Gaya Batang Dan Tegangan

IV.4. Gaya Batang Dan Tegangan

Jarak Gelagar memanjang Tetap 1.5 m dan jarak gelagar diafragma bervariasi pada kondisi pembebanan maksimum dengan nilai nominal beban yang sama Profil sama WF36×300 memanjang dan WF 10×68 Gelagar Diafragma.Berikut akan dibahas gaya- gaya batang dan Tegangan yang terjadi dengan mengambil nilai maksimum pada tiap gelagar memenjang. Universitas Sumatera Utara TABLE: Element Forces - Frames Frame ElemStation OutputCase P V2 V3 T M2 M3 Text M Text KN KN KN KN-m KN-m KN-m 1 COMB1 -504.54 1 3 COMB1 -470.153 1462.975 2 COMB1 -435.354 2.7852 1463.136 2 3 COMB1 -400.966 2.7852 2718.551 3 COMB1 -339.466 2.1504 2718.68 3 3 COMB1 -305.078 2.1504 3686.43 4 COMB1 -226.494 1.4392 3686.524 4 3 COMB1 -192.107 1.4392 4315.36 5 COMB1 -100.909 0.6555 4315.413 5 3 COMB1 -66.521 0.6555 4567.493 6 COMB1 67.144 -0.6555 4567.493 6 3 COMB1 101.532 -0.6555 4315.413 7 COMB1 192.73 -1.4392 4315.36 7 3 COMB1 227.117 -1.4392 3686.524 8 COMB1 305.701 -2.1504 3686.43 8 3 COMB1 340.089 -2.1504 2718.68 9 COMB1 401.589 -2.7852 2718.551 9 3 COMB1 435.977 -2.7852 1463.136 10 COMB1 470.776 1462.975 10 3 COMB1 505.163 7.64E-12 11 COMB1 -601.075 11 3 COMB1 -500.967 1654.931 12 COMB1 -483.115 2.2649 1654.867 12 3 COMB1 -383.007 2.2649 2955.919 13 COMB1 -377.178 1.7514 2955.87 13 3 COMB1 -277.07 1.7514 3939.112 14 COMB1 -276.497 1.145 3939.076 14 3 COMB1 -176.389 1.145 4620.275 15 COMB1 -182.793 0.4246 4620.252 15 3 COMB1 -82.685 0.4246 5020.337 16 COMB1 83.931 -0.4246 5020.337 16 3 COMB1 184.039 -0.4246 4620.252 17 COMB1 177.635 -1.145 4620.275 17 3 COMB1 277.743 -1.145 3939.076 18 COMB1 278.316 -1.7514 3939.112 18 3 COMB1 378.424 -1.7514 2955.87 19 COMB1 384.253 -2.2649 2955.919 19 3 COMB1 484.361 -2.2649 1654.867 20 COMB1 502.212 1654.931 20 3 COMB1 602.32 1.58E-11 21 COMB1 -633.818 21 3 COMB1 -529.043 1746.16 22 COMB1 -505.152 0.8591 1746.063 Universitas Sumatera Utara 22 3 COMB1 -400.377 0.8591 3106.224 23 COMB1 -391.165 0.6757 3106.143 23 3 COMB1 -286.39 0.6757 4124.343 24 COMB1 -289.005 0.4255 4124.285 24 3 COMB1 -184.23 0.4255 4836.006 25 COMB1 -192.483 0.1407 4835.975 25 3 COMB1 -87.708 0.1407 5258.129 26 COMB1 88.953 -0.1407 5258.129 26 3 COMB1 193.728 -0.1407 4835.975 27 COMB1 185.476 -0.4255 4836.006 27 3 COMB1 290.251 -0.4255 4124.285 28 COMB1 287.635 -0.6757 4124.343 28 3 COMB1 392.41 -0.6757 3106.143 29 COMB1 401.623 -0.8591 3106.224 29 3 COMB1 506.398 -0.8591 1746.063 30 COMB1 530.289 1746.16 30 3 COMB1 635.064 1.16E-11 31 COMB1 -633.818 31 3 COMB1 -529.043 1746.16 32 COMB1 -505.152 -0.8591 1746.063 32 3 COMB1 -400.377 -0.8591 3106.224 33 COMB1 -391.165 -0.6757 3106.143 33 3 COMB1 -286.39 -0.6757 4124.343 34 COMB1 -289.005 -0.4255 4124.285 34 3 COMB1 -184.23 -0.4255 4836.006 35 COMB1 -192.483 -0.1407 4835.975 35 3 COMB1 -87.708 -0.1407 5258.129 36 COMB1 88.953 0.1407 5258.129 36 3 COMB1 193.728 0.1407 4835.975 37 COMB1 185.476 0.4255 4836.006 37 3 