框架结构设计例题

框架构造设计例题 框架构造设计例题 --10---11-框架构造设计例题设计任务书设计资料1~4±0.000相当于确定标高10.00m，室内外高差600mm。建筑构造做法建筑构造做法选自华北地区建筑标准设计图集05J1。1。2300mm200mm，8.5kN/m3。05J1-271.5厚聚胺脂防水涂料刷基层处理剂一遍卫生间上人屋面非上人屋面顶棚承受轻钢龙骨纸面石膏板吊顶05J1顶7，自重0.14kN/205J1-271.5厚聚胺脂防水涂料刷基层处理剂一遍卫生间上人屋面非上人屋面表1 楼面及屋面构造做法名称厚度〔mm〕使用部位铺地砖楼面10厚地砖铺平拍实，水泥浆擦缝10〔30mm〕05J1-10201:4干硬性水泥砂浆结合层素水泥浆结合层一遍20一般楼面花岗石楼面20厚花岗石板铺平拍实，水泥浆擦缝20走廊〔50mm〕05J1-13301:4干硬性水泥砂浆结合层素水泥浆结合层一遍30门厅楼梯间10厚地砖铺平拍实，水泥浆擦缝10251:4干硬性水泥砂浆结合层2515厚水泥砂浆找平层1550C153050105~8，1:1水泥砂浆填缝10251:4干硬性水泥砂浆结合层25满铺0.15厚聚乙烯薄膜一层0.15上人屋面高聚物改性沥青防水卷材305J1-61:3水泥砂浆找平层20聚苯保温板1001:82%201001:3水泥砂浆找平层20涂料或粒料高聚物改性沥青防水卷材3非上人屋面1:3水泥砂浆找平层2005J1-6聚苯保温板1001:82%201001:3水泥砂浆找平层20图面平层准标1图图面平层顶屋2图图面平层顶屋⑧~①3图图面立侧，图面剖4图名称厚度〔mm〕 名称厚度〔mm〕 使用部位全部外墙面除卫生间外全部内墙面秞面砖墙面05J1-9152:1:8水泥石灰砂浆，分两次抹灰20%建筑胶4~5厚秞面砖，白水泥浆擦缝25卫生间内墙面刷素建筑胶水泥浆一遍，协作比为建筑胶:水泥浆=1:410面砖墙面152:1:8水泥石灰砂浆，分两次抹灰2005J1-13刷素水泥浆结合层一遍20%建筑胶8~10厚面砖，1:1水泥砂浆勾缝或水泥浆擦缝混合砂浆墙面刷素建筑胶水泥浆一遍，协作比为建筑胶:水泥浆=1:4151:1:6水泥石灰砂浆，分两次抹灰1505J1-551:0.5:3水泥石灰砂浆5刷素建筑胶水泥浆一遍，协作比为建筑胶:水泥浆=1:410使用荷载标准值屋2.0kN/m2；0.5kN/m2；楼2.0kN/m2；走廊、门厅、楼梯、厕所2.5kN/m2。4自然条件根本风压：0.40kN/m2；根本雪压：0.40kN/m2；最大冰冻深度0.6m。5．抗震设防抗震设防烈度为7度0.15；设计地震分组为第一组，场地类别为Ⅲ类。地质勘探资料场地较为平坦，自然地坪为确定高程9.200m。自上而下，各土层主要特征描述如下，3。①层：素填土，以粘土为主，局部含建筑垃圾、有机质较多，平均厚度约1.0m；②层：粉质粘土，场区普遍分布，平均厚度约2.5~3.0m，可塑，分布较均匀；③层：粉土，场区普遍分布，平均厚度约4~4.5m，可塑，分布较均匀；5m，可塑，场地内分布均匀。地下水最高水位为室外地坪下3.00m，地下水对混凝土及混凝土中的钢筋无侵蚀性。厚度层底深度 孔隙比 液性指数地基承载力特征值ak表厚度层底深度 孔隙比 液性指数地基承载力特征值ak层次土层描述〔m〕〔m〕〔e〕〔I〕Lf〔kPa〕1素填土1.01.019.72粉质粘土3.5~4.04.5~5.00.6710.5114019.53粉 土4.0~4.58.0~9.00.5820.1515020.04粉质粘土5m0.6760.4116019.5材料：混凝土：现浇，强度等级为C30或C35；钢筋：板内受力主筋承受HPB23512时承受HRB335级钢筋，板内分布筋承受HPB235级钢筋。梁柱内受力主筋承受HRB335级钢筋，箍筋承受HPB235级钢筋。3〕填充墙：室内地面以上填充墙为陶粒混凝土砌块砌体，砌块强度等级为MU5；砂浆承受强度等M7.5的水泥混合砂浆。MU10，砂浆承受强度等级M10的水泥砂浆。设计要求计算方法及内容确定构造构件尺寸；用底部剪力法计算水平地震作用下地震剪力。并取一榀框架，计算其内力；对上述框架用分层法或二次弯矩安排法计算竖向荷载下构件内力，并进展梁弯矩调幅，调幅系数=0.85；进展框架内力组合及截面设计；按弹性理论计算板及次梁的内力，并进展截面设计；计算书A4复印纸抄写计算书，字体工整，装订成册。图纸内容1〕构造平面配筋图比例1：100；注明轴线号，尺寸，墙厚，主、次梁截面尺寸，钢筋规格。2〕次梁配筋图要求绘制，弯矩包络图，纵、横剖面图，抽筋图。纵剖面：比例1:40，注明跨度；纵筋、架立筋、箍筋编号；钢筋断点位置。横剖面：比例1:25；注明截面尺寸，钢筋编号，根数，直径，箍筋直径，间距。框架配筋图框架立面图：比例1：40；注明跨度、层高、楼面标高、纵筋及箍筋、钢筋断点位置；梁柱加密区范围，次梁作用处加密箍筋或吊筋规格。梁柱截面配筋图：比例1:25，注明截面尺寸，钢筋直径、根数，箍筋直径、间距。根底施工图图5 多层框架构造设计的主要流程构造设计流程多层框架构造设计的主要流程如图5。构造方案选型与构造布置GB50011-2023105条，按本地区设防烈度实行抗震措施。本建筑高H=19.500m，局部高H=22.800m，属多层建筑，承受框架构造，现浇梁、板GB50011-20236.2.1条，框架抗震等级为三级。-2.50m，根底顶面标高为-1.30m。混凝土：主体构造梁、柱、板均承受C30级；构造柱、圈梁及过梁均承受C20级。钢HPB235级钢φHRB335级钢φ。焊条：承受E43E50型。抗震及抗风措施：填充墙在门口标高处设抗震带一道。框架柱柱截面尺寸根椐柱的允许轴压比[]按下式计算确定。 Nc c

