框架柱内力组合
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第8章 一榀框架计算8.7框架内力计算框架结构承受的荷载主要有恒载、活载、风荷载、地震作用。
其中恒载、活载为竖向荷载,风荷载和地震为水平作用。
手算多层多跨框架结构的内力和侧移时,采用近似方法。
求竖向荷载作用下的内力采用分层法,求水平荷载作用下的内力采用反弯点法、D 值法。
在计算各项荷载作用下的效应时,一般按标准值进行计算,然后进行荷载效应组合。
8.7.2框架内力计算1。
恒载作用下的框架内力 (1)计算简图将图8-12(a )中梁上梯形荷载折算为均布荷载。
其中a=1。
8m ,l=6.9m ,=1800/69000.26a α==,顶层梯形荷载折算为均布荷载值:232312+=120.26+0.2621.31=18.8kN m q αα-⨯-⨯⨯()(),顶层总均布荷载为18.8+4.74=23.54kN m 。
其他层计算方法同顶层,计算值为21.63kN m 。
中间跨只作用有均布荷载,不需折算。
由于该框架为对称结构,取框架的一半进行简化计算,计算简图见8-19。
(2)弯矩分配系数节点A 1:101044 1.18 4.72A A A A S i ==⨯=111144 1.33 5.32A B A B S i ==⨯=12120.940.94 1.61 5.796A A A A S i =⨯=⨯⨯=()0.622 1.3330.84415.836AS =++=∑1010 4.720.29815.836A A A A AS S μ===∑图8-19 恒载作用下计算简图(括号内数值为梁柱相对线刚度)1111 5.320.33615.836A B A B AS S μ===∑1212 5.7960.36615.836A A A A AS S μ===∑ 节点B 1:11112 1.12 2.24B D B D S i ==⨯=18.076BS =∑1111 5.320.29418.076B A B A BS S μ===∑1010 4.720.32118.076B B B B BS S μ===∑ 1212 5.7960.32118.076B B B B BS S μ===∑1111 2.240.12418.076B D B D BS S μ===∑节点A 2:()210.94 1.610.4170.94 1.610.776 1.33A A μ⨯⨯==⨯⨯++230.940.7760.20113.91A A μ⨯⨯==224 1.330.38213.91A B μ⨯==节点B 2:224 1.330.3294 1.330.94 1.61+0.940.7762 1.12B A μ⨯==⨯+⨯⨯⨯⨯+⨯210.94 1.610.35916.15B B μ⨯⨯==212 1.120.13916.15B C μ⨯==230.940.7760.17316.15B B μ⨯⨯==节点A 3 、A 4、A 5与A 2相同B 3、B 4、B 5与B 2相同。
柱顶N 193.6712.277.94-11.6311.63177.64柱底N 223.6212.277.94-11.6311.63206.39柱顶N 450.4859.5555.22-35.1335.13422.43柱底N 480.4359.5555.22-35.1335.13451.18柱顶N 707.21106.92102.59-67.9267.92657.53柱底N 737.16106.92102.59-67.9267.92686.28柱顶N 963.94154.29149.96-109.23109.23883.76柱底N 993.89154.29149.96-109.23109.23912.52柱顶N 1220.64201.65197.32-153.74153.741106.64柱底N 1250.59201.65197.32-153.74153.741135.39柱顶N 1477.13249.77245.44-206.60206.601320.99柱底N1525.64249.77245.44-206.60206.601367.56截面柱顶柱底柱顶柱底柱顶柱底柱顶柱底γRE (∑Mc=ηc ∑--116.8088.43130.58112.96146.70126.86γREN--495.50524.25798.80827.551110.961139.712SEk左震组合内力截面1层次6543层次 4.003.00SQk和雪载6.005.00SGk 表6.31(b) 横向框架C柱柱端组合弯矩设计值的调整6.00-18.62-2.81-2.3417.19-17.19-1.19-39.18-27.955.00-14.19-4.16-4.2128.44-28.4414.81-48.05-23.324.00-14.57-3.98-3.9837.16-37.1624.17-57.95-23.653.00-14.65-3.99-3.9943.64-43.6431.24-65.20-23.772.00-14.96-4.15-4.1548.20-48.2035.89-70.64-24.351.00-5.76-1.56-1.5656.36-56.3655.61-68.95-9.34M -38.18-3.10-1.92-62.7462.74-96.40N 239.5617.1611.25-11.4211.42223.50M 30.50 3.84 3.5038.45-38.4566.51N 269.5117.1611.25-11.4211.42252.25M -28.08-3.85-4.00-88.9488.94-121.37N 555.6192.0086.09-34.7334.73538.59M 28.84 3.84 3.8472.77-72.77105.21N 585.5692.0086.09-34.7334.73567.34M -28.84-3.84-3.84-109.89109.89-143.82N 871.74166.75160.84-69.0669.06842.25M 28.84 3.84 3.84101.43-101.43135.02N 901.69166.75160.84-69.0669.06871.00M -28.84-3.84-3.84-124.11124.11-158.60N 1187.87241.50235.59-110.63110.631138.38M 28.88 3.83 3.83124.11-124.11158.64N 1217.82241.50235.59-110.63110.631167.14M -28.74-3.87-3.87-137.07137.07-172.00N 1504.03316.26310.35-162.10162.101424.25M 31.82 3.54 3.54137.07-137.07174.80N 1533.98316.26310.35-162.10162.101453.00M -21.56-2.57-2.57-131.64131.64-158.84N 1819.50390.26384.35-207.98207.981714.91M 10.78 1.29 1.29214.79-214.79234.35N 1868.01390.26384.35-207.98207.981761.48柱顶N 239.5617.1611.25-11.4211.42223.50柱底N 269.5117.1611.25-11.4211.42252.25柱顶N 555.6192.0086.09-34.7334.73538.59柱底N 585.5692.0086.09-34.7334.73567.34柱顶N 871.74166.75160.84-69.0669.06842.25柱底N 901.69166.75160.84-69.0669.06871.00柱顶N 1187.87241.50235.59-110.63110.631138.38柱底N 1217.82241.50235.59-110.63110.631167.14柱顶N 1504.03316.26310.35-162.10162.101424.25柱底N1533.98316.26310.35-162.10162.101453.00SGk SQk和雪载SEk左震组合右震组合 1.35SGk+SQk 柱顶柱底柱顶柱底柱顶柱底柱顶柱底柱顶柱底柱顶柱底表6.33(a) 横向框架D柱弯矩和轴力组层次截面内力SGk SQk和雪载SEk 左震组合表6.32 横向框架C柱剪力组合(kN)层次SGk SQk和雪载SEk 左震组合65432层次截面内力3.002.001.006.005.004.00柱顶N 1819.50390.26384.35-207.98207.981714.91柱底N 1868.01390.26384.35-207.98207.981761.48截面柱顶柱底柱顶柱底柱顶柱底柱顶柱底γRE (∑Mc=ηc ∑--142.09122.15166.97157.94185.53186.44γREN--538.59567.34842.25871.001138.381167.14619.08 1.93 1.5128.11-28.1151.29-10.8327.69515.81 2.14 2.1844.92-44.9266.87-32.4023.48416.02 2.13 2.1358.70-58.7082.29-47.4423.76316.03 2.13 2.1368.95-68.9593.63-58.7523.77216.82 2.06 2.0676.15-76.15102.35-65.9424.7716.600.790.7970.70-70.7085.26-70.999.701表6.33(b) 横向框架C柱柱端组合弯矩设计值的调整层次 6.005.004.003.00表6.34 横向框架C柱剪力组合(kN)层次SGk SQk和雪载SEk 左震组合右震组合 1.35SGk+SQkN Nmin Nmax 