第四章框架剪力墙结构房屋设计

1、第7章 框架-剪力墙结构房屋设计计算实例及分析某10层房屋的结构平面及剖面示意图如图7.5.2所示，各层纵向剪力墙上的门洞尺寸均为1.5m2.4m，门洞居中。抗震设防烈度8度。场地类别类，设计地震分组为第一组。各层横梁截面尺寸：边跨梁300mm600mm，走道梁300mm450mm。柱截面尺寸：1、2层为550mm550mm，3、4层为500mm500mm，510层为450mm450mm。各层剪力墙厚度：1、2层为350mm，310层为200mm。梁、柱、剪力墙及楼板均为现浇钢筋混凝土。混凝土强度等级：16层为C30，710层为C20。经计算，集中于各层楼面处的重力荷载代表值为G1=9285k

2、N，G2=8785kN，G3= G4=G9=8570kN，G10=7140kN，G11=522kN。试按协同工作分析方法计算横向水平地震作用下结构的内力及位移。1. 基本计算参数（1）横向框架的剪切刚度框架横梁线刚度，计算结果见表。柱线刚度，计算结果见表7.5.2。框架柱侧向刚度按式（5.4.4）计算，其中柱侧向刚度修正系数按表5.4.1取值，值计算结果见表7.5.3。将表7.5.3各对应层的值相加，并乘以层高，即得，见表7.5.4。（b） （c）图 结构平面及剖面示意图表 梁线刚度（Nmm）梁类别层次边 框 架中 框 架一般梁7102.553006005.4008.1001093.4431.

3、08010104.590163.004.0505.400走道梁7102.553004502.2783.4171093.6314.5561094.841163.004.2715.695表7.5.2 柱线刚度（Nmm）层次层高（mm）)71036004504502.553.4172.4215636004504503.003.4172.8483436005005003.005.2084.340245005505503.007.6265.084155005505503.007.6264.159表7.5.3 中框架柱侧向刚度（N/mm）层次层高/mm边 柱中 柱81036001.8960.4871091

4、73.8950.66114817257340736002.0630.508113884.2390.679152212660905636001.8960.487128423.8960.661174313027303436001.2440.383153912.5560.56122544379350245001.0620.347104542.1820.52215727261810155001.2980.54589922.6680.67911202201940续表 边框架柱侧向刚度（N/mm）层次层高/mm边 柱中 柱81036001.4220.41693252.9220.59413316905647

5、36001.5480.43697743.1790.61413764941525636001.4220.416109702.9220.594156641065363436000.9330.318127791.9170.48919651129720245000.7970.28585861.6370.4501355788572155000.9740.49681832.0010.6251031273980表 各层框架剪切刚度层 次1234567810层 高5500450036003600360036002759203503825090704092663602423479041.517561.57672

6、1.832651.473361.296871.25245由式（）计算，即各层的值按高度加权取平均值（2）横向剪力墙截面等效刚度本例的4片剪力墙截面形式相同，但各层厚度及混凝土强度等级不同。这里以第一层剪力墙为例进行计算，其他各层剪力墙刚度的计算结果见表。表7.5.5 各层剪力墙刚度参数（一片墙）层次 (mm)（端柱）71020045045012002 6581.3271 710 0008.056582.054435620045045012002 6581.3271 710 0008.056582.416983420050050012002 6581.3271 790 0008.812462.6

7、43741235055055019402 4351.4233 095 25014.444974.33349图 剪力墙截面尺寸第一层墙厚350mm，端柱截面为550mm550mm，墙截面及尺寸如图所示。有效翼缘宽度应取翼缘厚度的6倍、墙间距的一半和总高度的1/20中的最小值，且不大于至洞口边缘的距离。经计算，。 由和，查表6.2.1得。将表7.5.5中各层的沿高度加权取平均值得将上述数据代入式（）得总剪力墙的等效刚度 (3)连梁的等效刚度为了简化计算，计算连梁刚度时不考虑剪力墙翼缘的影响，取墙形心轴为1/2墙截面高度处，如图7.5.4所示。另外，由于梁截面高度较小，梁净跨长与截面高度之比大于4，

8、故可不考虑剪切变形的影响。下面以第一层连梁为例，说明连梁刚度计算方法，其他层连梁刚度计算结果见表7.5.6。图 连梁计算简图连梁的转动刚度按式（）计算，其中刚域长度为另由表得。将上述数据代入式（7.2.10）得由式（）得 表 连梁剪切刚度层次层高bh (端柱)710360045045054000.5761.161782.668940.718047.413742.965505636004504501.366803.139940.844758.722053.488823436005005000.5813.264020.865049.066713.62668245005505500.5863.394

