沈阳东旭高中教学楼设计计算书

'摘要本工程是沈阳东旭高中教学楼，为多层钢筋混凝土框架结构，共五层，底层层高3.6米，其他层层高也为3.6米，建筑物总高度为18.9米。在遵循“适用、安全、经济、美观”的设计原则和国家有关现行建筑结构设计规范与标准的基础上，进行了教学楼的建筑与结构初步设计，获得了该建筑物初步设计阶段的建筑CAD设计图纸与技术指标，确定了结构布置方案与结构计算模型。先进行了层间荷载代表值的计算，然后按底部剪力法计算水平地震荷载作用下大小，进而求出在水平荷载作用下的结构内力（弯矩、剪力、轴力）。接着计算竖向荷载（恒载、活荷载以及雪荷载）作用下的结构内力，找出最不利的一组或几组内力组合。选取最安全的结果计算配筋并绘图。此外还进行了结构方案中的室内楼梯的设计（完成了平台板，梯段板，平台梁等构件的内力和配筋计算）、楼盖的设计（完成了板的配筋和次梁的配筋）、基础的设计（完成了基础的配筋）关键词：钢筋混凝土，框架，结构设计56 AbstractThisisateachingbuildingofaDongxuchoolinshenyang.Itisamulti-layerreinforcedconcreteframe.Ithasfivestories,theheightofthefirststoreyis3.6meters,andtheheightofotherstoriesarea3.6metersto.Theheightofthewholebuildingis18.9meters.Inaccordancewiththedesignprincipleof“applicability、safety、economy、aesthetic”andthepresentcodesandstandardsofthearchitecturalandstructuraldesign,theprimaryarchitecturalandstructuraldesignofbuildingiscarriedout.AftergettingthearchitecturaldrawingfromCADdesign,theanthordecidesthestructuralschemeandthestructuralcalculationmodelWhenthedirectionsoftheframesisdetermined,firstlytheweightofeachflooriscalculated.Thenmakingtheamountofthehorizontalseismicforcecanbegotbywayofthebottom-shearforcemethod.Theseismicforcecanbeassignedaccordingtotheshearingstiffnessoftheframesofthedifferentaxis.Thentheinternalforce(bendingmoment,shearingforce，axialforce＆snowforce)inthestructureunderthehorizontalloadscanbeeasilycalculated.Afterthedeterminationoftheinternalforceunderthedeadandliveloads,thecombinationofinternalforcecanbemadebyusingtheExcelsoftware,whosepurposeistofindoneorseveralsetsofthemostadverseinternalforceofthewalllimbsandthecoterminousgirders,whichwillbethebasisofprotractingthereinforcingdrawingsofthecomponents.Thedesignofthestairsisalsobeapproachedbycalculatingtheinternalforceandreinforcingsuchcomponentsaslandingslab,stepboard.Thedesignoffloorslabisalsobecompletedintheend.　　　　　　　　Keywords:reinforcedconcrete；frame；thedesignofthestructure56 引言土建类本科土木工程专业毕业设计是大学学校教学计划的最后一个重要环节，是学生综合素质与工程实践能力培养效果的全面检验。毕业设计的目的是培养学生综合应用所学基础课、技术基础课、专业课知识和相应技能，解决土木工程设计问题的综合能力和创新能力，提高学生的综合素质和分析、处理问题的能力。本组毕业设计题目为《某中学教学楼框架结构设计》。在进行建筑方案设计前，我温习了《房屋建筑学》、《结构力学》、《钢筋混凝土结构设计原理》、《建筑结构抗震设计》、《土力学地基基础》等专业课程，并且阅读了《抗震规范》、《混凝土规范》、《荷载规范》等相关规范。在这次设计中，我尽量全面综合运用所学的基本理论、专业知识和基本技能以及实习时所见所闻的积累，进行建筑，、结构设计并绘制施工图纸。特别是在设计期间，得到了老师的热情指导和审批及指正，本组成员齐心协力、分工合作，发挥了大家的团队精神。在毕业设计后期，主要进行设计手稿的电脑输入，使我圆满的完成了毕业设计任务，在此表示衷心的感谢。毕业设计的四个月里，在指导老师的热情帮助下，经过资料查阅、设计计算、计算说明撰写以及外文的翻译，加深了对新规范、规程、手册等相关内容的理解。巩固了专业知识、提高了综合分析、解决问题的能力。熟练掌握了AutoCAD、天正等绘图软件，从而从不同方面达到了毕业设计的目的与要求。框架结构设计的计算工作量很大，并且在计算过程中以手算为主，由于自己的知识结构还不够全面，在设计计算过程中难免有不妥和疏忽之处。56 1建筑方案设计1.1工程概况1.1.1建筑设计指标本方案建筑地点位于沈阳市康平县，占地面积为1230平方米，建筑面积为6447.74平方米，18间普通教室，每间建筑面积为56.7平方米；3间实验室，每间建筑面积为75.6平方米，两间计算机房，每间建筑面积为56.7平方米;2间语音教室，每间建筑面积为56.7平方米；卫生间每层2个，其他用房见详图。1.1.2建筑设计思路综合工程各条件，本教学楼采用框架结构体系。框架结构的最大特点是承重构件与围护构件有明确分工，建筑的内外墙处理十分灵活，应用范围很广。根据框架布置方向的不同，框架体系可分为横向布置、纵向布置及纵横双向布置三种。本建筑方案力求创新，在形象上追求现代气息，同时注重在建筑方案经济合理性，在里面造型上给人以美感，内部设计主要以内廊为中心线，左右布置教师；教学区和辅组教学区分开，在导向上给人明确的方向感，在教学楼内布置了三步楼梯，在交通上，疏散人流更加方便快捷。