/Afcc

ccGB50011-2023637比限值为[]=0.9。c为使构造在两个主轴方向的动力特性相近，柱截面承受方柱，柱的轴力设计值Nc按下式估算。N aSwnc G4B、4C、5B、5C处，则其最大轴力估算为：N aSwn=1.2×1.1×(6.6+3.0)/2×7.2×14×6=3558.3kNc G因此，主楼框架柱截面尺寸确定为：600×600。框架梁636200mm；截面高宽4；梁净跨与截面高度之比宜大于4。〔1〕A~D轴纵向框架梁：h=(1/8~1/14)l=(1/8~1/14)×7200=900~550h=750mm，b=300mm；〔2〕1~8轴AB段及CD段横向框架梁：h=(1/8~1/14)l=(1/8~1/14)×6600=825~471h=700mm，b=300mm；〔3〕1~8轴BC段横向框架梁按与AB段框架梁线刚度相等计算，即1 1bh3/l bh3/ll3 2l1300036600121l3 2l1300036600h h2 1

700

538mm故取h=550mm，b=300mm；楼面次梁h=(1/12~1/18)l=(1/12~1/18)×6600=550~367，取h=550mm；b=200mm；h=400mm；b=200mm。现浇板厚h=(1/30~1/35)l=(1/30~1/35)×3600=120~100，取h=110mm；6所示。图6 标准层构造平面布置简图荷载计算荷载分类计算屋面荷载屋面恒载依据构造做法计算，列于表4中。分析框架构造在竖向荷载作用下的内力时，屋面活载应取均布活载与雪载之间的较大2.0kN/m20.50kN/m2。抗震计算时，计算屋面重力荷载代表值时不考虑屋面活载，取雪载0.40kN/m2。楼面荷载楼面恒载依据构造做法计算，列于表5中。楼面活载：办公室、卫生间取2.0kN/m2；走廊：2.5kN/m2；屋顶设备用房：6.0kN/m2。楼梯间荷载恒载：水磨石地面楼梯踏步板板下抹灰30厚130厚20厚1.16×(0.3+0.15)/0.3=1.74kN/m2=5.51kN/m20.02×20/cos=0.45kN/m2合计：7.70kN/m2活载：2.50kN/m24．墙体荷载300200厚陶粒混凝土砌块，双侧摸灰。考虑到组砌时在洞口处、墙体底部和顶部混砌局部粘土砖，混砌比例取8:2，粘19kN/m3，则砌体容重为：=8.5×0.8+19×0.2=10.6kN/m3计入面层的做法，求得墙体的单位面积重量为：out外墙：q =0.3×10.6+0.55+0.02×20=4.13kN/m2out内墙：qin=0.2×10.62×0.02×20=2.92kN/m2表4 屋面恒载计算表厚度容重重量恒荷载名称及部位用料做法(mm)(kN/m3)(kN/m2)标准值105~8，1:1水泥砂浆填缝10200.20251:4干硬性水泥砂浆结合层25200.50高聚物改性沥青防水卷材30.10上人屋面1:3水泥砂浆找平层20200.40(19.500)聚苯保温板1003.00.306.3561:82%20100151.501:3水泥砂浆找平层20200.40钢筋混凝土楼板110252.75板底吊顶0.20高聚物改性沥青防水卷材30.101:3水泥砂浆找平层20200.40非上人屋面聚苯保温板1003.00.30(22.800)1:82%20100151.505.6561:3水泥砂浆找平层20200.40钢筋混凝土楼板110252.75板底吊顶0.20厚度容重重量名称及使用部位厚度容重重量名称及使用部位恒荷载〔mm〕〔kN/m3〕〔kN/m2〕标准值3.554.115.50铺地砖楼面10厚地砖铺平拍实，水泥浆擦缝10200.20〔办公室〕201:4干硬性水泥砂浆结合层20200.40〔30mm〕钢筋混凝土楼板110252.7510板底轻钢龙骨吊顶0.20花岗石楼面20厚花岗石板铺平拍实，水泥浆擦缝20280.56(走廊、楼梯间)301:4干硬性水泥砂浆结合层30200.60〔50mm〕钢筋混凝土楼板110252.7513板底轻钢龙骨吊顶20200.2010厚地砖铺平拍实，水泥浆擦缝10200.20铺地砖防水楼面251:4干硬性水泥砂浆结合层25200.50(卫生间)15厚水泥砂浆找平层15200.30〔102mm〕50C153050251.2527钢筋混凝土楼板110252.75板底吊顶0.50重力荷载代表值计算各层重力荷载代表值汇总于表6。将表中恒载与活载求和并除以总面积，可得框架单位w=12.8kN/m2w=14kN/m2是合理的。项次层号12~456梁自重项次层号12~456梁自重byby纵向框架梁Gbx1095.11095.11095.1391.1横向框架梁G668.3668.3668.3276.9G302.4302.4302.469.5G=G+G+Gb bx by by2065.82065.82065.8737.5Gc1664.01248.01248.0455.0楼、屋面恒载Gs2963.82963.82682.71349.6Gw3996.33186.12387.1501.5Gd38.538.523.24.0GG+G+G+G+Gb c s w d10728.49502.28406.83047.6楼、屋面活载Q1595.51595.51217.995.5G=G+0.5Qi11526.210300.09015.83095.4根本自振周期的计算构造刚度计算框架梁的惯性矩及线刚度先计算矩形截面梁的惯性矩然后考虑楼板的翼缘效应，将梁惯性矩乘以增大系数，即I=1.5II=2I，其中，I=1/12×b×h3。b 0 b 0 0 b bi=I/l7。b b框架柱的惯性矩及线刚度I=1/12×b×h3，i=I/h8。c b b c c框架柱的抗推刚度：9~11。方向层号横向 1~6纵向 1~6方向层号横向 1~6纵向 1~6梁号b×hb b(mm)I0(×10-2m4)Ib(×10-2m4)Ec(×107kPa)l(m)i=EI/lb Cb(kNm)BL1300×7000.85751.2863.006.600.585×105BL2300×5500.41590.6243.003.000.624×105ZL1300×7000.85751.7153.006.600.780×105ZL2300×5500.41590.8323.003.000.832×105BL1300×7501.05471.5823.007.20.659×105ZL1300×7501.05472.1093.007.20.879×1058柱的线刚度计算层砼b×h (mm)c cI(×10-2m4)cEc(×107kPa)h(m)i=EI/h(kNm)c cc1C30600×6001.083.005.200.623×1052~5C30600×6001.083.003.900.831×1056C30600×6001.083.003.300.982×105柱的类型根数K=柱的类型根数K=i/ibjC=(0.5+K)/(2+K)cD=·12i/h2(kN/m)边框架边柱边框架中柱440.9391.9410.4900.619c c0.135×1050.171×105D(kN/m)横向5.244×105纵向5.576×105中框架边柱121.2520.5390.149×105中框架中柱122.5870.6730.186×105边框架边柱41.0580.5090.141×105边框架中柱122.1160.6360.176×105中框架边柱41.4110.5600.155×105中框架中柱122.8220.6890.190×10510二层~五层框架柱的抗推刚度柱的类型根数K=i柱的类型根数K=i/(2i)=K/(2+K)D=·12i/h2(kN/m)D(kN/m)边框架边柱边框架中柱横向441212412412bj C0.7041.4550.9391.9411.0582.1161.4112.822c0.2600.4210.3190.4920.3460.6920.4140.827c c0.170×1050.276×1050.209×1050.323×1050.227×1050.454×1050.271×1050.543×1058.168×105中框架边柱中框架中柱纵向13.956×105中框架边柱中框架中柱柱的类型根数K=i/(2i)3、613、623、6轴框架中柱横向4、524、51A、D轴框架边柱A、D轴框架中柱B轴框架边柱B轴框架中柱C轴框架边柱C轴框架中柱2222222422222bj C1.1380.6951.4360.6950.7941.5421.6421.0071.3421.2311.6781.3431.790=K/(2+K)cD=·12i/h2(kN/m)D(kN/m)0.3630.2580.4180.2580.2840.4350.4510.3350.4020.3810.4560.4020.472c c0.393×1050.279×1050.452×1050.279×1050.307×1050.471×1050.488×1050.363×1050.435×1050.412×1050.493×1050.435×1050.511×1055.338×105纵向6.024×105T1的计算承受能量法进展计算，将集中在各楼层标高处的重力荷载代表值，作为水平荷载作用iu，然后按式〔1-2-14a〕计算根本自振周期T，结i1果见表12、13。其中，填充墙材料为陶粒混凝土，周期折减系数取T

