框架办公楼设计计算土木工程设计

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设计资料····················································41.1工程名称····················································41.2工程概况····················································41.3建筑等级····················································41.4设计荷载····················································41.5抗震设防····················································41.6气象资料····················································41.7材料选用····················································52 结构布置与计算简图·············································52.1结构平面布置················································52.2构件截面初估················································5 2.3计算简图····················································6 2.4框架梁柱线刚度计算··········································73恒载及其内力分析 ·············································83.1恒载标准值计算··············································83.2框架梁线荷载计算···········································113.3框架柱节点集中荷载计算·····································113.4恒荷载下框架固端弯矩·······································133.5节点分配系数计算···········································133.6恒载作用下框架的内力计算···································144活载及其内力分析·············································204.1 活载标准值计算············································204.2活载作用下梁线荷载计算·····································204.3框架柱节点集中荷载计算·····································214.4活载下框架的固端弯矩·······································225风载及其内力分析·············································235.1风载标准值计算···········································275.2侧移刚度及剪力分配系数计算·······························295.3风载作用下框架侧移计算·····································305.4风载下框架内力计算·········································316 水平地震荷载作用·············································35 6.1 重力荷载代表值计算······································35 6.2水平地震作用力的计算·······································36 6.3水平地震作用下框架的侧移验算·······························38 6.4水平地震作用下框架内力计算·································387 荷载内力组合················································427.1梁内力组合···············································427.2柱内力组合···············································48 8 