第四章框架剪力墻結(jié)構(gòu)房屋設(shè)計(jì)

1、第7章 框架-剪力墻結(jié)構(gòu)房屋設(shè)計(jì)計(jì)算實(shí)例及分析某10層房屋的結(jié)構(gòu)平面及剖面示意圖如圖7.5.2所示，各層縱向剪力墻上的門洞尺寸均為1.5m2.4m，門洞居中?？拐鹪O(shè)防烈度8度。場地類別類，設(shè)計(jì)地震分組為第一組。各層橫梁截面尺寸：邊跨梁300mm600mm，走道梁300mm450mm。柱截面尺寸：1、2層為550mm550mm，3、4層為500mm500mm，510層為450mm450mm。各層剪力墻厚度：1、2層為350mm，310層為200mm。梁、柱、剪力墻及樓板均為現(xiàn)澆鋼筋混凝土?；炷翉?qiáng)度等級(jí)：16層為C30，710層為C20。經(jīng)計(jì)算，集中于各層樓面處的重力荷載代表值為G1=9285k

2、N，G2=8785kN，G3= G4=G9=8570kN，G10=7140kN，G11=522kN。試按協(xié)同工作分析方法計(jì)算橫向水平地震作用下結(jié)構(gòu)的內(nèi)力及位移。1. 基本計(jì)算參數(shù)（1）橫向框架的剪切剛度框架橫梁線剛度，計(jì)算結(jié)果見表。柱線剛度，計(jì)算結(jié)果見表7.5.2?？蚣苤鶄?cè)向剛度按式（5.4.4）計(jì)算，其中柱側(cè)向剛度修正系數(shù)按表5.4.1取值，值計(jì)算結(jié)果見表7.5.3。將表7.5.3各對(duì)應(yīng)層的值相加，并乘以層高，即得，見表7.5.4。（b） （c）圖 結(jié)構(gòu)平面及剖面示意圖表 梁線剛度（Nmm）梁類別層次邊 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 柱線剛度（Nmm）層次層高（mm）)71036004504502.553.4172.4215636004504503.003.4172.8483436005005003.005.2084.340245005505503.007.6265.084155005505503.007.6264.159表7.5.3 中框架柱側(cè)向剛度（N/mm）層次層高/mm邊 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續(xù)表 邊框架柱側(cè)向剛度（N/mm）層次層高/mm邊 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 各層框架剪切剛度層 次1234567810層 高5500450036003600360036002759203503825090704092663602423479041.517561.57672

6、1.832651.473361.296871.25245由式（）計(jì)算，即各層的值按高度加權(quán)取平均值（2）橫向剪力墻截面等效剛度本例的4片剪力墻截面形式相同，但各層厚度及混凝土強(qiáng)度等級(jí)不同。這里以第一層剪力墻為例進(jìn)行計(jì)算，其他各層剪力墻剛度的計(jì)算結(jié)果見表。表7.5.5 各層剪力墻剛度參數(shù)（一片墻）層次 (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圖 剪力墻截面尺寸第一層墻厚350mm，端柱截面為550mm550mm，墻截面及尺寸如圖所示。有效翼緣寬度應(yīng)取翼緣厚度的6倍、墻間距的一半和總高度的1/20中的最小值，且不大于至洞口邊緣的距離。經(jīng)計(jì)算，。 由和，查表6.2.1得。將表7.5.5中各層的沿高度加權(quán)取平均值得將上述數(shù)據(jù)代入式（）得總剪力墻的等效剛度 (3)連梁的等效剛度為了簡化計(jì)算，計(jì)算連梁剛度時(shí)不考慮剪力墻翼緣的影響，取墻形心軸為1/2墻截面高度處，如圖7.5.4所示。另外，由于梁截面高度較小，梁凈跨長與截面高度之比大于4，