=0.8。从表中可以看出，框架在两个方向的根本自振周期相差不多，即两个方向的动力特性相近，满足抗震设计时的要求。层号G(kN)iV层号G(kN)iV(kN)iD(kN/m)iiiGui iGu2i iT1nGu2iiTni1Guiii1=0.711(s)163095.43095.45.338×1050.005800.24366754.225183.77459015.812023.28.168×1050.014710.237862144.498510.090410300.022311.28.168×1050.027320.223152298.445512.898310300.032511.28.168×1050.039800.195832023.049394.999210300.042811.28.168×1050.052410.156031607.109250.757111526.254337.45.244×1050.103620.103621194.345123.7581表13 纵向根本自振周期T1i层号G(kN)i

Vi(kN)

D(kN/m)

ui(m) Gu

Gu2 Ti i 1iii 63095.43095.46.024×1050.005140.18117iii 63095.43095.46.024×1050.005140.18117560.794101.59959015.812023.213.956×1050.008610.176031587.051279.369410300.022311.213.956×1050.015990.167421724.426288.703310300.032511.213.956×1050.023300.151431559.729236.190210300.042811.213.956×1050.030680.128131319.739169.098111526.254337.45.576×1050.097450.097451123.228109.459ii2 i1T nGuiii1=0.621(s)水平地震作用计算本工程建筑总高度H＜40m近似承受底部剪力法进展地震作用计算。地震作用标准值计算1水平地震作用影响系数17〔0.15可得计算参数： =0.12，T=0.45s，max g横向水平地震作用影响系数1

分别为：T

0.450.9横向： g

0.120.07951 T 21

max

0.711T

0.450.91

g1

2

0.120.08980.621水平地震作用标准值i集中在各层楼、屋盖标高处的重力荷载代表值G见表6，总重力荷载代表值为：iG Ei1

G=54537.4kNi构造底部总水平地震作用标准值为横向：F

=G=·0.85G

=0.0795×0.85×54537.4=3685.36kNEk 1 eq 1 eq纵向：F

=G=·0.85G

=0.0898×0.85×54537.4=4162.84kNEk 1 eq 1 eq各层楼、屋盖标高处的横向水平地震作用标准值及地震剪力作用标准值如表14。由于T

