【《某教学楼的建筑结构设计》18000字（论文）】

框架截面尺寸及线刚度计算2.1楼板厚度楼板采用现浇楼板，钢筋混凝土单向板跨厚比不大于30，双向板不大于40，且板的最小厚度应取80mm，故楼面板厚度取100mm，屋面板厚度为120mm。2.2梁截面尺寸主梁截面高度h为跨度的1/18~1/10，宽度b=(1/2~1/4)h；次梁截面高度h取梁跨度的1/18~1/12，宽度b=(1/2~1/4)h，对于该工程实例，选取eq\o\ac(○,3)号轴线对应一榀框架进行计算，则梁截面尺寸选取如下：AB梁：h=(1/18~1/10)×lAB=(1/18~1/10)×7500mm，取h=600mm；b=(1/4~1/2)×h=(1/4~1/2)×600mm，取b=250mm。纵梁：h=(1/18~1/10)×l=(1/18~1/10)×7800mm，取h=600mm；b=(1/4~1/2)×h=(1/4~1/2)×600mm，取b=250mm。AB梁：b×h=250mm×600mm纵梁：b×h=250mm×600mm次梁：b×h=250mm×550mm2.3柱截面尺寸柱截面尺寸可根据轴压比公式计算，根据《建筑抗震设计规范》（GB50011-2A柱：N=1.3×((7800/1000+7800/1000)/2×7500/1000/2)×14×5=2661.75kNA≥2661.75×1000/(0.85×14.3)=218983.96mm2B柱：N=1.25×((700/(0.85×14.3)=286363.64mm2D柱：N=1.3×((7800/1000+7800/1000)/2×7500/1000/2)×14×5=2661.75kNA≥2661.75×1000/(0.85×14.3)=218983.96mm2截面形式采（GB50011-2010）6.3.5规定柱截面尺寸，四级抗震时或楼层层数不超过2层时不宜小于300mm，ABCD柱尺寸保持一致，同时为满足规范中上下层侧向刚度剪切破坏。高最低为3600mm，H/h=3600/650=5.538461538，满足要求。2.4计算框架及计算单元取eq\o\ac(○,3)号轴为一榀框架。图2.1计算框架简图根据建筑设计资料，首层柱高应为楼层高度3600mm、室内外高差450mm以及基础顶到重力荷载计算部分如图2.2虚线区域所示，即是框架与框架之间的一半。图2.2计算单元简图3重力荷载计算3.1屋面荷载表3.1屋面做法及恒载计算名称做法厚度(mm)容重(kN/m3)荷载(kN/m2)防水层4厚SBS改性沥青防水4110.044找平层1:3水泥沙浆找平20200.40找坡层40厚水泥炉渣找坡40140.56隔热层40厚挤塑聚苯板400.50.02结构层现浇钢筋混凝土板120253.00抹灰层水泥砂浆板底抹灰10200.20合计4.2243.2楼面荷载表3.2楼面做法及恒载计算名称做法厚度(mm)容重(kN/m3)荷载(kN/m2)面层水磨石地面10mm面层0.65水磨石地面20mm水泥砂浆打底找平层10厚水泥砂浆找平10200.20结构层现浇钢筋混凝土板100252.50抹灰层水泥砂浆板底抹灰10200.20合计3.553.3墙体荷载女墙墙体宽度为200mm，墙体材料选用粉煤灰加气混凝土砌块（5.5kN/m3），并进行20mm厚混合砂浆粉刷。在计算过程中，不考虑门窗自重，将墙体当作为未开门洞的整墙进行计算，通过下列计算方式可得墙体的线荷载大小，以外墙为例：标准层墙体线荷载计算：墙体线荷载=砌块容重×(标准层层高-梁高)×墙体宽度×墙体单位长度+砂浆容5×(3.6-0.6)×0.2×1+20×0.02×(3.6-0.6)×1×2=5.700kN/m。底层墙体线荷载计算：墙体线荷厚度×(底层层高-梁高)×墙体单位长度×粉刷次数；即：5.5×(3.6-0.6)×0.2×1+20×0.02×(3.6-0.6)×1×2=5.700kN/m。女儿墙：×粉刷×0.3×0.2×1+20×0.02×0.3×1×2=0.57kN/m。3.4梁、柱自重标准层梁柱侧面同样进行20mm厚混合砂浆粉刷。AB梁线荷载计算：梁自荷载计算：梁自重=梁宽度×(梁高度-板厚度)×梁单位长度×容重×容重BC梁线荷载=0.25×(0.40-0.10)×25+0.02×[(0.40-0.10)×2+0.25]×20=2.215kN/mCD梁线荷载计算：梁自重=梁宽度×(梁高度-板厚度)×梁单位长度×容重粉刷层自框架=梁宽度×(梁高度-板厚度)×梁单位长度×容重粉刷层自重框架梁线荷载=梁自重+粉刷层自重纵梁线荷载=0.25×(0.60-0.10)×25+0.02×[(0.60-0.10)×2+0.25]×20=3.625kN/m柱线荷载计算：荷载=柱自重+粉刷层自重柱线荷载=0.65×0.65×25+0.02×0.65×4×20=11.603kN/m其余各层柱线×0.50×25+0.02×0.50×4×20=7.050kN/m3.5活荷载取值屋面活荷载0.5kN/m2，楼面活载为2.5kN/m2、3.5kN/m2。3.6雪荷载标准值屋面雪荷载标准值可按照下式进行计算：sk—雪荷载标准值（kN/m2）；μr—屋面积压（kN/m2）；sk=μr×s0=1.0×0.4=0.4kN/m2雪荷载与屋面活荷载不同时考虑，取二者较大值4侧移刚度的计算在计算水平荷载作用时，通常采用D值法进行计算，D值法又被称为改进后的反弯点法，是对框架如下表所示。表4.1节点转动影响系数αc和K计算公式楼层简图Kαc一般层底层D值法中，柱的抗侧移刚度为：根据上述计算方法，可对每一层不同柱的抗侧移刚度进行计算。第一层：A柱：K=(3.602)/(0.742+2)=0.453D=0.453×12×8.84×10^10/(5050)^2=18843N/mmC柱：K=(2.96×10^)/(0.742+2)=0.453D=0.453×1K=(0+3.60×10^10)/8.84×10^10=0.407α0.377×12×8.84×10^10/(5050)^2=15682N/mm表4.2框架柱侧移刚度计算表格层数类别Ec(N/mm2)柱宽b

(mm×mm)柱长h

(mm×mm)I0(mm4)hc(mm)EcIc/l*10^10

