第四章 水平地震作用計(jì)算及位移內(nèi)力分析.doc

揚(yáng)州市某辦公樓設(shè)計(jì) 揚(yáng)州大學(xué)畢業(yè)設(shè)計(jì)第四章 水平地震作用計(jì)算及位移內(nèi)力分析對(duì)于高度不超過40m，以剪切變形為主且質(zhì)量和剛度沿高度分布比較均勻的結(jié)構(gòu)，以及近似于單質(zhì)點(diǎn)體系的結(jié)構(gòu)，可以采用底部剪力法的簡(jiǎn)化方法計(jì)算水平地震作用。底部剪力法適用于本工程。此法是將結(jié)構(gòu)簡(jiǎn)化為作用于各樓層位置的多質(zhì)點(diǎn)葫蘆串，結(jié)構(gòu)底部總剪力與地震影響系數(shù)及各質(zhì)點(diǎn)的重力荷載代表值有關(guān)。為計(jì)算各質(zhì)點(diǎn)的重力荷載代表值，先分別計(jì)算各樓面層梁板柱的重量，各樓層墻體的重量，然后按以樓層為中心上下各半個(gè)樓層的重量集中于該樓層的原則計(jì)算各質(zhì)點(diǎn)的重力荷載代表值。水平地震作用計(jì)算還涉及結(jié)構(gòu)的自振周期，本工程采用假想頂點(diǎn)位移法確定。水平作用下內(nèi)力及位移分析均采用D值法計(jì)算。一 重力荷載代表值計(jì)算1. 各層梁、板、柱自重標(biāo)準(zhǔn)值見下表：柱重力荷載標(biāo)準(zhǔn)值層數(shù)柱編號(hào)截面尺寸/mm凈高/mgk/(kN/m)數(shù)量Gki/kNGki總和kN1KZ14505003.65.625 24486824.26KZ24506003.66.7512291.6GZ2402403.61.44946.662KZ14505003.65.625 24486829.44KZ24506003.66.7512291.6GZ2402403.61.441051.843KZ14505003.65.625 24486829.44KZ24506003.66.7512291.6GZ2402403.61.441051.844KZ14505003.65.625 24486829.44KZ24506003.66.7512291.6GZ2402403.61.441051.845KZ14505003.65.625 24486829.44KZ24506003.66.7512291.6GZ2402403.61.441051.84KZ1為框架柱，GZ為構(gòu)造柱梁重力荷載代表值層數(shù)截面尺寸/mm凈跨長(zhǎng)/mgk/(kN/m)數(shù)量Gki/kNGki總和/kN1300650主梁6.954.125 12344.025996.015.154.125 12254.925450250主梁3.452.187 33249300200次梁3.91 33128.7衛(wèi)生間41 283.361 13.361#、2#梯41 282均與1層相同996.013均與1層相同996.014均與1層相同996.015均與1層相同996.01樓、屋面重力荷載代表值 層數(shù)種類板面積/平方米gk/(kN/m)Gki/kNGki總和kN1露面549.4953.90 2143.0312350.823樓梯44.44.68 207.7922露面549.4953.90 2143.0312350.823樓梯44.44.68 207.7923露面549.4953.90 2143.0312350.823樓梯44.44.68 207.7924露面549.4953.90 2143.0312350.823樓梯44.44.68 207.792屋面593.8954.10 2434.972434.97注：表中樓梯部分板的gk按樓面的1.2倍考慮2.墻自重標(biāo)準(zhǔn)值：一層軸線號(hào)凈跨高度數(shù)量面積門窗數(shù)量面積門窗自重重量16.952.95120.50 00077.91 5.152.95115.19 00057.73 36.952.95117.42 1.42.213.11.23267.44 5.152.95115.19 00057.73 45.152.95115.19 00057.73 55.252.95115.49 00058.85 5.152.95115.19 00057.73 75.052.95114.90 00056.61 5.152.95115.19 00057.73 95.052.95114.90 00056.61 5.152.95115.19 00057.73 106.952.95117.42 1.42.213.11.23267.44 