1.2建筑构造设计1.2.1非上人屋面构造设计［1］(1)25mm厚1﹕3水泥砂浆(2)40mm厚SBS改性沥青防水卷材(3)20mm厚1：3水泥砂浆找平层56 (4)1：6水泥焦渣找坡层最薄处30mm厚(5)100mm厚阻燃型聚苯乙烯板保温层(6)120mm厚现浇钢筋混凝土屋面板(7)20mm厚板下混合砂浆抹灰1.2.2楼面构造设计(1)20mm厚水磨石地面(2)20mm厚1：3水泥砂浆结合层(3)120mm厚现浇钢筋混凝土板(4)20mm厚板下混合砂浆抹灰1.2.3外墙体构造设计(1)刮大白(2)20mm厚混合砂浆(3)墙体基层(4)外贴50mm厚阻燃型挤塑聚苯乙烯板(5)20mm厚1:3水泥砂浆(6)刷涂料56 2荷载计算2.1截面尺寸的选取2.1.1截面尺寸选取框架柱：根据轴压比公式初步估定柱截面尺寸：［2］（三级框架）混凝土强度为C30bc=hc=459mm取bc=hc=500×500mm框架梁：由挠度、裂度控制h=(1/12～1/8)Lb=(1/3～1/2)h纵向框架梁截面尺寸：bb×hb=250mm×600mm横向框架梁截面尺寸：bb×hb=250mm×600mm；次梁截面尺寸：bb×hb=250mm×600mm走廊梁截面尺寸：bb×hb=250mm×400mm楼板：取板厚：h=120mm56 2.2荷载汇集2.2.1恒载［1］［4］屋面：25mm厚1﹕3水泥砂浆0.025×20=0.5kN/m240mm厚SBS改性沥青防水卷材0.04×2.0=0.08kN/m220mm厚1：3水泥砂浆找平层0.02×20=0.4kN/m21：6水泥焦渣找坡层最薄处30mm厚0.09×14=1.26kN/m2100mm厚阻燃型聚苯乙烯板保温层［6］0.1×1.5=0.15kN/m2120mm厚现浇钢筋混凝土屋面板0.12×25=3kN/m220mm厚混合砂浆抹灰0.02×17=0.34kN/m2∑=5.73kN/m2楼面：［11］20mm厚水磨石地面0.65kN/m220mm厚1：3水泥砂浆结合层0.02×20=0.4kN/m2120mm厚现浇钢筋混凝土板3kN/m220mm厚板下混合砂浆抹灰0.34kN/m2∑=4.39kN/m2梁重：纵梁：梁自重：0.25×0.6×25=3.75kN/m粉刷：0.02×（0.6-0.12）×2×17=0.33kN/m∑=4.08kN/m56 横梁：自重：0.25×0.6×25＝3.75kN/m粉刷：0.02×（0.6-0.12）×2×17=0.33kN/m∑=4.08kN/m次梁：自重：0.25×0.6×25＝3.75kN/m粉刷：0.02×（0.6-0.12）×2×17=0.33kN/m∑=4.08kN/m走廊横梁：自重：0.25×0.4×25＝2.5kN/m粉刷：0.02×（0.4-0.12）×2×17=0.19kN/m∑=2.69kN/m墙重：（砌体与抹灰之和）外墙：0.37×11=4.07kN/m2内墙：0.24×11=2.64kN/m2女儿墙：0.24×18=4.32kN/m2柱：（考虑到柱子抹灰，取柱子自重27kN/m3）0.5×0.5×27=6.75kN/m门、窗：门：0.2kN/m2窗：0.45kN/m22.2.2活荷载［3］风压：0.55kN/m2雪压：0.5kN/m2厕所：2.0kN/m256 办公室（教室）：2.0kN/m2走廊、楼梯：2.5kN/m2不上人屋面：0.5kN/m22.3计算简图及层数划分如图图1计算简图56 图2框架简图2.4各层重力荷载代表值计算第五层的重力荷载代表值:五层上半层女儿墙：（42+15）×2×0.24×0.9×18=443.23kN屋面：42×15×5.73=3609.90kN纵梁：42×4.08×4=685.44kN横梁：6.3×4.08×16=411.26kN次梁：6.6×4.08×14=359.86kN走廊横梁：2.4×2.69×8=51.65kN56 柱子：×6.75×32=388.8kN外墙：116.4×（-0.6）×4.07=556.78kN内纵墙：6.0×（-0.6）×13×2.64=247.10kN内横墙：6.3×（-0.6）×8×2.64=159.67kN外墙窗洞：-(-0.6)×2.1×14×2×4.07=-287.18kN外墙窗：(-0.6)×2.1×14×2×0.45=31.75kN内门洞：-(2.1-）×0.9×16×2.64=-11.40kN内门：（2.1-）×0.9×16×0.2=0.86kN∑＝6651.25KN五层下半层柱子：×6.75×32=388.80kN外墙：114××4.07=835.16kN内纵墙：6.0××13×2.64=370.66kN内横墙：6.3××8×2.64=239.50kN外墙窗洞：-×2.1×14×2×4.07=-430.77kN外墙窗:×2.1×14×2×0.45=47.62kN内门洞：-×0.9×8×2×2.64=-68.42kN内门：×0.9×8×2×0.2=5.18kN∑＝1411.44kN2～4层的重力荷载代表值:四层上半层楼面：6.0×6.3×13×4.39+42×3×4.39+6.0×6.3×5.84=2931.14kN56 纵梁：42×4.08×4=685.44kN横梁：6.3×4.08×16=411.26kN次梁：6.6×4.08×14=359.86kN走廊横梁：2.4×2.69×8=51.65kN柱子：×6.75×32=388.8kN外墙：116.4×（-0.6）×4.07=556.78kN内纵墙：6.0×（-0.6）×13×2.64=247.10kN内横墙：6.3×（-0.6）×8×2.64=159.67kN外墙窗洞：-(-0.6)×2.1×14×2×4.07=-287.18kN外墙窗：(-0.6)×2.1×14×2×0.45=31.75kN内门洞:-(2.1-)×0.9×15×2.64=-14.26kN内门:(2.1-)×0.9×15×0.2=1.08kN∑＝5939.68kN四层下半层柱子：×6.75×32=388.80kN外墙：114××4.07=835.16kN内纵墙：6.0××13×2.64=370.66kN内横墙：6.3××8×2.64=239.50kN外墙窗洞：-×2.1×14×2×4.07=-430.77kN外墙窗:×2.1×14×2×0.45=47.62kN内门洞:-×0.9×15×2.64=-64.15kN56 内门:×0.9×15×0.2=4.86kN∑＝1411.44kN三层上半层等于四层上半层为：5539.68kN三层下半层等于四层下半层为：1411.44kN二层上半层等于三层上半层为：5539.68kN二层下半层等于三层下半层为：1411.44kN一层上半层楼面：6.0×6.3×13×4.39+42×3×4.39+6.0×6.3×5.84=2931.14kN纵梁：42×4.08×4=685.44kN横梁：6.3×4.08×16=411.26kN次梁：6.6×4.08×14=359.86kN走廊横梁：2.4×2.69×8=51.65kN柱子：×6.75×32=388.8kN外墙：116.4×（-0.6）×4.07=556.78kN内纵墙：6.0×(-0.6)×12×2.64=228.01kN内横墙：6.3×(-0.6)×7×2.64=139.71kN外墙窗洞：-(-0.6)×2.1×13×2×4.07=-266.67Kn外墙窗:(-0.6)×2.1×13×2×0.45=29.48kN内门洞:-(2.1-)×0.9×13×2.64=-9.27kN内门:(2.1-)×0.9×13×0.2=0.70kN雨篷:6.0×3.0×0.08×25=36kN56 ∑＝5581.75kN则恒载+0.5活载：=6651.25+0.5×0.5×42×15=6808.75kN1411.44+5939.68+0.5×[2.0×(6.0×6.3×13+5.4×6.3)+2.5×2.4×6.3+2.5×2.4×42]=7615.77kN1411.44+5939.68+0.5×[2.0×(6.0×6.3×13+5.4×6.3)+2.5×2.4×6.3+2.5×2.4×42]=7615.77kN1411.44+5939.68+0.5×[2.0×(6.0×6.3×13+5.4×6.3)+2.5×2.4×6.3+2.5×2.4×42]=7615.77kN1411.44+5581.75+664.65=7657.84kN56 3水平荷载作用下的框架内力分析3.1层间侧移刚度计算3.1.1梁线刚度在计算梁线刚度时，考虑楼板对梁刚度的有利影响，即板作为翼缘工作。