(N·mm)1A柱300006506501.488E+1050508.84B柱300006506501.488E+1050508.84C柱300006506501.488E+1050508.84D柱300006506501.488E+1050508.842A柱300005005005.208E+0936004.34B柱300005005005.208E+0936004.34C柱300005005005.208E+0936004.34ΣD1=DA+DB+DC+DD=15682+18843+18843+15682=69050N/mm取eq\o\ac(○,3)号轴分析，计算一榀框架的侧移刚度总和：表4.3横向框架层间侧移刚度ΣDi楼层12345ΣDi(N/mm)6905058188581885818858188Di/Di+11.191.001.001.00/5水平荷载计算5.1风荷载计算5.1.1荷载计算根据《建筑结构荷载规范》（GB5009-2012）8.1，垂直于建筑物表面上的风荷载标准值，应按下式确定，其中w0=0.45kN/m2，地面粗糙度为B类。为简化计算，通常将外墙面的风荷载以集中力的形式等效加在楼面处。需要注意的是，底层高度Hi是底层层高与室内外高差之和，μz的计算则是通过GB50009-2012建筑结构荷载规范中表8.2.1进行线性插值计算，hi以及hj则是以每一层楼板处位置作为参照的上下柱高，如图5.1所示。图5.1上下层柱高示意图计算如下表所示：5.2.3水平地震作用下层间位移验算水平地震作用下各层层间弹性位移角6竖向荷载作用下框架结构内力计算6.1横向框架计算简图板传至梁上的三角形或梯形荷载等效为均布荷载，荷载的传递示意图如图所示。图6.1荷载传递示意图按弹性理论设计计算梁的支座弯矩时，可按支座弯矩等效的原则，按下式将三角形荷载和梯形荷载等效为均布荷载pe：三角形荷载作用：梯形荷载作用：其中：g，q—分别为板面的均布恒荷载以及均布活荷载；l01，l02—分别为短跨、长跨的计算跨度。AB跨左板梯形荷载转换系数：α1=0./7.5=0.26BC跨左板梯形荷换系数：α1=0.5×3.9/7.5=0.26CD跨板梯形荷载转换系数：α1=0.5×3.9/7.5=0.26由第三章计算可知：表6.1荷载统计类型恒载活载墙体自重梁自重屋面楼面屋面办公室走廊标准层女儿墙AB跨BC跨CD跨荷载(kN/m2)4.2243.550.52.53.55.70.573.6252.2153.6256.1.1框架梁荷载计算AB跨梁荷载计算首先判断AB递给梁的荷载：恒载：4.224×(1-2×0.26^2+0.26^3)×3.9/2+-2×0.26^2+0.26^3)×3.9/2=14.54kN/m.26^2+0.26^3)×3.9/2=1.72kN/m（2）楼面板传递给梁的荷载：恒载：3.55×(1-2×0.26^2+0.26^3)×3.9/2+3.55×(1-2×0.26^2+0.26^3)×3.9/2=12.22kN/m9/2+2.5×(1-2×0.26^2+0.26^3)×3.9/2=8.6kN/mAB跨梁自重标准值：3.625kN/m；AB跨墙体自重标准值：5.7kN/m故AB跨梁均布荷载为：（3）屋面梁：恒载=AB跨递的荷载=1.72kN/m（4）楼面梁：恒载=AB跨梁递的荷载=8.6kN/mBC跨梁荷载计算首先判断BC跨板是否为双向板：l02/l01=7.8/2.7=2.89<3，为双向板（1）屋面板传递给梁的荷载：板为双向板，根据弹塑性分析可取折减系数取5/8恒载：4.224×5/8×2.7/2+4.224×5/8×2.7/2=7.12kN/m活载：0.5×5/8×2.7/2+0.5×5/8×2.7/2=1.28kN/m（2）楼面板传递给梁的荷载：恒载：3.重标准值：2.215kN/m；（3）屋面梁：恒载=BC：恒载=BC跨梁自重+楼面板传递的荷载=2.215+5.99+0=8.21kN/m活载=楼面板1.92<3，为双向板（1）屋面板传递给梁的荷载：恒载：4.224×(1-2×0.26^2+0.26^3)×3.9/2+4.224×(1-2×0.26^2+0.26^3)×3.9/2=14.54kN/m活载：0.5×(1-2×0.26^2+0.26^3)×3.9/2+0.5×(1-2×0.26^2+0.26^3)×3.9/2=1.72kN/m（2）楼面(1-2×0.26^2+0.26^3)×3.9/2+2.5×(1-2×0.26^2+0.26^3)×3.9/2=8.6kN/mCD跨梁自重标3.625kN/m；CD跨墙体自重标准值：5.7kN/m故CD跨梁均布荷载为：（3）屋面梁：恒载=CD跨梁自重+屋面板传递的荷载=3.625+14.54=18.17kN/m活载=屋面板传递的荷载=1.72kN/m（4）楼面梁：恒载=CD跨梁自重+楼面板传递的荷载+CD跨墙体自重=3.625+12.22+5.7=21.55kN/m活载=楼面板传递的荷载=8.6kN/m6.1.2柱集中荷载计算在计算出每一跨的均布荷载之后，还需要对每一个柱的集中荷载进行计算。A柱集.57×3.9+3.625×3.9+3.625×3.9+3.625×7.5/2+14.54×7.5/2+4.224×5/8×3.9/2×3.9+4.224×5/8×3.9/2×3.9+3.2725×7.5/4+3.2725×7.5/4=153.27kN梁柱偏心弯矩：M=0×153.27=0kN·m活载=AB跨板传5/8×3.9/2×3.9+0.5×5/8×3.9/2×3.9=11.20kN梁柱偏心弯矩：M=0×11.2=0kN·m（2）标准层柱：恒载=墙体：M=0×199.55=0kN·m活载=AB跨板传递的梯形荷载+AB跨板传递的三角形荷载=8.6×7.5/2+2.5×5/8×3.9/2×3.9+2.5×5/8×3.9/2×3.9=56.02kN梁柱偏心弯矩：M=0×56.02=0kN·mB柱集中荷载计算：（1）顶层柱：恒载=纵梁自重+AB梁自重+BC梁自重+AB跨板传递的梯形荷载+AB跨板传递的三角形5×3.9+3.625×3.9+3.625×7.5/2+2.215×2.7/2+0+0+14.54×7.5/2+4.224×5/8×3.9/2×3.9+4.224×5/8×3.9/2×3..9+7.12×2.7/2+3.2725×0/4+3.2725×7.5/4+3.2725×0/4+3.2725×7.5/4=203.55kN梁柱偏跨板传递的梯形荷载+AB跨板传递的三角形荷载+BC跨板传递的梯形荷载+BC跨板传递的三角形荷载=1.72×7.5/2+0.5×5/8×3.9/2×3.9+0.5×5/8×3.9/2×3.9+0.5×(1-2×0.17^2+0.17^3)×2.7/2×3.9+0.5×(1-2×0.17^217.92=0kN·m（2）标准层柱：恒载=纵梁自重+AB梁自重+BC梁自重+AB跨墙体自重+墙体自重+AB跨板传递的梯形荷载+AB跨板传递的三角形荷载+BC跨板传递的梯形荷载+BC跨板传递的三角形荷载+次×5/8×3.9/2×3.9+3.55×5/8×3.9/2×3.9+3.55×(1-2×0.17^2+0.17^3)×2.7/2×3.9+3.55×(1-2×0.17^2+0.17^3)×2.7/2×3.9+5.99×2.7/2+3.2725×0/4+3.2725×7.5/4+3.2725×0/4+3.2725×7.5/4=246.03kN梁柱偏心弯矩：M=0×246.03=0kN·m活载=AB跨板传递的梯形荷载+AB跨板传递的三角形荷载+BC跨板传递的梯形荷载+BC跨板传递的三角形荷载=8.6×7.5/2+2.5×5/8×3.9/2×3.9+2.5×5/8×3.9/2×3.9+3.5×(1-2×0.17^2+0.17^3)×2.7/2×3.9+3.5×(1-2×0.17^2+0.17^3)×2.7/2×3.9+5.91×2.7/2=98.90kN梁柱偏心弯矩：M=0×98.9=0kN·mC柱集中荷载计算：（1）顶层柱：恒载=纵梁自重+CD梁自重+BC梁自重+CD跨板传递的梯形荷载+BC跨板传递的梯形荷载+CD跨板传递的三角形荷载++BC跨板传递的三角形荷载+次梁自重=3.625×3.9+3.6259+4.224×(1-2×0.17^2+0.17^3)×2.7/2×3.9+4.224×5/8×3.9/2×3.9+4.224×5/8×3.9/2×3.9+7