MARIO PAZ 1.6 PAGE 19RESPON SISTEM BERDERAJAT KEBEBASAN TUNGGAL TAK TEREDAM MENGGUNAKAN MICROSOFT EXCEL
Diketahui : L = 120 inciEI = 1000000000 lb.inci²w = 5000 lbY₀ = 0.5 inciV₀ = 15 inci/detikg = 386 inci/detik²
Waktu (t) Gaya (F) Lendutan (y) Kecepatan (ẏ) Percepatan (ӱ) Momendetik lb inci inci/detik inci/detik² lbinci0.0 55555.5556 0.5 15 -4288.8889 833333.3333
0.10 -51894.9030 -0.4671 -22.3225 4006.2865 -778423.5451 0.20 46856.0003 0.4217 29.0521 -3617.2832 702840.0040 0.30 -40572.6730 -0.3652 -35.0101 3132.2104 -608590.0949 0.40 33211.7969 0.2989 40.0383 -2563.9507 498176.9528 0.50 -24968.8656 -0.2247 -44.0031 1927.5964 -374532.9838 0.60 16062.7990 0.1446 46.7993 -1240.0481 240941.9849 0.70 -6730.1287 -0.0606 -48.3526 519.5659 -100951.9310 0.80 -2781.2836 -0.0250 48.6217 214.7151 -41719.2535 0.90 12218.8292 0.1100 -47.5995 -943.2936 183282.4377 1.00 -21331.8612 -0.1920 45.3131 1646.8197 -319977.9174 1.10 29878.3512 0.2689 -41.8233 -2306.6087 448175.2673 1.20 -37631.3173 -0.3387 37.2227 2905.1377 -564469.7595 1.30 44384.8525 0.3995 -31.6335 -3426.5106 665772.7882 1.40 -49959.5932 -0.4496 25.2042 3856.8806 -749393.8979 1.50 54207.4826 0.4879 -18.1055 -4184.8177 813112.2385 1.60 -57015.7031 -0.5131 10.5259 4401.6123 -855235.5470 1.70 58309.6728 0.5248 -2.6668 -4501.5067 874645.0922 1.80 -58055.0257 -0.5225 -5.2631 4481.8480 -870825.3858
W
y
L/2 L/2
EI
1.90 56258.5249 0.5063 13.0533 -4343.1581 843877.8734 2.00 -52967.8827 -0.4767 -20.4967 4089.1205 -794518.2403 2.10 48270.4936 0.4344 27.3958 -3726.4821 724057.4037 2.20 -42291.1131 -0.3806 -33.5674 3264.8739 -634366.6969 2.30 35188.5446 0.3167 38.8474 -2716.5556 527828.1695 2.40 -27151.4216 -0.2444 -43.0957 2096.0897 -407271.3237 2.50 18393.1978 0.1655 46.1994 -1419.9549 275897.9672 2.60 -9146.4785 -0.0823 -48.0762 706.1081 -137197.1777 2.70 -343.1574 -0.0031 48.6761 26.4918 -5147.3614 2.80 9823.6796 0.0884 -47.9833 -758.3881 147355.1944 2.90 -19043.2997 -0.1714 46.0161 1470.1427 -285649.4961 3.00 27757.1586 0.2498 -42.8267 -2142.8526 416357.3791
Lendutan (y) maksimum = 0.52478705532 inci pada saat t = 1.70 detikKecepatan (ẏ) = 48.6760991336 inci/detik pada saat t = 2.70 detikPercepatan (ӱ) = 4481.84798548 inci/detik² pada saat t = 1.80 detikGaya maksimum = 58309.672813 lb pada saat t = 1.70 detikMomen maksimum = 874645.092195 lbinci pada saat t = 1.70 detik
RESPON SISTEM BERDERAJAT KEBEBASAN TUNGGAL TAK TEREDAM MENGGUNAKAN MICROSOFT EXCEL
Koefisien EI L w V₀ Y₀ 1/8 inci lb inci/detik inci
0.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.5
lb.inci²
tvtyy
tvtyy
tv
tyy
w
gk
gwk
m
k
jepitJepitL
EIk
sincos
