荷載內力分析計算過程案例綜述恒載計算節(jié)點分配系數將一榀框架梁柱節(jié)點進行編號：一榀框架節(jié)點圖豎向荷載內力分配采用彎矩二次分配法，即假定節(jié)點不平衡彎矩只對與該節(jié)點相交的各桿件的遠端有影響，而對其余桿件的影響忽略不計。計算時，先對各節(jié)點不平衡彎矩進行第一次分配，并向遠端傳遞，再將因傳遞彎矩而產生的新的不平衡彎矩進行第二次分配，整個彎矩分配和傳遞過程即結束。彎矩分配首先是以節(jié)點周邊的梁柱線剛度計算各節(jié)點的彎矩分配系數，在按照分配系數計算不平衡彎矩。以1號節(jié)點為例計算分配系數：μμ經匯總，各節(jié)點處分配系數見下圖：彎矩分配系數圖彎矩計算框架梁按照固支考慮，其控制截面彎矩如下：M鑒于彎矩分配是對節(jié)點部分即支座部分進行分配，以頂層為例對支座彎矩進行計算：MMM經計算匯總，各層彎矩如下：梁端彎矩表梁端彎矩梁AB梁BC梁CD5-85.552-5.694-85.5524-104.963-4.402-104.9633-104.963-4.402-104.9632-104.963-4.402-104.9631-104.963-4.402-104.963恒載內力計算使用Excel表對各節(jié)點處彎矩進行計算，過程如下：恒載彎矩二次分配表各節(jié)點處彎矩分配后，梁兩端彎矩大小不再一致，原跨中彎矩相應進行調整，按照總彎矩不變原理對跨中進行計算：M以頂層邊跨為例對跨中彎矩進行計算：M恒載工況彎矩圖EQ均布荷載下梁柱端剪力計算方式如下：VV以邊跨頂層為例，對梁端剪力和柱軸力進行計算：VV計算結果見下圖：恒載作用下剪力圖一榀框架軸力計算公式：N上式中，V為柱節(jié)點兩側的剪力差，G為柱自重，P為傳至柱上的集中力，以邊跨頂層為例，計算柱軸力：NN恒載作用下軸力圖活載計算活載梁端彎矩計算活載計算方法同恒載，計算結果如下：梁端活載彎矩表梁端彎矩梁AB梁BC梁CD第5層-6.000-0.365-6.000第4層-23.812-1.805-23.812第3層-23.812-1.805-23.812第2層-23.812-1.805-23.812第1層-23.81-1.80-23.81EQ活荷載彎矩二次分配法計算：活荷載彎矩二次分配表活載作用下彎矩圖活載柱端剪力與梁端剪力計算公式：VV計算結果如下：活載作用下剪力圖軸力計算公式：N活載作用下軸力圖雪荷載計算EQ根據荷載設計規(guī)范及建設地點，雪荷載標準值Sk=0.35kN/mm2EQ雪荷載為活荷載，僅作用于屋面即頂層，梁端彎矩計算如下：MMM風荷載內力計算風荷載屬于水平力，力的分配按照剛度分配，即：先對各軸反彎點進行計算：第A軸柱反彎點計算表層號h(m)Ky0y1y2y3yyh(m)53.601.580.380.000.000.000.381.3743.601.580.430.000.000.000.431.5533.601.580.480.000.000.000.481.7323.601.580.500.000.000.000.501.8014.602.020.550.000.000.000.552.53第B軸柱反彎點計算表層號h(m)Ky0y1y2y3yyh(m)53.604.690.450.000.000.000.451.6243.604.690.500.000.000.000.501.8033.604.690.500.000.000.000.501.8023.604.690.500.000.000.000.501.8014.605.990.550.000.000.000.552.53第C軸柱反彎點計算表層號h(m)Ky0y1y2y3yyh(m)53.604.690.450.000.000.000.451.6243.604.690.500.000.000.000.501.8033.604.690.500.000.000.000.501.8023.604.690.500.000.000.000.501.8014.605.990.550.000.000.000.552.53第D軸柱反彎點計算表層號h(m)Ky0y1y2y3yyh(m)53.601.580.380.000.000.000.381.3743.601.580.430.000.000.000.431.5533.601.580.480.000.000.000.481.7323.601.580.500.000.000.000.501.8014.602.020.550.000.000.000.552.53EQ對梁、柱彎矩進行計算，計算過程見下表MM中柱：MM邊柱：M以頂層邊跨為例：M第A軸梁柱節(jié)點彎矩（風荷載）：層號Vi(kN)Di∑DDi/∑DVim(kN)y(m)Mc上