COMB1 290.251 0.4255 4124.285 38 COMB1 287.635 0.6757 4124.343 38 3 COMB1 392.41 0.6757 3106.143 39 COMB1 401.623 0.8591 3106.224 39 3 COMB1 506.398 0.8591 1746.063 40 COMB1 530.289 1746.16 40 3 COMB1 635.064 8E-12 41 COMB1 -601.075 -3.6E-12 41 3 COMB1 -500.967 1654.931 42 COMB1 -483.115 -2.2649 1654.867 42 3 COMB1 -383.007 -2.2649 2955.919 43 COMB1 -377.178 -1.7514 2955.87 43 3 COMB1 -277.07 -1.7514 3939.112 44 COMB1 -276.497 -1.145 3939.076 44 3 COMB1 -176.389 -1.145 4620.275 45 COMB1 -182.793 -0.4246 4620.252 Universitas Sumatera Utara 45 3 COMB1 -82.685 -0.4246 5020.337 46 COMB1 83.931 0.4246 5020.337 46 3 COMB1 184.039 0.4246 4620.252 47 COMB1 177.635 1.145 4620.275 47 3 COMB1 277.743 1.145 3939.076 48 COMB1 278.316 1.7514 3939.112 48 3 COMB1 378.424 1.7514 2955.87 49 COMB1 384.253 2.2649 2955.919 49 3 COMB1 484.361 2.2649 1654.867 50 COMB1 502.212 1654.931 50 3 COMB1 602.32 1.22E-11 51 COMB1 -504.54 1.09E-11 51 3 COMB1 -470.153 1462.975 52 COMB1 -435.354 -2.7852 1463.136 52 3 COMB1 -400.966 -2.7852 2718.551 53 COMB1 -339.466 -2.1504 2718.68 53 3 COMB1 -305.078 -2.1504 3686.43 54 COMB1 -226.494 -1.4392 3686.524 54 3 COMB1 -192.107 -1.4392 4315.36 55 COMB1 -100.909 -0.6555 4315.413 55 3 COMB1 -66.521 -0.6555 4567.493 56 COMB1 67.144 0.6555 4567.493 56 3 COMB1 101.532 0.6555 4315.413 57 COMB1 192.73 1.4392 4315.36 57 3 COMB1 227.117 1.4392 3686.524 58 COMB1 305.701 2.1504 3686.43 58 3 COMB1 340.089 2.1504 2718.68 59 COMB1 401.589 2.7852 2718.551 59 3 COMB1 435.977 2.7852 1463.136 60 COMB1 470.776 1462.975 60 3 COMB1 505.163 2.18E-12 61 COMB1 -34.799 0.1611 2.7852 61 1.5 COMB1 -9.782 0.1611 37.3324 62 COMB1 -27.634 0.0974 39.5973 62 1.5 COMB1 6.716 0.0974 55.2856 63 COMB1 -17.175 -1E-13 56.1447 63 1.5 COMB1 17.175 -1E-13 56.1447 64 COMB1 -6.716 -0.0974 55.2856 64 1.5 COMB1 27.634 -0.0974 39.5973 65 COMB1 9.782 -0.1611 37.3324 65 1.5 COMB1 34.799 -0.1611 2.7852 66 COMB1 -61.501 0.1295 -0.6348 66 1.5 COMB1 -36.484 0.1295 73.9651 67 COMB1 -42.313 0.0809 73.4516 67 1.5 COMB1 -7.963 0.0809 111.1582 68 COMB1 -17.175 -8.7E-14 110.9749 Universitas Sumatera Utara 68 1.5 COMB1 17.175 -8.7E-14 110.9749 69 COMB1 7.963 -0.0809 111.1582 69 1.5 COMB1 42.313 -0.0809 73.4516 70 COMB1 36.484 -0.1295 73.9651 70 1.5 COMB1 61.501 -0.1295 -0.6348 71 COMB1 -78.584 0.0939 -0.7113 71 1.5 COMB1 -53.567 0.0939 99.5134 72 COMB1 -54.14 0.0581 98.907 72 1.5 COMB1 -19.79 0.0581 154.3549 73 COMB1 -17.175 -6.1E-14 154.1046 73 1.5 COMB1 17.175 -6.1E-14 154.1046 74 COMB1 19.79 -0.0581 154.3549 74 1.5 COMB1 54.14 -0.0581 98.907 75 COMB1 53.567 -0.0939 99.5134 75 1.5 COMB1 78.584 -0.0939 -0.7113 76 COMB1 -91.198 0.0537 -0.7837 76 1.5 COMB1 -66.181 0.0537 118.3617 77 COMB1 -59.778 0.0308 117.6413 77 1.5 COMB1 -25.428 0.0308 181.5454 78 COMB1 -17.175 -2.2E-14 181.2606 78 1.5 COMB1 17.175 -2.2E-14 181.2606 79 COMB1 25.428 -0.0308 181.5454 79 1.5 COMB1 59.778 -0.0308 117.6413 80 COMB1 66.181 -0.0537 118.3617 80 1.5 