高层住宅设计

1、高层住宅设计摘要本设计为某小区高层住宅设计，通过荷载汇集、解框架平面计算单元在风荷载作用下的内力及侧移，在竖向荷载作用下的内力。将求得的内力进行组合，考虑最不利布置，进行梁、住、楼板、楼梯等相关结构物的设计。关键词: 荷载，框架，内力，侧移abstractthis plan is upper layer residence. adopt to collet burden,solve framed plane calculating units internal force and lateral migration in the action of wind burden and vertic

2、al burden.make up abovementioned internal force, consider the worst disadvantageousarrangement,design the section of beam and column, floor, and stairs.key: burden, frame, internal force,lateral migration 目录摘要abstract一、 截面尺寸估算11 梁板截面尺寸估算12 柱截面尺寸估算1二、 荷载汇集21 竖向荷载2（1） 楼面荷载2（2） 屋面荷载32 水平风荷载3三、 水平荷载作用下框

3、架内力及侧移计算51 计算在风荷载作用下各楼层节点上集中力及各层剪力52 计算各梁柱的线刚度ib和ic63 计算搞侧移刚度d4 各柱剪力计算5 确定柱的反弯点高度比y6 计算柱端弯矩7 由柱端弯矩，并根据节点平衡计算梁端弯矩8 计算梁支座剪力及柱轴力9 梁柱弯曲产生的侧移四、 在竖向荷载作用下结构内力计算1 各层框架梁上荷载计算2 内力计算五、 内力组合六、 梁截面设计1 正截面承载力计算2 斜截面承载力七、 柱截面设计八、 楼板设计1 荷载计算2 按弹性理论计算（1） 弯矩计算（2） 配筋计算九、 楼梯设计1 梯段板计算（1） 荷载计算（2） 截面设计2 平台板（1） 荷载计算（2） 截面设

4、计3 平台梁计算（1） 荷载计算（2） 截面设计结论致谢参考文献一、 截面尺寸估算1 梁板截面尺寸估算梁板截面高度h，按梁跨度1/101/15确定，取梁高500mm，框架梁截面宽度取梁高的一半，梁宽250mm，板的最小厚度为l/50=6000/50=120mm，考虑到板的挠度及裂缝宽度的限制及在板中铺设管线等因素，根据经验取板厚150mm。2 柱截面尺寸估算根据柱支承的楼板面积计算竖向荷载作用下产生的轴力，并按轴压比控制估算柱截面面积，估算柱截面时，楼层荷载按1517kn/计，本工程边柱取17kn/，中柱取15 kn/。负荷面积为5.1×6/2的边柱轴力nv=5.1×6/2

5、×17×12=3121.2kn负荷面积为5.1×6的中柱轴力nv=5.1×6×15×12=5508kn各柱的轴力不同,但为施工方便和美观，将柱截面归并为一类，取轴力最大的估算截面面积本工程框架为三极抗震n=1.1nv=1.1×5508=6058kn柱轴压比n查有得n=0.9其中n=n/ac·fcac=n/n·fc=6058800/0.9×19.5=34523077mm设柱为正方形b=h=ac½=587.6故本工程取15层为0.6×0.6,612层为0.5×0.56层

6、底柱截面核算nv=5.1×6×15×7=3231knn=1.1nv=1.1×3213=3534.3knn/ac·fc=3534300/5002×19.5=0.72<0.97层底柱截面核算nv=5.1×6×15×6=2754knn=1.1nv=1.1××2751=3029.4knn/ac·fc=3029400/5002×15=0.81<0.轴压比满足要求。二、 荷载汇集1. 竖向荷载(1)楼面荷载取楼面活荷1.5kn/砼楼板(板厚15cm)25×

7、0.15=3.75kn/水泥砂浆抹灰(楼板上下各2cm厚)20×0.02×2=0.8kn/内隔墙为20cm和10cm厚陶粒砼砌块,砌块容重8 kn/,两侧各抹2cm 厚混合砂浆8×0.2+20×0.02×2=2.4 kn/8×0.1+20×0.02×2=1.6 kn/外墙为30cm厚陶粒砼砌块,墙外侧贴墙面砖,墙里侧抹混合砂浆2cm厚05+8×0.3+20×0.02×2=3.7kn/(2)屋面荷载防水卷材 0.35 kn/20厚砂浆找平层 20×0.02=0.4 kn/炉渣砼

