第4章內(nèi)力計(jì)算

1、第4章 內(nèi)力計(jì)算第4章 內(nèi)力計(jì)算4.1 風(fēng)荷載作用下框架內(nèi)力計(jì)算由D值法計(jì)算結(jié)構(gòu)在風(fēng)荷載作用下的內(nèi)力，計(jì)算過程及結(jié)果見表4-1。 表4-1風(fēng)荷載作用下柱端彎矩表(kN·m)層次邊柱D/DViyiM上M下50.2338.450.940.44653.272.6440.23318.481.270.457.105.8130.23327.971.490.59.789.7820.23336.571.860.512.7812.7810.24244.23.210.5521.9026.77層次中柱D/DViyiM上M下50.2678.451.410.453.723.0540.26718.481.490

2、.57.407.4030.26727.971.490.511.2011.2020.26736.571.650.514.6514.6510.25844.212.470.5523.3528.54梁端風(fēng)荷載彎矩、剪力、軸力 見表4-2,其中=KR/（KR+KL）。4.2 水平地震作用下框架內(nèi)力計(jì)算以12軸橫向框架為例進(jìn)行計(jì)算，在水平地震作用下的框架住彎矩計(jì)算采用D值法，其計(jì)算過程見表4-3。 表4-2梁端風(fēng)荷載彎矩(kN·m)、剪力(kN)、軸力(kN)層次邊柱處中柱處剪力軸力McMc1-Mc右Mc左ABBC邊柱中柱續(xù)表4-2層次邊柱處中柱處剪力軸力McMc1-Mc右Mc左ABBC邊柱中柱

3、53.273.720.310.692.571.150.822.140.821.3249.7410.450.310.697.213.242.406.013.224.93312.5918.600.310.6912.835.773.4010.696.6212.22222.5625.850.310.6917.848.015.6614.8712.2821.43134.6838.000.310.6926.2211.788.6021.8520.8834.68 風(fēng)荷載作用下框架的彎矩、剪力、軸力圖見圖4-1,4-2。 圖4-1風(fēng)荷載作用下的框架彎矩（單位KN.m） 圖4-2風(fēng)荷載作用下的剪力、軸力(單位KNm

4、)表4-3水平地震作用下框架柱彎矩計(jì)算柱層次層剪力總剛度各柱剛度D/DVikyhM下M上邊柱5748.611102920168700.015311.452.930.44715.3419.0141366.511102920168700.015320.912.930.4528.2334.5031847.601102920168700.015328.272.930.5 42.4142.41續(xù)表4-322191.891102920168700.015333.542.930.550.3150.3112470.0740992062300.015237.554.460.55 93.9776.88中柱5748

5、.611102920192800.017513.104.240.4517.6921.6241366.511102920192800.017523.914.240.535.87 35.8731847.601102920192800.017532.334.240.548.50 48.5022191.891102920192800.017538.364.240.557.54 57.54 12470.0740992066700.016340.266.450.55100.75 82.43水平地震作用下框架剪力、軸力計(jì)算見表4-4。表4-4水平地震作用下框架剪力、軸力層次邊柱中柱剪力軸力Mc梁端McMrM

6、labbc邊柱中柱519.01-19.010.6921.6214.926.704.7612.434.767.67449.84-49.840.6953.5636.9616.6012.3030.817.0626.17370.64-70.640.6984.3758.2226.1517.9248.5234.9856.77292.72-92.720.69106.0473.1732.8723.2660.9858.2494.491127.19-127.190.69139.9796.5843.3931.5980.4889.83143.38地震作用下框架的彎矩、剪力、軸力圖見圖4-3,4-4。圖4-3水平地震作

7、用下的框架彎矩圖（單位kN·m）圖4-4水平地震作用下的剪力、軸力圖（單位kN）4.3 恒載作用下框架內(nèi)力計(jì)算4.3.1 計(jì)算方法選用本工程荷載作用下的內(nèi)力計(jì)算采用分層法4.3.2 用彎矩分配法計(jì)算梁柱端彎矩注意：除底層外柱的線剛度需要乘以修正系數(shù)0.9，并且除底層柱外其它各層的彎矩傳遞系數(shù)取1/3。 修正后的梁柱線剛度見表4-5。表4-5 梁柱線剛度表（10-4E .m3）層次梁柱iAB(iCD)iBCiC2-56.9520.837.1116.9520.834.22中間層A點(diǎn)分配系數(shù)中間節(jié)點(diǎn)B節(jié)點(diǎn)分配系數(shù)底層A點(diǎn)分配系數(shù)底層B點(diǎn)分配系數(shù) 頂層A點(diǎn)分配系數(shù) 頂層B點(diǎn)分配系數(shù)固端彎矩及

