【《某大学4层活动中心楼建筑结构的内力计算案例》4700字】

某大学4层活动中心楼建筑结构的内力计算案例目录TOC\o"1-3"\h\u320某大学4层活动中心楼建筑结构的内力计算案例 1326471.1构件自重统计 1205421、板：25mm水泥砂浆和30mm大理石砖面1.3KN/㎡ 1325452、横向框架梁及横向次梁： 1174883、纵向框架梁： 283044、柱： 2259795、墙 3135111.2竖向荷载作用下内力分析 4111431、恒载内力 465432、活载计算： 1561561.3水平荷载作用下内力分析 22175431、水平地震作用内力 221.1构件自重统计1、板：25mm水泥砂浆和30mm大理石砖面1.3KN/㎡100mm厚混凝土板0.1×25=2.5KN/㎡石灰砂浆顶棚0.6KN/㎡小计4.4KN/㎡2、横向框架梁及横向次梁：（1）边跨（6000mm，700）:钢筋混凝土梁0.7−0.12石灰砂浆顶棚0.7−0.12小计4.63KN/m（2）中跨（3300mm）及横向次梁：钢筋混凝土梁0.5−0.12石灰砂浆顶棚0.5−0.12小计3.03KN/m3、纵向框架梁：（1）边梁：钢筋混凝土梁0.5−0.12外墙面砖0.5×0.62=0.31KN/m内墙涂料0.5−0.12小计3.27KN/m（2）中梁：钢筋混凝土梁0.5−0.12内墙涂料0.5−0.12小计3.06KN/m4、柱：（1）边柱：钢筋混凝土梁0.85×0.85×4.5×25=47.53KN/m外墙面砖、涂料（平均取比重）0.65×4.5×0.45=1.32KN/m内墙涂料0.85+小计50.75KN（2）中柱：钢筋混凝土0.85×0.85×4.5×25=47.53KN/m内墙涂料0.85×2+小计50.27KN5、墙（1）浆砌焦渣砖内墙（240mm）砌体4.5−0.7内墙涂料4.5−0.7小计14.90KN/m（2）浆砌焦渣砖外墙（240mm）砌体4.5−0.7内墙涂料4.5−0.7外墙面砖、涂料（平均取比重）4.5−0.7小计15.54KN/m（3）框架顶层自重计算：①板：防水屋面3.61KN/㎡120厚钢筋混凝土楼板0.12×25=3.0KN/㎡石灰砂浆顶棚0.24KN/㎡小计6.85KN/㎡②女儿墙：砌体1.0×0.24×14=3.36KN/m外墙面砖1.0×0.62=0.26KN/m内墙面20厚水泥粉刷1.0×0.02×20=0.4KN/m小计4.02KN/m③门窗1）木门0.2KN/㎡2）铝合金窗0.4KN/㎡3）玻璃门0.4KN/㎡1.2竖向荷载作用下内力分析1、恒载内力（1）梁、柱参数汇总表5-1第⑩轴框架梁几何参数断面b跨度l截面惯性矩I第⑩轴框架梁I=2i=0.30×0.706.008.58×17.16×9.30×0.30×0.503.303.13×6.26×6.17×表5-2第⑩轴框架柱几何参数柱类别楼层断面b(m)×ℎ(m)iℎKαD边柱40.85×0.8531.42×4.50.2960.1292401930.85×0.8531.42×4.50.2960.1292401920.85×0.8531.42×4.50.2960.1292401910.85×0.8531.42×4.50.2960.34764609中柱40.85×0.8531.42×4.50.4920.1973668030.85×0.8531.42×4.50.4920.1973668020.85×0.8531.42×4.50.4920.1973668010.85×0.8531.42×4.50.4920.39874105（2）弯矩计算利用二次弯矩分配法。计算固定端弯矩：梯形荷载折算公式：qeα1=l01顶层边跨等效均布荷载：αq中间层边跨等效均布荷载：αq则顶层固端弯矩：M中间层固定端弯矩：M图5-1恒载弯矩图由以上所求均布荷载，各杆固定端弯矩计算如图所示：图5-1恒载弯矩图图5-1恒载作用下弯矩二次分配简图图5-1恒载作用下弯矩二次分配简图图5-2恒载作用下弯矩图图5-2恒载作用下弯矩图（3）剪力计算为了方便计算，将梁上的均布荷载换算成集中荷载。