201.83273.72249.58230.58314.16285.52495.50667.70623.95524.25708.13659.89798.801061.65998.34827.551102.091034.281110.961455.611372.731139.711496.041408.671426.421849.511747.081455.171889.951783.021750.722243.902122.231797.292309.382180.45柱顶柱底柱顶柱底135.32164.17160.00248.561426.421455.171750.721797.29右震组合 1.35SGk+S Qk 1.2SGk+1.4SQk 红色字体绿色字体紫色字体1.002.00调整-26.28 -22.85 -23.06 -23.17 -23.76 -9.1025.95-54.64-50.16 247.25340.57311.50 -8.4645.0241.98 276.01381.00347.44 63.62-41.76-39.09 610.83842.07795.53 -46.1542.7739.98 639.58882.51831.47 84.76-42.77-39.98 985.901343.601279.54 -75.9642.7739.98 1014.651384.031315.48 99.54-42.77-39.98 1368.491845.121763.54 -99.5142.8240.02 1397.251885.561799.48 113.10-42.67-39.91 1761.422346.702247.60 -110.3146.5043.14 1790.172387.132283.54 114.97-31.68-29.47 2147.512846.592729.76 -212.4115.8414.74 2194.082912.072787.98 247.25340.57311.50 276.01381.00347.44 610.83842.07795.53 639.58882.51831.47 985.901343.601279.54 1014.651384.031315.48 1368.491845.121763.54 1397.251885.561799.48 1761.422346.702247.60 1790.172387.132283.54M轴力组合右震组合1.35SGk+SQk1.2SGk+1.4SQkMmax M1.2SGk+1.4SQk 剪力设计值右震组合1.35SGk+SQk红色字体绿色字体绿色字体紫色字体紫色字体1.2SGk+1.4SQkN Nmin Nmax红色字体2147.512846.592729.762194.082912.072787.98柱顶柱底柱顶柱底202.14204.07185.44304.661424.251453.001714.911761.4825.6021.9722.2122.2223.079.03调整2.00 1.001.2SGk+1.4SQk 剪力设计值。
内力组合《抗震规范》第条规定如下。
截面抗震验算结构构件的地震作用效应和其他荷载效应的基本组合,应按下式计算:G GE Eh Ehk Ev Evk w w wkS S S S S γγγψγ=+++ ()式中: S ——结构构件内力组合的设计值,包括组合的弯矩、轴向力和剪力设计值;γG ——重力荷载分项系数,一般情况应采用,当重力荷载效应对构件承载能力有利时,不应大于; γEh 、γEv ——分别为水平、竖向地震作用分项系数,应按表 采用; γw ——风荷载分项系数,应采用;s GE ——重力荷载代表值的效应,有吊车时尚应包括悬吊物重力标准值的效应; s Ehk ——水平地震作用标准值的效应,尚应乘以相应的增大系数或调整系数; s Evk ——竖向地震作用标准值的效应,尚应乘以相应的增大系数或调整系数; s wk ——风荷载标准值的效应 ;ψw ——风荷载组合值系数,一般结构取,风荷载起控制作用的高层建筑应采用。
注:本规范一般略去表示水平方向的下标。
表 地震作用分项系数结构构件的截面抗震验算,应采用下列设计表达式:RE RS γ=式中: γRE ——承载力抗震调整系数,除另有规定外,应按表采用;R ——结构构件承载力设计值。
表 承载力抗震调整系数当仅计算竖向地震作用时,各类结构构件承载力抗震调整系数均宜采用。
本次毕业设计,各截面不同内力的承载力抗震调整系数取值如下表结构安全等级设为二级,故结构重要性系数为0 1.0γ=根据《建筑结构荷载规范》和《建筑抗震设计规范》,组合三种工况:恒荷载控制下、活荷载控制下和有地震作用参加的组合。
其具体组合方法如下: 恒荷载控制下:Gk Qk S 1.35S 1.40.7S =+⨯ 活荷载控制下:Gk Qk S 1.2S 1.4S =+有地震作用参加的:Gk Qk Ehk S 1.2(S 0.5S ) 1.3S =+± Gk Qk Ehk S 1.0(S 0.5S ) 1.3S =+±对柱进行非抗震内力组合时,根据规范,对活载布置计算的荷载进行折减,折减系数由上而下分别为,,,,。