COMB1 91.198 -0.0537 -0.7837 81 COMB1 -133.665 2.34E-06 -1.3109 81 1.5 COMB1 14.551 2.34E-06 104.5359 82 COMB1 -152.064 -9.3E-11 103.6867 82 1.5 COMB1 67.086 -9.3E-11 167.4203 83 COMB1 -109.575 1.72E-14 167.139 83 1.5 COMB1 109.575 1.72E-14 167.139 84 COMB1 -67.086 9.29E-11 167.4203 84 1.5 COMB1 152.064 9.29E-11 103.6867 85 COMB1 -14.551 -2.3E-06 104.5359 85 1.5 COMB1 133.665 -2.3E-06 -1.3109 86 COMB1 -91.198 -0.0537 -0.7837 86 1.5 COMB1 -66.181 -0.0537 118.3617 87 COMB1 -59.778 -0.0308 117.6413 87 1.5 COMB1 -25.428 -0.0308 181.5454 88 COMB1 -17.175 3.71E-14 181.2606 88 1.5 COMB1 17.175 3.71E-14 181.2606 89 COMB1 25.428 0.0308 181.5454 89 1.5 COMB1 59.778 0.0308 117.6413 90 COMB1 66.181 0.0537 118.3617 90 1.5 COMB1 91.198 0.0537 -0.7837 91 COMB1 -78.584 -0.0939 -0.7113 Universitas Sumatera Utara 91 1.5 COMB1 -53.567 -0.0939 99.5134 92 COMB1 -54.14 -0.0581 98.907 92 1.5 COMB1 -19.79 -0.0581 154.3549 93 COMB1 -17.175 6.05E-14 154.1046 93 1.5 COMB1 17.175 6.05E-14 154.1046 94 COMB1 19.79 0.0581 154.3549 94 1.5 COMB1 54.14 0.0581 98.907 95 COMB1 53.567 0.0939 99.5134 95 1.5 COMB1 78.584 0.0939 -0.7113 96 COMB1 -61.501 -0.1295 -0.6348 96 1.5 COMB1 -36.484 -0.1295 73.9651 97 COMB1 -42.313 -0.0809 73.4516 97 1.5 COMB1 -7.963 -0.0809 111.1582 98 COMB1 -17.175 7.87E-14 110.9749 98 1.5 COMB1 17.175 7.87E-14 110.9749 99 COMB1 7.963 0.0809 111.1582 99 1.5 COMB1 42.313 0.0809 73.4516 100 COMB1 36.484 0.1295 73.9651 100 1.5 COMB1 61.501 0.1295 -0.6348 101 COMB1 -34.799 -0.1611 2.7852 101 1.5 COMB1 -9.782 -0.1611 37.3324 102 COMB1 -27.634 -0.0974 39.5973 102 1.5 COMB1 6.716 -0.0974 55.2856 103 COMB1 -17.175 8.97E-14 56.1447 103 1.5 COMB1 17.175 8.97E-14 56.1447 104 COMB1 -6.716 0.0974 55.2856 104 1.5 COMB1 27.634 0.0974 39.5973 105 COMB1 9.782 0.1611 37.3324 105 1.5 COMB1 34.799 0.1611 2.7852 Gelagar Gaya Geser Momen torsi Momen Lentur Memanjang V2Maksimum TMaksimum M3Maksimum Positf Negatif Positf Negatif Positf Negatif KN KN-m KN-m I 505.163 -504.540 2.7852 -2.7852 4567.4928 II 602.320 -601.075 2.2649 -2.2649 5020.3369 III 635.064 -633.818 0.8591 -0.8591 5258.1289 IV 635.064 -633.818 0.8591 -0.8591 5258.1289 V 602.320 -601.075 2.2649 -2.2649 5020.3369 VI 505.163 -504.540 2.7852 -2.7852 4567.4928 Universitas Sumatera Utara Gambar Diagram Lintang maksimum yang terjadi pada gelagar memanjang Gaya Geser Maksimum Yang Terjadi Gambar Diagram Torsi maksimum yang terjadi pada gelagar memanjang Momen Torsi Maksimum Yang Terjadi Gambar Diagram Momen Lentur maksimum yang terjadi pada gelagar memanjang Momen Lentur Maksimum Yang Terjadi Universitas Sumatera Utara Tegangan Yang Terjadi Pada Gelagar Pada suatu komponen struktur selalu timbul gaya-gaya dalam tidak hanya puntir tetapi juga terdapat gaya lintang, momen, dan normal. Oleh karena itu, pada tampang akan timbul tegangan-tegangan pada tampang komponen struktur. Untuk menentukan nilai tegangan akibat Geser,Torsi dan Momen Bending maksimum pada tampang