第五章竖向荷载作用下的框架内力计算

5.1计算单元的确定5.1计算单元的确定取6号轴线一榀框架进行计算，计算宽度为(6.6+6.6)/2=6.6m。如图下图所示5.2荷载计算5.2.1恒荷载的计算1、五层、q、q0、q(、q0〃分别为女儿墙、边跨横梁(走道纵梁)、走道横梁、次梁自重(扣除板自重)，为均布荷载形式；P为考虑梁粉刷自重时的放大系数，取P=1.05。女儿墙：q=3.47x0.9=3.12kN/m边跨横梁(走道纵梁)：q0=1.05x0.3x(0.6-0.1)x25=3.94kN/m走道横梁：q0‘=1.05x0.3x(0.4-0.1)x25=2.36kN/m次梁：q0〃=1.05x0.2x(0.5-0.1)x25=2.1kN/mq1.q{分别为屋面板自重传给横梁的梯形和三角形荷载等效为均布荷载值q1=[1-2x(3.3/6.6x2)2+(3.3/6.6x2)3]x4.38x3.3/2=6.44kN/mq1=5x4.38x3.0/2=4.11kN/m18q2、q2z分别为屋面板自重传给纵梁上的梯形和三角形荷载等效为均布荷载值梯形：q2=[1-2x(3.0/6.6x2)2+(3.0/6.6x2)3]x4.38x3.0/2=5.96kN/m三角形：q,=5x4.38x3.3/2=4.52kN/m28P1为由板传给次梁及次梁自重传给纵梁的集中力P1=q1x6.6+q0〃x6.6/2=49.43kNP2为由板传给外纵梁及外纵梁、女儿墙自重传给柱子的集中力尸2=(q{+q°+q)x3.3x2=76.42kNP3为由板传给内纵梁及内纵梁自重传给柱子的集中力。P3=(q2‘+q2+q0)x3.3x2=95.17kNP4为由板传给边框架横梁及边框架横梁自重传给柱子的集中力P4=q1x6.6+q0x6.6/2=55.51kNP5为由板传给走道横梁及走道横梁自重传给柱子的集中力尸5=q、'x6.6+q。'x3.0/2=30.67kNPA=P1+P2=125.85kNPC=P1+P3=144.6kNPD=P1+P3=144.6kNPE=P1+P2=125.85kN由于梁偏心作用而在梁端产生的弯矩MA=(PA)e=125.85x(0.6-0.3)/2=18.88kN•mMC=(PC)e=144.6x(0.6-0.3)/2=21.69kN•mMD=(PD)e=144.6x(0.6-0.3)/2=21.69kN•mMe=(PE)e=125.85x(0.6-0.3)/2=18.88kN•m2、一~四层：q、q0、q0'、q0〃分别为外纵梁、边跨横梁(走道纵梁)、走道横梁、次梁自重(扣除板自重，包括填充墙重)，为均布荷载形式；B为考虑梁粉刷自重时的放大系数，取P=1.05。外纵梁：q=1.05x0.3x(0.6-0.1)x25+2.77x3.3=13.08kN/m边跨横梁(走道纵梁)：q0=1.05x0.3x(0.6-0.1)x25+1.6x3.3=9.22kN/m走道横梁：q0'=1.05x0.3x(0.4-0.1)x25+1.6x3.3=7.64kN/m次梁：q0〃=1.05x0.2x(0.5-0.1)x25+1.6x3.3=7.38kN/mq1.q1'分别为楼面板自重传给横梁的梯形和三角形荷载等效为均布荷载值q1=[1-2x(3.3/6.6x2)2+(3.3/6.6x2)3]x3.39x3.3/2=4.98kN/mq'=5x3.39x3.0/2=3.18kN/m18q2、q2'分别为楼面板自重传给纵梁上的梯形和三角形荷载等效为均布荷载值梯形：q2=[1-2x(3.0/6.6x2)2+(3.0/6.6x2)3]x3.39x3.0/2=4.62kN/m三角形：q2'=5x3.39x3.3/2=3.50kN/m28P1为由板传给次梁及次梁自重传给纵梁的集中力P1=q1x6.6+q0〃x6.6/2=57.22kNP2为由板传给外纵梁及外纵梁自重传给柱子的集中力P=(q2'+q)x3.3x2=109.43kNP3为由板传给内纵梁及内纵梁自重传给柱子的集中力。尸3=(q2+q?+q°)x3.3x2=114.44kNP4为由板传给边框架横梁及边框架横梁自重传给柱子的集中力P4=q1x6.6+q0x6.6/2=46.70kNP5为由板传给走道横梁及走道横梁自重传给柱子的集中力尸5=qjx6.6+q。'x3.0/2=32.45kNPA=P1+P2=166.65kNPC=P1+P3=171.66kNPD=P1+P3=171.66kNPE=P1+P2=166.65kN由于梁偏心作用而在梁端产生的弯矩MA=(PA)e=166.65x(0.6-0.3)/2=25.00kN•mMC=(PC)e=171.66x(0.6-0.3)/2=25.75kN•mMD=(PD)e=171.66x(0.6-0.3)/2=25.75kN•mMe=(PE)e=166.65x(0.6-0.3)/2=25.00kN•m5.2.2活荷载计算《建筑结构荷载规范》5.1.2规定：当楼面梁从属面积超过25m2时，应取折减系数0.9。本设计中楼面梁的从属面积：6.6x3.3=21.78m2v25m2，故活荷载不需要折减。