.00139
-390.000
-390.000
-149.800
278.657
-313.657
-156.828
-60.238
224.109
-306.614
31365.66
5227.61
91.12
-0.00523
-0.00304
-0.00084
0.00135
-390.000
-390.000
-168.223
270.762
-313.657
-156.828
-67.646
217.759
-320.372
31365.66
5227.61
88.88
-0.00544
-0.00319
-0.00094
0.00131
-390.000
-390.000
-187.573
262.469
-313.657
-156.828
-75.428
211.090
-334.823
31365.66
5227.61
86.64
-0.00566
-0.00335
-0.00104
0.00127
-390.000
-390.000
-207.924
253.747
-313.657
-156.828
-83.611
204.075
-350.021
31365.66
5227.61
84.50
-0.00588
-0.00351
-0.00114
0.00122
-390.000
-390.000
-228.402
244.970
-313.657
-156.828
-91.846
197.017
-365.314
31365.66
5227.61
-390.000
-126.000
138.000
390.000
-313.657
-50.668
55.493
313.657
4.825
31365.66
1688.92
KONDISI TEKAN AKSIAL KECIL : Pn = 0.1 * fc' * b * h KONDISI BALANCE 151.52
-0.00195
-0.00063
0.00069
0.00201
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Ms3
Ms4
Ms
a
Cc
Mc
Pn
Mn
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
kNm
1463.16
31336.62
66461.89
121.22
618.22
55262.89
592.93
121.72
0.65
385.41
79.12
1358.23
31066.79
66252.03
119.32
608.52
54974.34
572.44
121.23
0.65
372.08
78.80
1249.89
30788.22
66035.36
117.41
598.81
54667.32
551.59
120.70
0.65
358.53
78.46
1137.99
30500.47
65811.55
115.51
589.11
54341.83
530.37
120.15
0.65
344.74
78.10
1022.34
30203.07
65580.24
113.61
579.40
53997.88
508.77
119.58
0.65
330.70
77.73
902.74
29895.55
65341.05
111.71
569.70
53635.45
486.76
118.98
0.65
316.40
77.33
779.00
29577.36
65093.58
109.80
559.99
53254.56
464.33
118.35
0.65
301.82
76.93
650.90
29247.95
64837.37
107.90
550.29
52855.19
441.45
117.69
0.65
286.94
76.50
518.20
28906.71
64571.96
106.00
540.58
52437.36
418.10
117.01
0.65
271.76
76.06
380.64
28553.00
64296.85
104.09
530.88
52001.06
394.24
116.30
0.65
256.26
75.59
237.96
28186.11
64011.50
102.19
521.17
51546.29
369.86
115.56
0.65
240.41
75.11
89.87
27805.30
63715.31
100.29
511.47
51073.05
344.92
114.79
0.65
224.20
74.61
Ф.Pn
Ф
kN
Ф.Mn kNm
-63.95
27409.76
63407.66
98.38
501.76
50581.35
319.40
113.99
0.65
207.61
74.09
-223.84
26998.61
63087.88
96.48
492.05
50071.17
293.25
113.16
0.65
190.61
73.55
-390.17
26570.92
62755.24
94.58
482.35
49542.53
266.43
112.30
0.65
173.18
72.99
-563.32
26125.67
62155.61
92.68
472.64
48995.41
246.52
111.15
0.65
160.24
72.25
-743.74
25661.74
61511.27
90.77
462.94
48429.83
226.76
109.94
0.65
147.39
71.46
-931.88
25177.95
60839.34
88.87
453.23
47845.78
206.57
108.69
0.65
134.27
70.65
-1128.25
24672.98
60138.00
86.97
443.53
47243.26
185.93
107.38
0.65
120.85
69.80
-1333.42
24145.42
59405.28
85.06
433.82
46622.27
164.79
106.03
0.66
109.20
70.26
-1547.97
23593.72
58639.02
83.16
424.12
45982.81
143.13
104.62
0.68
97.43
71.22
-1772.57
23016.18
57836.88
81.26
414.41
45324.88
120.91
103.16
0.70
84.55
72.13
-2007.94
22410.93
56996.26
79.35
404.71
44648.49
98.09
101.64
0.72
70.46
73.01
-2254.88
21775.95
56114.34
77.45
395.00
43953.62
74.63
100.07
0.74
55.06
73.83
-2514.26
21108.97
55187.98
75.55
385.30
43240.29
50.47
98.43
0.76
38.26
74.60
-2787.04
20407.53
54213.75
73.65
375.59
42508.48
25.57
96.72
0.78
19.91
75.32
-3061.53
19701.69
53233.43
71.83
366.31
41791.11
0.99
95.02
0.80
0.79
75.94
1849.77
31365.66
66270.01
128.79
656.82
56227.62
661.64
122.50
0.65
117.00
0.00
117.00
70.00
0.00
0.00
430.07
79.62
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
ANALISIS KEKUATAN KOLOM BETON BERTULANG DENGAN DIAGRAM INTERAKSI [C]2010 : M. Noer Ilham
KODE KOLOM
K3
INPUT DATA KOLOM
f c' = f y =
Kuat tekan beton, Tegangan leleh baja,
b= h= ds = n= D=
Lebar kolom, Tinggi kolom, Tebal brutto selimut beton, Jumlah tulangan, Diameter tulangan,
20
MPa
390
MPa
250
mm
250
mm
40
mm
8
buah
16
mm
PERHITUNGAN DIAGRAM INTERAKSI Es =
Modulus elastis baja,
2.E+05 MPa
β1 = 0.85
untuk f c' 30 MPa
β1 = 0.85 - 0.008 (f c' - 30)
untuk f c ' > 30 MPa
Faktor distribusi tegangan,
β1 =
0.85
2
1608
2
mm
Luas tulangan total,
As = n * p / 4 * D =
Jarak antara tulangan,
x = ( h - 2*d s ) / 2 = 85.000 mm
Rasio tulangan,
r = As / Ag =
Faktor reduksi kekuatan, f = 0.65 untuk P n ≥ 0.1 * fc' * b * h f=
0.80 untuk P n = 0
2.57%
Untuk : 0
≤
Pn ≤ 0.1 * f c' * b * h
f = 0.65 + 0.15 * ( Pno - Pn ) / Pno
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
1000 950 900 850 800 750 700
b=
250
mm
h=
250
mm
650 600 ) N k ( n
P . f
8
D
16
f c' =
20
MPa
f y =
390
MPa
Tul. :
550 500 450 400 350 300 250 200 150 100 50 0 0
2
4
6
8
10 12 14 1 6 18 20 22 2 4 26 28 30 3 2 34 36 3 8 40 42 44 4 6 48 50
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
Pu
Mu
(kN)
(kNm)
112.564
23.320
129.708
21.314
124.018
23.886
82.829
25.915
163.048
26.993
116.549
20.454
114.222
31.322
72.850
34.678
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
No
Luas masing-masing tulangan
Jarak tulangan thd. sisi beton 2
1
As1 = 3/8 * A s =
603
mm
2
As2 = 2/8 * A s =
402
mm
3
As3 = 3/8 * A s =
603
d1 = 2*x + d s =
210
mm
d2 = x + ds =
125
mm
2 2
mm
d3 = ds =
40
Pada kondisi tekan aksial sentris (M no = 0) : -3
Pno = 0.80*[ 0.85*f c' *b*h + A s*(f y - 0.85*f c')]*10 →
Pno =
1330
kN
-3
125
kN