.12×2.7/2+3.2725×7.5/4+3.2725×0/4+3.2725×7.5/4+3.2725×0/4=203.55kN梁柱偏心弯矩：M=0×203.55=0kN·m活载=CD跨板传递的梯形荷载+BC跨板传递的梯形荷载+CD跨板传递的三角形荷载+BC跨板传递的三角形荷载=1.72×7.5/2+0.5×(1-2.9+0.5×5/8×3.9/2×3.9+1.28×2.7/2=17.92kN梁柱偏心弯矩：M=0×17.92=0kN·m（2）标准层柱：恒载=纵梁自重+CD梁自重+BC梁自重+CD跨墙体自重+墙体自重+CD跨板传递的梯形荷载+CD跨板传递的三角形荷载+BC跨板传递的梯形荷载+BC跨板传递的三角形荷载+次梁自重=3.625×3.9+3.625×3.9+3.625×7.5/2+2.215×2.7/2+5.7×7.5/2+5.7×3.9+5.7×3.9+12.22×7.5/2+3.55×(1-2×0.17^2+0.17^3)×2.7/2×3.9+3.55×(1-2×0.17^2+0.17^3)×2.7/2×3.9+3.55+3.2725×7.5/4+3.2725×0/4=246.03kN梁柱偏心弯矩：M=0×246.03=0kN·m活载=CD跨板传递的梯形荷载+BC跨板传递的梯形荷载+CD跨板传递的三角形荷载+BC跨板传递的三角形荷载=8.6×7.5/2+3.5×(1-2×0.17^2+0.17^3)×2.7/2×3.9+3.5×(1-2×0.17^2+0.17^3)×2.7/2×3.9+2.5×5/8×3.9/2×3.9+2.5×5/8×3.9/2×3.9+5.91×2.7/2=98.90kN梁柱偏心弯矩：M=0×98.9=0kN·mD柱集中荷载计算：（1）顶层柱：恒载=女儿墙自重+纵梁自重+CD梁自重+CD跨板传递的梯形荷载+CD跨板传递的三角形荷载+次梁自重=0.57×3.9+0.57×3.9+3.625×3.9+3.625×3.9+3.625×7.5/2+14.54×7.5/2+4.224×5/8×3.9/2×3.9+4.224×5M=0×153.27=0kN·m活载=AB跨板传递的梯形荷载+AB跨板传递的三角形荷载=1.72×7.5/2+0.5×5/8×3.9/2×3.9+0.5×5/8×3.9/2×3.9=11.20kN梁柱偏心弯矩：M=0×11.2=0kN·m（2）标准层柱：恒载=墙体自重次梁自重=5.7×3.9+5.7×3.9+3.625×3.9+3.625×3.9+3.625×7.5/2+12.22×7.5/2+3.55×5/8×3.9/2×3.9+3.55×5/8×3.9/2×3.9+3.2725×7.5/4+3.2725×7.5/4=199.55kN梁柱偏心弯矩：M=0×199.55=0kN·m活载=CD跨板传递的梯形荷载+CD跨板传递的三角形荷载=8.6×7.5/2+2.5×5/8×3.9/2×3.9+2.5×5/8×3.9/2×3.9=56.02kN梁柱偏心弯矩：M=0×56.02=0kN·m6.2弯矩分配系数计算根据梁、柱的线刚度计算各个节点杆件的弯矩分配系数，各节点分配系数按下式进行计算：图6.2弯矩分配系数计算简图其余弯矩分配系数计算下表所示：表6.2弯矩分配系数计算楼层节点线刚度ib×10^10(N·mm)∑ib分配系数μi左梁右梁上柱下柱左梁右梁上柱下柱C柱2.963.64.344.3415.240.1940.2360.2850.285D柱3.604.344.3412.280.29300.3530.3532A柱03.64.344.3412.2800.2930.3530.353B柱3.62.964.344.3415.240.2360.1940.2850.285C柱2.963.64.344.3415.240.1940.2360.2850.285D柱3.604.344.3412.280.29300.3530.3531A柱03.64.348.8416.7800.2150.2590.527B柱3.62.964.348.8419.740.1820.150.220.448C柱2.963.64.348.8419.740.150.1820.220.448D柱3.604.348.8416.780.21500.2590.5276.3恒载杆端弯矩计算梁固端弯矩计算如下式所示：（以顺时针为正）表6.3恒载作用梁固端弯矩计算楼层均布荷载q（kN/m）跨度l（m）AB跨BC跨CD跨AB跨BC跨CD跨AB跨BC跨CD跨Mb左Mb右Mb左Mb右Mb左Mb右518.179.3418.177.52.77.5-85.1785.17-5.675.67-85.1785.17421.558.2121.557.52.77.5-101.02101.02-4.994.99-101.02101.02221.558.2121.557.52.77.5-101.02101.02-4.994.99-101.02101.02121.558.2121.557.52.77.5-101.02101.02-4.994.99-101.02101.026.4恒载下弯矩分配计算弯矩二次分配计算要点分为四步：第一步：将各节点的不平衡弯矩进行第一次分配；其余层弯矩二次分配具体过程及结果如下0.0000.5470.4530.33000.3980.2720.27200.3980.3300.45300.54750.00-85.1785.170.00-5.675.670.00-85.1785.170.000.0046.5938.58-26.240.00-31.64-21.6221.620.0031.6426.24-38.580.00-46.590.0017.83-13.1219.290.00-13.6810.81-10.810.0013.68-19.2913.120.00-17.830.00-2.58-2.13-5.420.00-6.53-4.474.470.006.535.422.130.002.580.0061.84-61.8472.810.00-51.86-20.9520.950.0051.86-72.8161.840.00-61.840.3530.3530.2930.2360.2850.2850.1940.1940.2850.2850.2360.2930.3530.35340.00-101.02101.020.00-4.994.990.00-101.02101.020.0035.6635.6629.60-22.66-27.37-27.37-18.6318.6327.3727.3722.66-29.60-35.66-35.6623.2917.83-11.3314.80-15.82-13.689.31-9.3115.8213.68-14.8011.33-23.29-17.83-10.52-10.52-8.731.271.541.541.05-1.05-1.54-1.54-1.278.7310.5210.5248.4442.97-91.4894.43-41.65-39.52-13.2613.2641.6539.52-94.4391.48-48.44-42.970.3530.3530.2930.2360.2850.2850.1940.1940.2850.2850.2360.2930.3530.35330.00-101.02101.