8、彎矩分配系數(shù)見表4-6。表4-6分層法分配系數(shù)及恒載作用下的固端彎矩計(jì)算結(jié)果節(jié)點(diǎn)單元ABEA上柱A下柱AB端BA端B上柱B下柱BE端E端分配系數(shù)頂層0.5060.4940.2840.2910.425-中間層0.3360.3360.3280.220.2250.2250.33-底層0.3890.2310.380.2420.2480.1470.363-固端彎矩頂層-50.3750.37-6.72-3.36中間層-70.4770.47-5.30-2.65底層-70.4770.47-5.30-2.65分配法計(jì)算過程見圖4-5圖4-7。4.3.3 跨中彎矩計(jì)算 根據(jù)求得的支座處彎矩，按平衡條件計(jì)算，框架梁

9、在實(shí)際荷載作用下按簡支梁計(jì)算的跨中彎矩M0，并查靜力手冊(cè)，在實(shí)際荷載分布下，框架的跨中彎矩計(jì)算按M=M0-（M左+M右）/2。結(jié)果見表4-7。表4-7實(shí)際荷載分布下分層法各單元跨中彎矩計(jì)算表（kN·m）位置按簡支計(jì)算跨中彎矩疊加后的跨中彎矩左端右端跨中AB、CD跨頂層75.5629.6748.2936.58中間層105.7153.1366.2346.03底層105.7149.7366.2247.74BC跨頂層10.0931.4031.40-21.31中間層7.9531.0831.08-23.13底層7.9534.4834.48-26.53圖4-5頂層彎矩分配法計(jì)算過程（單位kN

10、83;m）圖4-6中間層彎矩分配法計(jì)算過程（單位kN·m）圖4-7底層彎矩分配法計(jì)算過程（單位kN·m）4.3.4 由各層單元計(jì)算整個(gè)結(jié)構(gòu)在恒載作用下的彎矩將分層法求得的各層彎矩圖疊加，可得整個(gè)框架在豎向荷載的彎矩圖。很顯然 疊加后各框架節(jié)點(diǎn)彎矩并不能達(dá)到平衡，這是由于分層計(jì)算的誤差造成的。為了提高精 度，可將不平衡彎矩分配進(jìn)行一次修正，疊加后的框架梁跨中彎矩計(jì)算表見表4-8。表4-8疊加后的框架梁跨中彎矩計(jì)算位置按簡支計(jì)算跨中彎矩疊加后跨中彎矩左端右端跨中AB跨（CD跨）575.5634.0549.9533.564105.7150.5762.7649.053105.715

11、8.9568.8141.832105.7159.4568.9841.501105.7153.1067.6445.34BC跨510.0932.1032.10-22.0147.9536.2836.28-28.3337.9534.9434.94-26.9927.9535.2035.20-27.2517.9536.6136.61-28.66 4.3.5 梁端剪力及梁端控制界面的彎矩 梁端剪力計(jì)算用平衡條件可求出的梁端剪力及梁端柱邊剪力，計(jì)算結(jié)果見表4-9。 梁端柱邊剪力計(jì)算取柱軸心至柱邊這一端梁為隔離體，由平衡條件可求出的梁端柱邊的剪力值，對(duì)AB跨梁取圖 為隔離體，由豎向力平衡及幾何條件，可得 梁端柱

12、邊彎矩計(jì)算為內(nèi)力組合做準(zhǔn)備，需將梁端彎矩?fù)Q算為梁端柱邊彎矩，對(duì)本工程按下式計(jì)算 表4-9 梁端彎矩（kN·m）、剪力(kN)AB跨（CD跨）層次g1g2MabMbaVabVbaVabVba53.2617.4734.0549.9523.56 41.8821.1637.34 416.36 12.64 50.5762.76 45.5568.23 41.01 63.69316.36 12.6458.9568.8148.6667.80 44.12 63.26 216.3612.6459.4568.9848.8467.7444.30 63.20 116.3612.64 53.10 67.6446

13、.49 68.6741.95 64.13 BC跨層次g1g2VbcVcbVbcVcb53.2610.7519.3919.3917.6617.6643.267.7815.12 15.12 13.6913.6933.267.7815.1215.1213.6913.6923.267.7815.1215.1213.6913.6913.267.7815.1215.1213.6913.69梁端柱邊剪力、彎矩計(jì)算結(jié)果見表4-10。表4-10梁端柱邊剪力(kN)、彎矩(kN·m)計(jì)算層次梁端彎矩梁端柱邊剪力梁端柱邊彎矩MabMbaMbcVabVbaVbcMabMbaMbc534.0549.9532.