0.1 * f c' * b * h *10 =
mm
Pada kondisi balance : c = cb = 600 / (600 + f y) * d1 = 127.27 mm As = 1608
2
mm
Pada kondisi garis netral terletak pada jarak c dari sisi beton tekan terluar : Regangan pada masing-masing baja tulangan :
εsi = 0.003 * ( c - di ) / c
Tegangan pada masing-masing baja tulangan : Untuk | εsi | < f y / Es maka : f si = esi* Es Untuk
| εsi | f y / Es maka : f si =| εsi | / esi* f y Jumlah interval jarak grs netral =
URAIAN PERHITUNGAN Gaya-gaya internal pada masing-masing baja tulangan : Resultan gaya internal baja tulangan : Momen akibat gaya internal masing-masing baja tulangan : Momen total akibat gaya internal baja tulangan : Tinggi blok tegangan tekan beton, Gaya internal pada beton tekan : Momen akibat gaya internal tekan beton : Gaya aksial nominal : Momen nominal : Gaya aksial rencana : Momen rencana :
125
PERSAMAAN
→
Dc =
2.0000
UNIT -3
Fsi = Asi * f si * 10 -3 Cs = [ S Fsi ]*10 Msi = Fsi*(h/2 - di) Ms = S Msi a = β1 * c -3 Cc = 0.85 * f c' * b * a * 10 Mc = Cc * (h - a) / 2 Pn = Cs + Cc -3 Mn = (Mc + Ms)*10 Pu = f * Pn Mu = f * Mn
kN kN kNmm kNmm mm kN kNmm kN kNm kN kNm
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
1000 950 900 850 800 750 700 650 600 ) N k ( n
P . f
b=
250
mm
h=
250
mm
8
D
16
500
f c' =
20
MPa
450
f y =
390
MPa
Tul. :
550
400
Pu
Mu
350
(kN)
(kNm)
300
112.564
23.320
250
129.708
21.314
124.018
23.886
82.829
25.915
163.048
26.993
116.549
20.454
114.222
31.322
72.850
34.678
200 150 100 50 0 0
2
4
6
8
10 1 2 14 16 1 8 20 22 24 2 6 28 30 3 2 34 36 38 4 0 42 44 4 6 48 50
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
mm
f s1
f s2
f s3
Fs1
Fs2
Fs3
Cs
Ms1
Ms2
Ms3
Ms
a
MPa
MPa
MPa
kN
kN
kN
kN
kNmm
kNmm
kNmm
kNmm
mm
KONDISI TEKAN AKSIAL SENTRIS 275.000
0.00071
0.00164
0.00256
141.818
327.273
390.000
85.543
131.604
235.242
452.389
-7271.13
0.00
19995.61
12724.48
233.75
273.000
0.00069
0.00163
0.00256
138.462
325.275
390.000
83.518
130.801
235.242
449.561
-7099.03
0.00
19995.61
12896.58
232.05
271.000
0.00068
0.00162
0.00256
135.055
323.247
390.000
81.463
129.985
235.242
446.691
-6924.39
0.00
19995.61
13071.21
230.35
269.000
0.00066
0.00161
0.00255
131.599
321.190
390.000
79.378
129.158
235.242
443.779
-6747.16
0.00
19995.61
13248.45
228.65
267.000
0.00064
0.00160
0.00255
128.090
319.101
390.000
77.262
128.318
235.242
440.823
-6567.27
0.00
19995.61
13428.34
226.95
265.000
0.00062
0.00158
0.00255
124.528
316.981
390.000
75.114
127.466
235.242
437.822
-6384.66
0.00
19995.61
13610.94
225.25
263.000
0.00060
0.00157
0.00254
120.913
314.829
390.000
72.933
126.600
235.242
434.775
-6199.28
0.00
19995.61
13796.33
223.55
261.000
0.00059
0.00156
0.00254
117.241
312.644
390.000
70.718
125.721
235.242
431.682
-6011.06
0.00
19995.61
13984.55
221.85
259.000
0.00057
0.00155
0.00254
113.514
310.425
390.000
68.470
124.829
235.242
428.541
-5819.93
0.00
19995.61
14175.68
220.15
257.000
0.00055
0.00154
0.00253
109.728
308.171
390.000
66.186
123.923
235.242
425.352
-5625.82
0.00
19995.61
14369.79
218.45
255.000
0.00053
0.00153
0.00253
105.882
305.882
390.000
63.867
123.003
235.242
422.112
-5428.67
0.00
19995.61
14566.94
216.75
253.000
0.00051
0.00152
0.00253
101.976
303.557
390.000
61.511
122.068
235.242
418.821
-5228.40
0.00
19995.61
14767.20
215.05
251.000
0.00049
0.00151
0.00252
98.008
301.195
390.000
59.117
121.118
235.242
415.477
-5024.95
0.00
19995.61
14970.66
213.35
249.000
0.00047
0.00149
0.00252
93.976
298.795
390.000
56.685
120.153
235.242
412.080
-4818.22
0.00
19995.61
15177.39
211.65
247.000
0.00045
0.00148
0.00251
89.879
296.356
390.000
54.213
119.172
235.242
408.628
-4608.14
0.00
19995.61
15387.46
209.95
245.000
0.00043
0.00147
0.00251
85.714
293.878
390.000
51.702
118.175
235.242
405.119
-4394.64
0.00
19995.61
15600.97
208.25
243.000
0.00041
0.00146
0.00251
81.481
291.358
390.000
49.148
117.162
235.242
401.553
-4177.62
0.00
19995.61
15817.99
206.55
241.000
0.00039
0.00144
0.00250
77.178
288.797
390.000
46.553
116.132
235.242
397.927
-3957.00
0.00
19995.61
16038.61
204.85
239.000
0.00036
0.00143
0.00250
72.803
286.192
390.000
43.914
115.085
235.242
394.241
-3732.69
0.00
19995.61
16262.92
203.15
237.000
0.00034
0.00142
0.00249
68.354
283.544
390.000
41.230
114.020
235.242
390.493
-3504.59
0.00
19995.61
16491.02
201.45
235.000
0.00032
0.00140
0.00249
63.830
280.851
390.000
38.501
112.937
235.242
386.681
-3272.60
0.00
19995.61
16723.01
199.75
233.000
0.00030
0.00139
0.00248
59.227
278.112
390.000
35.725
111.835
235.242
382.803
-3036.64
0.00
19995.61
16958.97
198.05
231.000
0.00027
0.00138
0.00248
54.545
275.325
390.000
32.901
110.715
235.242
378.858
-2796.59
0.00
19995.61
17199.02
196.35
229.000
0.00025
0.00136
0.00248
49.782
272.489
390.000
30.028
109.574
235.242
374.844
-2552.35
0.00
19995.61
17443.26
194.65
227.000
0.00022
0.00135
0.00247
44.934
269.604
390.000
27.104
108.414
235.242
370.760
-2303.80
0.00
19995.61
17691.81
192.95
225.000
0.00020
0.00133
0.00247
40.000
266.667
390.000
24.127
107.233
235.242
366.603
-2050.83
0.00
19995.61
17944.78
191.25
223.000
0.00017
0.00132
0.00246
34.978
263.677
