《教学楼结构设计中的内力计算案例》3400字

II教学楼结构设计中的内力计算案例综述恒荷载内力计算弯矩分配系数由于所取一榀框架为对称结构，简化半结构进行计算。由于在荷载传递过程中，由板传递过来的荷载存在不均匀荷载如：梯形线荷载、三角形线荷载等，在计算过程中需要先将其转化为均匀荷载在进行内力计算。计算过程如下：梯形：三角形：图4-1荷载等效变换图恒载的计算，需采用弯矩二次分配法，要首先计算各节点之间的弯矩分配系数，详细节点编号如下：图4-2节点编号图以1号节点作为例子，计算过程如下：。其他节点求解过程如下：2节点：。4节点：5节点：13节点：14节点：结构固端弯矩梁的固端弯矩：恒载内力计算采用弯矩二次分配法，首先计算竖向荷载作用下的梁各个杆端的固端弯矩，再根据前面计算的节点弯矩分配系数对弯矩进行组合分配计算。两边固端下梁支座及跨中计算弯矩公式为：··································（4.1）按上述公式，以第五层作为例子，计算梁固端弯矩；，剩下层梁固端弯矩计算过程如下：，纵梁引起的柱端附加弯矩：内力计算弯矩二次分配借助于Excel表格进行计算，具体计算过程如下：表4-1恒载弯矩分配表上柱下柱右梁左梁上柱下柱右梁左梁0.4460.5540.4810.3870.132偏心弯矩偏心弯矩8.46-60.3660.36-7.56-6.03-3.0223.1528.7514.38-14.71-29.41-23.66-8.078.076.568.154.07-1.96-1.580.5429.71-38.1747.44-25.24-13.565.050.3080.3080.3840.3470.2790.2790.095偏心弯矩偏心弯矩9.70-65.1365.13-9.13-8.20-4.1017.0717.0721.2910.64-10.14-20.28-16.31-16.31-5.555.553.123.123.891.95-0.68-0.54-0.54-0.1820.2020.20-50.0956.76-16.85-16.85-13.941.450.3080.3080.3840.3470.2790.2790.095偏心弯矩偏心弯矩9.70-65.1365.13-9.13-8.20-4.1017.0717.0721.2910.64-10.14-20.28-16.31-16.31-5.555.553.123.123.891.95-0.68-0.54-0.54-0.1820.2020.20-50.0956.76-16.85-16.85-13.941.450.3080.3080.3840.3470.2790.2790.095偏心弯矩偏心弯矩9.70-65.1365.13-9.13-8.20-4.1017.0717.0721.2910.64-10.14-20.28-16.31-16.31-5.555.553.123.123.891.95-0.68-0.54-0.54-0.1820.2020.20-50.0956.76-16.85-16.85-13.941.450.3400.2360.4240.380.3050.2110.104偏心弯矩偏心弯矩9.70-65.1365.13-9.13-8.20-4.1018.8513.0823.5011.75-11.31-22.63-18.16-12.57-6.196.193.852.674.502.40-0.91-0.73-0.51-0.2522.6915.75-48.1455.74-18.89-13.07-14.642.09图4-3恒载弯矩图恒载作用下梁端剪力，在弯矩图中可知，其计算剪力分为两部分，一部分看做均布荷载在简支梁作用下产生的剪力值，另一部分看做两端梁弯矩下的固定剪力值；但是对于柱来说，杆件上没有垂直均布荷载作用，故仅考虑柱上下端弯矩下产生的固定弯矩值，故梁、柱相关剪力计算公式分别如下：···································（4.2）按上述公式，计算梁和柱的剪力，结果见下图：图4-4恒载剪力图轴力由两部分组成，一部分是由柱端集中荷载作用下产生的轴力，另一部分根据节点力平衡将柱节点旁的梁端剪力作为柱的轴力，公式如下：················································（4.3）上式中，V为柱节点两侧的梁端剪力差，P为上部结构传递下来的集中力，对于柱自身，需要考虑恒载作用下的自重，计算结果见下图。图4-5恒载轴力图活荷载作用下的内力计算本次设计近似采用对称结构对称荷载的形式进行简化计算。由于楼面活荷载<3.5kN/m2，故按活荷载满布的情况计算。杆件固端弯矩第五层横梁：标准层横梁：纵梁引起的柱端附加弯矩：顶层外纵梁M1=GA×l偏心距=14.4×0.125=1.8kN·m顶层中纵梁楼层外纵梁顶层中纵梁由于在荷载传递过程中，由板传递过来的荷载存在不均匀荷载如：梯形线荷载、三角形线荷载等，在计算过程中需要先将其转化为均匀荷载在进行内力计算。内力计算弯矩二次分配借助于Excel表格进行计算，具体计算过程如下：表4-2活载弯矩分配表上柱下柱右梁左梁上柱下柱右梁左梁0.4460.5540.4810.3870.132偏心弯矩偏心弯矩1.80-21.4221.42-3.20-2.05-1.038.7510.875.43-5.20-10.39-8.36-2.852.852.322.881.44-0.69-0.560.5411.07-12.8717.21-8.92-4.361.820.3080.3080.3840.3470.2790.2790.095偏心弯矩偏心弯矩1.80-21.4221.42-3.55-2.56-1.286.046.047.533.77-3.31-6.62-5.32-5.32-1.811.811.021.021.270.64-0.22-0.18-0.18-0.067.067.06-15.9218.98-5.50-5.50-4.430.530.3080.3080.3840.3470.2790.2790.095偏心弯矩偏心弯矩1.80-21.4221.42-3.55-2.56-1.286.046.047.533.77-3.31-6.62-5.32-5.32-1.811.811.021.021.270.64-0.22-0.18-0.18-0.067.067.06-15.9218.98-5.50-5.50-4.430.530.3080.3080.3840.3470.2790.2790.095偏心弯矩偏心弯矩1.80-21.4221.42-3.55-2.56-1.286.046.047.533.77-3.31-6.62-5.32-5.32-1.811.811.021.021.270.64-0.22-0.18-0.18-0.067.067.06-15.9218.98-5.50-5.50-4.430.530.3400.2360.4240.380.3050.2110.104偏心弯矩偏心弯矩1.80-21.4221.42-3.55-2.56-1.286.674.638.324.16-3.70-7.40-5.94-4.11-2.022.021.260.871.570.78-0.30-0.24-0.17-0.087.935.50-15.2318.67-6.18-4.27-4.670.74图4-6活载弯矩图活载作用下梁端剪力，在弯矩图中可知，其计算剪力分为两部分，一部分看做均布荷载在简支梁作用下产生的剪力值，另一部分看做两端梁弯矩下的固定剪力值；但是对于柱来说，杆件上没有垂直均布荷载作用，故仅考虑柱上下端弯矩下产生的固定弯矩值，故梁、柱相关剪力计算公式分别如下：····································（4.4）计算结果见下图所示：图4-7活载剪力图轴力由两部分组成，一部分是由柱端集中荷载作用下产生的轴力，另一部分根据节点力平衡将柱节点旁的梁端剪力作为柱的轴力，公式如下：Nc计算结果见下图：图4-8活载轴力图风荷载作用下的位移、内力计算风荷载作用下的位移计算表4-3一榀框架侧向刚度表Dj第A轴第Ｂ轴第Ｃ轴第Ｄ轴∑Dj1层8015854785478015331242层15270196901969015270699203层15270196901969015270699204层15270196901969015270699205层1527019690196901527069920表4-4风荷载作用下位移表楼层Wk.(kN)Vj(kN)∑D(kN/m)△uj(m)△uj/h58.998.99699200.000130.00004410.1519.14699200.000270.0000839.2628.40699200.000410.0001128.9937.39699200.000540.0001619.5546.94331240.001420.00028

