东南大学横向框架计算书

第一部分设计条件一、工程名称洪泽县文化中心二、建筑设计资料本建筑为洪泽县文化中心。采用钢筋砼全现浇框架结构，共五层楼，底层层高4.5m，二～五层层高为4.2m。本建筑总长为59.0m，总宽为21.0m，总高为建筑平面如下图所示：三、基本数据1、工程地质报告摘要建筑场地表层为素填土，厚为1.8m，其下为粉质粘土层，厚度为1.1m，再下为中密卵石土层，厚1m，再下依次为：2.4m稍密卵石土层；2.3m中密卵石土层；1.9m密实卵石土层；0.9m中密卵石土层；2.5m密实卵石土层；1.0m稍密卵石土层；1.6m密实卵石土层(二)、气象条件摘要主导风象：东南风基本风压：W0=0.7KN/m2基本雪压：S0=0.40KN/m2(三)、活荷载查《建筑结构荷载规范》可知楼面活荷载为5.0KN/m2，楼梯活荷载为3.5m2第二部分结构方案的选型及布置一、确定结构体系本工程采用框架承重，现浇整体式钢筋砼楼板，墙体240厚KP1空心砖墙。二、梁柱截面的确定1、横向框架梁(1)、截面高度h框架梁的高度可按照高跨比来确定，即梁高h=L。h=L1=×7200＝583~875mm取h=700mm(2)、截面宽度b=h=×700＝280~350mm取b=302、纵向框架梁(1)、截面高度h=L1=×7200＝583~875mm取h=700mm(2)、截面宽度b=h=×700＝280~350mm取b=303、框架柱按轴心受压公式≤[轴压比]计算中柱N=1.25×14×7.0×7.0×5=4287.5b≥==534mm边柱N=1.25×1.05×14×7.0×3.5×5=2251b≥==387.0mm故取中柱截面600×600mm，取边柱截面450×450mm。三、横向框架的布置标准层底层四、横向框架的跨度和柱高1、框架的跨度框架的跨度应取柱形心间的距离。2、框架底层柱的高度框架的底层柱高取基础扩大面至二层楼板顶面间的距离。根据地质资料综合分析，假定基础高度为1.5m，确定基础顶面标高为-0.60，二层板顶的标高为4.5，所以底层柱高应取为3、其余各层柱高除底层柱外的其余各层柱的柱高均取层高，故本设计其余各层柱高均为4.2m第三部分横向框架内力计算一、水平地震荷载下的横向框架(KJ-5)内力计算(一)、地震作用的计算地震作用的计算即地震荷载的计算。按《建筑抗震设计规范》规定，本设计的结构底部总剪力(即总地震荷载)可以按公式FEK=α1·Geq来计算，其中α1=αmax·。1、产生地震荷载的建筑物总质量Geq的计算(1)、作用于房屋上的恒载标准值①、屋面荷载防水层三毡四油热铺绿豆砂一层0.4KN/㎡找平层20厚1：3水泥砂浆找平层0.02*20=0.4KN/㎡保温层70厚水泥防水珍珠岩块保温层0.07*4=0.28KN/㎡找平层20厚1：3水泥砂浆找平层0.02*20=0.4KN/㎡结构层100厚现浇钢筋砼屋面板0.1*25=2.5KN/㎡粉刷层10厚1：3水泥砂浆粉平顶0.01*20=0.2KN/㎡Σ=4.18KN/㎡②、楼面荷载面层15厚1：2水泥白石子0.015*16=0.24KN/㎡找平层20厚1：3水泥砂浆找平层0.02*20=0.4KN/㎡垫层30厚C20细石砼0.03*18.5=0.555KN/㎡防水层1.5厚水乳型橡胶沥青防水涂料0.0015*10=0.015KN/㎡找平层20厚1：3水泥砂浆找平层0.02*20=0.4KN/㎡结构层100厚现浇钢筋砼楼板0.1*25=2.5KN/㎡粉刷层10厚1：3水泥砂浆粉平顶0.01*20=0.2KN/㎡Σ=4.31KN/㎡③、框架梁、柱重量a、700mm0.3*0.7*25+(0.6*2+0.3)*0.02*20=5.85KN/mb、框架柱0.6*0.6*25+0.6*4*0.02*20=9.96KN/m0.45*0.45*25+0.45*4*0.02*20=5.78KN/mc、门过梁0.2*0.1*25+(0.2*2+0.1)*0.02*20=0.70KN/m(2)、质点质量Gi的计算决定多层框架的地震荷载时，结构的计算简图可以认为是一多质点体系，产生地震荷载的建筑物重量集中于各层的楼盖处，各质点质量还应包括上下各半层范围内的恒载，50%的雪载或50%的楼面等效均布活荷载。①、集中于屋盖平面处的质点质量G５雪载（50%）0.5*0.4*59*14=165.2KN屋面恒载4.18*59*14=3452.68KN700高横向框架梁5.85*(7.0-0.6/2-0.45/2)*20=757.575KN700高纵向框架梁5.85*(7.0-0.6)*8+5.85*（3-0.6）*1+5.85*(7.0-0.45)*8*2+5.85*（3-0.45）*2=957.1KN门过梁0.7*1*17=11.9KN1m高女儿墙 0.24*1*(59+14)*2*19=665.76kN外墙 0.24*(2.1-0.7)*[(59+14)*2-3-3]*19=893.76kN

内墙0.24*(2.1-0.7)*[5*7+7*7+7-2+2+(7-1)*12+(4-1)]*19=1059.74kN柱9.96*2.1*10+5.78*2.1*20=451.92KN合计：=7553.64KN②、集中于四层顶盖处的质点质量G4楼面活载（50%）0.5*5.0*59*14=2065KN楼面恒载59*14*4.31=3560.06KN700高横向框架梁757.57KN700高纵向框架梁957.10KN过梁11.9KN外墙 0.24*(4.2-0.7)*[(59+14)*2-3-3]*19=2234.4kN

内墙0.24*(4.2-0.7)*[5*7+7*7+7-2+2+(7-1)*12+(4-1)]*19=2649.36kN

柱9.96*4.2*10+5.78*4.2*20=903.84KN合计:=13130.23KN③、集中于二、三层顶盖平面处的质点质量G2=G3=G4 =13130.23KN⑤、集中于一层顶盖处的质点质量G1楼面活载2065KN雪载（50%） 0.5*0.4*59*7=82.6KN楼面恒载 3560.06KN屋面恒载 4.18*59*7=1726.34700高横向框架梁5.85*(7.0-0.6/2-0.45/2)*30=1136.46KN700高纵向框架 5.85*(7.0-0.6)*16+5.85*(3-0.6)*2+5.85*(7.0-0.45)*8*2+5.85*（3-0.45）*2=1270KN柱9.96*(2.1+2.55)*20+5.78*(2.1+2.55)*20=1463.82KN外墙 0.24*2.1*[(59+14)*2-3-3]*19+0.24*(2.55-0.7)*[(59+21)*2-4*6-2*6-7]*19=2327.652KN设计时底层没有布置内隔墙，取底层内墙荷载为2.5kN/m2;则内墙荷载为 2.5/2*59*21+0.24*(2.1-0.7)*[5*7+7*7+7-2+2+(7-1)*12+(4-1)]*19=2608.49合计：G1=16240.42KN整个建筑物的重力荷载代表值如下图所示：2、梁和柱刚度的计算本工程柱、梁的砼均采用C35，EC=3.15*107KN/m2。