8、故可不考慮剪切變形的影響。下面以第一層連梁為例，說明連梁剛度計(jì)算方法，其他層連梁剛度計(jì)算結(jié)果見表7.5.6。圖 連梁計(jì)算簡圖連梁的轉(zhuǎn)動(dòng)剛度按式（）計(jì)算，其中剛域長度為另由表得。將上述數(shù)據(jù)代入式（7.2.10）得由式（）得 表 連梁剪切剛度層次層高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將表中各層的按高度加權(quán)取平均值 （4）結(jié)構(gòu)剛度特征值為了考察連梁的約束作用對(duì)結(jié)構(gòu)內(nèi)力和側(cè)移的影響，下面分別按連梁剛結(jié)和鉸結(jié)兩種情況計(jì)算?？紤]連梁約束作用時(shí)，按式（）計(jì)算，連梁剛度折減系數(shù)取0.55，則得不考慮連梁約束作用時(shí)，按式（）計(jì)算，即2. 水平地震作用(1)結(jié)構(gòu)自振周期計(jì)算該結(jié)構(gòu)的質(zhì)量和剛度沿高度分布比較均勻，基本自振周期可按下式計(jì)算式中，為計(jì)算結(jié)構(gòu)基本自振周期用的結(jié)構(gòu)頂點(diǎn)假想位移（m）；為結(jié)構(gòu)基本自振周期考慮非承重磚墻影響的折減系數(shù)，本例可取=0.8。對(duì)帶屋面局部

10、突出間的房屋，上式中的應(yīng)取主體結(jié)構(gòu)頂點(diǎn)位移。突出間對(duì)主體結(jié)構(gòu)頂點(diǎn)位移的影響，可按頂點(diǎn)位移相等的原則，將其重力荷載折算到主體結(jié)構(gòu)的頂層，如圖所示。對(duì)本例，其折算重力荷載可按下式計(jì)算均布荷載為結(jié)構(gòu)頂點(diǎn)位移為式中，均布荷載作用下結(jié)構(gòu)的頂點(diǎn)位移，將代入式（）得頂點(diǎn)集中荷載作用下結(jié)構(gòu)的頂點(diǎn)位移，將代入式（）得結(jié)構(gòu)自振周期的計(jì)算結(jié)果見表7.5.7。圖 計(jì)算簡圖 表 結(jié)構(gòu)自振周期計(jì)算類 別連梁剛結(jié)10.7438810172.1160.2190.0040.2230.642連梁鉸結(jié)1.4400.3250.0060.3310.782（2）水平地震作用計(jì)算該房屋主體結(jié)構(gòu)高度不超過40m，且質(zhì)量和剛度沿高度分布比較均

11、勻，故可用底部剪力法計(jì)算水平地震作用。結(jié)構(gòu)等效總重力荷載代表值結(jié)構(gòu)總水平地震作用標(biāo)準(zhǔn)值 頂部附加水平地震作用標(biāo)準(zhǔn)值質(zhì)點(diǎn)的水平地震作用標(biāo)準(zhǔn)值 和 的具體計(jì)算過程見表.表 水平地震作用計(jì)算層次連梁剛結(jié)連梁鉸結(jié)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為作用在各層樓面處的水平集中力。當(dāng)采用連續(xù)化方法計(jì)算框架-剪力墻結(jié)構(gòu)的內(nèi)力和側(cè)移時(shí)，應(yīng)將實(shí)際的地震作用分布轉(zhuǎn)化為均布水平力或倒三角形分布的連續(xù)水平力或頂點(diǎn)集中力。根據(jù)實(shí)際地震作用基本為倒三角形分布的特點(diǎn)，下面按基底剪力和基底傾覆力矩分別相等的條件，將實(shí)際地震作用分布圖（a