5.152.95115.19 00057.73 126.952.9519.52 6.11.81114.39240.58 5.152.9515.92 5.151.819.33.70826.21 衛(wèi)生間2.83.618.19 0.92.111.90.75631.88 A3.453.15941.92 3.451.895622.356181.64 3.453.1520.34 1.733.14218.5569.87 B83.3246.64 1.42.226.22.464179.70 C3.453.1517.09 1.23.213.81.51228.44 3.453.15215.58 1.42.226.22.46461.65 3.453.15221.74 00082.59 3.453.1518.89 0.92.2120.79234.56 D3.453.151070.88 2.11.8103815.12284.45 3.453.1516.46 2.12.114.41.76426.30 衛(wèi)生間3.453.319.50 0.92.111.90.75636.84 合計(jì)1813.69 二層16.952.95118.52 0.92.2120.79271.18 5.152.95115.19 00057.73 A3.453.151151.23 3.451.8116827.324222.01 B83.3246.64 1.42.226.22.464179.70 83.3121.34 2.32.215.12.02483.12 D3.453.151070.88 2.11.8103815.12284.45 3.453.1517.63 1.81.813.21.29630.28 8(增）5.052.95114.90 56.61 增加了8軸將1/A/B/更換2160.86 三五層與二層墻體相同2160.86 女兒墻（43.15+13.5）*2*0.6*3.8258.32 3.各層（各質(zhì)點(diǎn)）自重標(biāo)準(zhǔn)值計(jì)算一層（墻+梁+板+柱）：（1813.69+2160.86）/2+996.01+2350.823+(824.26+829.44)/2=6160.958 kN二層（墻+梁+板+柱）：2160.86+996.01+2350.823+829.44=6337.13kN三層（墻+梁+板+柱）：2160.86+996.01+2350.823+829.44=6337.13kN四層（墻+梁+板+柱）：2160.86+996.01+2350.823+829.44=6337.13kN五層（墻+梁+板+柱）：2160.86/2+258.32+996.01+2434.97+829.44/2=5184.45kN4.重力荷載代表值 重力荷載代表值G取結(jié)構(gòu)和構(gòu)件自重標(biāo)準(zhǔn)值和可變荷載組合值之和，各可變荷載組合值取為雪荷載：0.5；屋面活載：0.0；按等效均布荷載計(jì)算的樓面活載：0.5；即，G=恒載+0.5（樓板面積+樓梯面積）活載標(biāo)準(zhǔn)值。一層：G1=6160.958 +0.5（549.495*2.0+44.4*2.5）=6765.953KN二層：G2=6337.13+0.5（549.495*2.0+44.4*2.5）=6942.125KN三層：G3=6337.13+0.5（549.495*2.0+44.4*2.5）=6942.125KN四層：G4=6337.13+0.5（549.495*2.0+44.4*2.5）=6942.125KN五層：G5=5184.45+0.5593.895*0.2=5303.229KN重力荷載代表值二側(cè)移剛度的計(jì)算地震作用是根據(jù)各受力構(gòu)件的抗側(cè)移剛度來分配的，同時(shí)，若用頂點(diǎn)位移法求結(jié)構(gòu)的自振周期時(shí)也要用到結(jié)構(gòu)的抗側(cè)剛度，為此先計(jì)算各樓層柱的側(cè)移剛度。