(1)、梁和柱的线刚度计算①、梁的线刚度计算在计算框架梁的惯性矩时，考虑梁为矩形截面。框架梁截面的折算惯性矩计算时，对于现浇整体式结构，中框架的折算系数为2，边框架的折算系数为1.5。类型截面积b*h跨度截面惯性矩中框架边框架IB=2I0iBIB=1.5I0iB700高0.3*0.77.08.575*10-316.15*10-37267512.86*10-357870注：表中iB=(KNm)②、柱的线刚度计算a、中柱（600600mm层次层高(m)截面积b*h(m2)截面惯性矩IC=bh3线刚度iC底层5.10.6*0.610.8*10-366706其余层4.20.6*0.610.8*10-381000注：表中iC=(KNm)b、边柱（45045层次层高(m)截面积b*h(m2)截面惯性矩IC=bh3线刚度iC底层5.10.45*0.453.42*10-321106其余层4.20.45*0.453.42*10-325628注：表中iC=(KNm)(2)、柱的侧移刚度D值的计算a、中框架中柱(C柱)侧移刚度D值的计算层次截面(m2)层高(m)线刚度KαD=α·50.6*0.64.2810001.0540.3451901040.6*0.64.2810001.0540.3451901030.6*0.64.2810001.0540.3451901020.6*0.64.2810001.0540.3451901010.6*0.65.1667062.1790.64119727注：底层=，α=；非底层==4*42675/(2*81000)=1.054，α=中框架边柱（D柱）侧移刚度D值的计算层次截面(m2)层高(m)线刚度KαD=α·50.45*0.454.2256282.8360.5861021640.45*0.454.2256282.8360.5861021630.45*0.454.2256282.8360.5861021620.45*0.454.2256282.8360.5861021610.45*0.455.1211063.4430.7247050注：底层=，α=；非底层=，α=中框架边柱（B柱）侧移刚度D值的计算层次截面(m2)层高(m)线刚度KαD=α·50.45*0.454.2256282.8360.5861021640.45*0.454.2256282.8360.5861021630.45*0.454.2256282.8360.5861021620.45*0.454.2256284.2540.681185510.45*0.455.1211065.6720.8047829注：底层=，α=；非底层=，α=中框架边柱（A柱）侧移刚度D值的计算层次截面(m2)层高(m)线刚度KαD=α·10.45*0.455.1211063.4430.7247050e边框架中柱（C柱）侧移刚度D值的计算层次截面(m2)层高(m)线刚度KαD=α·50.6*0.64.2810001.4230.4162292240.6*0.64.2810001.4230.4162292230.6*0.64.2810001.4230.4162292220.6*0.64.2810001.4230.4162292210.6*0.65.1667061.7350.59818404注：底层=，α=；非底层=，α=e边框架边柱（D柱）侧移刚度D值的计算层次截面(m2)层高(m)线刚度αD=α·50.45*0.454.2256282.2580.530924040.45*0.454.2256282.2580.530924030.45*0.454.2256282.2580.530924020.45*0.454.2256282.2580.530924010.45*0.455.1211062.7420.6486310注：底层=，α=；非底层=，α=f边框架边柱（B柱）侧移刚度D值的计算层次截面(m2)层高(m)线刚度KαD=α·50.45*0.454.2256282.2580.530924040.45*0.454.2256282.2580.530924030.45*0.454.2256282.2580.530924020.45*0.454.2256283.3870.6291096510.45*0.455.1211065.4840.7807595注：底层=，α=；非底层=，α=f边框架边柱（A柱）侧移刚度D值的计算层次截面(m2)层高(m)线刚度KαD=α·10.45*0.455.1211062.7420.6846660(3)、各层柱侧移刚度之和(层间刚度)的计算层次中框架中柱中框架边柱边框架中柱边框架边柱∑D519010*88*2=16345622922*2=458449240*2*2=36960152080+163456+45844+36960=3983404152080163456458443696039834031520801634564584436960398340215208011855*8*2=1896804584410965*2*2=43860431464119727*8=1578167050*8+7829*8+7050*82+7595*2=519986310*2+6660*2=259404111863、结构基本自振周期T1的计算层次各层重量(KN)总重量(KN)层间刚度∑DiΔui=∑um=∑Δui57553.647553.643983400.0190.418413130.2320683.873983400.0520.399313130.2333814.13983400.0850.347213130.2346944.334314640.1090.262116240.4263184.754111860.1540.154T1=1.7*ΨT*=1.7*0.6*=0.659(s)＞Tg=1.4*0.4=0.56(s)注：上式中，对于民用建筑取ΨT=0.6~0.8，本设计取ΨT=0.6；对于Ⅱ类场地土近震取特征周期值Tg=0.4(s)4、横向水平地震作用的计算本设计的建筑为7°近震，地震影响系数αmax=0.08，则相应于基本自振周期的α1值为：α1＝αmax·()0.9=0.08*()0.9=0.0510所以结构总水平地震作用值为：FEK=α1·Geq=0.0510*0.85*63184.75=2739.06KN因为T1＞1.4Tg，由于高振型影响，根据对大量结构的地震反应直接动力分析证明，计算时结构顶部的地震剪力偏小，故须进行调整。方法是将结构的总地震作用的一部分作为集中力，作用于结构顶部，再将余下的地震作用按倒三角形分配给各质点。