由规范可知，楼层层间最大位移与层高之比的限值为1/550=0.00182，本框架层间最大位移与层高之比=0.00027<0.00182,故满足。风荷载作用下的内力计算柱沿侧向刚度分配的计算方式如下：············································（4.6）根据已知的柱的抗侧刚度，对反弯点进行查表计算，查均布水平力反弯点表的标准高度比，并按修正系数，对柱反弯点进行计算：表4-5A、D边柱反弯点位置表h(m)Ky0y1y2y3yyh(m)5-4321--表4-6B、C中柱反弯点位置表h(m)Ky0y1y2y3yyh(m)5-4321--EQ对梁、柱弯矩进行计算，计算过程见下表··················································（4.7）中柱：··············································（4.8）边柱：···················································（4.9）表4-7A、D轴梁柱节点弯矩：层号Vi(kN)∑DDiDi/∑DVi(kN)yh(m)Mc上

(kN.m)Mc下

(kN.m)Mb总

(kN.m)58.9969920152700.221.981.264.632.494.63419.1469920152700.224.211.449.096.0611.58328.4069920152700.226.251.6212.3810.1318.44237.3969920152700.228.231.8014.8114.5124.94146.943312480150.2411.272.8226.8231.7841.63表4-8B、C轴梁柱节点弯矩：层号Vi(kN)∑DDiDi/∑DVi(kN)yh(m)Mc上

(kN.m)Mc下

(kN.m)Mb左

(kN.m)Mb右

(kN.m)58.9969920196900.282.521.515.533.543.571.96419.1469920196900.285.361.6210.818.499.275.08328.4069920196900.287.951.8014.6014.0214.918.17237.3969920196900.2810.471.8018.8518.8521.2311.64146.943312485470.2612.212.5028.5734.9230.6316.79（B、C轴梁柱节点弯矩Mb左、Mb右相反，这里以B轴为参考）详细内力图如下所示：图4-9风荷载作用下弯矩图由于风荷载作用下，梁不承受均布荷载作用，故梁端剪力可直接由梁两端弯矩进行组合求解，公式如下：Vb图4-10风荷载作用下剪力图图4-11风荷载作用下轴力图

地震作用下的内力计算同样与求解风荷载方法相似，故对反弯点进行求解，查倒三角水平力反弯点表的标准高度比。表4-9A、D边柱反弯点位置表h(m)Ky0y1y2y3yyh(m)--0.00-表4-10B、C中柱反弯点位置表h(m)Ky0y1y2y3yyh(m)--0.00-EQ对梁、柱弯矩进行计算，计算过程见下表···················································（4.11）中柱：··············································（4.12）边柱：·····················································（4.13）

表4-11第A、D轴地震作用内力计算表Vi(kN)∑DDiDi/∑DVi(kN)y(m)Mc上

(kN.m)Mc下

(kN.m)Mb总

(kN.m)5247.76678308152700.025.580.3712.657.4320.084513.70678308152700.0211