14、10 21.1637.34 17.6629.8242.48 28.57 450.5762.76 36.2841.01 63.6913.6942.3750.02 33.26358.9568.8134.9444.12 63.26 13.6950.7556.1631.92259.4568.9835.20 44.30 63.20 13.6950.5956.3432.18 153.10 67.6436.61 41.95 64.13 13.6944.71 54.81 33.59 4.3.6 柱軸力計(jì)算柱軸力可通過對(duì)梁端剪力、縱向梁傳來剪力和柱自重疊加得到。柱軸力的計(jì)算過程見表4-11。表4-11柱軸力計(jì)算

15、(kN)Vab豎向力F柱自重軸力VbaVbc豎向力柱自重軸力23.5648.1512 頂71.7141.8819.3944.2712頂105.54底83.71底117.5445.5569.9012 頂115.45 68.2315.1284.7512頂168.10底127.45 底180.1048.66 69.9012 頂118.5667.8015.1284.7512頂167.67底130.56 底179.6748.8469.9012 頂118.74 67.7415.1284.7512頂167.61底130.74 底179.6146.49 69.9018.20 頂116.39 68.6715.1

16、284.7518.4頂168.54底134.59底186.94 4.3.7 彎矩調(diào)幅本工程考慮梁端彎矩調(diào)幅，調(diào)幅系數(shù)，恒載作用下的梁剪力、柱軸力 見圖4-8，調(diào)幅后的梁端柱邊彎矩及跨中彎矩見圖4-9。調(diào)幅后的梁端柱邊彎矩及跨中彎矩見表4-12。表4-12 調(diào)幅后的梁端、跨中彎矩層次AB跨（CD跨）BC跨Mab'Mm'Mba'Mbc'Mm'525.3544.8336.1124.28-14.19436.0166.4442.5228.27-20.32343.1460.2747.7427.13-19.18243.0060.2647.8927.35-19.4013

17、8.0063.4146.5928.55-20.60圖4-8恒載作用下的剪力、軸力圖(單位：kN)圖4-9恒載作用下經(jīng)調(diào)幅的柱邊彎矩圖(單位：kN·m)4.4 活載作用下的內(nèi)力計(jì)算 活載同時(shí)作用于所有框架梁上，按滿荷載分布考慮，不考慮活載的不利布置并采用分層法，跨中彎矩乘以1.1-1.2的放大系數(shù)，以考慮其不利布置可能產(chǎn)生的影響。 4.4.1 用彎矩分配法計(jì)算梁端彎矩 頂層： 其它層： 4.4.2 內(nèi)力計(jì)算活載作用下的梁端彎矩、剪力、柱軸力計(jì)算過程與恒載作用下的計(jì)算過程完全一樣。計(jì)算過程不再累述。計(jì)算結(jié)果見表4-13。表4-13梁端柱邊剪力計(jì)算(kN)ab跨梁端柱邊剪力計(jì)算層次g1g2

18、MabMbaVabVbaVabVba57.8012.722.0815.2322.8013.6721.2447.8016.2219.0116.5421.5814.9820.0237.8015.7418.7516.3621.6214.8020.0627.8015.8718.8017.4921.6015.9320.0417.8014.1718.4815.7821.8614.2220.30bc跨梁端柱邊剪力計(jì)算層次g1g2MbcVbcVbcVcb54.8013.175.764.84.846.007.977.26.06.036.008.367.26.06.026.008.297.26.06.016.00

19、9.657.26.06.0活荷載作用下的梁端柱邊彎矩計(jì)算見表4-14。表4-14活荷載作用下的梁端柱邊彎矩計(jì)算層次梁端彎矩梁端柱邊剪力梁端柱邊彎矩MabMbaMbcVabVbaVbcMabMbaMbc512.722.0813.1713.6721.244.89.9717.8312.21416.2219.017.9714.9820.026.013.2215.016.77315.7418.758.3614.8020.066.012.7814.747.16215.8718.808.2915.9320.046.012.6814.797.09114.1718.489.6514.2220.306.011.3

20、314.428.45 4.4.3彎矩調(diào)幅考慮梁端彎矩調(diào)幅，調(diào)幅系數(shù),調(diào)幅后的梁端柱邊彎矩及跨中彎矩見圖4-12。表4-15 調(diào)幅后的梁端、跨中彎矩(kN·m)層次AB跨（CD跨）BC跨Mab'Mm'Mba'Mbc'Mm'58.47116.61615.15710.379-6.919411.2416.43212.7555.755-1.435310.86316.73512.5276.086-1.766210.78116.75312.5736.027-1.70719.62717.48812.2577.183-2.863 風(fēng)荷載作用下的柱邊彎矩、剪力計(jì)算見表4-16。表4-16風(fēng)荷載作用下的柱邊彎矩、剪力計(jì)算層次梁端彎矩梁端剪力梁端柱邊彎矩MabMbaMbcVab'Vba'Vbc'Mab'Mba'Mbc&