框架梁、柱配筋··············································538.1 框架梁配筋···············································538.2框架柱配筋···············································579 板的配筋····················································619.1荷载标准值计算···········································61 9.2板内力和配筋计算·········································6110楼梯设计····················································6310.1楼梯板设计计算··········································6310.2平台板设计··············································6410.3平台梁计算··············································6511基础设计····················································6611.1确定基底尺寸··············································6611.2条形基础设计··············································6812电算校核及分析··············································69结语···························································118参考文献·······················································118绪论土木工程是具有很强的实践性的学科,这次毕业设计也就是对我们四年的大学学习一个很好的实践锻炼的机会。虽然说,随着计算机的普及,各类程序的逐渐成熟,使得设计周期变得越来越短,计算也越来越简单,可电脑毕竟是一个程序,它只会按照编好的一步一步计算,而结果是否合理,经济,计算的模型是否符合真实的工程,这就需要人为的去调整,去复核,这样就要求必须知道计算中的任何一步是怎么得来的,了解掌握其原理和过程。故本次毕业设计不但要求掌握PKPM的计算建模的方法,还需要手算一榀框架,进一步掌握和巩固所学的专业知识。本次毕业设计的题目是成都金凤集团综合办公楼设计,结构设计部分主要是先进行结构的选型,柱网的布置,梁柱截面的估计,再用PKPM建模计算整体的受力是否合理,调整后绘出整套的完整的施工图纸,手算任务为选取一榀有代表性的框架进行荷载统计,内力计算、组合及验算,主要:分层法计算荷载作用下的框架内力,D值法计算风荷载下框架内力,底部剪力法计算地震荷载作用下框架内力,再内力组合获得控制截面,最后进行各个构件的配筋及验算。以上的设计内容涵盖了整个大学所学的知识,将所学的知识系统化,整体化了。1 设计资料1.1工程名称成都金凤集团综合办公楼设计1.2工程概况建筑总高度为19.2m,共五层,层高为3.6m。室内外高差为450mm,底层室内设计标高±0.000,总占地面积约为900平方米。1.3 建筑等级建筑物耐久等级为二级,耐火等级为二级,建筑物等级为二级,设计使用年限50年。1.4设计荷载基本风压:0.3KN/m²,主导风向:夏季东南风,冬季西北风,采用50年一遇的风压值 ,地面粗糙度B类。基本雪压:0.10KN/m², 采用50年一遇的雪压值。1.5 抗震设防本工程建筑抗震设防类别均为丙类,抗震设防烈度7度,设计基本地震加速度值为0.10g,设计地震分组为第三组,建筑场地类别为类,建筑的设计特征周期为0.35s。框架抗震等级为三级,抗震构造措施为二级,内力调整及其他为三级。1.6 气象资料(1)极端温度:最高40 o C,最低-6 o C;(2)相对湿度:79%(夏季),76%(冬季);(3)基本风压:0.30KN/ 主导风向:夏季东南风,冬季西北风;(4)基本雪压:0.10KN/(5)最大降雨量:60mm/h1.7 材料选用(1)混凝土:梁、板、基础、柱均为C30(2)墙体: 外墙、内墙均采用240厚灰砂砖(3)钢筋: 柱、梁纵筋:冷轧带肋钢筋(HRB335) 板钢筋:HPB235 箍筋:HPB235 基础钢筋:HPB2352 结构布置与计算简图2.1结构平面布置 框架结构平面布置及计算单元简图如下图: 柱网布置图2.2构件截面初估: 由于建筑总高度<30m,初步确定框架的抗震等级为三级,按经验确定楼面荷载为15KN/m2,故柱子截面尺寸可按其轴压比限值确定为,而梁和板的截面尺寸可根据其跨度确定。 柱子、梁、板及其他构件砼强度等级均为C30。2.2.1 梁截面尺寸:(1) 主梁 因为梁的跨度较接近,可取跨度较大者进行计算,L=6000mm. h=(1/12-1/8)L=(1/12-1/8)6000=500-750mm,取h=700mm. b=(1/3-1/2)h=(1/3-1/2)700=233-350mm,取b=250mm. 