cossin
sincos
)(12
2
2
3
0.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.50.125 1000000000 120 5000 15 0.5
pada saat t = 1.70 detikpada saat t = 2.70 detikpada saat t = 1.80 detikpada saat t = 1.70 detikpada saat t = 1.70 detik
RESPON SISTEM BERDERAJAT KEBEBASAN TUNGGAL TAK TEREDAM MENGGUNAKAN MICROSOFT EXCEL
g k ω sin ωt cos ωt V₀/ωlb/inci rad/detik
386 111111.111 92.6163 0.0000 1 0.1619585439 8577.7777778386 111111.111 92.6163 0.1624 -0.98672075578 0.1619585439 8577.7777778386 111111.111 92.6163 -0.3205 0.94723569976 0.1619585439 8577.7777778386 111111.111 92.6163 0.4701 -0.88259349535 0.1619585439 8577.7777778386 111111.111 92.6163 -0.6072 0.79451094179 0.1619585439 8577.7777778386 111111.111 92.6163 0.7282 -0.68532737856 0.1619585439 8577.7777778386 111111.111 92.6163 -0.8299 0.55794255606 0.1619585439 8577.7777778386 111111.111 92.6163 0.9095 -0.41573962264 0.1619585439 8577.7777778386 111111.111 92.6163 -0.9649 0.26249527325 0.1619585439 8577.7777778386 111111.111 92.6163 0.9948 -0.10227944617 0.1619585439 8577.7777778386 111111.111 92.6163 -0.9982 -0.06065276839 0.1619585439 8577.7777778386 111111.111 92.6163 0.9751 0.22197413711 0.1619585439 8577.7777778386 111111.111 92.6163 -0.9261 -0.37740020826 0.1619585439 8577.7777778386 111111.111 92.6163 0.8525 0.52280310035 0.1619585439 8577.7777778386 111111.111 92.6163 -0.7562 -0.65432113234 0.1619585439 8577.7777778386 111111.111 92.6163 0.6399 0.76846138409 0.1619585439 8577.7777778386 111111.111 92.6163 -0.5066 -0.86219246305 0.1619585439 8577.7777778386 111111.111 92.6163 0.3598 0.93302501343 0.1619585439 8577.7777778386 111111.111 92.6163 -0.2035 -0.97907782978 0.1619585439 8577.7777778
ω²inci/detik²
386 111111.111 92.6163 0.0418 0.9991278189 0.1619585439 8577.7777778386 111111.111 92.6163 0.1211 -0.99264248337 0.1619585439 8577.7777778386 111111.111 92.6163 -0.2807 0.95979406392 0.1619585439 8577.7777778386 111111.111 92.6163 0.4329 -0.90145496491 0.1619585439 8577.7777778386 111111.111 92.6163 -0.5735 0.81917458463 0.1619585439 8577.7777778386 111111.111 92.6163 0.6990 -0.7151381656 0.1619585439 8577.7777778386 111111.111 92.6163 -0.8059 0.59210875787 0.1619585439 8577.7777778386 111111.111 92.6163 0.8913 -0.45335383653 0.1619585439 8577.7777778386 111111.111 92.6163 -0.9531 0.30255852255 0.1619585439 8577.7777778386 111111.111 92.6163 0.9896 -0.14372771156 0.1619585439 8577.7777778386 111111.111 92.6163 -0.9998 -0.01892029021 0.1619585439 8577.7777778386 111111.111 92.6163 0.9835 0.18106579767 0.1619585439 8577.7777778
CONTOH 2 - TANPA REDAMAN