1、 五层q「q1/分别为房间传给边横梁的梯形荷载和走道板传给走道横梁上的三角形荷载等效为均布荷载值q1=[1-2x(3.3/6.6x2)2+(3.3/6.6x2)3]x0.5x3.3/2=0.74kN/mq1"=5x0.5x3.0/2=0.47kN/m18q2、q2；分别为房间传给纵梁上的梯形和三角形荷载等效为均布荷载值梯形：q2=[1-2x(3.0/6.6x2)2+(3.0/6.6x2)3]x0.5x3.0/2=0.68kN/m三角形：q,=5x0.5x3.3/2=0.52kN/mP为房间通过纵梁传给柱的集中力PA=PE=q2x6.6=4.49kNPC=PD=(q2+q2‘)x6.6=7.92kNM为由于梁偏心作用而在梁端产生的弯矩MA=ME=(PA)e=4.49x(0.6-0.3)/2=0.67kN•mMC=MD=(PC)e=7.92x(0.6-0.3)/2=1.19kN•m2、 一~四层q「q1/分别为房间传给边横梁和走道横梁上的荷载等效为均布荷载值q1=[1-2x(3.3/6.6x2)2+(3.3/6.6x2)3]x2.0x3.3/2=2.96kN/mq'=5x2.0x3.0/2=1.88kN/m18q2、q2'分别为房间传给纵梁上的梯形和三角形荷载等效为均布荷载值梯形：q2=[1-2x(3.0/6.6x2)2+(3.0/6.6x2)3]x2.0x3.0/2=2.72kN/m三角形：q2'=5x2.0x3.3/2=2.08kN/mP为房间通过纵梁传给柱的集中力PA=PE=q2x6.6=17.95kNPc=PD=(q?+q；)x6.6=31.68kNM为梁偏心作用而在梁端产生的弯矩MA=Me=(PA)e=17.95x(0.6-0.3)/2=2.69kN•mMC=MD=(Pc)e=31.68x(0.6-0.3)/2=4.75kN•m表5.1横向框架恒荷载汇总表层数q。(kN/m)q0(kN/m)q1(kN/m)q「(kN/m)q0+q1(kN/m)q0'+q1'(kN/m)PA(Pe)(kN)Pc(pD)(kN)53.942.366.444.1110.386.47125.85144.61~49.227.644.983.1814.2010.82166.65171.66

ql212各层梁上作用的活荷载5.3内力计算梁端、柱端弯矩均采用弯矩二次分配法计算。5.3.1弯矩计算ql212各层梁上作用的活荷载5.3内力计算梁端、柱端弯矩均采用弯矩二次分配法计算。5.3.1弯矩计算层数q1(kN/m)(kN/m)PA(PE)(kN)PC(PD)(kN)50.740.474.497.921~42.961.8817.9531.68各层梁上作用的恒荷载弯矩计算简图恒荷载弯矩计算1、 五层由均布荷载产生的弯矩：MAc=-McA=-l/12xl0.38x6.62=-37.68kN・mMcD=-MDc=-l/12x6.47x3.02=-4.85kN・mMDE=-MED=-1/12x10-38x6-62=-37.68kN^m2、一~四层由均布荷载产生的弯矩：MAC=-MCA=-1/12x14.20x6.62=-51.55kN・mMCD=-MDC=-1/12x10.82x3.02=-8.12kN・mMDE=-MED=-1/12x14.20x6.62=-51.55kN・m活荷载弯矩计算1、五层由分布荷载产生的弯矩：MAC=-MCA=-1/12x0.74x6.62=-2.69kN・mMCD=-MDC=-1/12x0.47x3.02=-0.56kN・mMDE=-MED=-1/12x°.74x6.62=-2.69kN・m2、一~四层由分布荷载产生的弯矩：MAC=-MCA=-1/12x2.96x6.62=-6.82kN・mMCD=-MDC=-1/12x1.88x3.02=-1.41kN・mMDE=-MED=-1/12x2.96x6.62=-6.82kN^m5.3.2横向框架内力计算1、转动刚度

梁柱线刚度取前面计算结果，分配系数按与节点连接方式形式可得各个杆件的转动刚度比值计算。S分配系数按下式计算：卩二弓4ikMsiki=1式中：s为节点K第i根杆件的转动刚度ik构件类别转动刚度S(N-m)架梁A-C横梁S=4i=4x4.45xlOio=1.78xlOiiC-D横梁S=4i=4x3.2xlOio=1.28xlOiiD-E横梁S=4i=4x4.45x10io=1.78x10ii架柱首层S=4i=4x6.5xiOio=2.6xiOii标准层S=4i=4x8.72x1Oio=3.49x1Oii工S为节点K各杆件的转动刚度之和iki=1表5.3梁柱转动刚度2、分配系数表5.4分配系数卩层次节点工Sik左梁右梁上柱下柱五层65.268x1011——0.338——0.662126.548x10110.2720.195——0.533186.548x10110.1950.272——0.533245.268x10ii0.338————0.662二〜四层5（4、3）8.756x1011——0.2020.3990.39911（10、9）10.036x10110.1770.1270.3480.34817（16、15）10.036x10110.1270.1770.3480.34823（22、21）8.756x10110.202——0.3990.399首层27.868x10ii——0.2260.4440.33089.148x10110.1950.1400.3810.284149.148x10110.1400.1950.3810.284207.868x10ii0.226——0.4440.3303、由于是远端固定，传递系数为1/2。经整理两端弯矩为：1、五层（恒荷载）MAc=-MCA=-37.68kN・mMcD=-MDc=-4.85kN・mMDE=-MED=-37.68kN・mDEED2、一~四层（恒荷载）MAC=-MCA=-51.55kN・mMCD=-MDC=-8.12kN・mMDE=-MED=-51.55kN・m1、五层（活荷载）MAC=-MCA=-2.69kN・mMCD=-MDC=-0.56kN・mMDE=-MED=-2.69kN・mDEED2、一~四层（活荷载）MAC=-MCA=-6.82kN・mMCD=-MDC=-1.41kN・mMDE=-MED=-6.82kN・mDEED节点分布图3、 弯矩分配见下表