对于多层钢筋砼房屋，顶部附加地震作用系数δn可以按照特征周期Tg及结构的基本周期T1来确定，当Tg=0.3~0.4s时，δn=0.08T1+0.01=0.08*0.659+0.01=0.0627故附加的集中水平地震作用为：ΔFn=δn*FEK=0.0627*2663.87=167.0KN则各质点分配的地震作用为：Fi=*FEK(1-δn)层次层高(m)高度(m)重量(KN)Fi=×FEK(1-δn)剪力Vi54.221.97553.640.212076544.4672711.467244.217.713130.230.297946764.9231476.3934.213.513130.230.227247583.4162059.80624.29.313130.230.156548401.9092461.71515.15.116240.420.106184272.60842734.324(二)、水平地震荷载作用下的结构变形验算根据《建筑抗震设计规范》的要求，本结构须进行多遇地震作用下的抗震变形验算，要对结构的变形加以限制，使其层间弹性位移以及结构顶点位移不超过一定的限值。对于砌体填充墙的框架结构，其层间弹性位移限值为≤，其顶点弹性位移变形限值≤。本结构变形计算如下表所示：层次剪力Vi刚度Di层间位移ΔUi=iiiDViiihUΣΔUi5711.46723983400.0017861/2351.5180.02301941476.393983400.0037061/1133.1880.02123332059.8063983400.0051711/812.2260.01752622461.7154314640.0057051/736.13270.01235512734.3244111860.006651/631.59350.00665由上表可知，结构层间相对位移ihiU均小于，故其层间弹性位移满足要求。结构的顶点位移为==≤，ihiU故也满足要求。(三)、地震荷载作用下的横向框架内力计算由底部剪力法计算出来的每层的地震剪力，按照每榀框架的刚度比值分配到每榀框架上，而每榀框架的地震剪力按柱的刚度比值分配到每一根柱上，最后以反弯点法求结构的内力。现以KJ-5为例，其内力的计算如下：1、地震剪力的分配在每层结构中，KJ-5的地震剪力分配系数为：底层第二层其他层故地震剪力分配为：第五层=711.47*0.0990=70.44KNB柱(D柱)C柱V=Vim**70.44=18.24KN*70.44=33.95KN第四层=1476.39*0.0990=146.16KNB柱(D柱)C柱V=Vim**146.16=37.86KN*146.16=70.45KN

第三层=2059.81*0.0990=203.92KNB柱(D柱)C柱V=Vim*N*第二层=2461.72*0.0952=234.36KNB柱C柱D柱V=Vim*×*234.36=108.45*234.36第一层=2734.32*0.1013=276.99KNA柱B柱V=Vim*C柱D柱V=Vim*2、柱的反弯点高度计算位置系数BCDA第五层m=5n=5h=4.22.8361.054同B柱－y00.4420.353I11y100α2－－y2－－α311y3001.8561.483第四层m=5n=4h=4.22.8361.054同B柱－y00.450.403I11y100α211y200α311y3001.891.693位置系数BCDA第三层m=5n=3h=4.22.8361.054同B柱－y00.50.453I11y100α211y200α311y3002.11.90第二层m=5n=2h=4.24.2541.0542.836－y00.500.500.5I111y1000α2111y2000α31.2141.2141.214y30002.12.12.1第一层m=5n=1h=5.15.6722.1793.4433.443y00.5500.645．6320.550.55I－－－－y10000α20.8240.8240.8240.824y20000α3－－－－y300002.8053.2742.8052.805注：1.y0由m、n及查表得到。2.y1由α1及查表得到，α1=；当i1+i2＞i3+i4时，α1取倒数，即α1=并且y1值取负号“-”。3.y2由α2及查表得到，α2=h上/h本。4.y3由α3及查表得到，α3=h下/h本。5.=(y0+y1+y2+y3)h。

3、柱端弯矩计算设地震荷载从左向右作用柱下端弯矩M下=*V柱上端弯矩M上=(h-)*V柱端弯矩计算结果如下图所示：4、梁端弯矩计算——根据节点平衡来计算第五层：MDC=MBC=42.75KNmMCD=MCB=0.5*92.24=46.12KNm第四层：MDC=MBC=33.85+87.46=121.31KNmMCD=MCB=0.5*(176.62+50.35)=113.49KNm第三层：MDC=MBC=71.56+110.92=182.48KNmMCD=MCB=0.5*(119.27+226.04)=172.66KNm第二层：MDC=142.02+110.92=252.94KNmMBC=110.92+122.39=233.31KNmMCD=MCB=0.5*(227.75+186.73)=207.24KNm第一层：MDC=142.02+107.59=249.61KNmMAB=107.59KNmMCD=MCB=0.5*(227.75+239.52)=233.64KNmMBC=MBA=0.5*(122.39+119.48)=120.94KNm5、水平地震作用下的框架内力图(左向)框架的弯矩图由柱端弯矩和梁端弯矩可以直接做出，弯矩图画在构件的受拉边，不标正负号。框架的剪力图根据框架弯矩图，通过对梁或柱取脱离体，求某一点ΣM=0，则可以求出梁端和柱端剪力，然后即可做出剪力图。框架轴力图即柱轴力图，根据框架剪力图，取节点脱离体，求ΣY=0，即可求出柱的轴力图，轴力以柱受压为正。M图(KNm)

V图(KN)N图(KN)二、风荷载作用下的横向框架(KJ-5)内力计算(一)、风荷载计算(假定风从左向右吹)垂直于建筑物表面上的风荷载标准值应为：WK=βZμSμZw0。因结构高度H=21.9m＜30m，故取βZ=1.0；对于矩形截面，μS=1.3，本建筑物所在的地面粗糙度为有密集建筑群的大城市市区，故属C层次βZμSZ(m)μZw0(KN/m2)A(m2)PW(KN)51.01.321.90.870.3514.75.8241.01.317.70.740.3529.49.9031.01.313.50.740.3529.49.9021.01.39.30.740.3529.49.9011.01.35.10.740.3532.5510.96注：表中A为各层框架节点的受风面积。