在工程上，为简化计算，通常梁均先按矩形截面计算某惯性矩I0，然后乘以增大系数:中框架梁I=2.0I0边框架梁I=1.5I0梁采用C30混凝土，EC=3.0×107kN/m2(m4)(3-1)KB单位：kNm横向框架：表1框架梁线刚度计算部位截面m2跨度m截面惯性矩边框架中框架I=1.5I0KB=EI/LI=2.0I0KB=EI/L边跨0.25×0.66.34.5×106.8×103.3×109.0×104.3×10中跨0.25×0.42.41.3×102.0×102.5×102.6×103.3×103.1.2柱线刚度柱采用C30混凝土Ec=3.0×107kN/M2，首层高度4.55m,2-5层3.6m。柱截面：500mm×500mm则I1-4=I0==5.2×10-3m456 (3-2)表2柱的线刚度计算层次层高b×hEc/KN/M2Ic(m4)Kc=2-53.6m500×5003.0×105.2×104.3×1014.55m500×5003.0×105.2×103.4×103.1.3柱的侧移刚度D［6］一般层：=D=（3-3）首层：=D=（3-4）表3边框架柱子的侧移刚度部位层高M柱子刚度边跨梁线刚度中跨梁线刚度边框架边柱C1（4根）边框架中柱C2（4根）K1α1DC1K2α2DC22-53.64300033000250000.7670.277110291.3490.4031603714.554300033000250000.9710.49597551.7060.59511726表4中框架柱子的侧移刚度部位层高M柱子刚度边跨梁线刚中跨梁a线刚中框架边柱C1（14根）中框架中柱C2（14根）K1α1DC3K2α2DC42-53.64300043000330001.0000.333132581.7670.4691867314.553400043000330001.2650.541106622.2350.646127313.1.4层间侧移刚度的计算表5层间侧移刚度部位各层柱子侧移刚度层间刚度∑DC1∑DC2∑DC3∑DC4∑Di2-544116641481590962240764914361390204690612794415277236664256 ∑D1/∑D2=0.77﹥0.7满足要求3.2水平地震作用层间地震剪力和弹性位移的计算采用底部剪力法计算水平地震作用3.2.1框架水平地震作用及水平地震剪力计算［5］［6］自振周期计算L0=0.6T1=1.7×0.6×ΔT0.5(3-5)表6横向框架顶点位移计算层次Gi(KN)(KN)Di△i-△i-1=∑Gi/D△I(m)56808.756808.754914360.01390.250247615.7714424.524914360.02940.236337615.7722040.294914360.04480.0.6927615.7729656.054914360.06030.162117657.8437313.893666420.10180.1018T1=1.7×0.6×0.25020.5=0.51s横向地震作用计算:地震作用按7度设计,基本地震加速度为0.10g,Ⅱ类场地,地震分组按一组则Tg=0.35Sαmax=0.08采用底部剪力法计算由于T1=0.51>1.4×0.35=0.49故应考虑顶点附加地震作用取=0.08×0.52+0.01=0.052FEK=()0.9×αmax×0.85(3-6)=()0.9×0.08×0.85×37313.89=1808.12KN顶点附加地震作用为:△=0.051×1808.12=92.21KN(3-7)56 =(3-8)表7各层地震作用及楼层地震剪力层hiHiGiGiHiGiHi/∑GiHiFiVi53.618.956808.75129025.810.298511.34603.5543.615.357615.77116902.070.270463.301066.8533.611.757615.7789485.300.207355.191422.0423.68.157615.7762068.530.144247.091669.1314.554.557657.8434843.170.081138.991808.123.2.2水平地震作用下的层间位移和顶点位移计算表8层间位移和顶点位移层Vi(kN)hi(m)ΣDi(kN/m)Δuei=Vi/ΣDi(m)Δuei/hi5603.553.64914360.00121/300041066.853.64914360.00221/163631422.043.64914360.00291/124121669.133.64914360.00341/105911808.124.553666420.00491/929﹤所以满足规范规定的弹性位移要求。3.2.3水平地震作用下的剪力图56 图3水平地震作用下的剪力图3.3水平地震作用下框架柱剪力和柱弯矩（采用D值法）［6］将层间剪力分配到该层的各个柱子，即求出柱子的剪力，再由柱子的剪力和反弯点高度来求柱上、下端的弯矩。柱端剪力按下式来计算：（3-9）柱上、下端弯矩按下式来计算（3-10）（3-11）（3-12）—反弯点到柱下端结点的距离，即反弯点高度。—标准反弯点高度比。—上下横粱线刚度比对标准反弯点高度比的修正系数。56 —上层层高变化修正值。—下层层高变化修正值。根据框架总层数，该柱所在层数和梁柱线刚度比查表得。表9边柱（中框）层h(m)y0y1y2y3Y53.61.0000.350.0000.0000.0001.2643.61.0000.450.0000.0000.0001.6233.61.0000.450.0000.0000.0001.6223.61.0000.500.0000.0000.0001.8014.551.2650.650.0000.0000.0002.96表10中柱（中框）层h(m)y0y1y2y3Y53.61.7670.390.0000.0000.0001.4043.61.7670.450.0000.0000.0001.6233.61.7670.490.0000.0000.0001.7623.61.7670.500.0000.0000.0001.8014.552.2350.630.0000.0000.0002.87表11边柱（中框）层H(m)∑Di(kN/m)D(kN/mD/∑DiVi(kN)Vik(kN)YM下（kNm）M上(kNm)53.6491436132580.0270603.5516.281.2620.5138.1043.6491436132580.02701066.8528.781.6246.6256.9833.6491436132580.02701422.0438.361.6262.1470.0523.6491436132580.02701669.1340.031.8072.0575.9514.55366642106620.02911808.1252.582.96155.6483.6056 