020.00-4.994.990.00-101.02101.020.0035.6635.6629.60-22.66-27.37-27.37-18.6318.6327.3727.3722.66-29.60-35.66-35.6617.8317.83-11.3314.80-13.68-13.689.31-9.3113.6813.68-14.8011.33-17.83-17.83-8.59-8.59-7.130.770.930.930.63-0.63-0.93-0.93-0.777.138.598.5944.9044.90-89.8893.92-40.13-40.13-13.6713.6740.1340.13-93.9289.88-44.90-44.900.3530.3530.2930.2360.2850.2850.1940.1940.2850.2850.2360.2930.3530.353-6.91-6.91-5.740.030.040.040.03-0.03-0.04-0.04-0.035.746.916.9146.5841.83-88.4993.19-41.01-37.89-14.2814.2841.0137.89-93.1988.49-46.58-41.830.2590.5270.2150.1820.220.4480.1500.1500.220.4480.1820.2150.2590.52710.00-101.02101.020.00-4.994.990.00-101.02101.020.0026.1653.2421.72-17.48-21.13-43.02-14.4014.4021.1343.0217.48-21.72-26.16-53.2417.830.00-8.7410.86-13.680.007.20-7.2013.680.00-10.868.74-17.830.00-2.35-4.79-1.95-0.80-0.96-1.96-0.660.660.961.960.801.952.354.7941.6448.45-89.9993.61-35.77-44.98-12.8512.8535.7744.98-93.6189.99-41.64-48.4524.22-22.4922.49-24.226.5恒载跨中弯矩计算在实际分布荷载的作用下，框架梁跨中弯矩按下面的式子计算：表6.4跨中弯矩计算楼层均布荷载q（kN/m）跨度l（m）AB跨BC跨CD跨AB跨BC跨CD跨AB跨BC跨CD跨518.179.3418.177.52.77.560.43-12.4460.43221.558.2121.557.52.77.560.68-6.860.68121.558.2121.557.52.77.559.72-5.3759.726.6恒载柱端剪力计算图6.3受力分析图因此柱端剪力可按下式进行计算：表6.5柱端剪力计算楼层类别柱高柱端弯矩柱端剪力上下上下5A3.6061.8448.4430.6330.63B3.60-51.86-41.6525.9825.98C3.6051.8641.6525.9825.98D3.60-61.84-48.4430.6330.634A3.6042.9744.9024.4124.41B3.60-39.52-40.1322.1222.12C3.6039.5240.1322.1222.12D3.60-42.97-44.9024.4124.413A3.6044.9046.5825.4125.41B3.60-40.13-41.0122.5422.54C3.6040.1341.0122.5422.54D3.60-44.90-46.5825.4125.411A5.0548.4524.2214.3914.39B5.05-44.98-22.4913.3613.36C5.0544.9822.4913.3613.36D5.05-48.45-24.2214.3914.396.7恒载梁端内力计算计算梁端剪力梁平衡受力及柱轴力图如下：图6.4梁平衡受力图由梁的平衡条件，梁端剪力按下列公式求得：表6.6梁端剪力计算楼层均布荷载q（kN/m）跨度l（m）AB跨BC跨CD跨AB跨BC跨CD跨AB跨BC跨CD跨Vb左Vb右Vb左Vb右Vb左Vb右321.558.2121.557.502.707.5080.2781.3511.0811.0881.3580.27221.558.2121.557.502.707.5080.1981.4411.0811.0881.4480.19121.558.2121.557.502.707.5080.3381.2911.0811.0881.2980.33柱轴力按下列公式计算：表6.7竖向恒载作用下A柱轴力计算楼层柱高柱荷载（kN/m）集中荷载P柱自重GVb左Vb右Nc（kN）2上部3.607.05199.550.000.0080.191135.62下部25.380.000.001161.001上部5.0511.60199.550.000.0080.331440.88下部58.590.000.001499.47表6.8竖向恒载作用下B柱轴力计算楼层柱高柱荷载（kN/m）集中荷载P柱自重GVb左Vb右Nc（kN）2上部3.607.05246.030.0081.4411.081377.23下部25.380.000.001402.611上部5.0511.60246.030.0081.2911.081741.01下部58.590.000.001799.60表6.9竖向恒载作用下C柱轴力计算楼层柱高柱荷载（kN/m）集中荷载P柱自重GVb左Vb右Nc（kN）5上部3.607.05203.550.0012.6169.60285.76下部25.380.000.00311.144上部3.607.05246.030.0011.0881.21649.46下部25.380.000.00674.843上部3.607.05246.030.0011.0881.351013.30下部25.380.000.001038.682上部3.607.05246.030.0011.0881.441377.23下部25.380.000.001402.611上部5.0511.60246.030.0011.0881.291741.01下部58.590.000.001799.60表6.10竖向恒载作用下D柱轴力计算楼层柱高柱荷载（kN/m）集中荷载P柱自重GVb左Vb右Nc（kN）5上部3.607.05153.270.0066.680.00219.95下部25.380.000.00245.334上部3.607.05199.550.0080.420.00525.30下部25.380.000.00550.68内力图绘制：a)弯矩图b)剪力图c)轴力图图6.5内力图6.8活载杆端弯矩计算活载的计算与恒载完全一致，梁固端弯矩计算如下式所示：（以顺时针为正）表6.11活载作用梁固端弯矩计算楼层均布荷载q（kN/m）跨度l（m）AB跨BC跨CD跨AB跨BC跨CD跨AB跨BC跨CD跨Mb左Mb右Mb左Mb右Mb左Mb右51.721.281.727.52.77.5-8.068.06-0.780.78-8.068.0648.65.918.67.52.77.5-40.3140.31-3.593.59-40.3140.3138.65.918.67.52.77.5-40.3140.31-3.593.59-40.3140.3128.65.918.67.52.77.5-40.3140.31-3.593.59-40.3140.3118.65.918.67.52.77.5-40.3140.31-3.593.59-40.3140.316.9活载下弯矩分配计算活载弯矩二次分配计算与恒载完全一致，同样分为四步：第一步：将各节点的不平衡弯矩进行第一次分配；第二步：将分配后的弯矩向远端传送，传递系数均为0.5；第三步：第一次分配弯矩传递后的弯矩，再进行第二次弯矩分配，分配结果不再传递；第四步：将各杆端的所有杆端弯矩叠加即为各杆端的最后弯矩。