Diketahui : E = 20000 MPa 20000000000m = 200 kgk₃ = 0.2 EIu₀ = 2 cmv₀ = 10 cm/dtL₁ = 4 mL₂ = 2.5 mb = 150 mm 0.15h = 200 mm 0.2
Ditanya : 1. Kekakuan gabungan struktur2. Frekuensi alami struktur3. Persamaan gerak struktur4. Persamaan paeralihan setiap saat5. Peralihan dan kecepatan6. Peralihan maksimum7. Gaya geser pada saat peralihan maksimum8. Momen pada kolom9. Tegangan maksimum pada kolom
Waktu u(t) v(t) F(t) Momen pada Kolomdetik cm cm/dt N Kolom Kiri (Nm)0.0 2 10 23180 150000.1 1.9998 -10.2570 23177.3964 14998.3152 0.2 1.9643 -30.3333 22766.2536 14732.2607 0.3 1.8942 -49.8748 21953.8184 14206.5262
4 m
A A A A
k1k2
mk3
0.4 1.7907 -68.5373 20754.4115 13430.3785 0.5 1.6557 -85.9916 19189.1743 12417.4985 0.6 1.4914 -101.9303 17285.6967 11185.7399 0.7 1.3009 -116.0722 15077.5306 9756.8145 0.8 1.0875 -128.1682 12603.5985 8155.9093 0.9 0.8548 -138.0050 9907.5074 6411.2429 1 0.6071 -145.4092 7036.7804 4553.5680
1.1 0.3488 -150.2504 4042.0187 2615.6290 1.2 0.0842 -152.4431 976.0099 631.5853 1.3 -0.1818 -151.9488 -2107.2027 -1363.5911 1.4 -0.4446 -148.7762 -5153.2725 -3334.7320 1.5 -0.6996 -142.9811 -8108.5074 -5247.0928 1.6 -0.9423 -134.6658 -10920.8167 -7066.9651 1.7 -1.1683 -123.9767 -13540.6288 -8762.2706 1.8 -1.3738 -111.1024 -15921.7654 -10303.1268 1.9 -1.5550 -96.2697 -18022.2549 -11662.3737 2 -1.7088 -79.7401 -19805.0728 -12816.0523
2.1 -1.8325 -61.8049 -21238.7941 -13743.8271 2.2 -1.9239 -42.7803 -22298.1471 -14429.3445 2.3 -1.9814 -23.0017 -22964.4590 -14860.5214 2.4 -2.0040 -2.8176 -23225.9849 -15029.7573 2.5 -1.9912 17.4161 -23078.1151 -14934.0693 2.6 -1.9434 37.3429 -22523.4559 -14575.1440 2.7 -1.8612 56.6114 -21571.7842 -13959.3082 2.8 -1.7463 74.8821 -20239.8747 -13097.4168 2.9 -1.6006 91.8328 -18551.2045 -12004.6621 3 -1.4267 107.1649 -16535.5391 -10700.3057
KeteranganPerhitungan Excel
Peralihan Maksimum 2.0043 2 Kecepatan Maksimum 107.1649 Gaya Maksimum 23230 23180Momen Kolom Kiri Maksimum 15032.320658 15000Momen Kolom Kanan Maksimum 19241.3704423 19200Tegangan Kolom Kiri Maksimum 15.032320658 15.00Tegangan Kolom Kanan Maksimum 19.2413704423 19.20
Perhitungan Manual
N
mm
Momen pada Kolom Tegangan Kolom σ(t) I kKolom Kanan (Nm) σ Kiri (N/mm²) σ Kanan (N/mm²) m⁴ N/m
19200 15 19.2 0.0001 115900019197.8435 14.9983 19.1978 0.0001 115900018857.2937 14.7323 18.8573 0.0001 115900018184.3535 14.2065 18.1844 0.0001 1159000
A
2,5 m
200 mm
150 mm
POTONGAN A-A
17190.8844 13.4304 17.1909 0.0001 115900015894.3981 12.4175 15.8944 0.0001 115900014317.7471 11.1857 14.3177 0.0001 115900012488.7225 9.7568 12.4887 0.0001 115900010439.5639 8.1559 10.4396 0.0001 11590008206.3910 6.4112 8.2064 0.0001 11590005828.5671 4.5536 5.8286 0.0001 11590003348.0052 2.6156 3.3480 0.0001 1159000808.4292 0.6316 0.8084 0.0001 1159000