390.000
21.098
106.031
235.242
362.371
-1793.33
0.00
19995.61
18202.28
189.55
221.000
0.00015
0.00130
0.00246
29.864
260.633
390.000
18.014
104.807
235.242
358.063
-1531.16
0.00
19995.61
18464.44
187.85
219.000
0.00012
0.00129
0.00245
24.658
257.534
390.000
14.873
103.561
235.242
353.676
-1264.21
0.00
19995.61
18731.40
186.15
217.000
0.00010
0.00127
0.00245
19.355
254.378
390.000
11.675
102.291
235.242
349.208
-992.34
0.00
19995.61
19003.27
184.45
215.000
0.00007
0.00126
0.00244
13.953
251.163
390.000
8.417
100.999
235.242
344.658
-715.41
0.00
19995.61
19280.20
182.75
213.000
0.00004
0.00124
0.00244
8.451
247.887
390.000
5.097
99.681
235.242
340.021
-433.27
0.00
19995.61
19562.33
181.05
211.000
0.00001
0.00122
0.00243
2.844
244.550
390.000
1.715
98.339
235.242
335.297
-145.79
0.00
19995.61
19849.82
179.35
209.000
-0.00001
0.00121
0.00243
-2.871
241.148
390.000
-1.732
96.971
235.242
330.482
147.19
0.00
19995.61
20142.80
177.65
207.000
-0.00004
0.00119
0.00242
-8.696
237.681
390.000
-5.245
95.577
235.242
325.575
445.83
0.00
19995.61
20441.44
175.95
205.000
-0.00007
0.00117
0.00241
-14.634
234.146
390.000
-8.827
94.156
235.242
320.571
750.30
0.00
19995.61
20745.91
174.25
203.000
-0.00010
0.00115
0.00241
-20.690
230.542
390.000
-12.480
92.706
235.242
315.469
1060.78
0.00
19995.61
21056.38
172.55
201.000
-0.00013
0.00113
0.00240
-26.866
226.866
390.000
-16.205
91.228
235.242
310.266
1377.42
0.00
19995.61
21373.03
170.85
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Cc
Mc
Pn
Mn
kN
kNmm
kN
kNm
Ф
Ф.Pn
Ф.Mn
kN
kNm
1329.98
0.00
0.65
864.48
0.00
993.44
8071.68
1329.98
20.80
0.65
864.48
13.52
986.21
8851.26
1329.98
21.75
0.65
864.48
14.14
978.99
9618.55
1329.98
22.69
0.65
864.48
14.75
971.76
10373.56
1329.98
23.62
0.65
864.48
15.35
964.54
11116.29
1329.98
24.54
0.65
864.48
15.95
957.31
11846.74
1329.98
25.46
0.65
864.48
16.55
950.09
12564.91
1329.98
26.36
0.65
864.48
17.13
942.86
13270.79
1329.98
27.26
0.65
864.48
17.72
935.64
13964.39
1329.98
28.14
0.65
864.48
18.29
928.41
14645.71
1329.98
29.02
0.65
864.48
18.86
921.19
15314.74
1329.98
29.88
0.65
864.48
19.42
913.96
15971.49
1329.98
30.74
0.65
864.48
19.98
906.74
16615.96
1322.21
31.59
0.65
859.44
20.53
899.51
17248.15
1311.59
32.43
0.65
852.54
21.08
892.29
17868.06
1300.92
33.26
0.65
845.59
21.62
885.06
18475.68
1290.18
34.08
0.65
838.62
22.15
877.84
19071.02
1279.39
34.89
0.65
831.60
22.68
870.61
19654.08
1268.54
35.69
0.65
824.55
23.20
863.39
20224.85
1257.63
36.49
0.65
817.46
23.72
856.16
20783.34
1246.66
37.27
0.65
810.33
24.23
848.94
21329.55
1235.62
38.05
0.65
803.15
24.73
841.71
21863.48
1224.52
38.82
0.65
795.94
25.23
834.49
22385.13
1213.35
39.58
0.65
788.67
25.73
827.26
22894.49
1202.11
40.34
0.65
781.37
26.22
820.04
23391.57
1190.80
41.08
0.65
774.02
26.70
812.81
23876.37
1179.42
41.82
0.65
766.62
27.18
805.59
24348.88
1167.96
42.55
0.65
759.17
27.66
798.36
24809.11
1156.43
43.27
0.65
751.68
28.13
791.14
25257.06
1144.81
43.99
0.65
744.13
28.59
783.91
25692.73
1133.12
44.70
0.65
736.53
29.05
776.69
26116.12
1121.35
45.40
0.65
728.87
29.51
769.46
26527.22
1109.48
46.09
0.65
721.16
29.96
762.24
26926.04
1097.53
46.78
0.65
713.40
30.40
755.01
27312.58
1085.49
47.46
0.65
705.57
30.85
747.79
27686.83
1073.36
48.13
0.65
697.69
31.28
740.56
28048.80
1061.13
48.79
0.65
689.74
31.72
733.34
28398.49
1048.81
49.45
0.65
681.72
32.15
726.11
28735.90
1036.38
50.11
0.65
673.65
32.57
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
mm
f s1 s1
f s2 s2
f s3 s3
Fs1
Fs2
Fs3
Cs
Ms1
Ms2
Ms3
Ms
a
MPa
MPa
MPa
kN
kN
kN
kN
kNmm
kNmm
kNmm
kNmm
mm
199.000
-0 - 0.00017
0.00112
0.00240
-33.166
223.116
390.000
-20.005
89.720
235.242
304.957
1700.44
0.00
19995.61
21696.05
169.15
197.000
-0 - 0.00020
0.00110
0.00239
-39.594
219.289
390.000
-23.882
88.181
235.242
299.541
2030.01
0.00
19995.61
22025.62
167.45
195.000
-0 - 0.00023
0.00108
0.00238
-46.154
215.385
390.000
-27.839
86.611
235.242
294.014
2366.34
0.00
19995.61
22361.95
165.75
193.000
-0 - 0.00026
0.00106
0.00238
-52.850
211.399
390.000
-31.878
85.009
235.242
288.373
2709.65
0.00
19995.61
22705.26
164.05
191.000
-0 - 0.00030
0.00104
0.00237
-59.686
207.330
390.000
-36.002
83.372
235.242
282.613
3060.14
0.00
19995.61
23055.75
162.35
189.000
-0 - 0.00033
0.00102
0.00237
-66.667
203.175
390.000
-40.212
81.701
235.242
276.731
3418.05
0.00
19995.61
23413.66
160.65
187.000
-0 - 0.00037
0.00099
0.00236
-73.797
198.930
390.000
-44.513
79.995
235.242
270.724
3783.62
0.00
19995.61
23779.23
158.95
185.000
-0 - 0.00041
0.00097
0.00235
-81.081
194.595
390.000
-48.907
78.251
235.242
264.587
4157.09
0.00
19995.61
24152.70
157.25
183.000
-0 - 0.00044
0.00095
0.00234
-88.525
190.164
390.000
-53.397
76.469
235.242
258.315
4538.73
0.00
19995.61
24534.33
155.55
181.000
-0 - 0.00048
0.00093
0.00234
-96.133
185.635
390.000
-57.986
74.648
235.242
251.905
4928.79
0.00
19995.61
24924.40
153.85
179.000
-0 -0.00052
0.00091
0.00233
-1 -103.911
181.006
390.000
-62.677
72.787
235.242
245.352
5327.58
0.00
19995.61
25323.19
152.15
177.000
-0 -0.00056
0.00088
0.00232
-1 -111.864