上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱0.0000.5470.4530.33000.3980.2720.27200.3980.3300.45300.54750.00-8.068.060.00-0.780.780.00-8.068.060.000.004.413.65-2.400.00-2.90-1.981.980.002.902.40-3.650.00-4.410.007.11-1.201.830.00-5.230.99-0.990.005.23-1.831.200.00-7.110.00-3.23-2.680.800.000.960.66-0.660.00-0.96-0.802.680.003.230.008.29-8.298.280.00-7.17-1.111.110.007.17-8.288.290.00-8.290.3530.3530.2930.2360.2850.2850.1940.1940.2850.2850.2360.2930.3530.3530.3530.3530.2930.2360.2850.2850.1940.1940.2850.2850.2360.2930.3530.35330.00-40.3140.310.00-3.593.590.00-40.3140.310.0014.2314.2311.81-8.67-10.47-10.47-7.127.1210.4710.478.67-11.81-14.23-14.237.117.11-4.335.91-5.23-5.233.56-3.565.235.23-5.914.33-7.11-7.11-3.49-3.49-2.900.240.280.280.19-0.19-0.28-0.28-0.242.903.493.4917.8517.85-35.7337.79-15.41-15.41-6.966.9615.4115.41-37.7935.73-17.85-17.850.3530.3530.2930.2360.2850.2850.1940.1940.2850.2850.2360.2930.3530.35320.00-40.3140.310.00-3.593.590.00-40.3140.310.0014.2314.2311.81-8.67-10.47-10.47-7.127.1210.4710.478.67-11.81-14.23-14.237.115.22-4.335.91-5.23-4.043.56-3.565.234.04-5.914.33-7.11-5.22-2.82-2.82-2.34-0.05-0.06-0.06-0.040.040.060.060.052.342.822.8218.5216.62-35.1837.50-15.75-14.56-7.197.1915.7514.56-37.5035.18-18.52-16.620.2590.5270.2150.1820.220.4480.1500.1500.220.4480.1820.2150.2590.52710.00-40.3140.310.00-3.593.590.00-40.3140.310.0010.4421.248.67-6.68-8.08-16.45-5.515.518.0816.456.68-8.67-10.44-21.247.110.00-3.344.33-5.230.002.75-2.755.230.00-4.333.34-7.110.00-0.98-1.99-0.81-0.34-0.41-0.83-0.280.280.410.830.340.810.981.9916.5819.25-35.8037.62-13.72-17.28-6.626.6213.7217.28-37.6235.80-16.58-19.259.63-8.648.64-9.636.10活载跨中弯矩计算在实际分布荷载的作用下，框架梁跨中弯矩按下面的式子计算：表6.12跨中弯矩计算楼层均布荷载q（kN/m）跨度l（m）AB跨BC跨CD跨AB跨BC跨CD跨AB跨BC跨CD跨51.721.281.727.52.77.53.810.053.8148.65.918.67.52.77.524.88-2.3124.8838.65.918.67.52.77.523.71-1.5723.7128.65.918.67.52.77.524.13-1.824.1318.65.918.67.52.77.523.76-1.2423.766.11活载柱端剪力计算图6.6受力分析图因此柱端剪力可按下式进行计算：表6.13柱端剪力计算楼层类别柱高柱端弯矩柱端剪力上下上下5A3.608.2914.676.386.38B3.60-7.17-12.715.525.52C3.607.1712.715.525.52D3.60-8.29-14.676.386.384A3.6019.5817.8510.4010.40B3.60-16.49-15.418.868.86C3.6016.4915.418.868.86D3.60-19.58-17.8510.4010.403A3.6017.8518.5210.1010.10B3.60-15.41-15.758.668.66C3.6015.4115.758.668.66D3.60-17.85-18.5210.1010.102A3.6016.6216.589.229.22B3.60-14.56-13.727.867.86C3.6014.5613.727.867.86D3.60-16.62-16.589.229.221A5.0519.259.635.725.72B5.05-17.28-8.645.135.13C5.0517.288.645.135.13D5.05-19.25-9.635.725.726.12活载梁端内力计算计算梁端剪力梁平衡受力及柱轴力图如下：图6.7梁平衡受力图由梁的平衡条件，梁端剪力按下列公式求得：柱轴力按下列公式计算：表6.14梁端剪力计算楼层均布荷载q（kN/m）跨度l（m）AB跨BC跨CD跨AB跨BC跨CD跨AB跨BC跨CD跨Vb左Vb右Vb左Vb右Vb左Vb右51.721.281.727.502.707.506.456.451.731.736.456.4548.605.918.607.502.707.5031.9032.607.987.9832.6031.9038.605.918.607.502.707.5031.9832.527.987.9832.5231.9828.605.918.607.502.707.5031.9432.567.987.9832.5631.9418.605.918.607.502.707.5032.0132.497.987.9832.4932.01a)弯矩图b)剪力图c)轴力图图6.8内力图7横向框架内力组合7.1横向构件内力调幅前文计算所得内力是构件轴线处的内力，在内力组合时应将各种荷载作用下梁柱轴线的弯矩值换算到梁柱边缘处，再进行内力组合。