故风荷载下的计算简图为：(二)、风荷载下的横向框架内力计算—D值法1、风荷载下各柱剪力的分配：层数B柱C柱D柱A柱5=1.51=2.81同B柱－4=4.07=7.583=6.54=12.352=10.25=16.44*35.52=8.83－1*46.48=8.74*46.48=22.01*46.48=7.87同D柱2、柱的反弯点高度计算位置系数BCDA第五层m=5n=5h=4.22.8361.054同B柱－y00.4420.353I11y100α2－－y2－－α311y3001.8561.483第四层m=5n=4h=4.22.8361.054同B柱－y00.450.403I11y100α211y200α311y3001.891.693位置系数BCDA第三层m=5n=3h=4.22.8361.054同B柱－y00.50.453I11y100α211y200α311y3002.11.90第二层m=5n=2h=4.24.2541.0542.836－y00.500.500.5I111y1000α2111y2000α31.2141.2141.214y30002.12.12.1第一层m=5n=1h=5.15.6722.1793.4433.443y00.5500.6450.550.55I－－－－y10000α20.8240.8240.8240.824y20000α3－－－－y300002.8053.2902.8052.805注：1.y0由m、n及查表得到。2.y1由α1及查表得到，α1=；当i1+i2＞i3+i4时，α1取倒数，即α1=并且y1值取负号“-”。3.y2由α2及查表得到，α2=h上/h本。4.y3由α3及查表得到，α3=h下/h本。5.=(y0+y1+y2+y3)h。

3、柱端弯矩计算设风荷载从左向右作用柱下端弯矩M下=*V柱上端弯矩M上=(h-)*V柱端弯矩计算结果如下图所示：(C柱和A柱相同)4、梁端弯矩计算——根据节点平衡来计算第五层：MDC=MBC=3.54KNmMCD=MCB=0.5*7.63=3.82KNm第四层：MDC=MBC=2.80+9.40=12.20KNmMCD=MCB=0.5*(11.80+19.00)=15.4KNm第三层：MDC=MBC=7.69+13.73=21.42KNmMCD=MCB=0.5*(12.83+28.41)=20.62KNm第二层：MDC=13.73+21.53=35.26KNMBC=13.73+18.54=32.27KNMCD=MCB=0.5*(23.47+34.52)=29.00KN第一层：MDC=21.53+20.05=41.58KNmMAB=18.06KNMCD=MCB=0.5*(34.52+50.51)=42.52KNmMBC=MBA=0.5*(18.54+18.06)=18.30KNm5、风荷载作用下的框架内力图(左向)框架的弯矩图由柱端弯矩和梁端弯矩可以直接做出，弯矩图画在构件的受拉边，不标正负号。框架的剪力图根据框架弯矩图，通过对梁或柱取脱离体，求某一点ΣM=0，则可以求出梁端和柱端剪力，然后即可做出剪力图。框架轴力图即柱轴力图，根据框架剪力图，取节点脱离体，求ΣY=0，即可求出柱的轴力图，轴力以柱受压为正。M图(KNm)V图(KN)N图(KN)三、竖向恒载作用下的横向框架(KJ-5)内力计算(一)、竖向恒载计算1、屋面框架梁荷载标准值屋面恒载为4.18KN/m2主梁自重(含粉刷)为：5.85KN/m次梁自重(含粉刷)为：7*[0.2*(0.4-0.1)*25)+(0.3*2+0.2)*0.02*20]=12.74KN屋面板与次梁施加于主梁上的集中荷载为：12.74+4.18*3.5*7=115.15KN 12.74+4.18*2.5*7=85.89KN 12.74+4.18*2.25*7=78.57KN2、楼面框架梁荷载标准值楼面恒载为4.31KN/m2主梁自重(含粉刷)为：5.85KN/m次梁自重(含粉刷)为：12.74KN内墙自重 0.24*(4.2-0.7)*19=15.96KN/m主梁上的线荷载为5.85+15.96=21.81KN/m楼面板与次梁施加于主梁上的集中荷载为：12.74+4.31*3.5*7=118.34KN 12.74+4.31*2.5*7=88.16KN 12.74+4.31*2.25*7=80.62KN3、屋面框架节点集中荷载标准值(1)、边柱B(D、A)柱边柱纵向框架梁自重(含粉刷)5.85*7=40.95KN连系梁传来的屋面板自重1/2*3.5*7*4.18=51.205KN1m高女儿墙自重1*0.24*7*19=31.92KN女儿墙粉刷1*0.02*2*7*17=4.76KNGF=128.84KN(2)、中柱 C柱中柱纵向框架梁自重(含粉刷)5.85*7=40.95KN连系梁传来的屋面板自重1/2*(3.5+2)*7*4.18=80.46KNGD=GC=121.41KN4、楼面框架节点集中荷载标准值(1)、边柱(B,D柱)边柱纵向框架梁自重(含粉刷)40.95KN铝合金窗自重 3*3*0.35*2=6.3KN窗下墙自重 0.24*(4.2-3)*7*19=38.30KN窗边墙体自重 0.24*(7-3*2)*4.2*19=19.15KN粉刷 0.02*[(4.2-3)*7+(7-3*2)*4.2]*20*2=10.08KN框架柱自重(含粉刷)5.78*4.2=24.28KN连系梁传来的楼面板自重1/2*3.5*7*4.31=52.80KNGF=191.86KN(2)、中柱(C柱)中柱纵向框架梁自重(含粉刷) 40.95KN内纵墙自重(考虑门洞折减30%) 0.24*(4.2-0.7)*7*19*0.7=78KN粉刷 0.02*(4.2-0.7)*7*20*0.7*2=13.72KN框架柱自重(含粉刷)9.96*4.2=41.83KN连系梁传来的楼面板自重1/2*(3.5+2)*7*4.31=82.97KNGD=GC=257.47KN6、竖向恒载作用下的结构计算简图(二)、竖向荷载作用下横向框架(KJ-5)内力计算1、求各梁端的固端弯矩第五层MCD=-MDC=115.15*7/8+5.85*7/24=124.64KNmMCB=-153.36KNm MBC=144.7KNm第四层及以下各层 MCD=-MDC=192.61KNmMCB=-200.86KNm MBC=208.27KNm第一层MBA=MAB=*5.85*72=23.89KNm2、计算各梁和柱的分配系数各梁柱的线刚度及相对线刚度如下图所示：梁柱的分配系数如下表所示：层次五层四、三、二层底层节点DCBDCBDCBA转动刚度S左梁—3.443*43.443*4—3.443*43.443*4—3.443*43.443*43.443*4上柱———1.214*0.9*43.838*0.9*41.214*0.9*41.214*0.9*43.838*0.9*41.214*0.9*4—下柱1.214*0.9*43.838*0.9*41.214*0.9*41.214*0.9*43.838*0.9*41.214*0.9*41*43.838*41*41*4右梁3.443*43.443*4—3.443*43.443*4—3.443*43.443*43.443*4—ΣS18.1441.3618.1422.5155.1722.5122.1456.7135.9117.77分配系数左梁—0.3330.759—0.2500.612—0.2430.3830.775上柱———0.1940.2500.1940.1970.2440.1220下柱0.2410.3340.2410.1940.2500.1940.1810.2710.1110.225右梁0.7590.333—0.6120.250—0.6220.2430.383—注：在计算分配系数时，除底层柱外的其余各层柱，其线刚度均应乘以折减系数0.9。