因此框架主梁初选截面尺寸为bh=250700mm. 中间框架梁由于跨度小,截面尺寸取为bh=250500mm.(2)次梁截面尺寸估算:L=7200mm.高h =(1/18-1/12)L=(1/18-1/12)7200=400-600mm, 取 h = 500 宽b =(1/3-1/2)h 167-250mm 取 b =250 故次梁的截面尺寸初选为bh=250500mm(3)地梁及楼梯间其上有短柱的梁取250mm×500mm。2.2.2柱截面尺寸: A=N/0.90fc=231818.2mm2 a=481mm 故取柱截面尺寸为bh=500500mm,为计算简便,中柱边柱尺寸相同。2.2.3板 由民用建筑规范规定的板厚要大于等于60mm,且h=L/40=3600/40=90mm,所以取板厚为100mm。2.2.4填充墙 内外墙均取240mm,用混凝土空心小砌块砌筑;保温材料用金属绝热材(聚氨酯)复合板。2.3计算简图 采用柱下独立基础,基础的埋深为2.0,基础高度取为1.0,框架见图1-1所示。取顶层柱的形心线作为轴线,2-5层柱高度取为层高3.6,底层标高从基础顶面取至板底,取m.图2.3为横向框架计算简图。 图2.3框架计算简图 2.4 框架梁、柱线刚度计算 由于现浇楼面可以作为梁的有效翼缘,增大梁的有效刚度,减少框架侧移。考虑这一有利因素,边框架梁取,对中框架梁取。(为梁矩形截面惯性矩)边跨梁: =3.0×1071.07×10-2/6=6.42×104KNm中跨梁: =6.25×104KNm 柱:=5.21×10-3mm4 =3.0×1075.21×10-3/4.95=3.16×104KNm i2-5=3.0×107×5.21×10-3/3.6=4.34×104KNm相对线刚度: 取 i2-5=1.0,则其余各杆件相对线刚度为: =0.73 =1.44 =1.48框架梁、柱的相对线刚度如图24所示,将作为计算节点杆端弯矩分配系数的依据。 图2-4 梁柱相对线刚度 3 恒载及其内力分析3.1恒荷载计算(此部分为PKPM建模作准备)1. 屋面防水层(刚性):30mm厚C20细石混凝土防水 1.00kN/m2 防水层(柔性):三毡四油铺小石子 0.40kN/m2找平层:15mm厚水泥砂浆 0.01520 kN/m3=0.30kN/m2找坡层:平均40mm厚水泥焦渣找坡 0.04014 kN/m3=0.56kN/m2保温层:60mm厚1:10水泥膨胀珍珠岩 0.06012 kN/m3=0.72kN/m2结构层:100mm厚现浇钢筋混凝土板 0.10025 kN/m3=2.50kN/m2抹灰层:10mm厚混合砂浆 0.01017 kN/m3=0.17 kN/m2合计 5.65KN/2.各层楼面(含走廊)20厚地砖面层: 25×0.020=0.50 KN/m210厚粘合层: 20×0.010=0.20 KN/m225厚楼面面层: 20×0.025=0.50 KN/m2100厚现浇板: 25×0.100=2.50 KN/m220厚顶棚抹灰: 20×0.020=0.40 KN/m2合计: 4.10KN/m2 3. 梁自重(1).主梁自重 a.hb=250mm700mm梁自重: 0.25(0.7-0.1)25 kN/m3=3.75kN/m抹灰层:10mm厚混合砂浆 0.01(0.7-0.1+0.25/2) 217 kN/m3=0.25kN/m合计 4.00KN/m b.hb=250mm500mm梁自重: 0.25(0.5-0.1)25 kN/m3=2.5kN/m抹灰层:10mm厚混合砂浆 0.01(0.5-0.1+0.25/2) 217 kN/m3=0.18kN/m合计 2.68KN/m (2)次梁自重hb=250mm600mm梁自重: 0.25(0.6-0.1)25 kN/m3=3.13kN/m抹灰层:10mm厚混合砂浆 0.01(0.6-0.1+0.25/2) 217 kN/m3=0.21kN/m合计 3.34kN/m(3)基础梁自重b×h=250×500mm(基础梁)梁自重: 0.25×0.5×25kN/m3=3.13kN/m合计 3.13kN/m 4. 柱自重 hb=500mm500mm柱自重: 0.50.525 kN/m3=6.25kN/m抹灰层:10mm厚混合砂浆 0.01(0.5+0.5) 217 kN/m3=0.34kN/m 合计 6.59KN/m5. 外纵墙自重标准层:纵墙: (3.6-0.5-0.9)0.2418 kN=9.50kN/m铝合金窗(1.80.9): 0.90.35 kN=0.32kN/m贴瓷砖外墙面: (3.6-0.9) 0.5 kN=1.35kN/m水泥粉刷内墙面: (3.6-0.9)0.36 kN=0.97kN/m合计 12.14kN/m底层:纵墙: (4.95-0.5-0.5-2.1)0.2418 kN=7.99kN/m门(2.11.8): 2.10.35 kN=0.74kN/m贴瓷砖外墙面: (3.6-2.1) 0.5 kN=0.75kN/m水泥粉刷内墙面: (3.6-2.1)0.36 kN=0.54kN/m 合计 10.02kN/m6. 