=0.711s＞1.4T=0.63s，应考虑顶部附加地震作用系数：1 g 5=0.08T5

+0.01=0.08×0.711+0.01=0.066881F=5

=0.06688×3685.36=246.48kNEk各层楼、屋盖标高处的纵向水平地震作用标准值及地震剪力作用标准值如表15。由于T=0.621s＜1.4T=0.63s，故不考虑顶部附加地震作用系数。1 g 5层号G〔层号G〔kN〕H〔m〕iiGHi i6GHi iGHF i iiGHk k6F EkGHk k5V Fi6iF5(kN)i63095.424.174599.10.1031354.551063.6559015.820.8187528.60.2591891.011492.04410300.016.9174070.00.2405827.052319.09310300.013.0133900.00.1850636.192955.28210300.09.193730.00.1295445.343400.62111526.25.259936.20.0828284.743685.36∑54537.4723763.9V3V=3F。6 6 6GHi iGGHi iGHF i i层号G〔kN〕H〔m〕iiGHi i6iGHk k6FEkGHk kV Fi6i〔kN〕i63095.424.174599.10.1031429.191287.5759015.820.8187528.60.25911078.591507.78410300.016.9174070.00.24051001.162508.94310300.013.0133900.00.1850770.133279.07210300.09.193730.00.1295539.093818.16111526.25.259936.20.0828344.684162.84∑54537.4723763.916层间侧移横向i纵向层间侧移允许值层号ViDi=V/DViDi=V/D=H/550i(kN)(kN/m)(mm)(kN)(kN/m)(mm)(mm)61063.655.338×1051.991287.576.024×1052.146.0051492.048.168×1051.831507.7813.956×1051.087.0942319.098.168×1052.832508.9413.956×1051.807.0932955.288.168×1053.623279.0713.956×1052.357.0923400.628.168×1054.163818.1613.956×1052.747.0913685.365.244×1057.034162.845.576×1057.479.45i i iii ii由于本工程高宽比小于4，柱轴向变形引起的侧移无视不计，梁柱弯曲变形引起的层间16。从结果看，层间位移均满足要求。7中。地震作用 地震剪力 水平侧移 地震作用 地震剪力 横向 纵向图7 地震作用、地震剪力与水平侧移框架剪力标准值844轴框架及纵向B轴框架的各柱剪力1718。层剪力层抗侧刚度边柱中柱层号ViDi层剪力层抗侧刚度边柱中柱层号ViDiDijV=V·D/Dij i ij i(kN)DijV=V·D/D(kN)(kN/m)(kN/m)(kN/m)ij i ij i(kN)61063.655.338×1050.279×10555.590.471×10593.850.307×10561.170.488×10597.2351492.048.168×1050.209×10538.180.323×10559.004轴框架42319.098.168×1050.209×10559.340.323×10591.7132955.288.168×1050.209×10575.620.323×105116.8723400.628.168×1050.209×10587.010.323×105134.4813685.365.244×1050.149×105104.710.186×105130.72层剪力层抗侧刚度边柱中柱层号ViDi层剪力层抗侧刚度边柱中柱层号ViDiDijV=V·D/Dij i ij iDijV=V·D/Dij i ij iB轴框架(kN)(kN/m)(kN/m)(kN)(kN/m)(kN)61287.576.024×1050.412×10588.060.493×105105.3751507.7813.956×1050.271×10529.280.543×10558.5642508.9413.956×1050.271×10548.720.543×10597.4433279.0713.956×1050.271×10563.670.543×105127.3523818.1613.956×1050.271×10574.140.543×105148.2814162.845.576×1050.155×105115.720.190×105141.85水平地震作用下框架内力计算4D值法进展计算。其计算步骤如下：依据柱剪力及反弯点高度计算柱端弯矩0 1 2 yh按式〔5-2-2〕计算，即：yh=(y+y+y+y)h0 1 2 柱端弯矩按式〔5-2-5〕计算。柱下端弯矩：M=V

·yh；柱上端弯矩：MV

。19。

b ij

t ij层号柱剪力柱位置y柱端弯矩(kN·m)层号柱剪力柱位置y柱端弯矩(kN·m)V (kN)ijKy0y1y2y3yMbMt654321边柱55.590.6950.300.05—0.00.3564.21119.24中柱B93.851.5420.37710.0—0.00.3771116.79192.92中柱C97.231.6420.38210.0—0.00.3821122.60198.26边柱D61.170.7940.350—0.00.3570.65131.21边柱、D38.180.9390.450.00.00.00.4570.0181.90中柱、C59.001.9410.450.00.00.00.45103.55126.56边柱、D59.340.9390.450.00.00.00.45104.14127.28中柱、C91.711.9410.49710.00.00.00.4971177.80179.87边柱、D75.620.9390.45200.00.00.00.4520133.30161.62中柱、C116.871.9410.500.00.00.00.50227.90227.90边柱、D87.010.9390.500.00.0-0.03330.4667158.37180.97中柱、C134.481.9410.500.00.00.00.50262.24262.24边柱、D104.711.2520.6374—-0.009—0.6284342.16202.33中柱、C130.722.5870.5707—0.00—0.5707387.93291.81计算梁端弯矩及梁剪力利用节点平衡条件，梁端弯矩按式〔5-2-6〕计算，梁剪力由梁两端的弯矩之和除以梁20。M=MACol,ALM=MACol,ALABVAB=(M+MA B,L)/lB,L轴MM =M ·iCol,BAB AB BC/(i+i )Col,B(kN·m)M =M ·i /(iB,RCol,BBC AB BC+i)119.2430.1379.64192.92113.27146.1039.98117.75243.35125.60197.2950.67137.14283.42146.28265.7670.01196.30405.69209.39314.2783.55237.16490.13252.97360.7095.27268.09554.05285.96M=MDCol,DD轴M (kN·m)Col,D131.21131.21152.55152.55197.29197.29265.76265.76314.27314.27360.70360.70层号1轴M (kN·m)Col,A119.24146.10197.29265.76314.27360.70LBCV M +M )/lBC B,R C,L32.6784.7397.52139.59168.65190.64M =M ·i /(i +i )C,L Col,CBC BC CD102.33128.60146.28209.39252.97285.96C轴M (kN·m)Col,CM =M ·i /(i +i )C,R Col,CCD BC CD198.2695.93249.16120.56283.42137.14405.69196.30490.13237.16554.05268.09LCDV =(M+M)/lCD C D34.4241.3850.6770.0183.5595.27依据梁端剪力计算柱轴力边柱轴力 Nij