顶层边跨：F顶层中跨：F中间层边跨：F中间层中跨：F图5-2恒载作用下弯矩图图5-2恒载作用下弯矩图图图SEQ图\*ARABIC1图5-3图5-3顶层：边跨:取A端矩为零MA70.78=120.27×3+77.81+解得：V则：VB=61.31KN（↑）；同时，可将梁的跨中弯矩一并计算：对跨中截面取矩：MM中跨：按折算后的均布荷载计算:M三层：边跨:取A端矩为零M98.06=127.08×3+100.31+V解得：V则：VB=63.92KN（↑）；同时，可将梁的跨中弯矩一并计算：对跨中截面取矩：MM中跨：按折算后的均布荷载计算:M二层：边跨:取A端矩为零M96.57=127.08×3+99.46+V解得：V则：VB=64.02KN（↑）；同时，可将梁的跨中弯矩一并计算：对跨中截面取矩：MM中跨：按折算后的均布荷载计算:M一层：边跨:取A端矩为零MA94.17=127.08×3+98.39+解得：V则：VB=64.24KN（↑）；同时，可将梁的跨中弯矩一并计算：对跨中截面取矩：MM中跨：按折算后的均布荷载计算:M以上，此框架的剪力和弯矩计算如下：表5-3恒载作用下轴线处梁端剪力与跨中弯矩梁类型层数梁长m外荷载KN固端弯矩KN·m杆端剪力KN跨中弯矩左右左右A~B轴边跨46120.27-70.7877.8158.96-61.31-53.9636127.08-98.06100.3163.16-63.92-57.4726127.08-96.5799.4663.06-64.02-58.6416127.08-94.1798.3962.84-64.24-60.39D~C轴边跨46120.27-77.8170.7861.31-58.96-53.9636127.08-100.3198.0663.92-63.16-57.4726127.08-99.4696.5764.02-63.06-58.6416127.08-98.3994.1764.24-62.84-60.39中跨43.310-11.3611.365-57.2433.310-6.626.625-52.5023.310-7.567.565-53.4413.310-8.678.675-54.55由Vu表5-4恒荷载作用下轴线处柱端剪力柱类型层数柱高m固端弯矩KN·m杆端剪力KN上下上下A轴柱44.541.1631.70-16.19-16.1934.521.6126.65-11.61-11.6124.528.3431.06-13.20-13.2014.521.6410.83-7.22-7.22D轴柱44.5-41.16-31.7016.1916.1934.5-21.61-26.6511.6111.6124.5-28.34-31.0613.2013.2014.5-21.64-10.837.227.22B轴柱44.5-31.75-21.9412.8212.8234.5-21.51-22.279.739.7324.5-24.45-26.1711.2511.2514.5-18.36-9.196.126.12C轴柱44.531.7521.94-12.82-12.8234.521.5122.27-9.73-9.7324.524.4526.17-11.25-11.2514.518.369.19-6.12-6.12通过以上计算，绘出恒载作用下的剪力图：图5-3恒载作用下剪力图图5-3恒载作用下剪力图（4）轴力计算：以四层B柱为例，计算如下：根据恒载图可知，柱顶集中力F集根据恒载计算，可得柱两端的剪力分别为：Vl=61.31KN↓则，柱中轴力N表5-5恒载作用下柱中轴力柱类型楼层柱顶集中力KN邻梁剪力KN柱中轴力KN左梁右梁A轴柱4204.100.0058.96263.063276.300.0063.16602.522276.300.0063.06941.881276.300.0062.841281.02D轴柱4204.1058.960.00263.063276.3063.160.00602.522276.3063.060.00941.881276.3062.840.001281.02B轴柱4231.9261.315298.233301.4063.925668.552301.4064.0251038.971301.4064.2451409.61C轴柱4231.92561.31298.233301.40563.92668.552301.40564.021038.971301.40564.241409.61通过以上计算，绘出恒载作用下的轴力图：图5-4图5-4恒载作用下轴力图（单位：KN）图5-4恒载作用下轴力图图5-4恒载作用下轴力图2、活载计算：活载计算同恒载作用下的计算相同。（1）弯矩计算采用力矩二次分配法计算。计算固定端弯矩：梯形荷载折算公式：qeα1=l01顶层边跨等效均布荷载：αq中间层边跨等效均布荷载：αq则顶层、中间层固端弯矩：M图5-5活载弯矩二次分配简图由以上所求均布荷载，各杆固定端弯矩计算如图所示：图5-5活载弯矩二次分配简图图5-6活载作用下弯矩图图5-6活载作用下弯矩图（2）剪力计算将梁上的均布荷载换算成集中荷载。顶层边跨：F顶层中跨：F中间层边跨：F中间层中跨：F取不同梁、柱为单元，分别对两边取矩，写出平衡方程，便可计算出该梁端、柱端剪力值。