内纵墙、横墙自重标准层纵墙: (3.6-0.5)0.2418 kN=13.39kN/m 粉刷墙面: (3.6-0.5)0.362 kN=2.23kN/m 合计 15.62kN/m底层纵墙: (4.95-0.50) 0.2418 kN=19.22kN/m 粉刷墙面: (4.95-0.50) 0.362 kN=3.20kN/m 合计 22.42kN/m 7.女儿墙女儿墙墙重: 0.24×1.1×18kN=4.75kN/m混凝土压顶0.1m: 25×0.1×0.24=0.6kN/m三面粉刷: 0.34×(0.54+1.2×2)=1.0kN/m合计 6.35kN/m 3.2 框架梁线荷载计算 边跨(AB、CD)框架梁承担的由屋面板、楼面板传来的荷载为梯形,如下图3.1,为计算方便,按支座弯矩等效原则,将其化为矩形分布,其中: = =0.5×7.2 /6=0.60 图3.1梯形荷载、三角形荷载分布等效图屋面梁上线荷载:(恒载=梁自重+板传荷载) ×5.65×3.6×2+4.00=24.2KN/m楼面梁上线荷载:(恒载=梁自重+板传荷载+填充墙重) ×4.50×3.6×2+4.00+15.5=31.4KN/m中框梁(BC)承担的由屋面板、楼面板传来的荷载为三角形,为计算方便,按支座弯矩等效原则,将其化为矩形分布,则:屋面梁上线荷载:(恒载=梁自重+板传荷载)=5/8×5.65×1.25×2+3.34=8.83+3.34=12.17kN/m楼面梁上线荷载:(恒载=梁自重+板传荷载)=5/8×4.50×1.25×2+3.34=5.19+3.34=8.53kN/m3.3 框架柱节点集中荷载计算3.3.1 A、D轴柱纵向集中荷载的计算顶层柱恒载=女儿墙自重+梁自重+板传荷载 =6.35×7.2+4.00×(7.2-0.5)+5/8×5.65×3.6×7.2 =164.05kN标准层柱恒载=墙自重+梁自重+板传荷载 =12.14×(7.2-0.5)+4.00×(7.2-0.5)+5/8×4.50×3.6×7.2 =161.92kN基础顶面荷载=底层外纵墙自重+基础梁自重 =10.02×(7.2-0.5)+3.13×(7.2-0.5) =88.11kN3.3.2 B、C轴柱纵向集中荷载的计算顶层柱恒载=梁自重+板传荷载 =3.34×(7.2-0.5)+ 5/8×5.65×3.6×7.2+1-2(1.25/6)2+(1.25/6)3×5.65×1.25×7.2 =164.75KN标准层柱恒载=墙自重+梁自重+板传荷载 =15.62×(7.2-0.5)+3.34×(7.2-0.5)+5/8×4.50×7.2×3.6 +1-2(1.25/6)2+(1.25/6)3×4.50×1.25×7.2 =209.2KN基础顶面荷载=底层内墙自重+基础梁自重 =22.42×(7.2-0.5)+3.13×(7.2-0.5) =171.2KN恒载作用下框架受荷简图如下(图 3.2): 图3.2恒载作用下结构计算简图3.4 恒载作用下框架的固端弯矩采用力矩分配法计算框架弯矩屋面层梁的固端弯矩:=6.34标准层梁的固端弯矩:=3.5 节点分配系数计算为各杆件的相对线刚度与交汇于此结点的所有杆件的线刚度之和的比值,公式如下: (4-1)为修正分层法的误差,一般层柱的线性刚度降低0.9,相应的传递系数取1/3,底层柱的线性刚度不降低,相应的传递系数取1/2.根据对称性,只计算A、B节点:A轴各节点: A5点:=1.48/(1×0.9+1.48)=0.62=1.0×0.9/(1.0×0.9+48)=0.38 A4、A3、A2点:=1.0×0.9/(1.48+1.0×0.9+1.0×0.9)=0.27=1.48/(1.48+1.0×0.9+1.0×0.9)=0.46A1点:=1.48/(1.48+1.0×0.9+0.73)=0.48=1.0×0.9/(1.48+1.0×0.9+0.73)=0.29=0.73/(1.48+1.0×0.9+0.73)=0.23B轴各节点:B5点:=1.48/(1.48+1.0×0.9+1.44)=0.39=1.0×0.9/(1.48+1.0×0.9+1.44)=0.24=1.44/(1.48+1.0×0.9+1.44)=0.37B4、B3、B2点:=1.48/(1.48+1.44+1.0×0.9+1.0×0.9)=0.31=1.0×0.9/(1.48+1.44+1.0×0.9+1.0×0.9)=0.19=1.44/(1.48+1.44+1.0×0.9+1.0×0.9)=0.31 B1点:=1.48/(1.48+1.44+0.73+1.0×0.9)=0.33=1.44/(1.48+1.44+0.73+1.0×0.9)=0.32=0.73/(1.48+1.44+0.73+1.0×0.9)=0.15=1.0×0.9/(1.48+1.44+0.73+1.0×0.9)=0.203.6恒载作用下框架的内力计算3.6.1 恒荷载作用下内力分析采用力矩二次分配法 计算图见图3.3。 图3.3 恒载作用下框架的弯矩计算(KN·m)框架横梁的跨中弯矩计算公式为:,根据此公式计算各框架梁的跨中弯矩如下:2222222222恒载作用下框架受力弯矩图如下(图3.4) 图3.4 恒载作用下框架的弯矩图(单位:KN·m) 3.6.2 恒载作用下框架的剪力计算梁: 柱: 框架的剪力计算具体过程见下表,见剪力图(图3.5)。 