-1745.3966 -1.3636 -1.7454 0.0001 1159000-4268.4569 -3.3347 -4.2685 0.0001 1159000-6716.2788 -5.2471 -6.7163 0.0001 1159000-9045.7153 -7.0670 -9.0457 0.0001 1159000
-11215.7064 -8.7623 -11.2157 0.0001 1159000-13188.0024 -10.3031 -13.1880 0.0001 1159000-14927.8384 -11.6624 -14.9278 0.0001 1159000-16404.5469 -12.8161 -16.4045 0.0001 1159000-17592.0987 -13.7438 -17.5921 0.0001 1159000-18469.5610 -14.4293 -18.4696 0.0001 1159000-19021.4673 -14.8605 -19.0215 0.0001 1159000-19238.0893 -15.0298 -19.2381 0.0001 1159000-19115.6087 -14.9341 -19.1156 0.0001 1159000-18656.1844 -14.5751 -18.6562 0.0001 1159000-17867.9144 -13.9593 -17.8679 0.0001 1159000-16764.6935 -13.0974 -16.7647 0.0001 1159000-15365.9675 -12.0047 -15.3660 0.0001 1159000-13696.3913 -10.7003 -13.6964 0.0001 1159000
Satuan
cmcm/dt
NNmNm
N/mm²N/mm²
ω f cosωt sinωtrad/dt Hz
76.1249 12.1157 1 076.1249 12.1157 0.9912 0.1325 76.1249 12.1157 0.9649 0.2626 76.1249 12.1157 0.9216 0.3881
76.1249 12.1157 0.8621 0.5068 76.1249 12.1157 0.7873 0.6165 76.1249 12.1157 0.6987 0.7154 76.1249 12.1157 0.5978 0.8016 76.1249 12.1157 0.4863 0.8738 76.1249 12.1157 0.3663 0.9305 76.1249 12.1157 0.2398 0.9708 76.1249 12.1157 0.1091 0.9940 76.1249 12.1157 -0.0236 0.9997 76.1249 12.1157 -0.1558 0.9878 76.1249 12.1157 -0.2853 0.9584 76.1249 12.1157 -0.4097 0.9122 76.1249 12.1157 -0.5270 0.8499 76.1249 12.1157 -0.6349 0.7726 76.1249 12.1157 -0.7316 0.6817 76.1249 12.1157 -0.8155 0.5788 76.1249 12.1157 -0.8850 0.4656 76.1249 12.1157 -0.9389 0.3443 76.1249 12.1157 -0.9762 0.2169 76.1249 12.1157 -0.9963 0.0856 76.1249 12.1157 -0.9989 -0.0471 76.1249 12.1157 -0.9838 -0.1790 76.1249 12.1157 -0.9515 -0.3078 76.1249 12.1157 -0.9023 -0.4311 76.1249 12.1157 -0.8372 -0.5468 76.1249 12.1157 -0.7574 -0.6529 76.1249 12.1157 -0.6643 -0.7475
CONTOH 3 - DENGAN REDAMAN
Diketahui : E = 20000 MPa 20000000000m = 200 kgk₃ = 0.2 EIy₀ = 2 cmv₀ = 10 cm/dtξ = 0.05L₁ = 4 mL₂ = 2.5 mb = 150 mm 0.15h = 200 mm 0.2
Ditanya : 1. Kekakuan gabungan struktur2. Frekuensi alami struktur3. Persamaan gerak struktur4. Persamaan paeralihan setiap saat5. Peralihan dan kecepatan6. Peralihan maksimum7. Gaya geser pada saat peralihan maksimum8. Momen guling pada saat peralihan maksimum9. Tegangan maksimum pada kolom
Waktu y(t) ẏ(t) ÿ(t) F(t)
4 m
A A A A
k1
k2
mk3