8、找坡3% 1.4×0.15=2.1 kn/苯板60厚 0.1 kn/20厚砂浆找平层 20×0.02=0.4 kn/150厚钢筋砼板 25×0.15=3.75 kn/20厚混合砂浆 20×0.02=0.4 kn/7.5 kn/ 不上人屋面活荷 0.7 kn/ 基本雪压 0.4 kn/2水平风荷载基本风压0=1.1×0.45=0.495 kn/垂直于建筑物表面上的风荷载标准值wk按下式计算k=zsz0风荷载体型系数s=1.4风压高度变化系数z=1各层风荷载标准值计算结果见表3.1 表3.1 各层风荷载标准值距地高度hizzs0k=zsz034.6

9、11.1701.40.4950.81133.611.1571.40.4950.80230.811.121.40.4950.77628.011.0761.40.4950.74625.211.0281.40.4950.71222.410.9811.40.4950.68019.610.9311.40.4950.64516.810.8661.40.4950.60014.010.8021.40.4950.55611.210.7381.40.4950.5118.410.5981.40.4950.4145.610.5501.40.4950.3812.810.5401.40.4950.374010.541.4

10、0.4950.374三、 水平荷载作用下框架内力及侧移计算1. 计算在风荷载作用下各楼层节点上集中力及各层剪力计算风荷载作用下各楼层节点上集中力时,假定风荷载在层间为均匀分布,并假定上、下相邻各半层层高范围内的风荷载按集中力作用本层楼面上。12层顶处风荷载作用下楼层节点集中力计算: f12=(12+1×h12+1+12×h12/2)×b=(0.811×1+0.802×2.8/2)×5.1=9.86kn 11层顶处风荷载作用下楼层节点集中力计算: f12=(12×h12/2+11×h11/2)×b =0.8

11、02×1.4+0.776×2.8/2)×5.1 =11.27kn 表4.1 风荷载作用下水平集中力及层间剪力层号i层高hi风荷标准值ki各层集中力fi各层剪力i=fi(kn)女儿墙1008111228080298698611280776112721131028074610873217928071210414258828068099452527280645946619862806008897087528055682579124280511762867432804146609334228038156899021280374539104412 计算各梁柱的线刚度ib和i

12、c各梁柱线刚度计算结果见表4.2表4.2 各杆件惯性矩及线刚度表b×h(mm)i(mm)ec(n/mm²)i0=bh3/12(mm4)i=2ioi=ei/l(n·mm)梁250×500600030×10426×10952×109221×1010柱600×6002800325×104108×1091254×1010500×5002800325×10452×109603×1010500×500280030×1041045

13、2×109557×10103 计算抗侧移刚度dd值为使柱上、下端产生单位相对位移所需施加的水平力各柱抗侧移刚度见表4.34.各柱剪力计算设第i层第j个柱的d值dij，该层柱总数为m，该柱的剪力为ij=dij/dij·vi各柱剪力计算结果见表4.35.确定柱的反弯点高度比y 反弯点距柱下端为yh:y=y0+y1+y2+y3式y0-标准反弯点高度系数y1 y2 y3-当上下梁线刚度改变,上下层层高度变化时反弯点高度系数修正值。y0根结构总层数m及该柱所在层n及k值由表查得。6计算柱端弯矩根据各柱分配到的剪力及反弯点位置yh计算第i层第j个柱端弯矩 上端弯矩 m+ij=

14、vijh(1-y) 下端弯矩 mbij=vijyh7由柱端弯矩，并根据节点平衡计算梁端弯矩边跨外边缘处的梁端弯矩 mbi= m+ij+ mbi+lj中间支座处的梁端弯矩 mlbi=( m+ij+ mbi+l·j)ibl/ ibl + ibr mrbi=( m+ij+ mbi+l·j)ibr/ ibl + ibr框架在风荷载作用下的弯矩见图4.1表4.3 水平荷载作用下柱抗侧移刚度d及剪力vij计算表层/hi柱列轴号ic(×105)(kn.m)ib(×105)k=ib/ic底层k=ib/icdi=12ic/h2i(×105di(×105

15、)vij(kn012/2.8abcd0.3640.3640.3640.3640.5200.9920.9920.5200.7141.2661.2660.7140.0.2630.3880.3880.2630.1470.2160.2160.147726007260072600726002.583.803.802.5811/2.8abcd0.3640.3640.3640.3640.5200.9920.9920.5200.7141.2661.2660.7141.0.2630.3880.3880.2630.1470.2160.2160.147726007260072600726005.498.078.07