176.271
390.000
-67.475
70.883
235.242
238.650
5735.38
0.00
19995.61
25730.99
150.45
175.000
-0 -0.00060
0.00086
0.00231
-1 -120.000
171.429
390.000
-72.382
68.936
235.242
231.796
6152.50
0.00
19995.61
26148.10
148.75
173.000
-0 -0.00064
0.00083
0.00231
-1 -128.324
166.474
390.000
-77.403
66.943
235.242
224.783
6579.26
0.00
19995.61
26574.87
147.05
171.000
-0 -0.00068
0.00081
0.00230
-1 -136.842
161.404
390.000
-82.541
64.904
235.242
217.605
7016.00
0.00
19995.61
27011.61
145.35
169.000
-0 -0.00073
0.00078
0.00229
-1 -145.562
156.213
390.000
-87.801
62.817
235.242
210.258
7463.09
0.00
19995.61
27458.69
143.65
167.000
-0 -0.00077
0.00075
0.00228
-1 -154.491
150.898
390.000
-93.187
60.680
235.242
202.735
7920.88
0.00
19995.61
27916.49
141.95
165.000
-0 -0.00082
0.00073
0.00227
-1 -163.636
145.455
390.000
-98.703
58.491
235.242
195.030
8389.77
0.00
19995.61
28385.37
140.25
163.000
-0 -0.00087
0.00070
0.00226
-1 -173.006
139.877
390.000
-104.355
56.248
235.242
187.136
8870.16
0.00
19995.61
28865.77
138.55
161.000
-0 -0.00091
0.00067
0.00225
-1 -182.609
134.161
390.000
-110.147
53.950
235.242
179.045
9362.49
0.00
19995.61
29358.10
136.85
159.000
-0 -0.00096
0.00064
0.00225
-1 -192.453
128.302
390.000
-116.085
51.593
235.242
170.751
9867.21
0.00
19995.61
29862.82
135.15
157.000
- 0. 0.00101
0.00061
0.00224
- 20 202.548
122.293
390.000
-122.174
49.177
235.242
162.245
10384.78
0.00
19995.61
30380.39
133.45
155.000
- 0. 0.00106
0.00058
0.00223
- 21 212.903
116.129
390.000
-128.420
46.698
235.242
153.521
10915.72
0.00
19995.61
30911.33
131.75
153.000
- 0. 0.00112
0.00055
0.00222
- 22 223.529
109.804
390.000
-134.830
44.155
235.242
144.567
11460.53
0.00
19995.61
31456.14
130.05
151.000
- 0. 0.00117
0.00052
0.00221
- 23 234.437
103.311
390.000
-141.409
41.544
235.242
135.377
12019.78
0.00
19995.61
32015.38
128.35
149.000
-0 -0.00123
0.00048
0.00219
-2 -245.638
96.644
390.000
-148.165
38.863
235.242
125.940
12594.03
0.00
19995.61
32589.64
126.65
147.000
-0 -0.00129
0.00045
0.00218
-2 -257.143
89.796
390.000
-155.105
36.109
235.242
116.247
13183.92
0.00
19995.61
33179.53
124.95
145.000
-0 -0.00134
0.00041
0.00217
-2 -268.966
82.759
390.000
-162.236
33.279
235.242
106.285
13790.08
0.00
19995.61
33785.68
123.25
143.000
-0 -0.00141
0.00038
0.00216
-2 -281.119
75.524
390.000
-169.567
30.370
235.242
96.046
14413.19
0.00
19995.61
34408.80
121.55
141.000
-0 -0.00147
0.00034
0.00215
-2 -293.617
68.085
390.000
-177.106
27.379
235.242
85.515
15053.98
0.00
19995.61
35049.59
119.85
139.000
-0 -0.00153
0.00030
0.00214
-3 -306.475
60.432
390.000
-184.861
24.301
235.242
74.682
15713.21
0.00
19995.61
35708.82
118.15
137.000
-0 -0.00160
0.00026
0.00212
-3 -319.708
52.555
390.000
-192.843
21.134
235.242
63.533
16391.68
0.00
19995.61
36387.29
116.45
135.000
-0 -0.00167
0.00022
0.00211
-3 -333.333
44.444
390.000
-201.062
17.872
235.242
52.053
17090.26
0.00
19995.61
37085.87
114.75
133.000
-0 -0.00174
0.00018
0.00210
-3 -347.368
36.090
390.000
-209.528
14.513
235.242
40.228
17809.85
0.00
19995.61
37805.46
113.05
131.000
-0 -0.00181
0.00014
0.00208
-3 -361.832
27.481
390.000
-218.252
11.051
235.242
28.041
18551.42
0.00
19995.61
38547.03
111.35
129.000
-0 - 0.00188
0.00009
0.00207
-3 - 376.744
18.605
390.000
-227.247
7.481
235.242
15.477
19315.97
0.00
19995.61
39311.58
109.65
127.000
-0 -0.00196
0.00005
0.00206
-3 -390.000
9.449
390.000
-235.242
3.800
235.242
3.800
19995.61
0.00
19995.61
39991.22
107.95
125.000
-0 -0.00204
0.00000
0.00204
-3 -390.000
0.000
390.000
-235.242
0.000
235.242
0.000
19995.61
0.00
19995.61
39991.22
106.25
123.000
-0 -0.00212
-0 -0.00005
0.00202
-3 -390.000
-9.756
390.000
-235.242
-3.923
235.242
-3.923
19995.61
0.00
19995.61
39991.22
104.55
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Cc
Mc
Pn
Mn
kN
kNmm
kN
kNm
718.89
29 29061.03
1023.84
50.76
0.65
665.50
711.66
29 29373.87
1011.20
51.40
0.65
657.28
33.41
704.44
29 29674.43
998.45
52.04
0.65
648.99
33.82
697.21
29 29962.71
985.59
52.67
0.65
640.63
34.23
689.99
30 30238.70
972.60
53.29
0.65
632.19
34.64
682.76
30 30502.41
959.49
53.92
0.65
623.67
35.05
675.54
30 30753.84
946.26
54.53
0.65
615.07
35.45
668.31
30 30992.99
932.90
55.15
0.65
606.38
35.84
661.09
31 31219.86
919.40
55.75
0.65
597.61
36.24
653.86
31 31434.44
905.77
56.36
0.65
588.75
36.63
646.64
31 31636.74
891.99
56.96
0.65
579.79
37.02
639.41
31 31826.76
878.06
57.56
0.65
570.74
37.41
632.19
32 32004.49
863.98
58.15
0.65
561.59
37.80
624.96
32 32169.94
849.75
58.74
0.65
552.33
38.18
617.74
32 32323.11
835.34
59.33
0.65
542.97
38.57
610.51
32 32464.00
820.77
59.92
0.65
533.50
38.95
603.29
32 32592.61
806.02
60.51
0.65
523.91
39.33
596.06
32 32708.93
791.09
61.09
0.65
514.21
39.71
588.84
32 32812.97
775.97
61.68
0.65
504.38
40.09
581.61
32 32904.73
760.66
62.26
0.65
494.43
40.47
574.39
32 32984.20
745.14
62.85
0.65
484.34
40.85
567.16
33 33051.39
729.41
63.43
0.65
474.12
41.23
559.94
33 33106.30
713.46
64.02
0.65
463.75
41.61
552.71
33 33148.93
697.28
64.61
0.65
453.23
41.99
545.49
33 33179.28
680.86
65.19
0.65
442.56
42.38
538.26