nV ；kki中柱轴力 Nij

nki

k,L

V k,R21。

各梁剪力各柱轴力层号VAB(kN)V 各梁剪力各柱轴力层号VAB(kN)V (kN)BCVCD(kN)NANBNCND630.1332.6734.42-30.13-2.53-1.7234.42539.9884.7341.38-70.11-47.2941.6075.805450.6797.5250.67-120.78-94.1388.45126.47370.01139.5970.01-190.79-163.72158.03196.48283.55168.6583.55-274.34-248.65243.13280.03195.27190.6495.27-369.61-344.19338.50375.30绘制内力图左震作用下，横向48。右震作用下，内力一样，方向相反。竖向荷载作用下框架内力计算4负荷范围计算，导算为作用在梁及梁柱节点上的荷载，荷载值详见表22。由纵向传来的作239所示，括号内为活荷载。层号均布恒载〔kN/m〕T形荷载层号均布恒载〔kN/m〕T形荷载〔kN/m〕651~4651~4651~4g=5.00AB跨1g=10.7，p=0.9，a=1.822g=15.801g=17.82，p=7.2，a=1.822g=9.551g=12.78，p=7.2，a=1.82〔kN/m〕---g=3.80BC跨112---g=16.95，p=1.533g=14.60g=14.85，p=6.033g=3.801g=13.34，p=7.533g=14.50CD跨1g=20.34，p=1.8，a=1.822---节点弯矩〔kN·m〕Mg=92.2，Mq=2.92Mg=113.80，Mq=11.66Mg=129.82，Mq=11.66------〔kN〕------P=38.401g=12.60122Q=7.65g=5.001g=16.30，p=8.1，a=1.82211~4层层号柱自重ABCD表层号柱自重ABCD633.00G87.60Q5.40G135.53Q8.06G178.25Q11.87G129.94Q7.56539.00130.5336.72146.1747.34186.4377.82158.4660.482~439.00153.5936.72187.2451.62247.2755.56169.6234.02152.00153.5936.72187.2451.62247.2755.56169.6234.02Nk力轴Nk(力剪图力内架框轴4向横8图·Nk矩弯94轴框架上的竖向荷载竖向恒载作用下框架内力计算承受二次弯矩安排法。计算步骤如下：计算竖向荷载作用下各层梁端固端弯矩〔表24。AB跨BC跨CD跨表AB跨BC跨CD跨层号M*ABM*BAM*BCM*CBM*CDM*DC6-68.52(-2.85)68.52(2.85)-10.80(-0.70)10.80(0.70)-82.50(-5.69)82.50(5.69)5-113.73(-22.78)113.73(22.78)-19.30(-2.81)19.30(2.81)-86.17(-45.56〕86.17(45.56)1~4-58.58(-22.78)58.58(22.78)-9.10(-3.52)9.10(3.52)-141.52(-33.07)125.53(29.88)依据梁柱线刚度求梁柱转动刚度，并确定各节点处的安排系数，详见图11。n SiknikSiki1其中，Sikki根杆件的转动刚度，Sikk各杆件的转动刚度之和。杆件的转动刚度的计算方法如下：jS=4i；当利j用构造对称性而将杆件的另一端取为定向支座时，第jS=2i，i为杆件j的线刚度。进展弯矩的安排和传递，求得各节点处的杆端弯矩值。需要留意的是，A轴柱外侧的悬臂是静定构造，并不参节点弯矩的安排和传递。11。图10 用二次弯矩安排法计算竖向恒载作用下框架弯矩依据静力平衡条件计算各梁跨中弯矩。跨中弯矩取荷载实际分布并按两端简支的计算值与梁端弯矩叠加求得不肯定在跨度的中点处，应建立平衡方程求解，计算简图如图11。 211所示荷载作用下，距离A 21M

x 1 a2

x

〔1〕 gl

M M Mx 2

l 6

l

l l

B A l对上式求导，并令M0，可求得跨中最大弯矩的位置x如下：1 M Mx2l

B A12g g l12

〔2〕代回到式〔1〕中，即可求得跨中最大弯Mxmax。4层AB跨为例，l=6.6m，a=1.8m，1 2 A1 2 AM=-38.33kN·m，可求得：Bx=3.667m，M

=31.20kN·m。

图11 求解梁跨中最大弯矩的位置xxmaxx=l/2=3.30m，则由式〔1〕M

=30.00kN·m。中。度中点处的弯矩为跨中最大弯矩。由此得到竖向恒载下的弯矩图，如图12。图12 竖向恒载作用下框架弯矩图依据各梁、柱弯矩计算各梁、柱的剪力。梁柱剪力依据平衡条件进展计算，结果见表2425。柱轴力计算柱轴力按节点处平衡条件进展计算，如图13。柱顶截面轴力：--22---23-图13 图13 柱剪力计算简图NtnGi ji

V

VR,j

g j1

〔3a〕柱底截面轴力：NbnGi ji

V

VR,j

gj

〔3b〕式中 g——各层柱自重；iG——各层由纵向框架传来的竖向荷载；iVV、——分别为节点左侧、右侧梁剪力；VVL R26。竖向活载作用下框架内力计算跨满布时的状况，内力组合时将支座最大弯矩和跨中最大弯矩乘以放大系数1.1，以考虑活载的不利布置的影响。计算结果见表27~2914。AB跨MBA ABAB跨MBA ABVGbV =V +V (kN)左M GbV =V –V (kN)左 M GbMBCMCBV=(M -MBC跨MCB BC)/lVGbCD跨VGb65.2272.25111.41/-100.93左 MGb层号654321左端弯矩M -81.74AB-115.40-81.50-77.64-77.12-83.31右端弯矩M -51.59BA-94.47-38.33-37.1-37.19-33.77V=(M -M)/l4.573.176.546.146.057.5157.2094.9147.1761.7798.0853.7153.2153.2254.68-52.63-91.74-40.63-41.03-41.12-39.66-17.09-31.69-1.71-3.03-2.92-4.35-29.81-22.62-36.08-34.60-34.31-41.48-1.931.37-5.20-4.78-4.76-5.6318.4133.0415.71V =V +V (kN)左 M Gb16.4834.4110.5010.9310.9510.08V =V –V (kN)-20.34-31.67-20.92-20.49-20.47-21.34左 M GbMCD-73.64-85.25-129.74-131.83-132.09-126.8MDCV=(M -M )/lM DC CD-59.182.19-78.900.96-107.313.40-109.743.35-107.73.70-100.124.04V =V +V (kN)左 M Gb67.4173.21114.81114.76115.11115.45V =V –V (kN)-63.03-71.29-97.53-97.58-97.23-96.89VV0以使结点顺时针转动为正。 框架构造设计例题 框架构造设计例题 25恒载作用下柱端剪力计算层号654321Mt10.462.4330.2126.0927.1714.75A轴Mb-4.0318.1126.0925.5331.777.38V=-(Mt+Mt)/h1.955.2714.4413.2415.114.26Mt34.4926.8115.7217.0417.359.93B轴Mb35.9720.9117.0416.9319.494.96V=-(Mt+Mt)/h21.3514.808.408.729.452.86Mt-43.83-31.62-50.81-48.61-49.45-29.42C轴Mb-31.01-41.12-48.61-48.32-55.91-14.71V=-(Mt+Mt)/h-22.68-18.66-25.49-24.85-27.02-8.49Mt59.1837.1757.4354.8759.0433.76D轴Mb41.7349.8854.8757.0366.3616.86V=-(Mt+Mt)/h30.5622.3228.7928.6932.159.73V以使结点顺时针转动为正。层号V层号VLA轴G柱顶轴力Ni柱底轴力NiVLVB轴RG柱顶轴力Ni柱底轴力NiVLVC轴RG柱顶轴力Ni柱底轴力NiVRD轴G柱顶轴力Ni柱底轴力Ni65432133.0039.0039.0039.0039.0052.0061.7798.0853.7153.2153.2254.6887.60130.53153.59153.59153.59153.59149.37410.98657.28903.081148.891396.16182.37449.98696.28942.081187.891448.16-52.63-91.74-40.63-41.03-41.12-39.6616.4834.4110.5010.9310.9510.08135.53146.17187.24187.24187.24187.24204.64509.96787.331065.531343.841619.82237.64548.96826.331104.531382.841671.82-20.34-31.67-20.92-20.49-20.47-21.3467.4173.21114.81114.76115.11115.45178.25186.43247.27247.27247.27247.27266.00596.311018.311439.831861.682284.74299.00635.311057.311478.831900.682336.74-63.03-71.29-97.53-97.58-97.23-96.89129.94158.46169.92169.92169.92169.92192.97454.72761.171067.671373.821679.63225.97493.72800.171106.671412.821731.63--50---25-荷载作用效应组合下组合：无地震作用时SG