(kN.m)Mc下

(kN.m)Mb總

(kN.m)510.7817723917890.192.081.374.642.854.64422.0017723917890.194.251.558.726.5811.57332.3117723917890.196.241.7311.6810.7818.26242.4217723917890.198.191.8014.7414.7425.52153.1612078554390.2211.592.5323.9929.3238.73第B軸梁柱節(jié)點彎矩（風荷載）：層號Vi(kN)Di∑DDi/∑DVim(kN)y(m)Mc上

(kN.m)Mc下

(kN.m)Mb左

(kN.m)Mb右

(kN.m)510.7828172917890.313.311.626.555.362.214.34422.0028172917890.316.751.8012.1512.155.9011.61332.3128172917890.319.921.8017.8617.8610.1119.90242.4228172917890.3113.021.8023.4423.4413.9227.38153.1615642554390.2814.992.5331.0337.9218.3536.12第C軸梁柱節(jié)點彎矩（風荷載）：層號Vi(kN)Di∑DDi/∑DVim(kN)y(m)Mc上

(kN.m)Mc下

(kN.m)Mb左

(kN.m)Mb右

(kN.m)510.7828172917890.313.311.626.555.364.342.21422.0028172917890.316.751.8012.1512.1511.615.90332.3128172917890.319.921.8017.8617.8619.9010.11242.4228172917890.3113.021.8023.4423.4427.3813.92153.1615642554390.2814.992.5331.0337.9236.1218.35第D軸梁柱節(jié)點彎矩（風荷載）：層號Vi(kN)Di∑DDi/∑DVim(kN)y(m)Mc上

(kN.m)Mc下

(kN.m)Mb總

(kN.m)510.7817723917890.192.081.374.642.854.64422.0017723917890.194.251.558.726.5811.57332.3117723917890.196.241.7311.6810.7818.26242.4217723917890.198.191.8014.7414.7425.52153.1612078554390.2211.592.5323.9929.3238.73風荷載作用下彎矩圖以頂層邊跨為例，對水平荷載下梁端剪力進行求解：V風荷載作用下剪力圖對于柱軸力，由于水平作用下一榀框架梁上只存在剪力，無柱集中荷載，且不需考慮柱自重，故主要將對應的剪力逐層疊加即可。風荷載作用下軸力圖地震作用內力計算地震作用為水平方向作用，采用D值法進行計算，計算方式同風荷載，彎矩計算結果如下：第A軸地震作用內力計算表層號Vi(kN)Di∑DDi/∑DVi(kN)y(m)Mc上

(kN.m)Mc下

(kN.m)Mb總

(kN.m)5866.07177237343110.0217.320.3838.6623.6938.6641586.42177237343110.0231.730.4365.1149.1288.8032139.06177237343110.0242.780.4880.0873.92129.2022523.98177237343110.0250.480.5090.8690.86164.7812752.18120784435150.0382.570.55170.92208.90261.78第B軸地震作用內力計算表層號Vi(kN)Di∑DDi/∑DVi(kN)y(m)Mc上

(kN.m)Mc下

(kN.m)Mb左

(kN.m)Mb右

(kN.m)5866.07281727343110.0434.640.4568.5956.1223.1145.4841586.42281727343110.0463.460.50114.23114.2357.40112.9532139.06281727343110.0485.560.50154.01154.0190.38177.8622523.98281727343110.04100.960.50181.73181.73113.12222.6212752.18156424435150.04110.090.55227.89278.53138.02271.60第C軸地震作用內力計算表層號Vi(kN)Di∑DDi/∑DVi(kN)y(m)Mc上

(kN.m)Mc下

(kN.m)Mb左

(kN.m)Mb右

(kN.m)5866.07281727343110.0434.640.4568.5956.1245.4823.1141586.42281727343110.0463.460.50114.23114.23112.9557.4032139.06281727343110.0485.560.50154.01154.01177.8690.3822523.98281727343110.04100.960.50181.73181.73222.62113.1212752.18156424435150.04110.090.55227.89278.53271.60138.02第D軸地震作用內力計算表層號Vi(kN)Di∑DDi/∑DVi(kN)y(m)Mc上

(kN.m)Mc下

(kN.m)Mb總

(kN.m)5866.07177237343110.0217.320.3838.6623.6938.6641586.421