33 33197.34
664.20
65.79
0.65
431.73
42.76
531.04
33 33203.12
647.28
66.38
0.65
420.73
43.15
523.81
33 33196.62
630.10
66.98
0.65
409.56
43.54
516.59
33 33177.83
612.63
67.59
0.65
398.21
43.93
509.36
33 33146.76
594.88
68.20
0.65
386.67
44.33
502.14
33 33103.41
576.82
68.81
0.65
374.93
44.73
494.91
33 33047.78
558.45
69.44
0.65
362.99
45.13
487.69
32 32979.87
539.74
70.07
0.65
350.83
45.54
480.46
32 32899.67
520.69
70.71
0.65
338.45
45.96
473.24
32 32807.19
501.28
71.35
0.65
325.83
46.38
466.01
32 32702.43
481.49
72.01
0.65
312.97
46.81
458.79
32 32585.38
462.59
72.58
0.65
300.68
47.17
451.56
32 32456.05
451.56
72.45
0.65
293.52
47.09
444.34
32 32314.44
440.41
72.31
0.65
286.27
47.00
Ф
Ф.Pn
Ф.Mn
kN
kNm 32.99
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
εs3
mm
f s1 s1
f s2 s2
f s3 s3
Fs1
Fs2
Fs3
Cs
Ms1
Ms2
Ms3
Ms
a
MPa
MPa
MPa
kN
kN
kN
kN
kNmm
kNmm
kNmm
kNmm
mm
121.000
-0 -0.00221
-0 -0.00010
0.00201
-3 -390.000
-19.835
390.000
-235.242
-7.976
235.242
-7.976
19995.61
0.00
19995.61
39991.22
102.85
119.000
-0.00229
-0.00015
0.00199
-390.000
-30.252
390.000
-235.242
-12.165
235.242
-12.165
19995.61
0.00
19995.61
39991.22
101.15
117.000
- 0. 0.00238
- 0. 0.00021
0.00197
- 39 390.000
-41.026
390.000
-235.242
-16.497
235.242
-16.497
19995.61
0.00
19995.61
39991.22
99.45
115.000
- 0. 0.00248
- 0. 0.00026
0.00196
- 39 390.000
-52.174
390.000
-235.242
-20.980
235.242
-20.980
19995.61
0.00
19995.61
39991.22
97.75
113.000
- 0. 0.00258
- 0. 0.00032
0.00194
- 39 390.000
-63.717
387.611
-235.242
-25.622
233.801
-27.063
19995.61
0.00
19873.10
39868.71
96.05
111.000
- 0. 0.00268
- 0. 0.00038
0.00192
- 39 390.000
-75.676
383.784
-235.242
-30.431
231.493
-34.181
19995.61
0.00
19676.90
39672.51
94.35
109.000
- 0. 0.00278
- 0. 0.00044
0.00190
- 39 390.000
-88.073
379.817
-235.242
-35.416
229.100
-41.559
19995.61
0.00
19473.49
39469.10
92.65
107.000
-0.00289
-0.00050
0.00188
-390.000
-100.935
375.701
-235.242
-40.588
226.617
-49.213
19995.61
0.00
19262.48
39258.09
90.95
105.000
-0.00300
-0.00057
0.00186
-390.000
-114.286
371.429
-235.242
-45.957
224.040
-57.159
19995.61
0.00
19043.44
39039.05
89.25
103.000
-0.00312
-0.00064
0.00183
-390.000
-128.155
366.990
-235.242
-51.534
221.363
-65.413
19995.61
0.00
18815.88
38811.49
87.55
101.000
-0.00324
-0.00071
0.00181
-390.000
-142.574
362.376
-235.242
-57.333
218.580
-73.995
19995.61
0.00
18579.32
38574.93
85.85
99.000
-0.00336
-0.00079
0.00179
-390.000
-157.576
357.576
-235.242
-63.365
215.685
-82.923
19995.61
0.00
18333.19
38328.80
84.15
97.000
-0.00349
-0.00087
0.00176
-390.000
-173.196
352.577
-235.242
-69.646
212.670
-92.219
19995.61
0.00
18076.92
38072.53
82.45
95.000
-0.00363
-0.00095
0.00174
-390.000
-189.474
347.368
-235.242
-76.192
209.528
-101.907
19 19995.61
0.00
17809.85
37805.46
80.75
93.000
-0.00377
-0.00103
0.00171
-390.000
-206.452
341.935
-235.242
-83.019
206.251
-112.011
19 19995.61
0.00
17531.30
37526.91
79.05
91.000
-0.00392
-0.00112
0.00168
-390.000
-224.176
336.264
-235.242
-90.146
202.830
-122.559
19 19995.61
0.00
17240.51
37236.12
77.35
89.000
-0.00408
-0.00121
0.00165
-390.000
-242.697
330.337
-235.242
-97.594
199.255
-133.582
19 19995.61
0.00
16936.64
36932.25
75.65
87.000
- 0. 0.00424
-0.00131
0.00162
-390.000
-262.069
324.138
-235.242
-105.384
195.515
-145.111
19995.61
0.00
16618.81
36614.42
73.95
85.000
- 0. 0.00441
-0.00141
0.00159
-390.000
-282.353
317.647
-235.242
-113.541
191.600
-157.183
19995.61
0.00
16286.02
36281.63
72.25
83.000
- 0. 0.00459
-0.00152
0.00155
-390.000
-303.614
310.843
-235.242
-122.091
187.496
-169.837
19995.61
0.00
15937.19
35932.79
70.55
81.000
- 0. 0.00478
-0.00163
0.00152
-390.000
-325.926
303.704
-235.242
-131.063
183.190
-183.115
19995.61
0.00
15571.13
35566.74
68.85
79.000
- 0. 0.00497
-0.00175
0.00148
-390.000
-349.367
296.203
-235.242
-140.489
178.665
-197.066
19995.61
0.00
15186.54
35182.15
67.15
77.000
- 0. 0.00518
-0.00187
0.00144
-390.000
-374.026
288.312
-235.242
-150.405
173.906
-211.742
19995.61
0.00
14781.97
34777.58
65.45
75.000
- 0. 0.00540
-0.00200
0.00140
-390.000
-390.000
280.000
-235.242
-156.828
168.892
-223.179
19995.61
0.00
14355.82
34351.43
63.75
73.000
- 0. 0.00563
-0.00214
0.00136
-390.000
-390.000
271.233
-235.242
-156.828
163.604
-228.467
19995.61
0.00
13906.32
33901.93
62.05
71.000
- 0. 0.00587
-0.00228
0.00131
-390.000
-390.000
261.972
-235.242
-156.828
158.018
-234.053
19995.61
0.00
13431.50
33427.11
60.35
68.000
- 0. 0.00626
-0.00251
0.00124
-390.000
-390.000
247.059
-235.242
-156.828
149.022
-243.048
19995.61
0.00
12666.90
32662.51
57.80
10.714
390.000
-235.242
4.308
235.242
4.308
19995.61
0.00
19995.61
39991.22
108.18
KONDISI TEKAN AKSIAL KECIL : Pn = 0.1 * fc' * b * h KONDISI BALANCE 127
-0 -0.00195
0.00005
0.00206
-3 -390.000
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
Cc
Mc
Pn
Mn
kN
kNmm
kN
kNm
Ф
Ф.Pn
Ф.Mn
kN
kNm
437.11
32 32160.55
429.14
72.15
0.65
278.94
46.90
429.89
31 31994.38
417.72
71.99
0.65
271.52
46.79
422.66
31 31815.92
406.17
71.81
0.65
264.01
46.67
415.44
31 31625.18
394.46
71.62
0.65
256.40