detik cm cm/dt cm/dt² N0.0 2.0000 10.0000 -11666.1249 23180000.1 1.3758 -7.0552 -7919.0490 1594551.3722 0.2 0.9298 -14.2296 -5280.0974 1077684.0623 0.3 0.6172 -15.9837 -3454.9019 715315.4832 0.4 0.4019 -15.0091 -2214.6400 465779.3213 0.5 0.2562 -12.8694 -1386.7854 296950.7467 0.6 0.1594 -10.4257 -844.4696 184766.9706 0.7 0.0963 -8.1142 -496.3881 111631.4182 0.8 0.0560 -6.1238 -278.0955 64942.6401 0.9 0.0309 -4.5069 -144.9241 35846.5881 1 0.0157 -3.2459 -66.4571 18233.2525
1.1 0.0069 -2.2926 -22.3481 7960.0450 1.2 0.0020 -1.5900 0.7626 2268.2494 1.3 -0.0006 -1.0834 11.4717 -644.8562 1.4 -0.0017 -0.7252 15.1862 -1933.1449 1.5 -0.0020 -0.4765 15.2168 -2317.9249 1.6 -0.0019 -0.3068 13.5234 -2237.5075 1.7 -0.0017 -0.1932 11.2146 -1948.8298 1.8 -0.0014 -0.1184 8.8776 -1595.2757 1.9 -0.0011 -0.0702 6.7897 -1251.0984 2 -0.0008 -0.0398 5.0525 -949.9280
2.1 -0.0006 -0.0211 3.6740 -702.6458 2.2 -0.0004 -0.0100 2.6178 -508.2865 2.3 -0.0003 -0.0037 1.8307 -360.4594 2.4 -0.0002 -0.0004 1.2576 -250.9575 2.5 -0.0001 0.0012 0.8487 -171.6460 2.6 -0.0001 0.0019 0.5625 -115.3371 2.7 -0.0001 0.0019 0.3657 -76.0919 2.8 0.0000 0.0018 0.2327 -49.2213 2.9 0.0000 0.0015 0.1445 -31.1464 3 0.0000 0.0012 0.0871 -19.2083
KeteranganPerhitungan Excel
Peralihan Maksimum (y) 2.0043 2.0000 10.0000 15.2168
Gaya Maksimum 2322995 2318000Momen Kolom Kiri Maksimum 15032.320658 15000Momen Kolom Kanan Maksimum 19241.3704423 19200Tegangan Kolom Kiri Maksimum 15.032320658 15Tegangan Kolom Kanan Maksimum 19.2413704423 19.2
Perhitungan Manual
Kecepatan Maksimum (ẏ)
Percepatan Maksimum (ÿ)
N
mm
Momen pada Kolom Tegangan Kolom σ(t)
A
k2 2,5 m
200 mm
150 mm
POTONGAN A-A
Kolom Kiri (Nm) Kolom Kanan (Nm) σ Kiri (N/mm²) σ Kanan (N/mm²)15000 19200 15 19.2
10318.4946 13207.6731 10.3185 13.2077 6973.7968 8926.4599 6.9738 8.9265 4628.8750 5924.9600 4.6289 5.9250 3014.1026 3858.0513 3.0141 3.8581 1921.5967 2459.6438 1.9216 2.4596 1195.6448 1530.4253 1.1956 1.5304 722.3776 924.6433 0.7224 0.9246 420.2500 537.9201 0.4203 0.5379 231.9667 296.9174 0.2320 0.2969 117.9891 151.0261 0.1180 0.1510 51.5102 65.9331 0.0515 0.0659 14.6781 18.7879 0.0147 0.0188 -4.1729 -5.3413 -0.0042 -0.0053
-12.5096 -16.0122 -0.0125 -0.0160 -14.9995 -19.1994 -0.0150 -0.0192 -14.4791 -18.5333 -0.0145 -0.0185 -12.6111 -16.1422 -0.0126 -0.0161 -10.3232 -13.2137 -0.0103 -0.0132 -8.0960 -10.3629 -0.0081 -0.0104 -6.1471 -7.8683 -0.0061 -0.0079 -4.5469 -5.8200 -0.0045 -0.0058 -3.2892 -4.2101 -0.0033 -0.0042 -2.3326 -2.9857 -0.0023 -0.0030 -1.6240 -2.0787 -0.0016 -0.0021 -1.1107 -1.4217 -0.0011 -0.0014 -0.7464 -0.9553 -0.0007 -0.0010 -0.4924 -0.6303 -0.0005 -0.0006 -0.3185 -0.4077 -0.0003 -0.0004 -0.2016 -0.2580 -0.0002 -0.0003 -0.1243 -0.1591 -0.0001 -0.0002
Satuan
cmcm/dt
NNmNm
N/mm²N/mm²
cm/dt²
I k ω CωD