SQ

的根本组合，并考虑弯矩调幅；组合工况A：S=1.20SG组合工况B：S=1.35S

+1.40SQ+0.7×1.40SG Q由于本例抗震设防烈度为7度0.15，地震作用较大，同时水平风荷载较小。因此，无地震作用时，未考虑竖向荷载效应与水平风荷载效应的根本组合。通过比较并依据实际阅历可知，由于活荷载所占比例很小〔约占总荷载的15左右对框架梁、柱，起掌握作用的根本组合均为组合工况B。有地震作用时取重力荷载代表值的荷载效应(SG

+0.5SQ

SEh

的根本组合：组合工况C：S=1.20(SG

+0.5SQ

)±1.30SEh组合工况D：S=1.00(SG

+0.5SQ

)±1.30SEhV=(V=(M -M )/l0.150.390.320.330.33AB跨MBA AB0.33V02.1617.28BC跨0V=(M -M )/l-0.100.660.690.75CD跨MDC CDV00.730.724.3234.5624.31/-22.22层号654321MAB-3.82-21.58-21.95-21.98-22.04-21.15MBA-2.82-19.00-19.83-19.83-19.86-18.94V =V +V(kN)左 M 02.3117.6717.6017.6117.6117.61V =V -V(kN)左 M 0-1.99-16.89-16.96-16.95-16.95-16.95MBC0.07-3.43-4.82-4.81-4.77-5.68MCB-0.48-11.88-8.14-8.50-8.44-10.02V=(M -M )/lM CB BC-0.18-2.82-1.11-1.23-1.22-1.45V1.134.505.63V =V +V(kN)左 M 00.951.724.524.404.414.18V =V -V(kN)左 M 0-1.31-6.32-6.74-6.86-6.85-7.08MCD-6.79-41.63-31.23-30.89-30.94-29.75MDC-7.42-37.27-26.67-25.96-26.15-23.67V =V +V(kN)左 M 04.2235.2225.0025.0625.0425.03V =V -V(kN)左 M 0-4.42-33.90-22.91-22.97-22.95-22.94注：V0VV0以使结点顺时针转动为正。28活载作用下柱端剪力计算层号 654321Mt0.91-5.58-5.20-5.16-5.28-3.26A轴Mb-4.34-5.09-5.16-5.10-6.24-1.63V=-(Mt+Mt)/h-1.04-2.74-2.66-2.63-2.95-0.94Mt2.898.277.517.507.624.64B轴Mb7.297.497.507.468.622.32V=-(Mt+Mt)/h3.084.043.853.844.161.34Mt-6.31-15.26-10.83-11.19-11.38-6.86C轴Mb-14.49-12.27-11.19-11.13-12.87-3.43V=-(Mt+Mt)/h-6.30-7.06-5.65-5.72-6.22-1.98Mt7.4219.0912.2312.9813.317.97D轴Mb18.1814.4412.9812.8315.713.99V=-(Mt+Mt)/h7.768.606.467.397.442.30V以使结点顺时针转动为正。图14 竖向活载作用下框架弯矩图A轴D轴iA轴D轴i层号654321VL2.3117.6717.6017.6117.6117.61Q5.4036.7236.7236.7236.7236.72N7.7162.10116.42170.75225.08279.41iVL-1.99-16.89-16.96-16.95-16.95-16.95BVR0.951.724.524.404.414.18轴Q8.0647.3451.6251.6251.6251.62Ni11.0076.95150.05223.02296.00368.75VL-1.31-6.32-6.74-6.86-6.85-7.08CVR4.2235.2225.0025.0625.0425.03轴Q11.8777.8255.5655.5655.5655.56Ni17.40136.76224.06311.54398.99486.66VR-4.42-33.90-22.91-22.97-22.95-22.94Q7.5660.4834.0234.0234.0234.02N11.98106.36163.29220.28277.25334.21竖向荷载作用下的根本组合依据以上组合原则，竖向荷载作用下框架组合内力结果见表30~表33。内力及AB跨BC内力及AB跨BC跨CD跨层号QQQQQQ其组合MMMMMMMMMABzAByAB中BCzBCyBC中CDzCDyCD中MG-81.74-51.5937.82-17.09-29.81-6.46-73.64-59.1860.586M组合弯矩-3.83-114.48-2.82-72.691.0952.230.07-23.00-0.48-40.760.85-7.80-6.79-106.73-7.42-87.891.7283.6415%-97.31-61.7866.27-19.55-34.65-3.03-90.42-74.7198.23MG-115.40-94.4767.41-31.69-22.622.64-85.25-78.9049.425M组合弯矩-21.58-179.05-19.00-148.0215.03107.21-3.43-46.48-11.88-43.35-3.160.16-41.63-159.96-37.27-146.6931.18100.3315%-152.20-125.81131.74-39.51-36.846.89-135.97-124.69123.33MG-81.50-38.3330.00-1.71-36.08-4.61-129.74-107.3186.464M组合弯矩-21.95-133.69-19.83-73.1214.4356.06-4.82-7.50-8.14-57.48-0.86-7.15-31.23-208.81-26.67-173.6219.96138.2415%-113.63-62.1571.57-6.38-48.86-2.28-177.49-147.58166.92MG-77.64-37.132.54-3.03-34.60-4.54-131.83-109.7484.203M组合弯矩-21.98-128.51-19.83-71.4614.4159.46-4.81-9.28-8.50-55.87-1.03-7.24-30.89-211.27-25.96-176.1320.49135.7615%-109.23-60.7474.46-7.88-47.49-2.35-179.58-149.71164.81MG-77.12-37.1932.76-2.92-34.31-4.34-132.09-107.785.092M组合弯矩-22.04-127.87-19.86-71.6214.3759.71-4.77-9.08-8.44-55.41-0.98-6.91-30.94-211.67-26.15-173.5820.37136.8315%-108.69-60.8774.68-7.72-47.10-2.08-179.92-147.55165.72MG-83.31-33.7731.37-4.35-41.48-8.65-126.8-100.1291.521M组合弯矩-21.15-135.27-18.94-66.0115.2758.81-5.68-12.00-10.02-66.80-2.23-14.08-29.75-203.25-23.67-160.6822.21147.4915%-114.98-56.1173.91-10.20-56.78-8.17-172.76-136.58174.79注：1.MG、MQ分别为竖向恒荷载、活荷载作用下各掌握截面弯矩。 弯矩组合工况为：M=1.35MG+0.7×1.40MQ×1.1；其中，系数1.1为考虑活荷载最不利布置时，将满10%。15%15%，相应的跨中弯矩按平衡条件求得。层号内力及其组合VABz层号内力及其组合VABzAB跨VAByVAB中VBCzBC跨VBCyVBC中VCDzCD跨VCDyVCD中VG61.77-52.6316.48-20.3467.41-63.036VQ2.31-1.990.95-1.314.22-4.42组合剪力85.65-73.0023.18-28.7495.14-89.42VG98.08-91.7434.41-31.6773.21-71.295VQ17.67-16.891.72-6.3235.22-33.90组合剪力149.72-140.4048.14-48.95137.16*-129.46VG53.71-40.6310.50-20.92114.81-97.534VQ17.6-16.964.52-6.7425.00-22.91组合剪力89.76-72.5*18.93*-34.85179.49-154.12VG53.21-41.0310.93-20.49114.76-97.583VQ17.61-16.954.4-6.8625.06-22.97组合剪力89.09-72.9719.28-34.38179.48-154.24VG53.22-41.1210.95-20.47115.11-97.232VQ17.61-16.954.41-6.8525.04-22.95组合剪力89.10-73.07*19.31*-34.35179.94-153.7VG54.68-39.6610.08-21.34115.45-96.891VQ17.61-16.954.18-7.0825.03-22.94剪力组合91.076-71.3217.95-35.75180.39-153.28注：1.VG、VQ分别为竖向恒荷载、活荷载作用下各掌握截面剪力。2.组合工况为：V=1.35VG+0.7×1.40VQ，带“*V=1.20VG+1.40VQ。3.各跨跨中剪力均较小，对箍筋计算不起掌握作用，故表中未给出。表32 A、B柱竖向荷载下的柱端内力根本组合柱号 A柱 B柱层号