表12中柱（中框）层H(m)∑Di(kN/m)D(kN/m)D/∑DiVi(kN)Vik(kN)YM下（kNm）M上(kNm)53.6491436186730.0380603.5522.931.4032.1050.4543.6491436186730.03801066.8540.541.6265.6780.2733.6491436186730.03801422.0454.031.7695.0992.0623.6491436186730.03801669.1363.421.80114.16114.1614.55366642127310.03471808.1262.782.87174.53105.473.4水平地震作用下梁端弯矩计算［6］根据节点平衡由柱端弯矩求得梁轴线处弯矩µB1=KB1/(KB1+KB2)（3-13）MB1=(MC上+MC下)×µB1（3-14）µB2=KB2/(KB1+KB2)（3-15）MB2=(MC上+MC下)×µB2（3-16）表13水平地震作用下梁端弯矩层A轴B轴MC上MC下µB1MABMC上MC下µB1µB2MBAMBC50.0038.10138.00.0050.450.570.4328.7621.69420.5156.98177.4932.1080.270.570.4359.5648.32346.6275.951122.5765.6792.060.570.4389.9167.82262.1470.051132.1995.09114.160.570.43119.2789.98172.0583.601155.65114.16105.470.570.43125.1994.4456 3.5水平地震作用下的梁端剪力和柱轴力标准值［6］（3-17）（3-18）表14水平地震作用下梁端剪力和柱轴力层AB跨梁端剪力BC跨梁端剪力柱轴力LL边柱(KN)中柱(KN)56.338.1028.7610.612.421.6918.0818.0810.6118.0846.377.4959.5621.652.448.3240.2740.2740.2726.0936.3122.5789.9133.732.467.8256.5256.5256.5248.8826.3132.19119.2739.912.489.9874.9874.9874.9883.9516.3155.65125.1944.582.494.4478.7078.7078.70118.0756 3.6水平地震作用下的框架内力图图4水平地震作用下的框架内力图56 3.7横向风荷载计算自然情况：地区基本风压W0=0.55kN/m2，地面粗糙程度C类。3.7.1风荷载计算［3］风荷载标准值：（3-19）表15风荷载作用下的剪力层βZμSμZiW0WkiFWkiVi51.01.30.830.550.5939.609.6140.740.52911.4321.0430.740.52911.4332.4720.740.52911.4343.9010.740.52911.4355.33注：（1）在实际工程中，对于高度不大于30M，高宽比小于1.5的高层建筑，取风振系数βZ=1.0。（2）（3-20）3.7.2风荷载作用分布图图5风荷载作用分布图56 3.8风荷载作用下框架柱剪力和柱弯矩（D值法）表16边柱（中框）层H(m)∑Di(kN/m)D(kN/m)D/∑DiVi(kN)Vik(kN)YM下（kNm）M上(kNm)53.663862132580.2089.612.001.262.524.6843.663862132580.20821.044.381.627.108.6733.663862132580.20832.476.751.6210.9313.3723.663862132580.20843.909.131.8016.4316.4314.5546786106620.22955.3312.672.9637.5020.15表17中柱（中框）层H(m)∑Di(kN/m)D(kN/m)D/∑DiVi(kN)Vik(kN)YM下（kNm）M上(kNm)53.663862186730.2929.612.811.403.936.1843.663862186730.29221.046.141.629.9512.1633.663862186730.29232.479.481.7616.6817.4423.663862186730.29243.9012.821.8030.0830.0814.5546786127310.27255.3315.102.8743.3425.3756 3.9风荷载作用下梁端弯矩计算表18风荷载作用下梁端弯矩层A轴B轴MC上MC下µB1MABMC上MC下µB1µB2MBAMBC50.004.6814.680.006.180.570.433.522.6642.528.67111.193.9312.160.570.436.935.2337.1013.37120.479.9517.440.570.439.947.50210.9316.43127.3616.6830.080.570.4317.1512.93116.4320.15136.5830.0825.370.570.4314.4610.913.10风荷载作用下的梁端剪力和柱轴力标准值表19风荷载作用下的梁端剪力和柱轴力层AB跨梁端剪力BC跨梁端剪力柱轴力LL边柱(KN)中柱(KN)56.34.683.522.002.42.662.662.222.000.2246.311.196.932.862.45.235.234.364.881.7036.320.479.944.832.47.507.506.259.713.1226.327.3617.157.072.412.9312.9310.7816.786.8316.336.5814.468.102.410.9110.919.0924.887.8256 3.11风荷载作用下的框架内力图图6风荷载作用下的框架内力图56 4竖向荷载作用下的内力分析图7荷载传递路线4.1恒载4.1.1屋面梁上线荷载标准值梁重：横梁:边跨4.08kN/m,中跨2.69kN/m屋面板荷载：(按双向板计算)4.1.2屋面板及楼面板的折减系数边跨为梯形荷载:56 中跨为梯形荷载:5/8=0.6254.1.3屋面梁上线荷载标准值边跨：g1=5.73×3.0×0.90+4.08=19.55kN/m中跨：g2=5.73×2.4×0.625+2.69=11.29kN/m4.1.4楼面梁上线荷载标准值边跨：g1=4.39×3.0×0.90+4.08=15.93kN/m中跨：g2=4.39×2.4×0.625+2.69=9.28kN/m4.2活载屋面:边跨q1=0.5×3.0×0.90=1.35kN/m中跨q2=0.5×2.4×0.625=0.75kN/m楼面:边跨q1=2.0×3.0×0.90=10.96kN/m中跨q2=2.5×3.0×0.625=4.69kN/m4.3框架计算简图56 图8框架计算简图4.4梁固端弯矩梁端弯矩以绕杆端顺时针为正，反之为负M固=（4-1）表20竖向荷载作用下框架的固端弯矩荷载部位边跨中跨跨度均布荷载固端弯矩跨度均布荷载固端弯矩左右左右恒载顶层6.319.55-64.4464.662.411.29-5.425.42其他层6.315.93-52.6952.692.49.28-4.454.45活载顶层6.31.35-4.474.472.40.75-0.360.36其他层6.35.40-17.8617.862.43.75-1.801.8056 4.5内力分配系数计算表21转动刚度S及相对转动刚度计算构件名称转动刚度S（KNm）相对转动刚度框架梁边跨1.00中跨0.38框架柱顶层1.00一般层1.00底层分配系数计算：（4-2）56 表22各杆件分配系数表节点层()()边节点51.00+1.00=2.00-----0.50-----0.5041.00+1.00+1.00=3.00-----0.340.330.3331.00+1.00+1.00=3.00-----0.340.330.3321.00+1.00+1.00=3.00-----0.340.330.3311.00+0.79+1.00=2.79-----0.360.360.28中间节点51.00+1.00+0.38=2.380.420.16-----0.4241.00+1.00+1.00+0.38=3.380.290.110.300.3031.00+1.00+1.00+0.38=3.380.290.110.300.3021.00+1.00+1.00+0.38=3.380.290.110.300.3011.00+0.79+1.00+0.38=3.170.320.120.320.244.6弯矩分配与传递方法：首先将各点的分配系数填在相应方框内，将梁的固端弯矩填写框架横梁相应位置上，然后将节点放松，把各节点不平衡弯矩同时进行分配。