m⁴ N/m rad/dt rad/dt inch0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134 0.0001 1159000 76.1249 76.03 2.0134
tg α α
0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069 0.1158 6.6069
MARIO PAZ 2.2 PAGE 32SISTEM BERDERAJAT KEBEBASAN TUNGGAL TEREDAM
Diketahui : L = 120 inciEI = 1000000000 lb.inci²w = 5000 lbY₀ = 0.5 inciV₀ = 15 inci/detikg = 386 inci/detik²
0.1
Waktu y(t) ẏ(t) ÿ(t) F(t) Momen
detik cm cm/dt cm/dt² N lbinci0.0 5.00.E-01 1.50.E+01 -4.57.E+03 5.56.E+04 7.41.E+110.1 2.09.E-01 2.82.E+00 -1.84.E+03 23221.247 3.0962E+110.2 8.50.E-02 -1.51.E-01 -7.26.E+02 9441.99656 1.2589E+110.3 3.37.E-02 -5.60.E-01 -2.78.E+02 3740.10232 4.9868E+100.4 1.30.E-02 -4.14.E-01 -1.04.E+02 1443.26796 1.9244E+100.5 4.88.E-03 -2.36.E-01 -3.75.E+01 541.799691 7.2240E+090.6 1.78.E-03 -1.20.E-01 -1.30.E+01 197.23454 2.6298E+090.7 6.23.E-04 -5.64.E-02 -4.30.E+00 69.2280155 9.2304E+080.8 2.09.E-04 -2.54.E-02 -1.32.E+00 23.1900486 3.0920E+080.9 6.55.E-05 -1.10.E-02 -3.58.E-01 7.27277748 9.6970E+071 1.84.E-05 -4.61.E-03 -7.27.E-02 2.04884597 2.7318E+07
1.1 4.15.E-06 -1.88.E-03 -7.07.E-04 0.46113439 6.1485E+061.2 3.52.E-07 -7.49.E-04 1.08.E-02 0.03916276 5.2217E+051.3 -3.75.E-07 -2.90.E-04 8.59.E-03 -0.041717 -5.5623E+051.4 -3.49.E-07 -1.09.E-04 5.02.E-03 -0.0387628 -5.1684E+051.5 -2.14.E-07 -4.00.E-05 2.58.E-03 -0.0237651 -3.1687E+051.6 -1.13.E-07 -1.41.E-05 1.23.E-03 -0.0125015 -1.6669E+05
ξ =
W
y
L/2
1.7 -5.44.E-08 -4.77.E-06 5.55.E-04 -0.0060471 -8.0628E+041.8 -2.49.E-08 -1.51.E-06 2.42.E-04 -0.0027672 -3.6896E+041.9 -1.09.E-08 -4.34.E-07 1.02.E-04 -0.0012151 -1.6201E+042.0 -4.64.E-09 -1.02.E-07 4.17.E-05 -0.000516 -6.8802E+032.1 -1.92.E-09 -1.20.E-08 1.67.E-05 -0.0002129 -2.8382E+032.2 -7.69.E-10 6.70.E-09 6.48.E-06 -8.549E-05 -1.1399E+032.3 -3.01.E-10 7.12.E-09 2.45.E-06 -3.346E-05 -4.4609E+022.4 -1.15.E-10 4.52.E-09 9.01.E-07 -1.275E-05 -1.6999E+022.5 -4.25.E-11 2.41.E-09 3.20.E-07 -4.72E-06 -6.2936E+012.6 -1.52.E-11 1.18.E-09 1.09.E-07 -1.691E-06 -2.2545E+012.7 -5.23.E-12 5.43.E-10 3.48.E-08 -5.816E-07 -7.7552E+002.8 -1.71.E-12 2.40.E-10 1.02.E-08 -1.895E-07 -2.5273E+002.9 -5.13.E-13 1.02.E-10 2.50.E-09 -5.697E-08 -7.5957E-013 -1.33.E-13 4.24.E-11 3.58.E-10 -1.481E-08 -1.9746E-01
Lendutan (y) maksimum = 5.0000.E-01 inci pada saat t = 0,0 detikKecepatan (ẏ) = 1.5000.E+01 inci/detik pada saat t = 0,0 detikPercepatan (ӱ) = 1.0850.E-02 inci/detik² pada saat t = 1,2 detikGaya maksimum = 5.5556.E+04 lb pada saat t = 0,0 detikMomen maksimum = 7.4074.E+11 lbinci pada saat t = 0,0 detik
SISTEM BERDERAJAT KEBEBASAN TUNGGAL TEREDAM
k ω C tg αN/m rad/dt rad/dt inch
111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261
ωD
L/2