组合效应MM10.460.9115.0134.492.8949.39N149.377.71209.21204.6411.00287.046 M-4.03-4.34-9.6935.977.2955.70N182.377.71253.76237.6411.00331.59V1.95-1.041.6121.353.0831.84柱顶MN2.43410.98-5.5862.10-2.19615.6826.81509.968.2776.9544.30763.865柱底MN18.11449.98-5.0962.1019.46668.3320.91548.967.4976.9535.57816.51V5.27-2.744.4314.804.0423.94柱顶MN30.21657.28-5.20116.4235.691001.4215.72787.337.51150.0528.581209.954柱底MN26.09696.28-5.16116.4230.161054.0717.04826.337.50150.0530.351262.59V14.44-2.6616.898.403.8515.47*柱顶MN26.09903.08-5.16170.7530.161386.4917.041065.537.50223.0230.351657.033柱底MN25.53942.08-5.10170.7529.471439.1416.931104.537.46223.0230.171709.68V13.24-2.6315.308.723.8415.84*柱顶MN27.171148.89-5.28225.0831.511771.5817.351343.847.62296.0030.892104.262柱底MN31.771187.89-6.24225.0836.771824.2319.491382.848.62296.0034.762156.91V15.11-2.9517.519.454.1617.16柱顶MN14.751396.16-3.26279.4116.722158.649.931619.824.64368.7517.952548.131柱底MN7.381448.16-1.63279.418.372228.844.961671.822.32368.758.972618.33V4.26-0.944.832.861.345.31*柱底注：组合工况为：S=1.35SG+0.7×1.40SQ。柱顶6柱底柱顶5柱底柱顶4柱底柱顶6柱底柱顶5柱底柱顶4柱底柱顶3柱底柱顶2柱底柱顶1柱底柱号C柱D柱层号恒载效应活载效应组合效应恒载效应活载效应组合效应M-43.83-6.31-65.3559.187.4287.16N266.0017.40376.15192.9711.98272.25M-31.01-14.49-56.0641.7318.1874.15N299.0017.40428.80224.9711.98315.45V-22.68-6.30-36.7930.567.7648.86弯矩M -31.62-15.26-57.6437.1719.0968.89N596.31136.76939.04454.72106.36718.10M-41.12-12.27-67.5449.8814.4481.49N635.31136.76991.69493.72106.36770.75V-18.66-7.06-32.28*22.328.6038.56M-50.81-10.83-79.2157.4312.2389.52N1018.31224.061594.30761.17163.291187.60M-48.61-11.19-76.5954.8712.9886.79N1057.31224.061646.95800.17163.291240.25V-25.49-5.65-39.9528.796.4645.20M-48.61-11.19-76.5954.8712.9886.79N1439.83311.542249.081067.67220.281657.23M-48.32-11.13-76.1457.0312.8389.56N1478.83311.542301.731106.67220.281709.88V-24.85-5.72-39.1528.697.3945.97弯矩M -49.45-11.38-77.9159.0413.3192.75N1861.68398.992904.281373.82277.252126.36M-55.91-12.87-88.0966.3615.71104.98N1900.68398.992956.931412.82277.252179.01V-27.02-6.22-42.5732.157.4450.69弯矩M -29.42-6.86-46.4433.767.9753.39N2284.74486.663561.331679.63334.212595.03M-14.71-3.43-23.2216.863.9926.67N2336.74486.663631.531731.63334.212665.23V-8.49-1.98-13.409.732.3015.39注：组合工况为：S=1.35S+0.7×1.40S。G Q水平地震作用效应与竖向荷载作用效应的根本组合水平地震作用下的梁端及跨中内力的根本组合依据以上组合原则，水平地震作用下框架梁组合内力结果见表34及表35。内力及AB跨BC内力及AB跨BC跨CD跨其组合M MABz AByM M MAB中 BCz BCyM M M MBC中 CDz CDy CD中MG-81.74-51.5937.82-17.09-29.81-6.46-73.64-59.1860.58MQ-3.83-2.821.090.07-0.480.85-6.79-7.421.72M ±79.64±19.8±113.27±102.33±5.47±95.93±131.21±17.64E1-85.52-54.2058.43-17.39-30.68-2.95-78.92-64.5386.492-240.54-157.7484.17-164.64-163.704.16-203.63-235.10109.42371.3650.34130.20102.9847.68107.68MG-115.40-94.4767.41-31.69-22.622.64-85.25-78.9049.42MQ-21.58-19.0015.03-3.43-11.88-3.16-41.63-37.2731.18M ±117.75±14.18±125.60±128.60±1.50±120.56±152.55±15.99E1-129.81-107.02111.71-34.25-29.746.73-110.31-101.3998.562-319.75-260.09130.14-197.52-196.918.68-267.04-299.70119.35363.7449.10129.87138.6150.66100.77MG-81.50-38.3330.00-1.71-36.08-4.61-129.74-107.3186.46MQ-21.95-19.8314.43-4.82-8.14-0.86-31.23-26.6719.96M ±137.14±30.08±146.28±146.280±137.14±197.29±30.08E1-95.44-50.2258.38-4.45-41.37-2.06-149.85-124.42141.132-351.92-228.5097.48-194.61-231.53-2.06-328.13-380.90180.233164.00130.03186.04150.0132.92135.83MG-77.64-37.132.54-3.03-34.60-4.54-131.83-109.7484.20MQ-21.98-19.8314.41-4.81-8.50-1.03-30.89-25.9620.49M ±196.30±34.73±209.39±209.390±196.30±265.76±34.73E1-91.52-48.9760.95-5.79-40.06-2.08-151.80-126.50139.122-437.01-304.16106.10-278.00-312.27-2.08-406.99-471.98184.263256.85208.18266.77233.36107.92222.76MG-77.12-37.1932.76-2.92-34.31-4.34-132.09-107.785.09MQ-22.04-19.8614.37-4.77-8.44-0.98-30.94-26.1520.37M ±237.16±38.56±252.97±252.970±237.16±314.27±38.56E1-91.03-49.0861.16-5.65-39.73-1.85-152.09-124.52139.962-499.58-357.38111.28-334.52-368.59-1.85-460.40-533.08190.083320.41261.19323.56290.33160.75287.78MG-83.31-33.7731.37-4.35-41.48-8.65-126.8-100.1291.52MQ-21.15-18.9415.27-5.68-10.02-2.23-29.75-23.6722.21M ±268.09±46.31±285.96±285.960±268.09±360.70±46.31E1-96.84-45.0760.24-7.62-47.93-6.95-146.03-115.40147.552-565.76-393.59120.44-379.37-419.68-6.95-494.54-584.32207.753375.03305.28364.56325.26206.84356.96层号654321注：1.M、M、M分别为竖向恒荷载、竖向活荷载、水平地震作用下各掌握截面弯矩标准值。G Q E1M=1.20M+0.6M15%2：支座最大负弯矩及G Q1结果+1.3M3=1.3M-1.0M-0.5M。E E G Q表35 水平地震作用下的梁端剪力根本组合ABAB跨BC跨CD跨层号内力及其组合VABzVAByVBCzVBCyVCDzVCDyVG61.77-52.6316.48-20.3467.41-63.03V2.31-1.990.95-1.314.22-4.426QVE30.1330.1332.6732.6734.4234.42组合114.68-103.5262.82-67.67128.17-123.03VG98.08-91.7434.41-31.6773.21-71.29V5Q17.67-16.891.72-6.3235.22-33.90VE39.9839.9884.7384.7341.3841.38组合180.27-172.20152.47-151.95162.78-159.68VG53.71-40.6310.50-20.92114.81-97.53V17.64Q-16.964.52-6.7425.00-22.91VE50.6750.6797.5297.5250.6750.67组合140.88-124.80142.09-155.92218.64-196.65VG53.21-41.0310.93-20.49114.76-97.58V17.61-16.954.4-6.8625.06-22.973QVE70.0170.01139.59139.5970.0170.01组合165.43-150.42197.22-210.17243.76-221.89VG53.22-41.1210.95-20.47115.11-97.23V17.61-16.954.41-6.8525.04-22.952QVE83.5583.55168.65168.6583.5583.55组合183.05-168.13235.03-247.92261.77-239.06VG54.68-39.6610.08-21.34115.45-96.89V17.61-16.954.18-7.0825.031Q-22.94VE95.2795.27190.64190.6495.2795.27组合200.03-181.61262.44-277.69277.41-253.88注：1.V、V分别为竖向恒荷载、活荷载作用下各掌握截面剪力。G Q2.组合工况为：V=1.20(V+1.40V)+1.30V。G Q E2水平地震作用下的柱端内力的根本组合由于框架柱的纵向钢筋配筋梁与弯矩及轴力有关响，因此应同时组合弯矩轴力及剪力，以期得到同一组合工况下的内力。框架柱组合内力应取以下几种最不利组合。①Nmax②Nmin

M，V③Mmax

及相应的N，V

max

及相应的N，V36~39表36 A柱水平地震作用下的柱端内力根本组合层号

活载

组合④MM10.460.91119.24-141.91165.93168.11-144.10N149.377.71-30.13223.04114.06144.70192.39M-4.03-4.3464.21-90.9177.2776.03-89.67N182.377.71-30.13262.64147.06184.30225.396柱底

1.95

-1.04

55.59

-70.55

73.70

73.98

-70.84M柱顶2.43-5.5881.90-106.90106.11106.04-106.83N410.9862.10-70.11621.58350.89439.29533.175柱底M18.11-5.0970.01-72.34106.58109.69-75.45N449.9862.10-70.11668.38389.89486.09572.17

5.27

-2.74

38.18

-44.95

53.53

54.31

-45.73M柱顶30.21-5.20127.28-132.33193.07198.60-137.85N657.28116.42-120.781015.60558.48701.57872.504柱底M26.09-5.16104.14-107.17158.89163.59-111.87N696.28116.42-120.781062.40597.48748.37911.50

14.44

-2.66