3、用弯矩分配法计算梁、柱端的弯矩注：各节点间的传递系数均为1/2。顶层在恒荷载作用下的弯矩分配分配系数0.240.760.330.330.330.760.24下柱1右梁1左梁2下柱2右梁2左梁3下柱3固媏弯距-124.64124.64-153.36144.701.3.5传递30.0494.60—>47.300.002.4.6传递-3.09<—-6.19-6.21-6.19—>-3.091.3.5传递0.752.35—>1.17-53.74<—-107.48-34.132.4.6传递8.75<—17.5017.5617.50—>8.751.3.5传递-2.11-6.64—>-3.32-3.32<—-6.64-2.112.4.6传递1.11<—2.212.222.21—>1.111.3.5传递-0.27-0.84—>-0.42-0.42<—-0.84-0.272.4.6传递0.14<—0.280.280.28—>0.141.3.5传递-0.03-0.11—>-0.05-0.05<—-0.11-0.032.4.6传递0.02<—0.040.040.04—>0.020.00-0.01—>-0.01-0.01<—-0.010.000.00<—0.000.000.00—>0.00结果28.37-28.37183.1613.89-197.0536.54-36.54顶层在恒荷载作用下的弯矩图标准层在恒荷载作用下的弯矩分配节点DCB12345678910分配系数0.1940.1940.6120.250.250.250.250.6120.1940.194上柱1下柱1右梁1左梁2上柱2下柱2右梁2左梁3上柱3下柱3固媏弯距-192.61192.61-200.86208.2737.3737.37117.88—>58.94-63.73<—-127.46-40.40-40.401.63<—3.263.263.263.26—>1.63-0.32-0.32-1.00—>-0.50-0.50<—-1.00-0.32-0.320.12<—0.250.250.250.25—>0.12-0.02-0.02-0.08—>-0.04-0.04<—-0.08-0.02-0.020.01<—0.020.020.020.02—>0.010.000.00-0.01—>0.000.00<—-0.010.000.000.00<—0.000.000.000.00—>0.0037.0237.02-74.05254.543.533.53-261.6081.49-40.75-40.75标准层在恒荷载作用下的弯矩图底层在恒荷载作用下的弯矩分配分配系数0.1970.1810.6220.2430.2440.2710.2430.3830.1220.1110.3830.7750.225上柱1下柱1右梁1左梁2上柱2下柱2右梁2左梁3上柱3下柱3右梁3左梁4下柱4固媏弯距-192.61192.61-200.86208.27-23.8923.8937.9434.86119.80—>59.90-35.31<—-70.62-22.49-20.47-70.62—>-35.31-1.99<—-3.97-3.99-4.43-3.97—>-1.994.42<—8.852.570.390.361.24—>0.62-0.47<—-0.93-0.30-0.27-0.93—>-0.47-0.02<—-0.04-0.04-0.04-0.04—>-0.020.18<—0.360.110.000.000.01—>0.01-0.03<—-0.06-0.02-0.02-0.06—>-0.030.00<—0.010.010.010.01—>0.000.01<—0.020.010.000.000.00—>0.000.00<—-0.010.000.00-0.01—>0.000.00<—0.000.000.000.00—>0.000.00<—0.000.00结果38.3435.22-73.56249.13-4.02-4.46-240.67134.65-22.81-20.76-90.89-2.682.68底层在恒荷载作用下的弯矩图4、各层弯矩迭加5、根据弯矩图利用平衡条件及实际荷载求跨中弯矩、剪力及轴力(1)跨中弯矩（KNm）层数CD跨CB跨BA跨5127.0999.614179.44127.863169.56128.292169.02128.71175.64118.048.35（2）梁剪力（KN）层数D右C左C右B左B右A左557.33-98.77128.79-76.624118.13-159.18161.73-127.83112.09-158.93161.48-128.052112.01-159161.61-127.921111.56-159.45152.49-137.0432.33-8.62（3）柱剪力（KN）层数柱D柱C柱B柱A5-19.04-5.0928622.566674-21.34-1.7623.426193-21.2071-1.9523823.63812-22.1857-0.2642918.804761-9.703921.4058825.662745-0.78824（4）柱轴力（KN）层数柱D柱C柱B柱A5186.17348.97205.464496.16927.35525.123800.111505.23845.0321103.982083.311164.8111407.42652.721493.71137.466、进行弯矩调幅弯矩调幅时：支座调幅0.85，跨中调幅0.15。（1）支座弯矩调幅层数DC左C右B左B右5原始弯矩-37.74182.77-197.4546.85-调幅弯矩-32.08155.35-167.8339.82-4原始弯矩-87.39253.09-263.0597.26-调幅弯矩-74.28215.12-223.5982.67-3原始弯矩-89.15253.95-262.1998.12-调幅弯矩-75.78215.86-222.8683.40-2原始弯矩-89.42253.91-262.2394.46-调幅弯矩-76.01215.82-222.9080.29-1原始弯矩-81.24248.85-240.96139.85-85.69调幅弯矩-69.05211.52-204.81118.87-72.84（2）跨中弯矩调幅原始弯矩调幅后弯矩层数CD跨CB跨BA跨层数CD跨CB跨BA跨5127.0999.615146.15114.554179.44127.864206.36147.043169.56128.293194.99147.532169.02128.72194.37148.011175.64118.048.351201.99135.759.607．