图3.5 恒载作用下框架剪力图(KN) 恒载作用下梁剪力计算层号MaMb-Mb+Mc-Mc+MdQaQb-Qb+Qc-Qc Qd5-40.38-59.03-28.13-28.13-59.03-40.3875.71-69.4915.21-15.2169.49-75.714-70.58-82.12-24.27-24.27-82.12-70.5896.12-92.2810.66-10.6692.28-96.123-70.08-82.3-24.1-24.1-82.3-70.0896.24-92.1610.66-10.6692.16-96.242-70.51-82.44-23.96-23.96-82.44-70.5196.19-92.2110.4-10.492.21-96.191-62.79-77.8-27.9-27.9-77.8-62.7996.7-91.710.4-10.491.7-96.7 恒载作用下柱剪力计算层号Ma+ Ma- Mb+Mb- Mc+ Mc- Md+ Md- Qa Qb Qc Qd540.3835.83-30.73-28.6330.7328.63-40.38-35.83-21.1716.49-16.4921.17434.7535.04-29.21-29.129.2129.1-34.75-35.04-19.3916.2-16.219.39335.0434.79-29.1-29.0229.129.02-35.04-34.79-19.416.14-16.1419.40235.7340.64-29.46-32.1729.4632.17-35.73-40.64-21.2117.12-17.1221.21122.1511.07-17.13-8.8717.138.87-22.15-11.07-6.715.25-5.256.71 3.6.3 恒载作用下框架的轴力计算 恒载作用下框架的轴力计算,包括梁传来的荷载和框架柱自重。 柱自重: 底层: 6.59×4.95=32.62KN 标准层:6.59×3.6=23.72KN 框架在恒载作用下轴力计算如下表,轴力图如下(图3.6)恒载作用下柱轴力计算(A、D轴)层号QaQPiPGiGNa575.3175.31164.05164.0523.7223.72263.08496.12171.43161.92325.9723.7247.44544.84396.24267.67161.92487.8923.7271.16826.72296.19363.86161.92649.8123.7294.881128.55196.70460.5688.11737.9232.62127.501325.98恒载作用下柱轴力计算(B、C轴)层号QbQPiPGiGNb569.4969.49164.75164.7523.7223.72257.96492.28161.77209.2373.9523.7247.44583.16392.16253.93209.2583.1523.7271.16908.24292.21346.14209.2792.3523.7294.881233.37191.70437.84171.2963.5532.62127.501528.89 图3.6 恒载作用下框架轴力图(KN)4 活荷载及其内力分析4.1 活荷载标准值查规范得活荷载值如下:(1) 屋面活荷载: 上人屋面 2.0KN/m2(2)办公楼楼面活荷载为 2.0KN/m2(3)走廊活荷载 2.5KN/m2(4)雪荷载 (式中ur为屋面积雪分布系数),屋面活荷载与雪荷载不同时考虑,两者取大值。 4.2活载作用下梁线荷载计算 边跨(AB、CD)框架梁承受的由屋面板、楼面板传来的活荷载形式为梯形,与恒荷载相同,为计算方便,可按支座弯矩等效原则将其简化为矩形分布,计算过程如下:屋面梁、楼面梁上线荷载:(活载=板传荷载)×2.0×3.6×2=12.20KN/m 中跨梁(BC) 承担的由屋面板、楼面板传来的荷载为三角形,为计算方便,按支座弯矩等效原则,将其化为矩形分布,则 屋面梁上线荷载:(活载=板传荷载)=5/8×2.0×1.25×2=3.13KN/m楼面梁上线荷载:(活载=板传荷载)=5/8×2.5×1.25×2=3.91KN/m4.3 活载作用下框架柱节点集中荷载计算4.3.1 A、D轴柱纵向集中荷载的计算顶层、标准层柱活载=板传荷载 =5/8×2.0×3.6×7.2 =32.4KN4.3.2 B、C轴柱纵向集中荷载的计算顶层柱活载=板传荷载 = 5/8×2.0×3.6×7.2+1-2(1.2/6)2+(1.2/6)3×2.0×1.25×7.2 =49.1KN标准层柱活载=板传荷载 = 5/8×2.0×3.6×7.2+1-2(1.2/6)2+(1.2/6)3×2.5×1.25 ×7.2 =53.3KN 活载作用下框架受荷简图如下(图 4.1) 图4.1框架受荷简图4.4 活载作用下框架的固端弯矩采用力矩分配法计算框架弯矩屋面层梁的固端弯矩:=标准层梁的固端弯矩:采用分层法近似计算,为了减少计算误差作出如下修正:(1)把除底层柱以外的其它个层柱的线刚度乘以修正系数0.9;(2)杆端分配弯矩向远端传递是,底层柱和各层梁的传递系数仍按远端为固定支撑取1/2;(3)其它各柱的传递系数考虑为弹性支撑取1/3;各杆的修正线刚度和传递系数同恒载,计算示意图同恒载。 