梁支座边缘处的弯矩为：剪力计算值也应按支座边缘处计算：在竖向作用下，可考虑框架梁梁端塑性变形内力重分布对梁端负弯矩乘以调幅系数进行调幅，装配调幅：梁跨中弯矩调幅：7.2梁的内力组合计算框架结构在恒荷载、活荷载、风荷载以及地震荷载作用下的内力求出后，要计算框架梁柱各控制截面上可能发生的最不利内力==，本工程的内力组合形式按如下计算：（1）一般荷载组合1.3恒荷载+1.5×活荷载1.3恒荷载+1.5×(活荷载-0.6右风)1.3恒荷载+1.5×(0.7活荷载+左风)1.3恒荷载+1.5×(0.7活荷载-右风)（2）考虑地震作用效应组合1.2重力载-1.3右震表7.2框架梁内力组合（一般组合）楼层截面

位置内力恒载活载风1.3恒+1.5×活1.3恒+1.5×(活+0.6风)1.3恒+1.5×(0.7活+风)|M|max及对应VMmin及对应V|V|max及对应M左风右风左风右风V(kN)65.066.02-1.3393.6092.4194.8088.9092.8994.8094.8094.80CD跨中M(kN·m)70.535.05-0.7899.2798.5699.9795.8298.1699.9795.82D支座M(kN·m)-38.39-5.67-5.42-58.43-63.30-53.55-64.00-47.75-64.00-64.00-63.30V(kN)-62.14-6.02-1.33-89.81-91.01-88.61-89.09-85.10-89.09-89.09-91.014A支座M(kN·m)-60.67-22.3714.75-112.43-99.16-125.70-80.24-124.48-125.70-125.70-125.70V(kN)75.0329.75-3.78142.17138.77145.57123.11134.45145.57145.57145.57AB跨中M(kN·m)72.5130.221.53139.60140.97138.22128.29123.70140.97123.70B支座左M(kN·m)-63.01-24.43-11.69-118.56-129.07-108.04-125.09-90.03-129.07-129.07-129.07V(kN)-75.82-30.45-3.78-144.24-147.65-140.84-136.21-124.87-147.65-147.65-147.65B支座右M(kN·m)-8.92-4.848.47-18.85-11.24-26.47-3.98-29.37-29.37-29.37-29.37V(kN)5.695.83-7.7016.159.2223.081.9725.0725.0725.0725.07BC跨中M(kN·m)-3.79-1.160.00-6.66-6.66-6.66-6.14-6.14-6.66-6.66C支座左M(kN·m)-8.92-4.84-8.47-18.85-26.47-11.24-29.37-3.98-29.37-29.37-29.37V(kN)-5.69-5.83-7.70-16.15-23.08-9.22-25.07-1.97-25.07-25.07-25.07C支座右M(kN·m)-63.01-24.4311.69-118.56-108.04-129.07-90.03-125.09-129.07-129.07-129.07V(kN)75.8230.45-3.78144.24140.84147.65124.87136.21147.65147.65147.65CD跨中M(kN·m)72.5130.22-1.53139.60138.22140.97123.70128.29140.97123.70D支座M(kN·m)-60.67-22.37-14.75-112.43-125.70-99.16-124.48-80.24-125.70-125.70-125.70V(kN)-75.03-29.75-3.78-142.17-145.57-138.77-134.45-123.11-145.57-145.57-145.573A支座M(kN·m)-59.34-23.5825.81-112.51-89.28-135.74-63.18-140.62-140.62-140.62-135.74V(kN)74.8829.83-6.59142.09136.16148.02118.78138.55138.55138.55148.02AB跨中M(kN·m)73.4129.222.77139.26141.76136.77130.27121.96141.76121.96B支座左M(kN·m)-62.55-25.21-20.28-119.12-137.38-100.87-138.20-77.36-138.20-138.20-137.38V(kN)-75.96-30.37-6.59-144.31-150.24-138.38-140.52-120.75-140.52-140.52-150.24B支座右M(kN·m)-9.27-4.2214.70-18.38-5.15-31.615.57-38.53-38.53-38.53-38.53V(kN)5.695.83-13.3616.154.1228.17-6.5233.5633.5633.5633.56BC跨中M(kN·m)-4.14-0.530.00-6.17-6.17-6.17-5.93-5.93-6.17-6.17C支座左M(kN·m)-9.27-4.22-14.70-18.38-31.61-5.15-38.535.57-38.53-38.53-38.53V(kN)-5.69-5.83-13.36-16.15-28.17-4.12-33.566.52-33.56-33.56-33.56C支座右M(kN·m)-62.55-25.2120.28-119.12-100.87-137.38-77.36-138.20-138.20-138.20-137.38V(kN)75.9630.37-6.59144.31138.38150.24120.75140.52140.52140.52150.24CD跨中M(kN·m)73.4129.22-2.77139.26136.77141.76121.96130.27141.76121.96D支座M(kN·m)-59.34-23.58-25.81-112.51-135.74-89.28-140.62-63.18-140.62-140.62-135.74V(kN)-74.88-29.83-6.59-142.09-148.02-136.16-138.55-118.78-138.55-138.55-148.022A支座M(kN·m)-58.18-23.1140.43-110.30-73.91-146.68-39.26-160.54-160.54-160.54-146.68V(kN)74.8029.79-10.29141.93132.