柱边梁端弯矩（将节点处内力转化为梁端柱边内力）（1）梁端柱边剪力（根据公式V=V’-(g+p)*b/2）层数D右C左C右B左B右5.0056.01-97.02127.04-75.304.00113.22-152.64159.98-122.893.00107.18-152.39159.73-123.142.00107.10-152.46159.86-123.011.00106.65-152.91150.74-132.1331.01（2）梁端柱边弯矩（根据公式M’=M-V’×b/2）层数DC左C右B左B右5.00-19.47126.25-129.7222.884.00-48.81169.33-175.6055.023.00-51.66170.14-174.9455.692.00-51.91170.09-174.9452.611.00-45.06165.65-159.5989.14-65.86四、竖向活载作用下的横向框架(KJ-5)内力计算(一)、竖向活载计算1、屋面框架梁荷载标准值屋面活载为0.7KN/m2屋面板通过次梁传给边跨主梁的集中荷载为：0.7*7.0*3.5=17.15KN/m 0.7*7.0*(2+2.5)/2=11.02 0.7*7.0*2.5=12.25KN/m2、楼面框架梁荷载标准值仓库楼面活载为5.0KN/m2；楼面板通过次梁传给边跨主梁的集中荷载为：5*7.0*3.5=122.5KN/m 5*7.0*(2+2.5)/2=78.85KN/m 5*7.0*2.5=87.5KN/m3、屋面框架节点集中荷载标准值边柱集中力：0.7*7.0*3.5/2=8.58KN 中柱集中力：0.7*7*(3.5+2)/2=13.47KN4、楼面框架节点集中荷载标准值边柱集中力：5*7.0*3.5/2=61.25KN中柱集中力：5*7*(3.5+2)/2=96.25KN(二)、竖向荷载作用下横向框架(KJ-5)内力计算1、竖向活载作用下的结构计算简图2、求各梁端的固端弯矩第五层MCD=-MDC=17.15*7/8=15.01KNmMCB=-18.28KNm MBC=17.15KNm第四层及以下各层 MCD=-MDC=107.19KNmMCB=-130.68KNm MBC=122.59KNm第一层MBA=MAB=17.15*7/8=15.01KNm3、计算各梁和柱的分配系数各梁柱的线刚度及相对线刚度如下图所示：梁柱的分配系数如下表所示：层次五层四、三、二层底层节点DCBDCBDCBA转动刚度S左梁—3.443*43.443*4—3.443*43.443*4—3.443*43.443*43.443*4上柱———1.214*0.9*43.838*0.9*41.214*0.9*41.214*0.9*43.838*0.9*41.214*0.9*4—下柱1.214*0.9*43.838*0.9*41.214*0.9*41.214*0.9*43.838*0.9*41.214*0.9*41*43.838*41*41*4右梁3.443*43.443*4—3.443*43.443*4—3.443*43.443*43.443*4—ΣS18.1441.3618.1422.5155.1722.5122.1456.7135.9117.77分配系数左梁—0.3330.759—0.2500.612—0.2430.3830.775上柱———0.1940.2500.1940.1970.2440.1220下柱0.2410.3340.2410.1940.2500.1940.1810.2710.1110.225右梁0.7590.333—0.6120.250—0.6220.2430.383—注：在计算分配系数时，除底层柱外的其余各层柱，其线刚度均应乘以折减系数0.9。4、用弯矩分配法计算梁、柱端的弯矩（1）顶层在活载作用下的弯矩图分配系数0.240.760.330.330.330.760.24下柱1右梁1左梁2下柱2右梁2左梁3下柱3固媏弯距-15.0115.01-18.2817.153.6211.39—>5.70-6.51<—-13.02-4.130.68<—1.361.361.36—>0.68-0.16-0.52—>-0.26-0.26<—-0.52-0.160.09<—0.170.170.17—>0.09-0.02-0.07—>-0.03-0.03<—-0.07-0.020.01<—0.020.020.02—>0.010.00-0.01—>0.000.00<—-0.010.00结果3.43-3.4321.961.56-23.530.004.32-4.322）标准层在活荷载作用下的弯矩分配分配系数0.1940.1940.6120.250.250.250.250.6120.1940.194上柱1下柱1右梁1左梁2上柱2下柱2右梁2左梁3上柱3下柱3固媏弯距-107.19107.19-130.68122.5920.7920.7965.60—>32.80-37.51<—-75.03-23.78-23.783.53<—7.057.057.057.05—>3.53-0.68-0.68-2.16—>-1.08-1.08<—-2.16-0.68-0.680.27<—0.540.540.540.54—>0.27-0.05-0.05-0.17—>-0.08-0.08<—-0.17-0.05-0.050.02<—0.040.040.040.04—>0.020.000.00-0.01—>-0.01-0.01<—-0.010.000.00结果20.0520.05-40.11146.457.637.63-161.7349.05-24.52-24.52（3）底层在活荷载作用下的弯矩分配分配系数0.1970.1810.6220.2430.2440.2710.2430.3830.1220.1110.3830.7750.225上柱1下柱1右梁1左梁2上柱2下柱2右梁2左梁3上柱3下柱3右梁3左梁4下柱4固媏弯距-107.19107.19-130.68122.59-15.0115.0121.1219.4066.67—>33.34-20.60<—-41.20-13.12-11.94-41.20—>-20.601.31<—2.612.622.912.61—>1.312.17<—4.331.26-0.26-0.24-0.81—>-0.41-0.67<—-1.33-0.42-0.39-1.33—>-0.670.13<—0.260.260.290.26—>0.130.26<—0.520.15-0.03-0.02-0.08—>-0.04-0.07<—-0.15-0.05-0.04-0.15—>-0.070.01<—0.030.030.030.03—>0.010.03<—0.060.020.000.00-0.01—>0.00-0.01<—-0.02-0.010.00-0.02—>-0.010.00<—0.000.000.000.00—>0.000.00<—0.010.00结果20.8319.14-39.97142.982.923.24-149.120.0081.34-13.60-12.37-55.250.00-1.431.43注：各节点间的传递系数均为1/2。