假定远端固定进行传递（不向滑动端传递），右（左）梁分配弯矩向左（右）梁传递，上（下）分配弯矩向下（上）柱传递（传递系数均为0.5）。第一次分配弯矩传递后，再进行第二次弯矩分配。［8］56 恒载作用下的力矩分配图9恒荷载作用下的力矩分配56 活载作用下的力矩分配图9活荷载作用下的力矩分配56 重力荷载作用下的力矩分配图10重力荷载作用下的力矩分配56 恒荷载作用下的弯矩图图11恒荷载作用下的弯矩图56 活荷载作用下弯矩图:图12活荷载作用下的弯矩图56 重力荷载作用下的弯矩图图13重力荷载作用下的弯矩图56 表23恒载作用下的弯矩楼层BC跨CD跨左端中间右端-左端=右端中间MMMMM5-42.9050.5749.9312.45-4.324-47.4330.0250.9010.48-3.973-45.1131.8949.4611.13-4.452-45.1631.9149.3911.08-4.401-41.3435.3246.3911.53-4.85表24活载作用下的弯矩楼层BC跨CD跨左端中间右端-左端=右端中间MMMMM5-4.142.793.680.370.314-14.7111.4116.052.75-0.053-15.3310.8316.602.580.122-15.4310.0816.552.560.141-14.1412.0415.372.97-0.27表25重力荷载作用下的弯矩楼层BC跨CD跨左端中间右端-左端=右端中间MMMMM5-44.9851.8252.0612.72-4.324-54.7735.4559.2011.86-.3833-52.5437.3057.7212.41--4.8356 2-52.8637.0757.8712.36-4.331-48.4141.2154.0413.69-5.66注:弯矩符号逆时针为正4.7梁端剪力均布荷载下:(4-3)(4-4)V’=V—q×(4-5)表26恒载作用下梁端剪力(BC跨)BC跨梁端剪力层qkN/mLmqL/2（kN）(kN)(kN)(kN)（kN）(kN)519.556.361.581.2260.3662.8055.4757.91415.936.350.190.5549.6450.7445.6646.75315.936.350.190.6949.5050.8845.5246.90215.936.350.190.6749.5250.8645.5446.88115.936.350.190.8019.3950.9945.4147.01表27恒载作用下梁端剪力(CD跨)CD跨梁端剪力层qkN/MLqL/2（kN）(kN)(kN)(kN)（kN）(kN)511.292.413.55013.5513.5510.7310.7549.282.411.14011.1411.149.089.0839.282.411.14011.1411.149.089.0829.282.411.14011.1411.149.089.0819.282.411.14011.1411.149.089.0856 表28活载作用下梁端剪力(BC跨)BC跨梁端剪力层qkN/mLmqL/2（kN）(kN)(kN)(kN)（kN）(kN)51.356.34.250.074.184.323.843.9845.46.317.010.2116.8017.2215.4515.8735.46.317.010.2016.8117.2115.4615.8625.46.317.010.1816.8317.1915.4815.8415.46.317.010.2016.8117.2115.4615.86表29活载作用下梁端剪力(CD跨)CD跨梁端剪力层q(kN/m)L(m)qL/2（kN）(kN)(kN)(kN)（kN）(kN)50.752.40.900.90.90.710.7143.752.44.504.54.53.563.5633.752.44.504.54.53.563.5623.752.44.504.54.53.563.5613.752.44.504.54.53.563.564.8柱轴力和剪力表30荷载作用下的柱轴力剪力(边柱)（1）边柱(单位:KN)层截面楼屋盖恒荷楼屋盖活荷墙重梁自重柱自重恒荷引起轴力活荷引起轴力恒荷引起剪力活荷引起剪力5顶130.889.4570.7976.1624.3207.049.4519.5462.94底231.344顶82.9737.870.7976.1624.3461.3747.2511.784.43底485.673顶82.9737.870.7976.1624.3644.885.0512.394.2356 底669.12顶82.9737.870.7976.1624.3899.13122.8513.864.74底923.431顶82.9737.870.7976.1624.31153.43160.654.971.62底1184.17表31荷载作用下的柱轴力剪力(中柱)（1）中柱(单位:KN)层截面楼屋盖恒荷楼屋盖活荷墙重梁自重柱自重恒荷引起轴力活荷引起轴力恒荷引起剪力活荷引起剪力5顶149.5513.0572.4785.9624.3235.5113.0516.882.56底259.814顶114.5852.272.4785.9624.3532.8265.2510.163.99底557.123顶114.5852.272.4785.9624.3830.13117.4510.613.85底854.432顶114.5852.272.4785.9624.31127.44169.6511.624.22底1151.741顶114.5852.272.4785.9624.31424.75221.854.931.78底1455.4656 5内力组合5.1竖向荷载作用下梁端弯矩的调幅由于钢筋混凝土结构具有塑性内力重分布性质，因此在重力荷载作用下对梁端弯矩进行调幅，去调幅系数为0.8。