46.55
408.21
31 31422.16
381.15
71.29
0.65
247.75
46.34
400.99
31 31206.85
366.81
70.88
0.65
238.42
46.07
393.76
30 30979.26
352.20
70.45
0.65
228.93
45.79
386.54
30 30739.39
337.32
70.00
0.65
219.26
45.50
379.31
30 30487.24
322.15
69.53
0.65
209.40
45.19
372.09
30 30222.81
306.67
69.03
0.65
199.34
44.87
364.86
29 29946.09
290.87
68.52
0.65
189.06
44.54
357.64
29 29657.09
274.71
67.99
0.65
178.56
44.19
350.41
29 29355.81
258.19
67.43
0.65
167.83
43.83
343.19
29 29042.24
241.28
66.85
0.65
156.83
43.45
335.96
28 28716.39
223.95
66.24
0.65
145.57
43.06
328.74
28 28378.26
206.18
65.61
0.65
134.02
42.65
321.51
28 28027.85
187.93
64.96
0.65
122.15
42.22
314.29
27 27665.16
169.18
64.28
0.65
109.96
41.78
307.06
27290.18
149.88
63.57
0.65
97.42
41.32
299.84
26902.92
130.00
62.84
0.65
84.50
40.84
292.61
26503.38
109.50
62.07
0.67
73.21
41.50
285.39
26091.55
88.32
61.27
0.69
61.30
42.52
278.16
25667.44
66.42
60.45
0.72
47.84
43.54
270.94
25231.05
47.76
59.58
0.74
35.47
44.25
263.71
24782.38
35.25
58.68
0.76
26.71
44.47
256.49
24321.43
22.43
57.75
0.77
17.34
44.64
245.65
23606.97
2.60
56.27
0.80
2.07
44.84
459.77
32 32602.07
464.08
72.59
0.65
81.25
0.00
81.25
50.00
0.00
0.00
301.65
47.19
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
ANALISIS KEKUATAN KOLOM BETON BERTULANG DENGAN DIAGRAM INTERAKSI [C]2010 : M. Noer Ilham
KODE KOLOM
K2
INPUT DATA KOLOM
f c' = f y =
Kuat tekan beton, Tegangan leleh baja, Lebar kolom, Tinggi kolom, Tebal brutto selimut beton, Jumlah tulangan, Diameter tulangan,
20
MPa
390
MPa
b= h= ds =
250
mm
250
mm
40
mm
n= D=
4
buah
19
mm
PERHITUNGAN DIAGRAM INTERAKSI Es = 2.E+05 MPa
Modulus elastis baja, β1 = 0.85
untuk f c' 30 MPa
β1 = 0.85 - 0.008 (f c' - 30)
untuk f c' > 30 MPa β1 =
Faktor distribusi tegangan, Luas tulangan total, Jarak antara tulangan, Rasio tulangan, Faktor reduksi kekuatan, f = 0.65 untuk Pn ≥ 0.1 * fc' * b * h f = 0.80 untuk Pn = 0
0.85 2
2
As = n * p / 4 * D = 1134 mm x = h - 2*ds = 170.00 mm r = As / Ag = 1.81%
Untuk : 0
≤
Pn ≤ 0.1 * f c' * b * h
f = 0.65 + 0.15 * ( Pno - Pn ) / Pno
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
No Luas masing-masing tulangan Jarak tulangan thd. sisi beton 2 As1 = 2/4 * A s = 567 mm d1 = x + ds = 1 210 mm 2
As2 = 2/4 * A s = 567 As =
2
mm
d2 = ds =
40
mm
2
1134 mm
-3
Pada kondisi tekan aksial sentris (M no = 0) :
Pno = 0.80*[ 0.85*f c' *b*h + A s*(f y - 0.85*f c')]*10 = 1188 kN -3
0.1 * f c' * b * h *10 =
125
c = cb = 600 / (600 + f y) * d1 = 127.3 mm
Pada kondisi balance : Pada kondisi garis netral terletak pada jarak c dari sisi beton tekan terluar : Regangan pada masing-masing baja tulangan :
εsi = 0.003 * ( c - di ) / c
Tegangan pada masing-masing baja tulangan : Untuk | εsi | maka f si = esi* Es Untuk
| εsi | maka f si =| εsi | / esi* f y Jumlah interval jarak grs netral =
URAIAN PERHITUNGAN Gaya-gaya internal pada masing-masing baja tulangan : Resultan gaya internal baja tulangan : Momen akibat gaya internal masing-masing baja tulangan : Momen total akibat gaya internal baja tulangan : Tinggi blok tegangan tekan beton, Gaya internal pada beton tekan : Momen akibat gaya internal tekan beton : Gaya aksial nominal : Momen nominal : Gaya aksial rencana : Momen rencana :
kN
→
112
Dc = 2.2321
PERSAMAAN
UNIT -3
Fsi = Asi * f si * 10 -3 Cs = [ S Fsi ]*10 Msi = Fsi*(h/2 - di) Ms = S Msi a = β1 * c -3 Cc = 0.85 * f c' * b * a * 10 Mc = Cc * (h - a) / 2 Pn = Cs + Cc -3 Mn = (Mc + Ms)*10 Pu = f * Pn Mu = f * Mn
kN kN kNmm kNmm mm kN kNmm kN kNm kN kNm
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
1000 950 900 850 800 750 700
) N k ( n
650
b=
250
mm
600
h=
250
mm
550
4
D
19
500
f c' =
20
MPa
450
f y =
390
MPa
P . f
400
Pu
Mu
350
(kN)
(kNm)
300
112.6
11.7
250
129.7
10.7
124.0
11.9
82.8
13.0
163.0
13.5
116.5
10.2
114.2
15.7
72.9
17.3
200 150 100 50 0 0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
42 44
f.Mn (kNm)
ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI
46 48 50
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
mm
f s1
f s2
Fs1
Fs2
Cs
Ms1
Ms2
Ms
a
Cc
Mc
Pn
Mn
MPa
MPa
kN
kN
kN
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
kNm
KONDISI TEKAN AKSIAL SENTRIS
1188.42
0.00
Ф 0.65
Ф.Pn
Ф.Mn
kN
kNm
772.47
0.00
275.00
0.00071 0.00256
141.82 390.00
80.42
221.15
301.57
-6835.62 18797.96
11962.34
233.75
993.44
8071.68
1188.42
20.03
0.65
772.47
13.02
272.77
0.00069 0.00256
138.07 390.00
78.29
221.15
299.45
-6654.90 18797.96
12143.06
231.85
985.37
8940.95
1188.42
21.08
0.65
772.47
13.70
270.54
0.00067 0.00256
134.26 390.00
76.13
221.15
297.28
-6471.19 18797.96
12326.76
229.96
977.31
9794.92
1188.42
22.12
0.65
772.47
14.38
268.30
0.00065 0.00255
130.38 390.00
73.93
221.15
295.09
-6284.43 18797.96
12513.52
228.06
969.25 10633.59
1188.42
23.15
0.65
772.47
15.05
266.07
0.00063 0.00255
126.44 390.00
71.70
221.15
292.85
-6094.54 18797.96
12703.42
226.16
961.18 11456.96
1188.42
24.16
0.65
772.47
15.70
263.84
0.00061 0.00255
122.44 390.00
69.43
221.15
290.58
-5901.43 18797.96
12896.53
224.26
953.12 12265.03
1188.42
25.16
0.65
772.47
16.36
261.61