IWF dengan menggunakan gaya-gaya dalam yang diperoleh pada sistem balok bersilang sebelumnya, akan diuraikan cara menentukan tegangan maksimum yang terjadi pada balok tersebut. Data-data yang digunakan sebagai Berikut: • Balok IWF 36x300 • V2 Geser Maksimum = 635.064 KN • T Torsi Maksimum = 2.7852 KNm • M3 Momen Lentur = 5258,189 KNm Table: Frame Section Properties 01 - General, Part 1 of 6 SectionName Material Shape t3 t2 tf tw Text Text Text m m m m W30X99 STEEL IWide Flange 0.754380 0.266700 0.017018 0.013208 W33X118 STEEL IWide Flange 0.835660 0.292100 0.018796 0.013970 W33X130 STEEL IWide Flange 0.840740 0.292100 0.021717 0.014732 W36X135 STEEL IWide Flange 0.904240 0.304800 0.020066 0.015240 W36X150 STEEL IWide Flange 0.911860 0.304800 0.023876 0.015875 W36X194 STEEL IWide Flange 0.927100 0.307340 0.032004 0.019431 W36X210 STEEL IWide Flange 0.932180 0.309880 0.034544 0.021082 W36X230 STEEL IWide Flange 0.911860 0.419100 0.032004 0.019304 W36X260 STEEL IWide Flange 0.922020 0.421640 0.036576 0.021336 W36X300 STEEL IWide Flange 0.932180 0.424180 0.042672 0.024003 Table: Frame Section Properties 01 - General, Part 2 of 6 SectionName t2b tfb Area TorsConst I33 I22 AS2 Text m m m2 m4 m4 m4 m2 W36X210 0.309880 0.034544 0.039871 0.000012 0.005494 0.000171 0.019652 W36X230 0.419100 0.032004 0.043613 0.000012 0.006243 0.000391 0.017603 W36X260 0.421640 0.036576 0.049355 0.000017 0.007201 0.000454 0.019672 W36X300 0.424180 0.042672 0.056968 0.000027 0.008449 0.000541 0.022375 Universitas Sumatera Utara Table: Material Properties 03 - Design Steel Material Fy Fu Text KNm2 KNm2 STEEL 250000.00 410000.00 TABLE: Material Properties 01 - General Material Type DesignType UnitMass UnitWeight E γ G Text Text Text KN- s2m4 KNm3 KNm2 Unitless KNm2 STEEL Isotropic Steel 7.849 77 199900000 0.3 76884615.4 t2 = t2 = 0.424180 m tf = ttb = 0.042672 m tw = 0.024003 m t3 = 0.932180 m Wx = 0.18128 m 3 Ix = 0.008449 m 4 J = 0.000027 m 4 Iy = 0.000541 m 4 Universitas Sumatera Utara Tegangan yang terjadi akibat Momen lentur maksimum M3 Momen Lentur maksimum = 5258,189 KNm 29009.9743 KNm 2 Tegangan yang terjadi akibat V2 Gaya Geser maksimum V2 Geser Maksimum = 635.064 KN Qmax = V2 Max F Bruto Badan = F Bruto Badan = F Bruto Badan = 38.83597884 m 2 Universitas Sumatera Utara 24.52869809 KN m 2 Tegangan yang terjadi akibat Torsi maksimum T Torsi Maksimum = 2.7852 KNm Konstanta Puntir J = 0.000027 m 4 Konstanta Pelengkungan Cw = Iy . Konstanta Pelengkungan Cw = Iy . = 0.000541 m 4 . Konstanta Pelengkungan Cw = 0.000117527 m 6 Universitas Sumatera Utara λ 2 = = λ 2 = 0.088359402 λ = 0.297253093 Tegangan Geser yang terjadi akibat Puntir Murni = [1- ] Tegangan Geser Akibat Puntir Murni maksimum Untuk Z = 0 maka: = [1- ] = [1- ] • Flens tf = 0.042672 m = [1- ] = 202.0144 KNm 2 • Badan tw = 0.024003 m = [1- ] = 113.6331 KNm2 Universitas Sumatera Utara

IV.5 Penurunan Matriks Kekakuan Bila Sumbu Tidak Rigid Sendi