表32梁端弯矩的调幅表层数梁左端MGKMGK，，MQKMQK，，M1MGEBC跨542.9034.324.143.3144.9858.61447.4337.9414.7111.7754.7743.82345.1136.0915.3312.2652.5442.03245.1636.1315.4312.3452.8642.29141.3433.0714.1411.3148.4138.73CD跨512.459.960.370.3012.7210.18410.488.382.752.2011.869.49311.138.902.582.0612.419.93211.088.862.562.0512.369.89111.539.222.972.3813.6910.95表33梁跨中弯矩的调幅表层数梁跨中MGKMGK，，MQKMQK，，M2MGEBC跨550.5759.852.793.5751.8261.52430.0239.8511.4114.4935.4546.85331.8941.3510.8314.0237.3048.36231.9141.3710.8014.0137.0748.14135.3244.0912.0414.9941.4051.65CD跨5-4.32-1.830.310.38-4.32-1.794-3.79-1.69-0.050.50-3.83-1.463-4.45-2.220.120.64-4.83-2.352-4.40-2.180.140.65-4.33-1.661-4.85-2.54-0.270.38-5.66-2.9256 表34梁端弯矩的调幅表层数梁右端MGKMGK，，MQKMQK，，M3MGEBC跨549.9339.943.682.9452.0640.04450.9040.7216.0512.8459.2047.36349.4639.5716.6013.2857.7246.18249.3939.5716.6513.3257.8746.30146.3937.1115.3712.3054.0443.23CD跨512.459.960.370.3012.7210.18410.488.382.752.2011.869.49311.138.902.582.0612.419.93211.088.862.562.0513.3610.69111.539.222.972.3813.6910.95注：①；(5-1)②=(5-2)(5-3)③；(5-4)；(5-5)④56 5.2控制截面及其内力组合5.2.1控制截面梁：梁端及跨中柱：上下柱端截面5.2.2竖向荷载作用下梁控制截面处剪力表35控制截面处剪力表(梁左端)层b梁左端BC跨50.555.473.8457.2358.6121.6240.545.6615.4553.3943.8230.4930.545.5215.4653.2542.0328.9120.545.5415.4853.2842.2928.9910.545.4115.4653.1438.7325.49CD跨50.510.730.7111.0910.187.2340.59.083.5610.919.496.7630.59.083.5610.919.937.2220.59.083.5610.919.897.1610.59.083.5610.9110.957.70表36控制截面处剪力表(梁右端)层b梁右端BC跨50.557.913.9859.9040.0425.0740.546.7515.8754.6947.3633.6930.546.9015.8654.8346.1832.4720.546.8815.8454.8046.3032.6010.547.0115.8654.9443.2329.5050.510.750.7111.1110.187.4056 D跨40.59.083.5610.869.496.7830.59.083.5610.869.937.2220.59.083.5610.8610.697.9810.59.083.5610.8610.958.24注：；(5-6)(5-7)5.2.3梁控制截面处弯矩表37梁控制截面处弯矩表(梁左端)层b梁左端BC跨50.534.3255.4720.453.313.842.3540.537.9445.6626.5311.7715.457.9130.536.0945.5224.7112.2615.468.4020.536.1345.5424.7512.3415.488.4710.533.0745.4121.7211.3115.467.45CD跨50.59.9610.737.280.301.710.1240.58.389.086.112.23.561.3130.58.909.086.630.063.561.1720.58.869.086.592.053.561.1610.59.229.086.952.383.561.49表38梁控制截面处弯矩表(梁右端)层b梁右端BC跨50.539.9457.9125.462.943.981.9540.540.7246.7529.0312.8415.878.8756 30.539.5746.9027.8513.2815.869.3220.539.5146.8827.7913.3215.849.3210.537.1147.0125.3612.3015.868.34CD跨50.59.9610.757.270.300.710.1240.58.389.086.112.203.561.3130.58.909.086.632.063.561.1720.58.869.086.592.053.561.1610.59.229.086.952.383.561.49注：(5-8)(5-9)5.2.4水平地震作用下梁控制截面处的内力表39水平地震作用下梁控制截面处的内力表层V（kN）b(m)梁左端梁右端跨中BC跨510.610.538.1035.4528.7626.114.67421.650.577.4972.0859.5654.158.97333.730.5122.57114.1489.9181.4816.33239.910.5132.19122.21119.27109.296.46144.580.5155.65144.44125.19114.0515.23CD跨518.080.521.6917.1721.6917.170.000440.270.548.3238.2548.3238.250.000356.520.567.8253.6967.8253.690.000274.980.589.9871.2489.9871.240.000178.700.594.4474.7794.4474.770.000注：(5-10)56 5.3基本组合公式5.3.1框架梁内力组合［7］(1)梁端负弯矩组合公式:①(5-11)②(5-12)③(5-13)(2)梁端正弯矩组合公式:④(5-14)(3)梁跨中正弯矩组合公式:⑤(5-15)⑥(5-16)⑦(5-17)(4)梁端剪力组合公式:⑧(5-18)⑨(5-19)⑩(5-20)表40梁的内力组合表(边跨5层)位置楼层内力及组合梁左端梁跨中梁右端MK(kN)VK(kN)MK(kN)VK(kN)MK(kN)VK(kN)边跨梁5永久荷载-20.4555.4759.85-1.2225.46-57.91可变荷载-2.353.843.75-0.071.95-3.98重力荷载代表值-21.6257.3961.64-1.2626.44-59.90地震作用左来35.45-10.614.67-10.6126.11-10.61右来-35.4510.61-4.6710.61-26.1110.61-MMAX(梁端)①-27.8671.9432.28-70.0656 ②-29.9178.6536.28-82.08③-54.0362.0049.25-64.25+MMAX(梁端)④18.35-53.395.6334.58+MMAX(跨中)⑤76.82-1.56⑥84.30-1.72⑦60.11-11.47VMAX(梁端)⑧-27.8371.9432.28-70.06⑨-29.9178.6536.28-82.08⑩-61.2370.2655.82-68.74表41梁的内力组合表(边跨4层)位置楼层内力及组合梁左端梁跨中梁右端MK(kN)VK(kN)MK(kN)VK(kN)MK(kN)VK(kN)边跨梁4永久荷载-26.5345.6639.85-0.5529.03-46.75可变荷载-7.9115.4514.49-0.218.87-15.87重力荷载代表值-30.4953.3947.10-0.5633.47-54.69地震作用左来72.08-21.658.97-21.6554.15-21.65右来-72.0821.65-8.9721.65-54.1521.65-MMAX(梁端)①-42.9176.4247.25-78.32②-43.5776.7847.88-78.67③-97.5369.1982.91-70.32+MMAX(梁端)④47.41-61.1527.6919.91+MMAX(跨中)⑤68.11-0.95⑥67.00-0.95⑦51.13-21.70VMAX(梁端)⑧-42.9176.4247.25-78.32⑨-43.5776.7847.88-78.67⑩-110.7578.3893.9879.71-表42梁的内力组合表(边跨3层)位置楼层内力及组合梁左端梁跨中梁右端MK(kN)VK(kN)MK(kN)VK(kN)MK(kN)VK(kN)边跨梁3永久荷载-24.7145.5241.35-0.6927.85-46.90可变荷载-8.415.4614.02-0.209.32-15.86重力荷载代表值-28.9153.2548.36-0.7932.51-54.83地震作用左来114.14-33.7316.33-33.7381.48-33.73右来-114.1433.73-16.3333.73-81.4833.73-MMAX(梁端)①-41.4176.2746.47-78.48②-41.5976.6046.73-78.86③-137.3180.81108.70-82.23+MMAX(梁端)④89.60-72.8255.068.24+MMAX(跨中)⑤69.25-1.1156 ⑥69.56-1.13⑦59.45-33.60VMAX(梁端)⑧-41.4176.2746.47-78.48⑨41.5976.6046.73-78.86⑩-155.6191.59123.20-93.20表43梁的内力组合表(边跨2层)位置楼层内力及组合梁左端梁跨中梁右端MK(kN)VK(kN)MK(kN)VK(kN)MK(kN)VK(kN)边跨梁2永久荷载-24.7545.5441.37-0.6727.79-46.88可变荷载-8.4715.4814.01-0.819.36-15.84重力荷载代表值-28.9953.2848.38-0.7632.47-54.80地震作用左来122.21-39.916.46-39.91109.29-39.91右来-122.2139.91-6.4639.91-109.2939.91-MMAX(梁端)①-41.5676.3246.45-78.43②-41.7176.6546.69-78.81③-145.2486.86135.78-88.23+MMAX(梁端)④97.41-78.8782.212.19+MMAX(跨中)⑤69.26-1.06⑥69.58-1.08⑦49.84-39.59VMAX(梁端)⑧-41.5676.3246.45-78.43⑨-41.7176.6546.69-78.81⑩-164.6197.78148.37-100.00表44梁的内力组合表(边跨1层)位置楼层内力及组合梁左端梁跨中梁右端MK(kN)VK(kN)MK(kN)VK(kN)MK(kN)VK(kN)边跨梁1永久荷载-21.7245.4144.09-0.825.36-47.01可变荷载-7.4515.4614.99-0.28.43-15.86重力荷载代表值-25.4553.1451.59-0.929.58-54.94地震作用左来144.44-44.5615.32-44.56114.05-44.56右来-144.4444.56-15.3244.56-114.0544.56-MMAX(梁端)①-36.4976.1442.11-78.62②-36.6276.4542..41-79.01③-163.7391.27137.78-92.89+MMAX(梁端)④121.74-83.3089.05-2.24+MMAX(跨中)⑤73.89-1.24⑥74.21-1.28⑦61.36-44.2656 VMAX(梁端)⑧-36.4976.1442.11-78.62⑨-36.6276.4542.41-79.01⑩-185.57103.44156.20-105.28注：角标K表示内力标准值；表45梁的内力组合表(中跨5层)位置楼层内力及组合梁左(右)端梁跨中MK(kN)VK(kN)MK(kN)VK(kN)中跨梁5永久荷载-7.2810.73-1.830.00可变荷载-0.120.710.380.00重力荷载代表值-7.3411.09-1.640.00地震作用左来17.17-18.080.00-18.08右来-17.1718.080.0018.08-MMAX(梁端)①-8.9013.87②-9.9515.18③-23.45127.61+MMAX(梁端)④11.24-25.95+MMAX(跨中)⑤-1.660.00⑥-2.100.00⑦-1.48-17.26VMAX(梁端)⑧-8.9013.87⑨-9.9515.18⑩-26.4631.29表46梁的内力组合表(中跨4层)位置楼层内力及组合梁左(右)端梁跨中MK(kN)VK(kN)MK(kN)VK(Kn)中跨梁4永久荷载-6.119.08-1.690.00可变荷载-1.313.560.500.00重力荷载代表值-6.7610.86-1.440.00地震作用左来38.25-40.270.00-40.27右来-38.2515.880.0040.27-MMAX(梁端)①-9.1715.75②-9.5349.04③-43.38-63.21+MMAX(梁端)④32.22-47.41+MMAX(跨中)⑤-1.330.00⑥-1.790.00⑦-1.3039.26VMAX(梁端)⑧-9.1715.8856 ⑨-9.5315.75⑩-49.1655.58表47梁的内力组合表(中跨3层)位置楼层内力及组合梁左(右)端梁跨中MK(kN)VK(kN)MK(kN)VK(kN)中跨梁3永久荷载-6.639.08-2.220.00可变荷载-1.173.560.640.00重力荷载代表值-7.2210.86-1.900.00地震作用左来53.69-56.520.00-56.52右来-53.6956.520.0056.52-MMAX(梁端)①-9.5915.88②-10.1015.75③-58.8564.88+MMAX(梁端)④46.93-63.25+MMAX(跨中)⑤-1.770.00⑥-2.380.00⑦-1.71-55.12VMAX(梁端)⑧-9.5915.88⑨-10.1015.75⑩-66.6973.53表48梁的内力组合表(中跨2层)位置楼层内力及组合梁左(右)端梁跨中MK(kN)VK(kN)MK(kN)VK(kN)中跨梁2永久荷载-6.599.08-2.180.00可变荷载-1.163.560.650.00重力荷载代表值-7.1610.86-1.850.00地震作用左来71.24-74.980.00-74.98右来-71.2474.980.0074.98-MMAX(梁端)①-9.5315.88②-10.0315.75③-75.9082.88+MMAX(梁端)④64.09-81.26+MMAX(跨中)⑤-1.710.00⑥-2.310.00⑦-1.67-73.01VMAX(梁端)⑧-9.5315.8856 ⑨-10.0315.75⑩-86.0294.48表49梁的内力组合表(中跨1层)位置楼层内力及组合梁左(右)端梁跨中MK(kN)VK(kN)MK(kN)VK(kN)中跨梁1永久荷载-6.959.08-2.540.00可变荷载-1.493.560.380.00重力荷载代表值-7.7010.86-2.730.00地震作用左来74.77-78.700.00-78.70右来-74.7778.700.0078.70-MMAX(梁端)①-10.4315.88②-10.8415.75③-79.8386.51+MMAX(梁端)④67.13-84.88+MMAX(跨中)⑤-2.510.00⑥-3.060.00⑦-2.46-76.73VMAX(梁端)⑧-10.4315.58⑨-10.8415.75⑩-90.4798.0456 5.3.2框架柱内力组合［7］考虑地震作用时：①1.3×地+1.2×(恒+0.5×活)不考虑地震作用时：②γ0(1.35×恒+0.7×1.4×活)③γ0(1.2×恒+1.4×活)表50柱的内力组合表楼层截面位置内力种类内力值组合结果恒载活载代表值地震作用|Mmax|NminNmax左来右来①②③5边柱上端M42.94.1444.98-38.1038.10103.5161.9757.65N207.049.15211.77-10.6110.61267.92288.77261.68V-19.54-2.94-21.0116.28-16.28-46.38-29.26-27.56下端M27.456.4430.66-20.5120.5163.4543.3742.06N231.349.45236.07-10.6110.61279.08321.57290.84V-19.54-2.94-21.0116.28-16.28-46.38-29.26-27.56中柱上端M-37.47-3.32-39.13-50.4550.45112.54-53.84-49.60N235.5113.05242.04-7.477.47300.16330.73300.88V16.682.5617.9622.93-22.9351.3625.3023.6下端M-23.28-5.88-26.22-32.1032.10-73.20-37.19-36.17N259.8113.05266.34-7.477.47329.32363.53328.84V16.882.5617.9622.93-22.9351.3625.3023.844边柱上端M19.988.2724.1-56.9856.98103.0035.0835.55N461.3747.25484.99-32.2632.26623.93669.15619.79V-11.78-4.43-13.9928.78-28.78-54.20-20.24-20.34下端M22.447.6626.27-46.6246.6292.1337.8037.65N485.6747.25509.30-32.2632.26653.10701.96648.95N-11.78-4.43-13.9928.78-28.78-54.20-20.24-20.34中柱上端M-17.41-7.42-21.11-80.2780.27-129.68-30.78-31.28N542.8265.25565.45-26.0926.09712.46783.25730.73V10.163.9912.1640.54-40.5467.2917.6317.78下端M-19.17-69.96-22.65-65.6765.67-112.5532.70-32.75N557.1265.25589.75-26.0926.09741.62816.06759.89V10.163.9912.1640.54-40.5467.2917.6317.783边柱上端M22.447.6626.27-75.9575.95130.2637.8037.65N64.4885.05687.33-65.9965.99910.58953.83892.8356 V-12.39-4.23-14.5138.36-38.36-67.28-20.87-20.79下端M22.187.5725.96-62.1462.14119.9337.3637.21N669.185.05709.35-65.9965.99937.01986.63921.99V-12.39-4.23-14.5138.36-38.36-67.28-20.87-20.79中柱上端M-19.17-6.96-22.65-92.0692.06-146.86-32.70-32.75N830.13117.45888.86-48.8848.881130.181235.781160.59V10.613.8512.5454.03-54.0385.2918.1018.12下端M-19.04-6.91-22.46-95.0995.09-150.57-32.48-32.52N850.43117.45909.06-48.8848.881154.541263.181184.95V10.613.8512.5454.03-54.0385.2918.1018.12(续表)楼层截面位置内力种类内力值组合结果恒载活载代表值地震作用|Mmax|NminNmax左来右来①②③2边柱上端M22.857.8426.88-70.0570.05123.1938.5338.40N899.13122.85960.56-105.90105.901290.341334.221250.95V-13.86-4.74-16.2340.03-40.03-71.52-23.36-23.27下端M27.069.2431.67-72.0572.05131.6745.5945.41N923.43122.85984.86-105.90105.901319.501367.021280.11V-13.86-4.74-16.2340.03-40.03-71.52-23.36-23.27中柱上端M-19.487.07-22.98-114.16114.06-175.98-33.23-33.27N1127.44169.651212.27-83.9583.951563.861688.301590.44V16.624.2218.7363.42-63.42104.9226.5725.85下端M-22.36-8.12-26.41-114.16114.16-180.1-38.14-38.20N1151.74169.651239.57-83.9583.951596.621721.111619.60V16.624.2218.7363.42-63.42104.9226.5725.851边柱上端M14.284.8516.72-83.6083.60128.7424.0323.93N1153.46169.751238.34-150.48150.481681.631723.531621.80V-4.76-1.62-5.5752.58-52.58-75.04-8.01-7.98下端M7.142.458.36-155.64155.64212.3612.0412.00N1184.17169.751269.05-150.48150.481718.481764.981658.65V-4.76-1.62-5.5752.58-52.58-75.04-8.01-7.98中柱上端M-11.84-4.28-13.97-105.47105.47-153.88-20.18-20.20N1424.75221.851535.68-118.07118.071997.512140.832020.29V4.931.785.8262.78-62.7888.608.408.41下端M-5.92-2.14-6.99-174.53174.53-235.28-10.09-10.1N1455.46221.851566.39-118.07118.072033.162182.282057.14V4.931.785.8262.78-62.7888.608.408.4156 56'