14、）轉(zhuǎn)換為倒三角形連續(xù)地震作用圖7.5.6（b）和頂點(diǎn)集中水平地震作用圖7.5.6（c）,即式中，。 (a) (b) (c)圖 水平地震作用的轉(zhuǎn)換由上式可得由表中的有關(guān)數(shù)據(jù)及上式，可得連梁剛結(jié)時(shí)連梁鉸結(jié)時(shí)3. 水平位移驗(yàn)算 倒三角形水平荷載和頂點(diǎn)集中水平荷載作用下的位移分別按式（）和式（7.3.19）計(jì)算，結(jié)果見表7.5.9。表 水平位移計(jì)算表層次連梁剛結(jié)連梁鉸結(jié)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由上表可見，無論連梁剛結(jié)還是鉸結(jié)，各層層間位移角均小于1/800，滿足彈性層間位移角限值的要求。此外當(dāng)考慮連梁的約束作用時(shí)，結(jié)構(gòu)側(cè)移減?。?127）。4. 水平地震作用下總剪力墻、總框架和總連梁的內(nèi)力計(jì)算（1）連梁鉸結(jié)時(shí)總框架、總剪力墻內(nèi)力倒三角形分布荷載及頂點(diǎn)集中荷載作用下的內(nèi)力分別按式（）（7.3.17）和（7.3.21）（7.3.23）計(jì)算，結(jié)果見表7.5.10。表 總框架及總剪力墻內(nèi)力（連梁鉸結(jié)）層次Hi(m)倒三角形荷載頂點(diǎn)集中力總內(nèi)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）連梁剛結(jié)時(shí)總框架、總剪力墻及總連梁內(nèi)力表為倒三角形分布荷載和頂點(diǎn)集中荷載作用下的內(nèi)力計(jì)算結(jié)果，表7.5.12為兩種荷載共同作用下的內(nèi)力。連梁剛結(jié)和鉸結(jié)時(shí)總剪力墻、總框架及總連梁內(nèi)力沿高度的分布見圖。由此圖及上述計(jì)算結(jié)果可見，對(duì)本例而言，考慮連梁的約束作用時(shí)，總水平地震作用增大16.3；在結(jié)構(gòu)上部，剪力墻彎矩增大，下部彎矩減小，

20、最大彎矩減小7.5；剪力墻承擔(dān)的剪力增大，框架承擔(dān)的剪力減小。表總框架、總剪力墻及總連梁內(nèi)力（連梁剛結(jié)）層次（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圖 總剪力墻、總框架及總連梁內(nèi)力分布圖表 倒三角形荷載及頂點(diǎn)集中荷載作用下內(nèi)力計(jì)算（連梁剛結(jié)）層次（m）倒三角形荷載頂點(diǎn)集中荷載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： ，分別表示總剪力墻和總框架的名義剪力，分別按式（）、（7.3.17）以及（7.3.22）、（7.3.23）計(jì)算。5.連梁剛結(jié)時(shí)構(gòu)件內(nèi)力計(jì)算(1)框架梁、柱內(nèi)力計(jì)算考慮連梁約束作用時(shí)，框架-剪力墻結(jié)構(gòu)底部總剪力為，由表可見，第14,9,10層的總框架剪力小于，應(yīng)予以調(diào)整。另外，所以調(diào)整后的取1350.05kN。框架柱的剪力和彎矩用值法計(jì)算，表為軸框架柱剪力和彎矩的計(jì)算結(jié)果，其余框架計(jì)算從略。表中反彎點(diǎn)高度比按式（5.4.9）確定，其中標(biāo)準(zhǔn)反彎點(diǎn)高度比由附表5.2.2查取。 梁端彎矩、剪力及柱軸力

26、計(jì)算結(jié)果見表，柱軸力按調(diào)整前的梁端剪力計(jì)算。(2)連梁內(nèi)力計(jì)算 本例的4根連梁受力情況相同，只需要計(jì)算出1根連梁的內(nèi)力即可。下面以第10層連梁內(nèi)力計(jì)算為例，說明連梁內(nèi)力計(jì)算過程，其它各層的計(jì)算結(jié)果見表。 由式（），并根據(jù)表7.5.6和表7.5.12中的有關(guān)數(shù)據(jù)，得 另由式（）得 由式()得連梁剛域端的彎矩 由式（）得連梁端剪力(3)剪力墻內(nèi)力計(jì)算本例的4 片墻受力情況相同，可用式（）計(jì)算每片墻的彎矩，每片墻的剪力用式（）計(jì)算，計(jì)算結(jié)果見表7.5.16,表中。剪力墻軸力用式（7.5.8）計(jì)算，計(jì)算結(jié)果見表7.5.15。表連梁內(nèi)力及剪力墻軸力計(jì)算層次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彎矩及剪力計(jì)算層次 邊 柱中 柱 y調(diào)整前調(diào)整后 y調(diào)整前調(diào)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：，分別表示本層柱的上端和下端彎矩，量綱為；分別為調(diào)整前、后的總框架剪力，其中。表7.5.14 水平地震

33、作用下梁端彎矩、剪力及柱軸力計(jì)算層次AB跨梁端彎矩、剪力BC跨梁端彎矩、剪力柱軸力調(diào)整前調(diào)整后調(diào)整前調(diào)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：表中剪力和軸力的量綱為kN；彎矩的量綱為表 一片剪力墻彎矩及剪力計(jì)算層次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