67151.19113.09143.96143.96143.96151.19AB跨中M(kN·m)74.3129.584.40140.97144.93137.01134.26121.06144.93121.06B支座左M(kN·m)-61.90-24.96-31.64-117.91-146.39-89.44-154.14-59.23-154.14-154.14-146.39V(kN)-76.05-30.41-10.29-144.48-153.74-135.22-146.23-115.36-146.23-146.23-153.74B支座右M(kN·m)-9.78-4.4222.91-19.341.28-39.9617.01-51.72-51.72-51.72-51.72V(kN)5.695.83-20.8316.15-2.6034.89-17.7244.7744.7744.7744.77BC跨中M(kN·m)-4.66-0.720.00-7.14-7.14-7.14-6.81-6.81-7.14-7.14C支座左M(kN·m)-9.78-4.42-22.91-19.34-39.961.28-51.7217.01-51.72-51.72-51.72V(kN)-5.69-5.83-20.83-16.15-34.892.60-44.7717.72-44.77-44.77-44.77C支座右M(kN·m)-61.90-24.9631.64-117.91-89.44-146.39-59.23-154.14-154.14-154.14-146.39V(kN)76.0530.41-10.29144.48135.22153.74115.36146.23146.23146.23153.74CD跨中M(kN·m)74.3129.58-4.40140.97137.01144.93121.06134.26144.93121.06D支座M(kN·m)-58.18-23.11-40.43-110.30-146.68-73.91-160.54-39.26-160.54-160.54-146.68V(kN)-74.80-29.79-10.29-141.93-151.19-132.67-143.96-113.09-143.96-143.96-151.19考虑地震效应的荷载组合首先需计算其重荷载代表值，其计算公式为：在设计时对框架梁提出了梁端的斜截面受剪承载力应高于正截面受弯承载力的要求，即“强剪弱弯”的设计概念。《建筑抗震设计规范》（GB50011-2012）的第6.2.4条对此作出了规定，对于一、二、三级的框架梁和抗震墙的连梁，其梁端截面组合的剪力设计值应按下式调整：表7.3框架梁内力组合（考虑地震效应）楼层截面

位置内力恒载活载地震重力荷载VGb1.2重力荷载+1.3地震强剪弱弯调整|M|max及对应VMmin及对应V|V|max及对应M左震右震V(kN)-8.07-1.30-30.66-8.0713.17-49.5430.1857.02-49.54-49.54-49.54C支座右M(kN·m)-47.10-5.6746.35-47.103.74-116.77-116.77-116.77-116.77V(kN)65.066.02-15.9365.0679.9357.3698.78104.3598.7898.7898.78CD跨中M(kN·m)70.535.05-9.4170.5372.4096.8796.8772.40D支座M(kN·m)-38.39-5.67-65.16-38.39-130.7838.63-130.78-130.78-130.78V(kN)-62.14-6.02-15.93-62.1479.93-95.27-53.86104.35-95.27-95.27-95.274A支座M(kN·m)-60.67-22.37123.90-71.8674.85-247.30-247.30-247.30-247.30V(kN)75.0329.75-32.0389.91108.5766.25149.53155.00149.53149.53149.53AB跨中M(kN·m)72.5130.2211.8187.62120.5089.79120.5089.79B支座左M(kN·m)-63.01-24.43-100.28-75.22-220.6340.10-220.63-220.63-220.63V(kN)-75.82-30.45-32.03-91.05108.57-150.90-67.62155.00-150.90-150.90-150.90B支座右M(kN·m)-8.92-4.8472.55-11.3480.71-107.92-107.92-107.92-107.92V(kN)5.695.83-65.968.6114.74-75.4296.08109.0596.0896.0896.08BC跨中M(kN·m)-3.79-1.160.00-4.37-5.24-5.24-5.24-5.24C支座左M(kN·m)-8.92-4.84-72.55-11.34-107.9280.71-107.92-107.92-107.92V(kN)-5.69-5.83-65.96-8.6114.74-96.0875.42109.05-96.08-96.08-96.08C支座右M(kN·m)-63.01-24.43100.28-75.2240.10-220.63-220.63-220.63-220.63V(kN)75.8230.45-32.0391.05108.5767.62150.90155.00150.90150.90150.90CD跨中M(kN·m)72.5130.22-11.8187.6289.79120.50120.5089.79D支座M(kN·m)-60.67-22.37-123.90-71.86-247.3074.85-247.30-247.30-247.30V(kN)-75.03-29.75-32.03-89.91108.57-149.53-66.25155.00-149.53-149.53-149.53V(kN)-74.88-29.83-45.21-89.80108.57-166.53-48.98173.98-166.53-166.53-166.532A支座M(kN·m)-58.18-23.11237.85-69.73225.52-392.88-392.88-392.88-392.88V(kN)74.8029.79-60.6989.70108.5728.74186.53196.24186.53186.53186.53AB跨中M(kN·m)74.3129.5825.4289.10139.9673.87139.9673.87B支座左M(kN·m)-61.90-24.96-187.02-74.38-332.38153.86-332.38-332.38-332.38V(kN)-76.05-30.41-60.69-91.26108.57-188.41-30.61196.24-188.41-188.41-188.41B支座右M(kN·m)-9.78-4.42135.46-11.99161.71-190.49-190.49-190.49-190.49V(kN)5.695.83-123.158.6114.74-149.77170.42190.84170