上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱右梁左梁0.6620.3380.2720.5330.1950.1950.5330.2720.3：18.88-37.6837.6821.69-4.854.85-21.69-37.6837.612.456.35-14.83-29.06-10.6310.6329.0614.83-6.35.30-7.413.18-12.045.32-5.3212.04-3.187.41.400.720.961.890.69-0.69-1.89-0.96-0.738.02-38.0226.99-17.52-9.479.4717.52-26.9938.(0.3990.3990.2020.1770.3480.3480.1270.1270.3480.3480.1770.2(25.00-51.5551.5525.75-8.128.12-25.75-51.5551.510.5910.595.36-12.24-24.07-24.07-8.798.7924.0724.0712.24-5.36.225.30-6.122.68-14.53-12.044.39-4.3914.5312.04-2.686.-2.15-2.15-1.093.456.786.782.48-2.48-6.78-6.78-3.451.(14.6638.74-53.4045.44-31.82-3.58-10.0410.0431.82-3.58-45.4453.40.3990.3990.2020.1770.3480.3480.1270.1270.3480.3480.1770.2(25.00-51.5551.5525.75-8.128.12-25.75-51.5551.510.5910.595.36-12.24-24.07-24.07-5.525.5224.0724.0712.24-5.35.305.30-6.122.68-12.04-12.042.76-2.7612.0412.04-2.686.-1.78-1.78-0.903.306.496.492.37-2.37-6.49-6.49-3.300.914.1139.11-53.2145.29-29.63-3.88-8.518.5129.633.88-45.2953.：0.3990.3990.2020.1770.3480.3480.1270.1270.3480.3480.1770.2(25.00-51.5551.5525.75-8.128.12-25.75-51.5551.510.5910.595.36-12.24-24.07-24.07-7.757.7524.0724.0712.24-5.35.305.89-6.122.68-12.04-13.183.88-3.8812.0413.18-2.686.-2.02-2.02-1.023.306.496.492.37-2.37-6.49-6.49-3.301.(13.8739.47-53.3345.29-29.62-5.01-9.639.6329.625.01-45.2953.30.4440.330.2260.1950.3810.2840.140.140.3810.2840.1950.2：25.00-51.5551.5525.75-8.128.12-25.75-51.5551.511.798.766.00-13.49-26.36-19.65-9.699.6926.3619.6513.49-6.(5.30-6.753.00-12.044.84-4.8412.04-3.006.7

0.640.480.330.821.601.190.59—0.59—1.60—1.19—0.82—0・：17.7334.24—51.9741.88—36.807.29—12.3812.3836.80—7.29—41.8851.9图5-5恒荷载弯矩分配及传递图上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱右梁左梁0.6620.3380.2720.5330.1950.1950.5330.2720.330.67-2.692.691.19-0.560.56-1.19-2.692.61.340.68—0.90—1.77—0.650.651.770.90—0.60.82—0.450.34—1.770.32—0.321.77—0.340.4—0.25—0.130.300.590.22—0.22—0.59—0.300.12.58—2