16、5.4910/2.8abcd0.3640.3640.3640.3640.5200.9920.9920.5200.7141.2661.2660.7142.0.2630.3880.3880.2630.1470.2160.2160.147726007260072600726008.2412.1212.128.249/2.8abcd0.3640.3640.3640.3640.5200.9920.9920.5200.7141.2661.2660.7143.0.2630.3880.3880.2630.1470.2160.2160.1477260072600726007260010.8215.9015.90

17、10.828/2.8abcd0.3640.3640.3640.3640.5200.9920.9920.5200.7141.2661.2660.7144.0.2630.3880.3880.2630.1470.2630.2630.1477260072600726007260013.2219.4319.4313.227/2.8abcd0.3950.3950.3950.3950.5200.9920.9920.5200.6581.2561.2560.6580.2480.3860.3860.2480.1500.2330.2330.1507660076600766007660014.9323.2123.21

18、14.936/2.8abcd0.8820.8820.8820.8820.5200.9920.9920.5200.2950.5620.5620.2950.1290.2190.2190.1290.1740.2960.2960.1749400094000940009400014.8725.3025.3014.875/2.8abcd0.8820.8820.8820.8820.5200.9920.9920.5200.2950.5620.5620.2950.1290.2190.2190.1290.1740.2960.2960.1749400094000940009400016.5528.1528.1516

19、.554/2.8abcd0.8820.8820.8820.8820.5200.9920.9920.5200.2950.5620.5620.2950.1290.2190.2190.1290.1740.2960.2960.1749400094000940009400018.0430.6930.6918.043/2.8abcd0.8820.8820.8820.8820.5200.9920.9920.5200.2950.5620.5620.2950.1290.2190.2190.1290.1740.2960.2960.1749400094000940009400019.3032.8432.8419.3

20、02/2.8abcd0.8820.8820.8820.8820.5200.9920.9920.5200.2950.5620.5620.2950.1290.2190.2190.1290.1740.2960.2960.1749400094000940009400020.3434.6034.6020.341/2.8abcd0.8820.8820.8820.8820.2600.4960.4960.2600.2950.5620.5620.2950.3460.4150.4150.3460.4670.5600.5600.46720540020540020540020540026.0931.2931.2926

21、.09表 4.4 风荷载作用下柱反弯点高度比及柱端弯矩层h柱轴线号k123y0=ym+ij(kn.m)mbij(kn.m)12/2.803970794079403971111000011110197030030019740160960940110126126110111/2.8039707940794039711111111111102985040040029857671119111976732774674632710/2.803970794079403971111111111110348504470447034851060156915691060567126812685679/2.80397

22、079407940397111111111111039850450450398513272066206613278791691698798/2.8039707940794039711111111111104004504504017713007300717711442462461447/2.80397079407940397111111111111044850450450448517713007300717711442462461446/2.803970794079403971111111111110433504504504335205530233023205515772473247315775

23、/2.80176035203520176111111111111038804504503882373396039602373150432432415044/2.80176035203520176111111111111045045045045233843414341233819133552355219133/2.80176035203520176111111111111056705050567198042474247198025934247424725932/2.801760352035201761111111111110764057605760764114538213821114536251

24、95193621/2.801760352035201761111111111111278085208521278-18.7811641164-18.788631669966998631上表中y=y1+y2+y3+y0,其中y1 ,y2,y3均为零，所以y= y0表 5.1 垂直荷载作用下框架梁固端弯矩值层数ab跨bc跨cd跨左支座右支座左支座右支座左支座右支座121110987654321-120.51-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36120.51-103.36-103.36

25、-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-120.51-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36120.51-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-120.51-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36

26、-103.36-103.36120.51-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36-103.36表5.2 各杆节点弯矩分配系数层数abcd上柱下柱梁上柱下柱梁左梁右上柱下柱梁左梁右上柱下柱梁12111098765432100.4100.4100.4100.4100.4100.3960.2870.4550.4550.4550.4550.6940.4100.4100.4100.4100.4100.4290.5960.4550.4550.4550.4550.3060.1800.1800.1800.180

27、0.1800.1750.1170.0890.0890.0890.08900.3760.3760.3760.3760.3760.3640.2710.1260.4260.4260.4260.6020.3760.3760.3760.3760.3760.3950.5640.4360.4360.4360.4360.2650.1660.1660.1660.1660.1660.1610.1110.0850.0850.0850.0850.1330.0820.0820.0820.0820.0820.080.0550.0430.0430.0430.04300.3760.3760.3760.3760.3760.36

28、40.2710.1260.4260.4260.4260.6020.3760.3760.3760.3760.3760.3950.5640.4360.4360.4360.4360.2650.1660.1660.1660.1660.1660.1610.1110.0850.0850.0850.0850.1330.0820.0820.0820.0820.0820.080.0550.0430.0430.0430.04300.4100.4100.4100.4100.4100.3960.2870.4550.4550.4550.4550.6940.4100.4100.4100.4100.4100.4290.59