9、410.886067.543133.01725155005505503.394410.886066.171652.46866将表中各层的按高度加权取平均值 （4）结构刚度特征值为了考察连梁的约束作用对结构内力和侧移的影响，下面分别按连梁刚结和铰结两种情况计算。考虑连梁约束作用时，按式（）计算，连梁刚度折减系数取0.55，则得不考虑连梁约束作用时，按式（）计算，即2. 水平地震作用(1)结构自振周期计算该结构的质量和刚度沿高度分布比较均匀，基本自振周期可按下式计算式中，为计算结构基本自振周期用的结构顶点假想位移（m）；为结构基本自振周期考虑非承重砖墙影响的折减系数，本例可取=0.8。对带屋面局部

10、突出间的房屋，上式中的应取主体结构顶点位移。突出间对主体结构顶点位移的影响，可按顶点位移相等的原则，将其重力荷载折算到主体结构的顶层，如图所示。对本例，其折算重力荷载可按下式计算均布荷载为结构顶点位移为式中，均布荷载作用下结构的顶点位移，将代入式（）得顶点集中荷载作用下结构的顶点位移，将代入式（）得结构自振周期的计算结果见表7.5.7。图 计算简图 表 结构自振周期计算类 别连梁刚结10.7438810172.1160.2190.0040.2230.642连梁铰结1.4400.3250.0060.3310.782（2）水平地震作用计算该房屋主体结构高度不超过40m，且质量和刚度沿高度分布比较均

11、匀，故可用底部剪力法计算水平地震作用。结构等效总重力荷载代表值结构总水平地震作用标准值 顶部附加水平地震作用标准值质点的水平地震作用标准值 和 的具体计算过程见表.表 水平地震作用计算层次连梁刚结连梁铰结1142.452222 1330.011 6469.052 927.7257.082 420.191038.87 140277 0320.145 67864.33(819.57)65 335.32714.50(749.59)56 806.69935.28 570301 6640.158 62941.1833 129.54778.0327 386.66831.68 570270 8120.142

12、 39844.9226 699.47698.4622 071.34728.08 570239 9600.126 27748.6720 962.76618.8917 328.92624.48 570209 1080.109 95652.4115 918.80539.3213 159.41520.88 570178 2560.093 73556.1511 567.92459.759 562.80417.28 570147 4040.077 51459.907 910.28380.176 538.92313.68 570116 5520.061 28363.644 945.50300.604 088

13、.16210.08 78587 8500.046 19274.092 740.90226.582 265.8015.59 28551 0680.026 85159.33876.32131.71724.41857221 901 8396753.24193 014.535 654.68162353.30按上述方法所得的水平地震作用为作用在各层楼面处的水平集中力。当采用连续化方法计算框架-剪力墙结构的内力和侧移时，应将实际的地震作用分布转化为均布水平力或倒三角形分布的连续水平力或顶点集中力。根据实际地震作用基本为倒三角形分布的特点，下面按基底剪力和基底倾覆力矩分别相等的条件，将实际地震作用分布图（a

14、）转换为倒三角形连续地震作用图7.5.6（b）和顶点集中水平地震作用图7.5.6（c）,即式中，。 (a) (b) (c)图 水平地震作用的转换由上式可得由表中的有关数据及上式，可得连梁刚结时连梁铰结时3. 水平位移验算 倒三角形水平荷载和顶点集中水平荷载作用下的位移分别按式（）和式（7.3.19）计算，结果见表7.5.9。表 水平位移计算表层次连梁刚结连梁铰结1038.83.619.869.2929.151/110224.5112.3736.881/805935.23.617.818.0825.881/108821.7010.7132.411/804831.63.615.706.8822.5

15、81/107318.869.0727.931/808728.03.613.515.7119.221/106616.007.4823.471/820624.43.611.254.5915.841/107813.135.9619.091/849520.83.68.973.5312.501/111910.304.5514.851/904417.23.66.722.569.291/12077.603.2610.861/1000313.63.64.601.706.311/13825.122.147.261/1174210.04.52.720.983.701/18282.981.224.201/15971

16、5.55.50.920.321.241/44350.990.391.381/3995由上表可见，无论连梁刚结还是铰结，各层层间位移角均小于1/800，满足弹性层间位移角限值的要求。此外当考虑连梁的约束作用时，结构侧移减小（1127）。4. 水平地震作用下总剪力墙、总框架和总连梁的内力计算（1）连梁铰结时总框架、总剪力墙内力倒三角形分布荷载及顶点集中荷载作用下的内力分别按式（）（7.3.17）和（7.3.21）（7.3.23）计算，结果见表7.5.10。表 总框架及总剪力墙内力（连梁铰结）层次Hi(m)倒三角形荷载顶点集中力总内力 1038.81.00.00-1150.451150.450.00