0.00059 0.00254
118.36 390.00
67.12
221.15
288.27
-5705.02 18797.96
13092.93
222.37
945.06 13057.80
1188.42
26.15
0.65
772.47
17.00
259.38
0.00057 0.00254
114.22 390.00
64.77
221.15
285.92
-5505.24 18797.96
13292.72
220.47
936.99 13835.28
1188.42
27.13
0.65
772.47
17.63
257.14
0.00055 0.00253
110.00 390.00
62.38
221.15
283.53
-5301.99 18797.96
13495.97
218.57
928.93 14597.45
1188.42
28.09
0.65
772.47
18.26
254.91
0.00053 0.00253
105.71 390.00
59.94
221.15
281.10
-5095.18 18797.96
13702.78
216.67
920.86 15344.32
1188.42
29.05
0.65
772.47
18.88
252.68
0.00051 0.00253
101.34 390.00
57.47
221.15
278.62
-4884.71 18797.96
13913.25
214.78
912.80 16075.90
1188.42
29.99
0.65
772.47
19.49
250.45
0.00048 0.00252
96.90 390.00
54.95
221.15
276.10
-4670.49 18797.96
14127.46
212.88
904.74 16792.17
1180.84
30.92
0.65
767.54
20.10
248.21
0.00046 0.00252
92.37 390.00
52.38
221.15
273.53
-4452.42 18797.96
14345.53
210.98
896.67 17493.15
1170.21
31.84
0.65
760.64
20.70
245.98
0.00044 0.00251
87.77 390.00
49.77
221.15
270.92
-4230.39 18797.96
14567.56
209.08
888.61 18178.83
1159.53
32.75
0.65
753.70
21.29
243.75
0.00042 0.00251
83.08 390.00
47.11
221.15
268.26
-4004.30 18797.96
14793.66
207.19
880.55 18849.21
1148.81
33.64
0.65
746.73
21.87
241.52
0.00039 0.00250
78.30 390.00
44.40
221.15
265.55
-3774.02 18797.96
15023.93
205.29
872.48 19504.29
1138.04
34.53
0.65
739.72
22.44
239.29
0.00037 0.00250
73.43 390.00
41.64
221.15
262.79
-3539.45 18797.96
15258.50
203.39
864.42 20144.06
1127.21
35.40
0.65
732.69
23.01
237.05
0.00034 0.00249
68.47 390.00
38.83
221.15
259.98
-3300.47 18797.96
15497.49
201.50
856.36 20768.55
1116.34
36.27
0.65
725.62
23.57
234.82
0.00032 0.00249
63.42 390.00
35.96
221.15
257.12
-3056.94 18797.96
15741.02
199.60
848.29 21377.73
1105.41
37.12
0.65
718.52
24.13
232.59
0.00029 0.00248
58.27 390.00
33.04
221.15
254.20
-2808.73 18797.96
15989.22
197.70
840.23 21971.61
1094.43
37.96
0.65
711.38
24.67
230.36
0.00027 0.00248
53.02 390.00
30.07
221.15
251.22
-2555.71 18797.96
16242.24
195.80
832.17 22550.19
1083.38
38.79
0.65
704.20
25.22
228.13
0.00024 0.00247
47.67 390.00
27.03
221.15
248.18
-2297.75 18797.96
16500.21
193.91
824.10 23113.47
1072.29
39.61
0.65
696.99
25.75
225.89
0.00021 0.00247
42.21 390.00
23.94
221.15
245.09
-2034.68 18797.96
16763.27
192.01
816.04 23661.46
1061.13
40.42
0.65
689.73
26.28
223.66
0.00018 0.00246
36.65 390.00
20.78
221.15
241.93
-1766.37 18797.96
17031.59
190.11
807.97 24194.14
1049.91
41.23
0.65
682.44
26.80
221.43
0.00015 0.00246
30.97 390.00
17.56
221.15
238.71
-1492.64 18797.96
17305.31
188.21
799.91 24711.53
1038.62
42.02
0.65
675.11
27.31
219.20
0.00013 0.00245
25.17 390.00
14.27
221.15
235.43
-1213.34 18797.96
17584.61
186.32
791.85 25213.61
1027.27
42.80
0.65
667.73
27.82
216.96
0.00010 0.00245
19.26 390.00
10.92
221.15
232.07
-928.29 18797.96
17869.66
184.42
783.78 25700.40
1015.86
43.57
0.65
660.31
28.32
214.73
0.00007 0.00244
13.22 390.00
7.50
221.15
228.65
-637.32
18797.96
18160.63
182.52
775.72 26171.89
1004.37
44.33
0.65
652.84
28.82
212.50
0.00004 0.00244
7.06 390.00
4.00
221.15
225.16
-340.23
18797.96
18457.72
180.63
767.66 26628.08
992.81
45.09
0.65
645.33
29.31
210.27
0.00000 0.00243
0.76 390.00
0.43
221.15
221.59
-36.84
18797.96
18761.11
178.73
759.59 27068.97
981.18
45.83
0.65
637.77
29.79
208.04
-0.00003 0.00242
-5.67 390.00
-3.21
221.15
217.94
273.06
18797.96
19071.02
176.83
751.53 27494.55
969.47
46.57
0.65
630.15
30.27
205.80
- 0.00006 0.00242
-12.23 390.00
-6.94
221.15
214.21
589.69
18797.96
19387.65
174.93
743.47 27904.85
957.68
47.29
0.65
622.49
30.74
203.57
-0.00009 0.00241
-18.95 390.00
-10.74
221.15
210.41
913.26 18797.96
19711.22
173.04
735.40 28299.84
945.81
48.01
0.65
614.78
31.21
201.34
-0.00013 0.00240
-25.81 390.00
-14.64
221.15
206.52
1244.01 18797.96
20041.96
171.14
727.34 28679.53
933.86
48.72
0.65
607.01
31.67
199.11
-0.00016 0.00240
-32.83 390.00
-18.61
221.15
202.54
1582.17 18797.96
20380.12
169.24
719.27 29043.92
921.81
49.42
0.65
599.18
32.13
196.88
-0.00020 0.00239
-40.00 390.00
-22.68
221.15
198.47
1928.00 18797.96
20725.95
167.34
711.21 29393.01
909.68
50.12
0.65
591.29
32.58
194.64
-0.00024 0.00238
-47.34 390.00
-26.84
221.15
194.31
2281.76 18797.96
21079.71
165.45
703.15 29726.81
897.46
50.81
0.65
583.35
33.02
192.41
-0.00027 0.00238
-54.85 390.00
-31.10
221.15
190.05
2643.72 18797.96
21441.68
163.55
695.08 30045.30
885.13
51.49
0.65
575.34
33.47
Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi
c
εs1
εs2
mm
f s1
f s2
Fs1
Fs2
Cs
Ms1
Ms2
Ms
a
Cc
Mc
Pn
Mn
MPa
MPa
kN
kN
kN
kNmm
kNmm
kNmm
mm
kN
kNmm
kN
kNm
Ф
Ф.Pn
Ф.Mn
kN
kNm
190.18
-0.00031 0.00237
-62.54 390.00
-35.46
221.15
185.69
3014.19
18797.96
21812.15
161.65
687.02 30348.50
872.71
52.16
0.65
567.26
33.90
187.95
-0.00035 0.00236
-70.40 390.00
-39.92
221.15
181.23
3393.46
18797.96
22191.41
159.75
678.96 30636.40
860.19
52.83
0.65
559.12
34.34
185.71
-0.00039 0.00235
-78.46 390.00
-44.49
221.15
176.66
3781.84
18797.96
22579.79
157.86
670.89 30908.99
847.55
53.49
0.65
550.91
34.77
183.48
-0.00043 0.00235