EI
111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261
111111.1111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261111111.111111111 92.62 92.15 0.5435 0.4261
pada saat t = 0,0 detikpada saat t = 0,0 detikpada saat t = 1,2 detikpada saat t = 0,0 detikpada saat t = 0,0 detik
α
23.077 1.00.E+00 0.9200 -0.392023.077 3.96.E-01 0.9709 -0.239623.077 1.57.E-01 0.9967 -0.081023.077 6.21.E-02 0.9968 0.079723.077 2.46.E-02 0.9712 0.238323.077 9.75.E-03 0.9205 0.390723.077 3.86.E-03 0.8461 0.533123.077 1.53.E-03 0.7498 0.661723.077 6.06.E-04 0.6341 0.773223.077 2.40.E-04 0.5021 0.864823.077 9.50.E-05 0.3571 0.934123.077 3.76.E-05 0.2029 0.979223.077 1.49.E-05 0.0435 0.999123.077 5.90.E-06 -0.1170 0.993123.077 2.34.E-06 -0.2746 0.961623.077 9.26.E-07 -0.4250 0.905223.077 3.67.E-07 -0.5645 0.8254
e-ξωt cos(ωDt-α) sin(ωDt-α)
23.077 1.45.E-07 -0.6894 0.724423.077 5.75.E-08 -0.7965 0.604623.077 2.28.E-08 -0.8830 0.469323.077 9.03.E-09 -0.9468 0.321823.077 3.57.E-09 -0.9861 0.166023.077 1.42.E-09 -1.0000 0.006023.077 5.61.E-10 -0.9880 -0.154223.077 2.22.E-10 -0.9506 -0.310523.077 8.80.E-11 -0.8886 -0.458723.077 3.48.E-11 -0.8037 -0.595123.077 1.38.E-11 -0.6980 -0.716123.077 5.47.E-12 -0.5743 -0.818623.077 2.16.E-12 -0.4358 -0.900023.077 8.57.E-13 -0.2860 -0.9582
GETARAN BEBAS UNDAMPED
Diketahui : m = 2k = 18 ton/cmy(0) = 1 cmẏ(0) = -3 cm/detC = 0A = 1B = -1
t y(t) ẏ(t) ωdetik cm cm/det rad/dt
0 1 -3 30.1 0.6598 -3.7526 30.2 0.2607 -4.1699 30.3 -0.1617 -4.2148 30.4 -0.5697 -3.8832 30.5 -0.9268 -3.2047 30.6 -1.2010 -2.2399 30.7 -1.3681 -1.0751 30.8 -1.4129 0.1858 30.9 -1.3315 1.4301 31 -1.1311 2.5466 3
1.1 -0.8297 3.4357 31.2 -0.4542 4.0178 31.3 -0.0382 4.2411 31.4 0.3813 4.0855 31.5 0.7667 3.5650 31.6 1.0837 2.7260 31.7 1.3038 1.6435 31.8 1.4075 0.4142 31.9 1.3854 -0.8521 32 1.2396 -2.0423 3
2.1 0.9830 -3.0500 3
ton det²/cm
k
m
ttty
ttty
Persamaan
3cos33sin3)(
3sin3cos)(
:
.
2.2 0.6387 -3.7853 32.3 0.2373 -4.1825 32.4 -0.1853 -4.2061 32.5 -0.5914 -3.8539 32.6 -0.9446 -3.1575 32.7 -1.2134 -2.1790 32.8 -1.3739 -1.0059 32.9 -1.4116 0.2570 33 -1.3232 1.4970 3
cosωt sinωt
1 00.9553 0.2955 0.8253 0.5646 0.6216 0.7833 0.3624 0.9320 0.0707 0.9975 -0.2272 0.9738 -0.5048 0.8632 -0.7374 0.6755 -0.9041 0.4274 -0.9900 0.1411 -0.9875 -0.1577 -0.8968 -0.4425 -0.7259 -0.6878 -0.4903 -0.8716 -0.2108 -0.9775 0.0875 -0.9962 0.3780 -0.9258 0.6347 -0.7728 0.8347 -0.5507 0.9602 -0.2794 0.9999 0.0168
0 0.5 1 1.5 2 2.5 3 3.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
GRAFIK HUBUNGAN ANTARA PERALIHAN
DAN WAKTU
TIME
DIS
PLA
CEM
EN
T
ttty
ttty
Persamaan
3cos33sin3)(
3sin3cos)(
:
.