17、558.02685.710.00-592.421836.15935.20.907-2724.01-377.791158.352014.87563.01680.72-709.14185.221839.07831.60.814-2819.44312.051173.124065.76578.07665.661246.32890.111838.78728.00.722-561.81931.401182.426189.33603.45640.285627.521534.861822.70624.40.6293815.431491.361175.198423.56639.63604.1012238.992

18、130.991779.29520.80.53610116.712001.911141.4110808.4687.24556.4920925.102689.151697.90417.20.44318180.892472.201071.9513386.4747.14496.5931567.323219.341568.54313.60.35127878.322910.62958.4016203.8820.39423.3444082.123731.011381.74210.00.25839108.543325.02792.9419310.9908.32335.4158419.404233.341128

19、.3515.50.14255193.063820.49501.8323687.21041.27202.4778880.304861.76704.300077832.194410.960.0029949.31243.730.00107781.445654.690.00（2）连梁刚结时总框架、总剪力墙及总连梁内力表为倒三角形分布荷载和顶点集中荷载作用下的内力计算结果，表7.5.12为两种荷载共同作用下的内力。连梁刚结和铰结时总剪力墙、总框架及总连梁内力沿高度的分布见图。由此图及上述计算结果可见，对本例而言，考虑连梁的约束作用时，总水平地震作用增大16.3；在结构上部，剪力墙弯矩增大，下部弯矩减小，

20、最大弯矩减小7.5；剪力墙承担的剪力增大，框架承担的剪力减小。表总框架、总剪力墙及总连梁内力（连梁刚结）层次（m）(kN.m)(kN.m)(kN)(kN)(kN)1038.80.00-1478.101553.0074.901339.42935.2-3622.62-556.221565.011008.781349.77831.6-4141.04251.981588.721840.701370.22728.0-1907.13977.761607.352585.111386.30624.42833.711649.191605.843255.031385.00520.89932.992292.2215

21、70.263862.481354.30417.219333.452931.721487.234418.961282.70313.631066.803592.431343.504935.931158.73210.045254.944299.881125.345425.22970.5715.566782.225291.87725.466017.33625.690.099749.366750.240.006750.240.00图 总剪力墙、总框架及总连梁内力分布图表 倒三角形荷载及顶点集中荷载作用下内力计算（连梁刚结）层次（m）倒三角形荷载顶点集中荷载Mw(kN.m)(kN)(kN)m(kN)Vw(

22、kN)Vf(kN)Mw(kN.m)(kN)(kN)m(kN)Vw(kN)Vf(kN)1038.80.00-1814.111814.11974.03-840.08840.080.00336.011078.32578.97914.98499.35935.2-4840.03-989.731842.96989.5290.80853.441217.42342.501071.82575.48917.99496.34831.6-6626.95-110.261906.861023.83913.57883.032841.91362.251052.08564.88927.13487.20728.0-5749.50

23、581.771975.321060.591642.36914.733842.37395.951018.33546.76942.76471.57624.4-2517.711204.132021.571085.432289.56936.155351.42445.06969.27520.42965.48448.85520.82865.591780.892021.561085.422866.31936.147067.40511.33903.00484.84996.17418.16417.210276.772334.351952.981048.603382.95904.399056.68597.3781

24、6.95438.641036.01378.31313.619670.622885.911794.43963.473849.37830.9611396.17706.52707.81380.041086.55327.77210.031078.593456.901524.57818.584275.47706.0014176.35842.98571.34306.761149.75264.5815.548345.214231.73996.96535.294767.02461.6718437.011060.14354.18190.171250.31164.020.074558.215335.910.000

25、.005335.910.0025191.231414.320.000.001414.320.00注： ，分别表示总剪力墙和总框架的名义剪力，分别按式（）、（7.3.17）以及（7.3.22）、（7.3.23）计算。5.连梁刚结时构件内力计算(1)框架梁、柱内力计算考虑连梁约束作用时，框架-剪力墙结构底部总剪力为，由表可见，第14,9,10层的总框架剪力小于，应予以调整。另外，所以调整后的取1350.05kN。框架柱的剪力和弯矩用值法计算，表为轴框架柱剪力和弯矩的计算结果，其余框架计算从略。表中反弯点高度比按式（5.4.9）确定，其中标准反弯点高度比由附表5.2.2查取。 梁端弯矩、剪力及柱轴力