.42170.42170.42BC跨中M(kN·m)-4.66-0.720.00-5.02-6.02-6.02-6.02-6.02C支座左M(kN·m)-9.78-4.42-135.46-11.99-190.49161.71-190.49-190.49-190.49V(kN)-5.69-5.83-123.15-8.6114.74-170.42149.77190.84-170.42-170.42-170.42C支座右M(kN·m)-61.90-24.96187.02-74.38153.86-332.38-332.38-332.38-332.38V(kN)76.0530.41-60.6991.26108.5730.61188.41196.24188.41188.41188.41CD跨中M(kN·m)74.3129.58-25.4289.1073.87139.96139.9673.87D支座M(kN·m)-58.18-23.11-237.85-69.73-392.88225.52-392.88-392.88-392.88V(kN)-74.80-29.79-60.69-89.70108.57-186.53-28.74196.24-186.53-186.53-186.53V(kN)-73.33-29.22-57.48-87.93106.24-180.24-30.80189.12-180.24-180.24-180.247.3柱内力组合计算在地的抗弯承载力，根据《建筑抗震设计规范》（GB50011—2010）的第6.2.2条可知，一、二、三、四级框架的梁柱节点处，柱端组合的弯矩设计值应符合下列要求：对于框架柱“强剪弱弯”调整，一、二、三、四级框架柱和框支柱组合的剪力设计值按下式调整：将柱子的内力进行汇总：表7.4框架柱控制截面的内力汇总楼层截面位置恒载作用下内力活载作用下内力风荷载作用下内力地震作用下内力MNVMNVMNVMNV5A柱柱顶61.84219.95-30.638.2917.65-6.38-5.75-1.332.32-69.14-15.9327.88柱底48.44245.33-30.6314.6717.65-6.38-2.60-1.332.32-31.23-15.9327.88B柱柱顶-51.86285.7625.98-7.1726.105.52-7.63-1.223.42-91.72-14.7341.13柱底-41.65311.1425.98-12.7126.105.52-4.69-1.223.42-56.35-14.7341.13C柱柱顶51.86285.76-25.987.1726.10-5.52-7.631.223.42-91.7214.7341.13柱底41.65311.14-25.9812.7126.10-5.52-4.691.223.42-56.3514.7341.13D柱柱顶-61.84219.9530.63-8.2917.656.38-5.751.332.32-69.1415.9327.88柱底-48.44245.3330.63-14.6717.656.38-2.601.332.32-31.2315.9327.884A柱柱顶42.97525.30-24.4119.58105.57-10.40-13.09-5.116.06-100.68-47.9646.61柱底44.90550.68-24.4117.85105.57-10.40-8.73-5.116.06-67.12-47.9646.61B柱柱顶-39.52649.4622.12-16.49165.588.86-18.33-5.148.94-140.98-48.6668.77柱底-40.13674.8422.12-15.41165.588.86-13.86-5.148.94-106.59-48.6668.77C柱柱顶39.52649.46-22.1216.49165.58-8.86-18.335.148.94-140.9848.6668.77柱底40.13674.84-22.1215.41165.58-8.86-13.865.148.94-106.5948.6668.77D柱柱顶-42.97525.324.41-19.58105.5710.40-13.095.116.06-100.6847.9646.61柱底-44.90550.6824.41-17.85105.5710.40-8.735.116.06-67.1247.9646.613A柱柱顶44.90830.50-25.4117.85193.57-10.10-18.73-11.709.46-120.96-93.1761.09柱底46.58855.88-25.4118.52193.57-10.10-15.33-11.709.46-98.97-93.1761.09B柱柱顶-40.131013.322.54-15.41304.988.66-26.11-11.9113.96-168.54-95.4190.13柱底-41.011038.6822.54-15.75304.988.66-24.15-11.9113.96-155.92-95.4190.13C柱柱顶40.131013.3-22.5415.41304.98-8.66-26.1111.9113.96-168.5495.4190.13柱底41.011038.68-22.5415.75304.98-8.66-24.1511.9113.96-155.9295.4190.13D柱柱顶-44.90830.525.41-17.85193.5710.10-18.7311.709.46-120.9693.1761.09柱底-46.58855.8825.41-18.52193.5710.10-15.3311.709.46-98.9793.1761.09表7.5框架柱内力组合（一般组合）楼层截面

位置内力恒载活载风1.3恒+1.5×活1.3恒+1.5×(活+0.6风)1.3恒+1.5×(0.7活+风)|M|max及对应N,VNmin及对应M,VNmax及对应M,V左风右风左风右风5A柱柱顶M61.848.29-5.7592.8387.6598.0080.4797.7298.0080.4798.00N219.9517.65-1.33312.41311.21313.61302.47306.46313.61302.47313.61V-30.63-6.382.32-49.39-47.30-51.48-43.04-50.00-51.48-43.04-51.48柱底M48.4414.67-2.6084.9882.6487.3274.4882.2887.3274.4887.32N245.3317.65-1.33345.40344.21346.60335.47339.46346.60335.47346.60V-30.63-6.382.32-49.39-47.30-51.48-43.04-50.00-51.48-43.04-51.48B柱柱顶M-51.86-7.17-7.63-78.17-85.04-71.30-86.39-63.50-86.39-86.39-71.30N285.7626.10-1.22410.64409.54411.74397.06400.72397.06397.06411.74V25.985.523.4242.0545.1338.9744.70