（一） 梁柱線剛度計(jì)算梁的線剛度Kb=EcIb/lEc混凝土的彈性模量；l梁的計(jì)算跨度；Ib梁的截面慣性矩，對(duì)于現(xiàn)澆的樓面，中框架梁Ib=2.0Io,邊框架梁Ib=1.5Io；柱的線剛度Kb=EcIb/hEc混凝土的彈性量；h柱的計(jì)算跨度；Iz柱的截面慣性矩；中框架梁截面特性計(jì)算表層數(shù)梁編號(hào)截面尺寸mmmm梁跨/mm混凝土彈性模量Ec/pa截面慣性矩Ib/mm4(Ib=2Iz)線剛度i/N*mm(i=EI/l)剛度比15AC跨3006507500300001.37310105.49310100.76CD跨3006505700300001.37310107.22710101邊框架梁截面特性計(jì)算表層數(shù)梁編號(hào)截面尺寸mmmm梁跨/mm混凝土彈性模量Ec/pa截面慣性矩Ib/mm4(Ib=1.5Iz)線剛度i/N*mm(i=EI/l)15AC跨3006507500300001.0310104.1210100.57CD跨3006505700300001.0310105.4210100.75柱截面特性計(jì)算表層數(shù)柱編號(hào)截面尺寸mmmm柱高/mm混凝土彈性模量Ec/pa截面慣性矩Ib/mm4(Ib=Iz)線剛度i/N*mm(i=EI/l)15A/D4505003600300000.46910103.90610100.54B4506003600300000.8110106.7510100.93注：混凝土強(qiáng)度C30.梁柱相對(duì)線剛度如圖所示.梁、柱相對(duì)線剛度計(jì)算簡(jiǎn)圖如下(CD梁線剛度為1)：12 (二)柱側(cè)移剛度計(jì)算中框架柱側(cè)移剛度層數(shù)/軸i1i2i3i4icKcic/(105)Di/(105)根數(shù)1/A0.760.541.4074070.5597830.39060.2024547101/C0.7610.931.8924730.6146410.6750.3841506101/D10.541.8518520.6105770.39060.22082531025層/A0.760.760.541.4074070.4130430.39060/C0.7610.7610.931.8924730.4861880.6750.30386741025層/D110.541.8518520.4807690.39060.173878210邊框架柱側(cè)移剛度層數(shù)/軸i1i2i3i4icKcic/(105)Di/(105)根數(shù)1/A0.570.541.0555560.5090910.39060.184121221/C0.570.750.931.4193550.5613210.6750.350825521/D0.750.541.3888890.5573770.39060.2015847225層/A0.570.570.541.0555560.3454550.39060.1249394225層/C0.570.750.570.750.931.4193550.4150940.6750.259434225層/D0.750.750.541.3888890.4098360.39060.1482242橫向框架層間側(cè)移剛度層次12345Di(105)9.5473685987.3364914647.3364914647.3364914647.33649146同時(shí)可以得出：Di 0.7Di+1，說明該結(jié)構(gòu)豎向規(guī)則. 三自振周期計(jì)算 對(duì)于質(zhì)量和高度分布比較均勻的框架結(jié)構(gòu)，框架剪力墻結(jié)構(gòu)和剪力墻結(jié)構(gòu)，一般多采用頂點(diǎn)位移法計(jì)算結(jié)構(gòu)基本周期，公式為：考慮非結(jié)構(gòu)墻體剛度影響的周期折剪系數(shù)，當(dāng)采用實(shí)砌填充磚墻時(shí)取0.6-0.7，本工程取0.7：假想集中在各樓層面處的重力荷載代表值Gi為水平荷載，按彈性方法所求得的結(jié)構(gòu)頂點(diǎn)假想位移橫向框架頂點(diǎn)假想位移（T）計(jì)算表 層數(shù)Gi/KnVGi/KnDi/(kN/m)u/KnNu/m55303.2295303.229733649.1460.0072290.12014446942.12512245.35733649.1460.0166910.11291636942.12519187.48733649.1460.0261530.09622526942.12526129.6733649.1460.0356160.07007116765.95332895.56954736.85980.0344550.034455 故由上表得，uT=0.120144m；所以T1=1.70.7=0.4125s4 橫向地震作用計(jì)算1.水平地震作用及樓層地震剪力計(jì)算地震作用按GB50011-2001 A. 揚(yáng)州場(chǎng)地，抗震設(shè)防烈度為7度，0.15g，設(shè)計(jì)地震第一組，則Tg=0.35s,max=0.12，=0.05。