图4.2 活载作用下框架的弯矩计算(KN·m) 框架横梁的跨中弯矩计算公式为:,根据此公式计算各框架梁的跨中弯矩如下: 2 2 2 2 2 2 2= 2 2框架在活载作用下的梁柱轴力、剪力计算如下表:活载作用下柱轴力计算(A、D轴)层号QaQPiPNa5 38.1138.1132.432.470.51437.3075.4132.464.8140.21337.41112.8232.497.2210.022 37.39150.2132.4129.6279.81137.60187.810.00129.6317.41活载作用下柱轴力计算(B、C轴)层号QbQPiPNb539.0039.0049.149.188.10440.7879.7853.3102.4182.18340.68120.4653.3155.7276.13240.70161.1653.3209.0370.16140.50201.660.00209.0410.66 活载作用下梁剪力计算层号MaMb-Mb+Mc-Mc+MdQaQb-Qb+Qc-QcQd5-19.56-28.64-13.40-13.40-28.64-19.5638.11-35.093.91-3.9135.09-38.114-28.13-32.35-9.35-9.35-32.35-28.1337.30-35.894.89-4.8935.89-37.303-27.20-32.07-9.63-9.63-32.07-27.2037.41-35.794.89-4.8935.79-37.412-27.37-32.12-9.58-9.58-32.12-27.3737.39-35.814.89-4.8935.81-37.391-24.37-30.34-11.10-11.10-30.34-24.3737.60-35.614.89-4.8935.61-37.60活载作用下柱剪力计算层号Ma+Ma-Mb+Mb-Mc+Mc-Md+Md-QaQbQcQd519.5615.07-15.16-11.9615.1611.96-19.56-15.07-9.627.53-7.539.62413.0613.60-11.05-11.2211.0511.22-13.06-13.60-7.416.19-6.197.41313.6013.50-11.22-11.1911.2211.19-13.60-13.50-7.536.23-6.237.53213.8715.78-11.36-12.4011.3612.40-13.87-15.78-8.246.60-6.608.2418.594.30-6.84-3.426.843.42-8.59-4.30-2.602.07-2.072.60 活载作用下框架所受弯矩、剪力以及轴力见下图: 图4.3 活载作用下框架的弯矩图(KNm) 图4.4 活载作用下框架的轴力图(KN) 图4.5 活载作用下框架轴力图(KN)5 风荷载作用5.1 风荷载标准值风荷载标准值的计算公式为: (6-1)式中:基本风压0=0.30KN/风载体型系数 ,迎风面取0.8,背风面取-0.5,故0.8(0.5)1.3;风振系数Z,由于高度H=19.20m<30m,且高宽比H/B=19.20/14.50=1.35< 1.5,应采用风振系数未考虑风压脉动影响,故Z=1.0;风压高度系数,地面粗糙度为B类;由得沿房屋高度的分布风荷载标准值为:K1.3×Z××0.30 (6-2)根据各楼层的高度 (从室外地面算起),由荷载规范,查取,得风压高度变化系数µZ 值(见表5.1数值)代入上式可得各楼层标高处的K如下: 底层:K =Z µZ µS0 =1.0001.01.30.30=0.390KN/二层:K =Z µZ µS0 =1.0001.01.30.30=0.390KN/三层:K =Z µZ µS0 =1.0001.0631.30.30=0.415KN/四层:K =Z µZ µS0 =1.0001.1591.30.30=0.452KN/五层:K =Z µZ µS0 =1.0001.2381.30.30=0.483KN/风荷载的线荷载标准值qk: 底层:qk =K 7.2=0.390×7.2=2.81KN/m 二层:qk =K 7.2=0.390×7.2=2.81N/m 三层:qk =K 7.2=0.415×7.2=2.99KN/m四层:qk =K 7.2=0.452×7.2=3.25KN/m 五层:qk =K 7.2=0.483×7.2=3.48KN/m为简化计算,将矩形分布的风荷载折算成节点集中力Fk: 第五层:=3.48 (3.6+1.1)÷2=8.18KN 第四层:=(3.48+3.25)÷23.6=12.11KN 第三层:=(3.25+2.99)÷23.6=11.77KN 第二层:=(2.99+2.81)÷23.6=10.44KN 底层: =(2.81+2.81)÷2(3.6+0.45)=11.38KN
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