.582.43—1.76—0.670.671.76—2.432.50.3990.3990.2020.1770.3480.3480.1270.1270.3480.3480.1770.202.69-6.826.824.75-1.411.41-4.75-6.826.81.651.650.83—1.80—3.54—3.54—1.291.293.543.541.80—0.80.670.82—0.900.42—0.88—1.770.65—0.650.881.77—0.420.9—0.24—0.24—0.120.280.550.550.20—0.20—0.55—0.55—0.280.12.084.93—7.005.72—3.870.00—1.851.853.870.00—5.727.00.3990.3990.2020.1770.3480.3480.1270.1270.3480.3480.1770.202.69-6.826.824.75-1.411.41-4.75-6.826.81.651.650.83—1.80—3.54—3.54—0.690.693.543.541.80—0.80.820.82—0.900.42—1.77—1.770.34—0.341.771.77—0.420.9—0.30—0.30—0.150.490.970.970.35—0.35—0.97—0.97—0.490.12.174.86—7.045.93—4.340.41—1.401.404.34—0.41—5.937.00.3990.3990.2020.1770.3480.3480.1270.1270.3480.3480.1770.202.69-6.826.824.75-1.411.41-4.75-6.826.81.651.650.83—1.80—3.54—3.54—1.111.113.543.541.80—0.80.820.92—0.900.42—1.77—1.940.56—0.561.771.94—0.420.9—0.34—0.34—0.170.480.950.950.35—0.35—0.95—0.95—0.480.12.144.92—7.055.92—4.350.23—1.621.624.35—0.23—5.927.00.4440.330.2260.1950.3810.2840.140.140.3810.2840.1950.222.69-6.826.824.75-1.411.41-4.75-6.826.81.831.360.93-1.98-3.87-2.89-1.421.423.872.891.98-0.90.82-0.990.47-1.770.71-0.711.77-0.470.90.070.050.040.120.220.170.08-0.08-0.22-0.17-0.12-0.02.734.11-6.845.42-5.412.03-2.042.045.41-2.03-5.426.8图5-6活荷载弯矩分配及传递图5.3.3梁端剪力及柱轴力计算表5.6恒荷载代表值下的梁端剪力(kN)梁类层次l(m)q(kN/m)V2M/1K二V―工M/1左V亠二V+2M/1右A-C梁56.610.3834.25-1.6735.9232.5846.614.246.86-1.2148.0745.6536.614.246.86-1.248.0645.6626.614.246.86-1.2248.0845.6416.614.246.86-1.5348.3945.33C-D梁53.06.4721.35——21.3521.3543.010.8235.71——35.7135.7133.010.8235.71——35.7135.7123.010.8235.71——35.7135.7113.010.8235.71——35.7135.71D-E梁56.610.3834.251.6732.5835.9246.614.246.861.2145.6548.0736.614.246.861.245.6648.0626.614.246.861.2245.6448.0816.614.246.861.5345.3348.39注：V、V均为轴线处剪力。左右梁端剪力可由梁上竖向荷载引起的剪力与梁端弯矩引起的剪力相叠加而得；柱轴力可由梁端剪力和节点集中力叠加得到，计算柱底轴力还需要考虑柱的自重。柱自重：底层：l.lx0.6x0.6x5.2x25=51.48kN标准层：1.1x0.6x0.6x3.9x25=38.61kN表5.7恒荷载代表值作用下柱轴力计算表柱类别层次截面横梁剪力P(kN)柱重(kN)AN(kN)柱轴向力(kN)A、E轴柱51-135.92125.8538.61161.77161.772-2200.38200.3841-148.07166.6538.61214.72415.12-2253.33453.7131-148.06166.6538.61214.71668.422-2253.32707.03

21-148.08166.6538.61214.73921.762-2253.34960.3711-148.39166.6551.48215.041175.412-2266.521226.89C、D轴柱51-153.93144.638.61198.53198.532-2237.14237.1441-181.36