0.9502 0.3115 0.8157 0.5784 0.6084 0.7937 0.3466 0.9380 0.0540 0.9985 -0.2435 0.9699 -0.5193 0.8546 -0.7486 0.6630 -0.9111 0.4121
0 0.5 1 1.5 2 2.5 3 3.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
GRAFIK HUBUNGAN ANTARA PERALIHAN
DAN WAKTU
TIME
DIS
PLA
CEM
EN
T
SISTEM SDOF UNDAMPED TANPA GAYA LUAR
Diketahui : w = 980 tonk = 25 ton/cmy(0) = 5 cm
5 cm/dt (kecepatan setelah 1/2 osilasi)g = 980m = 1A = 5B = -1
t y(t) ẏ(t) ω cosωtdetik cm cm/det rad.dt
0 5 -5 5 130 4.2111 14.3757 5 0.6993 60 0.8893 25.1044 5 -0.0221 90 -2.9675 20.7329 5 -0.7302
120 -5.0393 3.8906 5 -0.9990 150 -4.0800 -15.2919 5 -0.6670 180 -0.6666 -25.2763 5 0.0662 210 3.1478 -20.0571 5 0.7596 240 5.0688 -2.7735 5 0.9961 270 3.9409 16.1783 5 0.6334 300 0.4426 25.3989 5 -0.1103 330 -3.3219 19.3421 5 -0.7876 360 -5.0883 1.6511 5 -0.9912
ẏ(π) =cm/dt²ton dt²/cm
k
m
SISTEM SDOF UNDAMPED TANPA GAYA LUAR
sinωt
0-0.7149 -0.9998 -0.6833 0.0442 0.7451 0.9978 0.6504 -0.0883 -0.7738 -0.9939 -0.6162 0.1322
0 50 100 150 200 250 300 350 400
-6
-4
-2
0
2
4
6
GRAFIK HUBUNGAN ANTARA PERALIHAN
DAN WAKTU
TIME
DIS
PLA
CEM
EN
T
ttty
ttty
Persamaan
5cos55sin25)(
5sin5cos5)(
:
.
GETARAN BEBAS DAMPED
Diketahui : k = 320 ton/cmC = 4 cmm = 5x(0)= 1 cm
7.6 cm/dtA = 1B = 1
t x ẋ F c/2m ωdetik cm cm/dt N rad/dt
0 1.0000 7.6 320 0.4 80.1 1.3586 -0.7022 434.7573 0.4 80.2 0.8958 -7.9557 286.6458 0.4 80.3 -0.0549 -10.0028 -17.5768 0.4 80.4 -0.9004 -6.0474 -288.1388 0.4 80.5 -1.1548 1.1376 -369.5282 0.4 80.6 -0.7148 7.1054 -228.7301 0.4 80.7 0.1091 8.4625 34.8989 0.4 80.8 0.8058 4.7702 257.8664 0.4 80.9 0.9782 -1.4256 313.0098 0.4 81 0.5657 -6.3120 181.0096 0.4 8
1.1 -0.1457 -7.1344 -46.6129 0.4 81.2 -0.7172 -3.7246 -229.4973 0.4 81.3 -0.8257 1.5994 -264.2165 0.4 81.4 -0.4434 5.5795 -141.8742 0.4 81.5 0.1686 5.9933 53.9646 0.4 81.6 0.6350 2.8731 203.2130 0.4 81.7 0.6945 -1.6860 222.2413 0.4 81.8 0.3436 -4.9095 109.9422 0.4 81.9 -0.1811 -5.0163 -57.9664 0.4 82 -0.5597 -2.1837 -179.0936 0.4 8
ton dt²/cm
ẋ(0)=
k, C
m
)8cos88sin8()8sin8(cos4,0)(
)8sin8(cos)(
:
4,04,0.
4,0
ttettetx
ttetx
Persamaan
tt
t
cosωt sinωt
1 00.6967 0.7174 -0.0292 0.9996 -0.7374 0.6755 -0.9983 -0.0584 -0.6536 -0.7568 0.0875 -0.9962 0.7756 -0.6313 0.9932 0.1165 0.6084 0.7937 -0.1455 0.9894 -0.8111 0.5849 -0.9847 -0.1743 -0.5610 -0.8278 0.2030 -0.9792 0.8439 -0.5366 0.9728 0.2315 0.5117 0.8592 -0.2598 0.9657 -0.8737 0.4864 -0.9577 -0.2879
0 0.2 0.4 0.6 0.8 1 1.2 1.4
-1.5000
-1.0000
-0.5000
0.0000
0.5000
1.0000
1.5000
2.0000
GRAFIK HUBUNGAN ANTARA PERALIHAN DAN WAKTU
TIME
DIS
PLA
CEM
EN
T
)8cos88sin8()8sin8(cos4,0)(
)8sin8(cos)(
:
4,04,0.
4,0
ttettetx
ttetx
Persamaan
tt
t
0 0.2 0.4 0.6 0.8 1 1.2 1.4
-1.5000
-1.0000
-0.5000
0.0000
0.5000
1.0000
1.5000
2.0000
GRAFIK HUBUNGAN ANTARA PERALIHAN DAN WAKTU
TIME
DIS
PLA
CEM
EN
T
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