5、各层弯矩迭加6、根据弯矩图利用平衡条件及实际荷载求跨中弯矩、剪力及轴力1)梁剪力层数D右C左C右B左B右A左56.77-10.3814.23-9.04446.85-75.65102.94-63.41347.71-75.09102.42-63.93247.37-75.13102.69-63.66147.2-75.28100.85-65.515.82-1.332）柱剪力层数柱D柱C柱B柱A5-6.71-2.538.244-11.75-4.3614.373-11.48-4.3314.232-12.03-0.6911.281-5.560.823.46-0.423）柱轴力层数柱D柱C柱B柱A515.3538.0817.624123.45312.92142.283232.41586.68267.462341.03860.75392.371449.481133.13534.949.914）跨中弯矩层数CD跨CB跨BA跨515.28.884119.0879.523117.6477.22117.3778.521121.1484.953.247、进行弯矩调幅弯矩调幅时：支座调幅0.85，跨中调幅0.15。（1）支座弯矩调幅层数DC左C右B左B右5原始弯矩-8.5021.12-24.3810.52调幅弯矩-7.2317.95-20.728.944原始弯矩-44.90145.69-162.4954.93调幅弯矩-38.16123.84-138.1246.693原始弯矩-48.29145.18-163.0059.05调幅弯矩-41.04123.41-138.5550.192原始弯矩-48.44145.58-162.6156.82调幅弯矩-41.18123.74-138.2248.301原始弯矩-44.12142.36-149.7484.47-52.12调幅弯矩-37.50121.01-127.2871.80-44.302）跨中弯矩调幅原始弯矩调幅后弯矩层数CD跨CB跨BA跨层数CD跨CB跨BA跨515.28.88517.4810.2124119.0879.524136.94291.4483117.6477.23135.28688.782117.3778.522134.975590.2981121.1484.953.241139.31197.69253.726第四部分梁、柱的内力组合一、梁的内力组合在进行梁的内力组合时，每层的框架梁均取边跨左支座、边跨跨中、边跨右支座、中跨支座和中跨跨中五个截面来进行。在组合时，梁的弯矩以梁下部受拉为正，上部受拉为负；梁的剪力以使梁产生顺时针转动为正，反之为负。梁的弯矩、剪力组合（见下页）梁剪力设计值根据公式求得本结构为三级框架，=0.75，=1.1，各梁净跨=7.0-（0.6+0.45）/2=6.47m层次截面位置内力SGkSQkSwkSEk1.2SGk+1.4*0.9(SQk+Swk)rRE[1.2(SGk+0.5SQk)+1.3SEk)]1.35SGk+1.4*0.7SQk1.2SGk+1.4SQkMmaxVbDM-19.47-8.503.5442.75-29.61-38.5320.33-63.03-34.61-35.2663.0390.15五层V56.015.77-1.05-12.7073.1675.8140.6265.3981.2775.2981.27DC跨中M146.1517.480.001.68197.40197.40141.04137.76214.43199.85214.43C左M-126.25-21.12-3.82-46.12-182.92-173.30-168.10-78.16-191.14-181.07191.14V-97.02-10.38-1.05-12.70-130.83-128.18-104.37-79.61-141.15-130.96141.15C右M-129.72-24.383.8246.12-181.57-191.20-82.75-172.69-199.01-189.80199.0178.02V127.0414.23-1.05-12.70169.05171.70108.36133.12185.45172.37185.45CB跨中M114.5510.210.001.68150.32150.32109.33106.05164.65151.75164.65BM-22.88-10.52-3.54-42.75-45.17-36.25-67.0116.36-41.20-42.1867.01V-75.30-9.04-1.05-12.70-103.07-100.43-84.22-59.46-110.51-103.02110.510.00DM-48.81-38.1612.20121.31-91.28-122.0357.18-179.38-103.29-112.00179.38176.97四层V113.2246.85-3.40-33.54190.61199.1890.28155.68198.76201.45201.45DC跨中M146.15136.940.003.91347.92347.92196.97189.35331.50367.10367.10C左M-169.33-123.84-15.40-113.49-378.64-339.83-318.78-97.47-349.96-376.57378.64V-152.64-75.65-3.40-33.54-282.77-274.20-204.12-138.72-280.20-289.08289.08C右M-175.60-138.1215.40113.49-365.35-404.16-109.54-330.85-372.42-404.09404.16148.07V159.98102.94-3.40-33.54317.40325.96157.60223.01316.85336.09336.09CB跨中M114.5591.450.003.91252.68252.68148.06140.43244.26265.49265.49BM-55.02-46.69-12.20-121.31-140.23-109.48-188.8147.75-120.03-131.39188.81V-122.89-63.41-3.40-33.54-231.65-223.08-171.84-106.43-228.04-236.24236.240.00DM-51.66-48.2921.42182.48-95.85-149.83109.69-246.14-117.07-129.60246.14191.21三层V107.1847.71-6.01-50.73181.16196.3068.47167.39191.45195.41196.30DC跨中M194.99135.290.004.91404.45404.45241.16231.58395.82423.39423.39C左M-170.14-123.41-20.62-172.66-385.65-333.68-377.00-40.32-350.63-376.94385.65V-152.39-75