26、计算结果见表，柱轴力按调整前的梁端剪力计算。(2)连梁内力计算 本例的4根连梁受力情况相同，只需要计算出1根连梁的内力即可。下面以第10层连梁内力计算为例，说明连梁内力计算过程，其它各层的计算结果见表。 由式（），并根据表7.5.6和表7.5.12中的有关数据，得 另由式（）得 由式()得连梁刚域端的弯矩 由式（）得连梁端剪力(3)剪力墙内力计算本例的4 片墙受力情况相同，可用式（）计算每片墙的弯矩，每片墙的剪力用式（）计算，计算结果见表7.5.16,表中。剪力墙轴力用式（7.5.8）计算，计算结果见表7.5.15。表连梁内力及剪力墙轴力计算层次103.61553.005590.8000.25

27、0.2611397.700364.850364.850326.389326.38993.61565.015634.0360.250.2611408.509367.621367.697328.913655.30283.61588.725719.3920.250.2611429.848373.190373.268333.896989.19873.61607.355786.4600.250.2611446.615377.567377.645337.8111327.00963.61605.845781.0240.250.2611445.256377.212377.290337.4941664.5035

28、3.61570.265652.9360.250.2611413.234368.854368.930330.0161994.51943.61487.235354.0280.250.2611338.507349.350349.423312.5662307.08633.61343.504836.6000.250.2611209.150315.588315.653282.3592589.44524.51125.345064.0300.250.2611266.008330.428330.496295.6362885.08115.5725.463990.0300.250.261997.508260.349

29、260.403232.9363118.017表 水平地震作用下框架柱弯矩及剪力计算层次 边 柱中 柱 y调整前调整后 y调整前调整后103.61339.42347904109170.0310.3942.0392.3059.0142.3693.0359.48148170.0430.4557.05112.9592.4157.50113.8593.1593.61349.77347904109170.0310.4442.3685.3967.0942.3685.4167.10148170.0430.4957.49105.54101.4157.50105.57101.4383.61370.22347904

30、109170.0310.4543.0085.1369.6543.0085.1369.65148170.0430.5058.36105.04105.0458.36105.04105.0473.61386.30360242113880.0320.5043.8278.8878.8843.8278.8878.88152210.0420.5058.57105.43105.4358.57105.43105.4363.61385.00409266128420.0310.4943.4679.7976.6643.4679.7976.66174310.0430.4958.99108.30104.0658.9910

31、8.30104.0653.61354.30409266128420.0310.5042.5076.4976.4942.5076.4976.49174310.0430.5057.68103.83103.8357.68103.83103.8343.61282.70509070153910.0300.5038.7869.8069.8040.8273.4773.47225440.0440.5056.80102.25102.2559.79107.62107.6233.61158.73509070153910.0300.5035.0363.0663.0640.8273.4773.47225440.0440

32、.5051.3192.3792.3759.79107.62107.6224.5970.57350382104540.0300.5028.9665.1665.1640.2890.6390.63157270.0450.5043.5698.0298.0260.60136.34136.3415.5625.6927592089920.0330.6420.3940.3771.7744.0087.11154.87112020.0410.5725.4060.0879.6454.81129.63171.83注：，分别表示本层柱的上端和下端弯矩，量纲为；分别为调整前、后的总框架剪力，其中。表7.5.14 水平地震

33、作用下梁端弯矩、剪力及柱轴力计算层次AB跨梁端弯矩、剪力BC跨梁端弯矩、剪力柱轴力调整前调整后调整前调整后A柱B柱106.092.3054.9724.5593.0355.4124.742.457.9857.9848.3158.4458.4448.70-24.55-23.7796.0144.4096.3440.12144.8896.7140.272.4101.61101.6184.68102.00102.0085.00-64.67-68.3286.0152.22100.4842.12152.24100.4942.122.4105.97105.9788.31105.98105.9888.32-10

34、6.79-114.5276.0148.54102.4441.83148.54102.4441.832.4108.04108.0490.03108.04108.0490.03-148.61-162.7266.0158.67104.0343.78158.67104.0343.782.4109.71109.7191.42109.71109.7191.42-192.40-210.3656.0153.15101.1842.39153.15101.1842.392.4106.70106.7088.92106.70106.7088.92-234.79-256.8946.0146.30100.3041.101

35、49.96102.9142.152.4105.78105.7888.15108.53108.5390.44-275.89-303.9436.0132.8694.7237.93146.94104.7541.952.499.8999.8983.24110.48110.4892.06-313.82-349.2526.0128.2192.6636.81164.10118.7447.142.497.7297.7281.44125.22125.22104.35-350.63-393.8816.0105.5376.9530.41177.74129.4551.202.481.1581.1567.62136.52136.52113.77-381.04-431.09注：表中剪力和轴力的量纲为kN；弯矩的量纲为表 一片剪力墙弯矩及剪力计算层次1038.80-1478.100.250388.2518.73935.2-3622.63-556.220.25-905.66391.25252.20831.6-4141.04251.980.25-1035.26397.18460.18728.0-1907.13977.760.25-476.78401.84646.286