29、60.4550.4550.4550.4550.3060.1800.1800.1800.1800.1800.1750.1170.0890.0890.0890.0898.计算梁支座剪力及柱轴力根据力平衡原理，由梁端弯矩和作用在梁上的竖向荷载来求出梁支座剪力；柱轴力可由计算截面之上的梁端剪力之和求得，框架在风荷载作用下的梁剪力及柱轴力见图4.2。9.梁柱弯曲产生的侧移因为h<50m,h/b<4,所以只考虑柱弯曲变形产生的侧移。第i层结构的层间变形为ui, ui=vi/d得u12=9.86/76800=1.3×10-4 u11=21.13/768000=2.8×10-4

30、 u10=32.17/76800=4.2×10-4 u9=42.58/76800=5.5×10-4 u8=52.52/76800=6.8×10-4 u7=61.98/76800=8.1×10-4 u6=70.87/76800=9.1×10-4 u5=79.12/88600=8.9×10-4 u4=86.74/88600=9.8×10-4 u3=93.34/88600=10.5×10-4 u2=99.02/88600=11.2×10-4 u1=104.41/58400=4.0×10-4 则顶总侧移

31、为u=ui=82.2×10-4 m顶点相对位移u/h82.2×10-4/3.36<1/500满足最大层间相对位移u/h=11.2×10-4 /2.8<1/450满足四、 在竖向荷载作用下结构内力计算1. 各层框架梁上荷载计算屋面梁梯形荷载 17.5×1.2+0.7×1.47×5.1=50.90kn/m屋面梁均布荷载0. 25×0.5×25×1.2=3.75 kn/m 111层框架梁上荷载梁自重 0.25×0.5×2.5×1.2=3.75 kn/m200厚陶粒砌块墙

32、高2.3m2.4×2.3×1.2=6.62 kn/m各跨楼面均布荷载3.75+6.62=10.37 kn/m2 内力计算多层多跨框架在竖向荷载作用下的内力近似分层法计算,除底层外,上层各柱线刚度均乘以0.9进行修正，这些柱的传递系数取-1/3，底层传递系数取-1/2，竖向荷载引起的各层框架固端弯矩见表5.1，弯矩分配系数计算公式j=ij/ij各节点弯矩分配系数计算结果见表5.2。内力分层计算结果见图5.2图5.6，竖向荷载作用下弯矩图见图5.7，竖向荷载作用下柱轴力及梁剪力见图5.8。五、 内力组合 在内力组合之前，应先将竖向荷载作用下的弯矩进行调幅，梁支座弯矩调幅系数取0

33、.8，梁跨中正弯矩按平衡条件重新计算，且应1/2按简支梁计算的跨中弯矩；由于未考虑活荷不利布置，活荷载引起的跨中弯矩乘以1.1的放大系数，然后将调幅后的竖向荷载引起的内力与风荷载引起的内力按公式s=rgckgk+rq1cq1kq1k+wrwcwk进行组合（注：本设计中恒、活荷载分项系数已在竖向荷载作用下的内力计算中考虑了）。一层顶、六层顶、十二层顶梁内力组合值及a、b、c轴柱组合内力见表6.1表6.3表6.1 框架一层顶梁内力组合部位组号内力竖向荷载作用下风荷载作用下组合内力ab跨左支座1mmaxv94.24×0.8=75.4101.117.421×1.4=24.398.2

34、×1.4=11.4899.79112.582mminv75.4101.1-24.39-11.4851.0289.62跨中1mmax54×1.1=59.4(31.77-17.42)×1.4/2=10.0569.45右支座1mmaxv107.62×0.8=86.1105.631.77×1.4=44.488.2×1.4=11.48103.58117.082mminv86.1105.6-44.48-11.4841.6294.12bc跨左支座1mmaxv103.56×0.8=82.8103.431.77×1.4=44.481

35、0.6×1.4=14.84127.28118.242mminv104.45103.4-44.48-14.8459.6588.56跨中1mmax52×1.2=57.2057.2右支座1mmaxv103.56×0.8=82.8103.431.77×1.4=44.48106×1.4=14.48127.28118.242mminv104.45103.4-44.48-14.4859.6588.56cd跨左支座1mmaxv86.1105.644.4811.48130.58117.082mminv86.1105.6-44.4811.4841.6294.12跨