由此計(jì)算相應(yīng)的結(jié)構(gòu)基本自振周期的水平地震影響系數(shù)為1= ()0.9max=0.1035 結(jié)構(gòu)等效總重力荷載 Geq= 0.85Gi=0.8532895.56=27961.23kN由于T1=0.4125s1.4Tg=0.49 s，故應(yīng)不考慮頂點(diǎn)附加地震作用，結(jié)構(gòu)底部剪力為：FEK =1Geq= 0.103527961.23=2894kN2.各質(zhì)點(diǎn)水平地震作用的標(biāo)準(zhǔn)值Fi= FEK= 2894計(jì)算結(jié)果見下表各質(zhì)點(diǎn)橫向水平地震作用及樓層地震剪力計(jì)算表層數(shù)Hi/mGi/KNGiHi/(kN*m)GiHi/GjHjFi/KNVi/KN5185303.22995458.1220.276899801.3444801.3444414.46942.12599966.60.289976839.19191640.536310.86942.12574974.950.217482629.39392269.9327.26942.12549983.30.144988419.59592689.52613.66765.95324357.4310.070654204.4739289432895.557344740.412894 水平地震作用分布 層間剪力分布 五變形驗(yàn)算 水平地震作用下框架結(jié)構(gòu)的層間位移i=Vi/Dij和頂點(diǎn)位移i=i，其計(jì)算機(jī)構(gòu)見下表；表中還計(jì)算了各層的層間彈性位移角：e=i/hi. 由表得最大層間彈性位移角發(fā)生在第二層，其值為1/792e=1/550。滿足要求！其中e鋼筋混凝土框架彈性位移角限值。橫向水平地震作用下的位移驗(yàn)算 層次 VGi/kN Di/(kN/m)ui/muT/mhi/me=i/hi5801.3444401733649.1460.0010922720.0010922723.60.00030340941640.536302733649.1460.0022361320.0033284043.60.00062114832269.930198733649.1460.0030940270.0064224313.60.00085945222689.526129733649.1460.0036659570.0100883883.60.00101832112894954736.85980.0030312020.0131195893.60.000842ui=Vi/DiuT=ui六、水平地震作用下框架內(nèi)力計(jì)算 對(duì)2軸線橫向框架內(nèi)力進(jìn)行計(jì)算?？蚣茉谒焦?jié)點(diǎn)荷載作用下，采用D值法分析內(nèi)力。1.計(jì)算依據(jù)柱端剪力：Vij=下端彎矩：Mb=Vijyh上端彎矩：MU=Vij(1-y)h上式中，y=y0+y1+y2+y3。其中y0查表得，y1由于各層梁線剛度一致，y1=0；y2、y3為層高對(duì)y的修正，查表可得。橫向水平地震作用下KJ-2軸框架各層柱端彎矩及剪力計(jì)算表層次軸號(hào)hi/mVGi/kN Di/(kN/m)Di/(kN/m)Vi/kNk-yMb/(kN/m)Mu/(kN/m)5A3.6801.34444733649.14614938.4116.32 1.41 0.3721.73 37.01 C30386.7433.19 1.89 0.39547.20 72.29 D17387.8218.99 1.85 0.39326.87 41.50 4A3.61640.5363733649.14614938.4133.40 1.41 0.4250.51 69.75 C30386.7467.95 1.89 0.445108.85 135.76 D17387.8238.88 1.85 0.44362.01 77.97 3A3.62269.9302733649.14614938.4146.22 1.41 0.4778.20 88.19 C30386.7494.02 1.89 0.495167.54 170.92 D17387.8253.80 1.85 0.49395.48 98.19 2A3.62689.52613733649.14614938.4154.76 1.41 0.52102.52 94.63 C30386.74111.40 1.89 0.545218.56 182.47 D17387.8263.74 1.85 0.543124.60 104.87 1A3.62894954736.859820245.4761.37 1.41 0