.09-6.01-50.73-285.05-269.91-220.40-121.48-279.31-287.99287.99C右M-174.94-138.5520.62172.66-358.52-410.48-51.45-388.14-371.95-403.90410.48163.39V159.73102.42-6.01-50.73313.15328.30140.38239.31316.01335.06335.06CB跨中M147.5388.780.004.91288.90288.90177.52167.94286.17301.33301.33BM-55.69-50.19-21.42-182.48-157.06-103.08-250.62105.21-124.37-137.09250.62V-123.14-63.93-6.01-50.73-235.89-220.75-189.06-90.13-228.89-237.27237.270.00DM-51.91-41.1835.26252.94-69.75-158.61181.37-311.87-110.43-119.94311.87204.65二层V107.1047.37-9.18-65.74176.64199.7753.61181.80191.01194.84199.77DC跨中M194.37134.980.0022.85403.32403.32257.95213.40394.68422.22422.22C左M-170.09-123.74-29.00-207.24-396.56-323.48-410.82-6.70-350.89-377.34410.82V-152.46-75.13-9.18-65.74-289.18-266.05-235.12-106.93-279.45-288.13289.18C右M-174.94-138.2229.00207.24-347.55-420.63-17.59-421.70-371.62-403.44421.70173.49V159.86102.69-8.75-62.94310.20332.25128.72251.45316.45335.60335.60CB跨中M148.0190.300.0013.03291.39291.39186.55161.14288.31304.03304.03BM-52.61-48.30-32.27-233.31-164.65-83.33-296.56158.39-118.36-130.75296.56V-123.01-63.66-8.75-62.94-238.85-216.80-200.72-77.99-228.45-236.74238.850.00DM-45.06-37.5041.58249.61-48.93-153.71185.94-300.80-97.58-106.57300.80207.93一层V106.6547.20-12.01-69.04172.32202.5849.91184.54190.23194.06202.58DC跨中M201.99139.310.007.99417.92417.92252.27236.69409.21437.42437.42C左M-165.65-121.01-42.52-233.64-404.83-297.68-431.3424.26-342.22-368.19431.34V-152.91-75.28-12.01-69.04-293.48-263.21-238.81-104.18-280.20-288.88293.48C右M-159.59-127.2842.52233.64-298.31-405.4626.89-428.71-340.18-369.70428.71172.43V150.74100.85-8.69-50.65297.01318.91131.66230.43302.33322.08322.08CB跨中M135.7597.690.0056.35285.99285.99221.08111.19279.00299.67299.67B左M-89.14-71.80-18.30-120.94-220.49-174.38-230.455.38-190.70-207.49230.45V-132.13-65.50-8.69-50.65-252.04-230.14-197.78-99.01-242.57-250.26252.04B右M-65.86-44.3018.30120.94-111.79-157.9138.71-197.13-132.33-141.05197.1351.42V31.0115.820.00-32.6457.1557.153.2066.8557.3759.3666.85BA跨中M9.603.730.006.6716.2216.2216.823.8216.6216.7416.82AM-2.28-1.22-18.06-107.59-27.0318.48-107.50102.30-4.27-4.44107.50V31.01-15.820.00-32.6417.2817.28-11.0352.6126.3615.0652.61二、柱的内力组合(1)、外柱的内力组合(B柱)在进行柱的内力组合，假定弯矩以使柱右侧受拉为正，使左侧受拉为负；剪力以使柱顺时针转动为正，反之为负；轴力以柱受压为正，受拉为负。1)横向框架B柱弯矩和轴力组层次截面位置内力SGkSQkSwkSEk1.2SGk+1.4*0.9(SQk+Swk)rRE[1.2(SGk+0.5SQk)+1.3SEk)]1.35SGk+1.4*0.7SQk1.2SGk+1.4SQkNMM轴压比1.1*∑Mb∑Mc剪力设计值5.00柱顶M-46.85-10.52-3.54-42.75-73.94-65.01-94.49-5.57-73.56-70.95-94.49-5.22-73.5649.05N205.4617.621.0512.70270.08267.43218.91192.49294.64271.22205.23192.49294.640.087126柱底M47.9324.12.833.8591.4184.3592.7822.3888.3291.2692.7820.9888.32N229.7417.621.0512.70299.21296.56242.21215.80327.41300.35299.21215.80327.410.0968174.00柱顶M-49.33-30.83-9.40-87.46-109.89-86.20-153.1128.80-96.81-102.36-153.1127-96.81207.6863245.9075.64N525.12142.284.4546.24815.02803.81620.50524.32848.35829.34581.7246.24848.350.25086柱底M49.0629.527.6971.56105.7686.38135.69-13.1695.16100.20135.69-12.3395.16N549.40