36、中1mmax59.410.0569.45右支座1mmaxv75.4101.124.3911.4899.79112.582mminv75.4101.1-24.39-11.4851.0289.62表6.2 框架6、12层顶梁内力组合部位组号内力竖向荷载作用下风荷载作用下组合内力12层ab跨左支座1mmaxv91.57×0.8=73.3100.539.51×1.4=55.311.9×1.4=16.7128.6117.22mminv73.3100.5-5.53-16.71883.8跨中1mmax55×1.2=60.5（39.5-32.17）×1.4/2

37、=5.165.6右支座1mmaxv108.76×0.8=119.6106.232.17×1.4=45.011.9×1.4=16.7164.6122.92mminv119.6106.2-45.0-16.774.689.5bc跨左支座1mmaxv103.69×0.8=82.95103.432.17×1.4=45.0410.7×1.4=14.98127.99118.382mminv82.95103.4-45.04-14.9837.9188.42跨中1mmax52×1.2=57.2057.2右支座1mmaxv103.69×

38、0.8=82.95103.432.17×1.4=45.0410.7×1.4=14.98127.99118.382mminv82.95103.4-45.04-14.9837.9188.42cd跨左支座1mmaxv108.76×0.8=119.6106.232.17×1.4=45.011.9×1.4=16.9164.6122.92mminv119.6106.2-45.0-16.774.989.5跨中1mmax55×1.1=60.5（39.5-32.17）×1.4/2=5.165.6右支座1mmaxv73.3100.555.316

39、.7128.6117.22mminv73.3100.5-55.3-16.71883.86层ab跨左支座1mmaxv85.33×0.8=68.26112.34.01×1.4=5.61.2×1.4=1.773.861142mminv68.26112.3-5.6-1.762.66110.6跨中1mmax71×1.1=78.1（4.01-3.04）×1.4/2=0.6878.78右支座1mmaxv134.34×0.8=107.47128.73.04×1.4=4.261.2×1.4=1.7111.73130.42mminv1

40、07.47128.7-4.26-1.7103.21127bc跨左支座1mmaxv120.51×0.8=96.41120.53.04×1.4=4.261.0×1.4=1.4100.67121.92mminv96.41120.5-4.26-1.492.15119.1跨中1mmax81×1.1=89.1089.1右支座1mmaxv120.51×0.8=96.41120.53.0×1.4=4.261.0×1.4=1.4100.67121.92mminv96.41120.5-4.26-1.492.15119.1cd跨左支座1mmaxv

41、107.47128.74.261.7111.73130.42mminv107.47128.7-4.26-1.7103.21127跨中1mmax78.10.6873.78114右支座1mmaxv68.26112.35.61.762.662mminv68.26112.3-5.6-1.7110.66.3 a d轴柱部分截面内力组合楼层部位组号内力竖向荷载作用下风荷载作用下组合内力1层顶柱上端1/mmax/v47.1220181.4×18.78=26.321.4×（-99.8）=-139.7273.441878.282mnmax47.1220181.4×(-18.74)=

42、-26.321.4×99.8=139.7220.82157.72柱下端1/mmax/n23.5620181.4×86.31=120.831.4×(-99.8)=139.72144.391878.282mnmax23.5620181.4×(-86.31)=-120.831.4×99.8=139.72-97.272157.725层顶柱上端1/mmax/n61.813261.4×23.73×1.4=33.22(-52.9)×1.4=-74.0658.8622272mnmax3.4222271.4×(-23.73

43、)=-33.2252.9×1.4=74.06-52.022227柱下端1/mmax/n47.12132615.04×1. 4=21.06-52.9×1.4=-74.0668.181251.942mnmax47.121326-15.04×1.4=21.06-52.9×1.4=-74.0626.061400.0612层顶柱上端1/mmax/n85.331764.01×1.4=5.61-1.2×1.4=-1.6890.94174.322mnmax85.33176-4.01×1.4=-5.611.2×1.4=1.

44、6879.72177.68柱下端1/mmax/n85.391761.01×1.4=1.41-1.2×1.4=-1.6886.8174.322mnmax85.39176-1.01×1.4=-1.411.2×1.4=1.6883.98177.681层顶柱上端1/mmax/n2.0333391.4×11.64=16.31.4×(-2.8)=-3.9218.333335.082mnmax2.0333391.4×(-11.64)=-16.31.4×2.8=3.92-14.273342.92柱下端1/mmax/n1.0233391.4×66.99=-93.791.4×2.8=3.9294.813335.082mnmax1.0233391.4×(-66.99)=-93.791.4×2.8=3.92-92.7