-86.72 390.00
-49.17
221.15
171.98
4179.67
18797.96
22977.62
155.96
662.83 31166.29
834.81
54.14
0.65
542.63
35.19
181.25
-0.00048 0.00234
-95.17 390.00
-53.97
221.15
167.18
4587.30
18797.96
23385.25
154.06
654.77 31408.29
821.95
54.79
0.65
534.27
35.62
179.02
-0.00052 0.00233
-103.84 390.00
-58.88
221.15
162.27
5005.10
18797.96
23803.05
152.17
646.70 31634.99
808.97
55.44
0.65
525.83
36.03
176.79
-0.00056 0.00232
-112.73 390.00
-63.92
221.15
157.23
5433.44
18797.96
24231.40
150.27
638.64 31846.39
795.87
56.08
0.65
517.31
36.45
174.55
-0.00061 0.00231
-121.84 390.00
-69.09
221.15
152.06
5872.74
18797.96
24670.70
148.37
630.57 32042.49
782.64
56.71
0.65
508.71
36.86
172.32
-0.00066 0.00230
-131.19 390.00
-74.39
221.15
146.76
6323.43
18797.96
25121.38
146.47
622.51 32223.29
769.27
57.34
0.65
500.03
37.27
170.09
-0.00070 0.00229
-140.79 390.00
-79.83
221.15
141.32
6785.94
18797.96
25583.89
144.58
614.45 32388.79
755.77
57.97
0.65
491.25
37.68
167.86
-0.00075 0.00229
-150.64 390.00
-85.42
221.15
135.73
7260.75
18797.96
26058.70
142.68
606.38 32538.99
742.12
58.60
0.65
482.38
38.09
165.63
-0.00080 0.00228
-160.75 390.00
-91.16
221.15
130.00
7748.36
18797.96
26546.31
140.78
598.32 32673.90
728.32
59.22
0.65
473.41
38.49
163.39
-0.00086 0.00227
-171.15 390.00
-97.05
221.15
124.10
8249.29
18797.96
27047.25
138.88
590.26 32793.50
714.36
59.84
0.65
464.33
38.90
161.16 -0.00091 0.00226 -181.83 390.00 -103.11
221.15
118.05
8764.10 18797.96
27562.06
136.99
582.19 32897.81
700.24
60.46
0.65
455.15
39.30
158.93 -0.00096 0.00224 -192.81 390.00 -109.33
221.15
111.82
9293.37 18797.96
28091.33
135.09
574.13 32986.81
685.95
61.08
0.65
445.87
39.70
156.70 -0.00102 0.00223 -204.10 390.00 -115.74
221.15
105.41
9837.72 18797.96
28635.68
133.19
566.07 33060.52
671.48
61.70
0.65
436.46
40.10
154.46 -0.00108 0.00222 -215.72 390.00 -122.33
221.15
98.83 10397.80 18797.96
29195.76
131.29
558.00 33118.93
656.83
62.31
0.65
426.94
40.50
152.23 -0.00114 0.00221 -227.68 390.00 -129.11
221.15
92.04 10974.31 18797.96
29772.26
129.40
549.94 33162.04
641.98
62.93
0.65
417.29
40.91
150.00 -0.00120 0.00220 -240.00 390.00 -136.09
221.15
85.06 11567.97 18797.96
30365.93
127.50
541.88 33189.84
626.93
63.56
0.65
407.51
41.31
147.77 -0.00126 0.00219 -252.69 390.00 -143.29
221.15
77.86 12179.57 18797.96
30977.53
125.60
533.81 33202.35
611.67
64.18
0.65
397.59
41.72
145.54 -0.00133 0.00218 -265.77 390.00 -150.71
221.15
70.45 12809.93 18797.96
31607.89
123.71
525.75 33199.56
596.20
64.81
0.65
387.53
42.12
143.30 -0.00140 0.00216 -279.25 390.00 -158.35
221.15
62.80 13459.93 18797.96
32257.89
121.81
517.68 33181.47
580.48
65.44
0.65
377.31
42.54
141.07 -0.00147 0.00215 -293.16 390.00 -166.24
221.15
54.91 14130.50 18797.96
32928.45
119.91
509.62 33148.09
564.53
66.08
0.65
366.95
42.95
138.84 -0.00154 0.00214 -307.52 390.00 -174.38
221.15
46.77 14822.63 18797.96
33620.58
118.01
501.56 33099.40
548.33
66.72
0.65
356.41
43.37
136.61 -0.00161 0.00212 -322.35 390.00 -182.79
221.15
38.36 15537.37 18797.96
34335.33
116.12
493.49 33035.41
531.85
67.37
0.65
345.70
43.79
134.38 -0.00169 0.00211 -337.67 390.00 -191.48
221.15
29.67 16275.87 18797.96
35073.82
114.22
485.43 32956.12
515.10
68.03
0.65
334.82
44.22
132.14 -0.00177 0.00209 -353.51 390.00 -200.46
221.15
20.69 17039.31 18797.96
35837.27
112.32
477.37 32861.54
498.06
68.70
0.65
323.74
44.65
129.91 -0.00185 0.00208 -369.90 390.00 -209.75
221.15
11.40 17828.99 18797.96
36626.94
110.42
469.30 32751.65
480.70
69.38
0.65
312.46
45.10
127.68
-0.00193 0.00206
-386.85 390.00 -219.37
221.15
1.78
18646.28
18797.96
37444.23
108.53
461.24 32626.47
463.02
70.07
0.65
300.97
45.55
125.45
-0.00202 0.00204
-390.00 390.00 -221.15
221.15
0.00
18797.96
18797.96
37595.91
106.63
453.18 32485.99
453.18
70.08
0.65
294.56
45.55
123.21
-0.00211 0.00203
-390.00 390.00 -221.15
221.15
0.00
18797.96
18797.96
37595.91
104.73
445.11 32330.20
445.11
69.93
0.65
289.32
45.45
120.98
-0.00221 0.00201
-390.00 390.00 -221.15
221.15
0.00
18797.96
18797.96
37595.91
102.83
437.05 32159.12
437.05
69.76
0.65
284.08
45.34
118.75
-0.00231 0.00199
-390.00 390.00 -221.15
221.15
0.00
18797.96
18797.96
37595.91
100.94
428.98 31972.74
428.98
69.57
0.65
278.84
45.22
116.52
-0.00241 0.00197
-390.00 390.00 -221.15
221.15
0.00 18797.96
18797.96
37595.91
99.04
420.92 31771.06
420.92
69.37
0.65
273.60
45.09
114.29
-0.00251 0.00195
-390.00 390.00 -221.15
221.15
0.00 18797.96
18797.96
37595.91
97.14
412.86 31554.08
412.86
69.15
0.65
268.36
44.95
112.05
-0.00262 0.00193
-390.00 385.82 -221.15
218.78
-2.37 18797.96
18596.32
37394.28
95.25
404.79 31321.80
402.42
68.72
0.65
261.57
44.67
109.82
-0.00274 0.00191
-390.00 381.46 -221.15
216.31
-4.84 18797.96
18386.49
37184.45
93.35
396.73 31074.22
391.89
68.26
0.65
254.73
44.37
107.59
-0.00286 0.00188
-390.00 376.93 -221.15
213.74
-7.41 18797.96
18167.96
36965.91
91.45
388.67 30811.35
381.25
67.78
0.65
247.82
44.06
105.36 -0.00298 0.00186 -390.00 372.20 -221.15
211.06
-10.09 18797.96 17940.16
36738.12
89.55
380.60 30533.17
370.51
67.27
0.65
240.83
43.73