计算简图如下：（计算同恒载一样）图5-7图5-7顶层：边跨:取A端矩为零M15.96=27×3+19.38+解得：V则：VB=14.07KN（↑）；同时，可将梁的跨中弯矩一并计算：对跨中截面取矩：MM中跨：按折算后的均布荷载计算:M表5-6活载作用下轴线处梁端剪力与跨中弯矩梁类型层数梁长m固端弯矩KN·m杆端剪力KN跨中弯矩左右左右A~B轴边跨46-11.9619.3814.07-12.93-13.6136-19.7119.9713.50-13.50-11.4426-18.2520.3313.85-13.15-11.9916-17.7920.1313.89-13.11-12.32D~C轴边跨46-19.3811.9612.93-14.07-13.6136-19.9719.7113.50-13.50-11.4426-20.3318.2513.15-13.85-11.9916-20.1317.7913.11-13.89-12.32中跨43.3-2.72.70.000.002.733.3-1.031.030.000.001.0323.3-1.281.280.000.001.2813.3-1.501.500.000.001.50表5-7活荷载作用下轴线处柱端剪力柱类型层数柱高m固端弯矩KN·m杆端剪力KN上下上下A轴柱44.511.917.75-4.37-4.3734.512.606.55-4.26-4.2624.57.658.15-3.51-3.5114.51.602.81-1.87-1.87D轴柱44.5-11.91-7.754.374.3734.5-12.60-6.554.264.2624.5-7.65-2.813.513.5114.5-1.60-10.831.871.87B轴柱44.5-8.17-4.922.912.9134.5-4.40-4.471.971.9724.5-4.97-1.302.282.2814.5-3.71-1.861.241.24C轴柱44.58.174.92-2.91-2.9134.54.404.47-1.97-1.9724.54.971.30-2.28-2.2814.53.711.86-1.241.24图5-8活载作用下剪力图图5-8活载作用下剪力图（3）轴力计算表5-8恒载作用下柱中轴力柱类型楼层柱顶集中力KN邻梁剪力KN柱中轴力KN左梁右梁A轴柱4270.0014.0741.073270.0013.5081.572270.0013.85122.421270.0013.89163.31D轴柱42714.070.0041.0732713.500.0081.5722713.850.00122.4212713.890.00163.31B轴柱456.7012.930.0069.63364.1313.500.00147.26264.1313.150.00224.54164.1313.110.00301.78C轴柱456.700.0012.9369.63364.130.0013.50147.26264.130.0013.15224.54164.130.0013.11301.78图5-9活载作用下轴力图（单位：KN）图5-9活载作用下轴力图（单位：KN）1.3水平荷载作用下内力分析1、水平地震作用内力（1）一层的梁柱1）计算各个柱分配剪力底层四柱D值分别为：底层边柱（A、D柱）：D=64609底层中柱（B、C柱）：D=74105底层层间剪力：V=按照D值法将层间剪力分配给各柱：底层边柱：V底层中柱：V2）反弯点高度yh=根据此框架情况，y1=0；y3=0。由前面计算可知，A、D轴柱：K=0.296，α=0.347，查表得y0=0.85，y2=−0.10D轴柱：yh=C轴柱：yh=柱端弯矩计算边柱：MA上M中柱：MM表5-9左地震作用下柱端弯矩计算层数层高m层间剪力KN单层刚度A、D轴柱D值剪力值KN反弯点高度mMM44.5776.5312139824019153.641.13-517.77-173.6134.51351.4312139824019267.381.80-721.93-481.2824.51739.712139824019344.212.70-619.58-929.3714.51958.7827742864609456.173.38-510.91-1541.85层数层高m层间剪力KN单层刚度B、C轴柱D值剪力值KN反弯点高度mMM44.5776.5312139836680232.960.9-838.66-209.6634.51351.4312139836680401.431.35-1277.1-547.3324.51739.712139836680521.911.8-1409.16-939.4414.51958.7827742874105587.632.93-922.58-1721.76注：所求弯矩以使柱顺时针转动为正。梁端弯矩计算以底层边跨梁为例，进行隔离体计算：（b）（b）左端弯矩列平衡方程：M可解得：M右端弯矩列平衡方程：M可解得：M左右梁按照线刚度分配：MM根据以上方法，可将各个梁的梁端弯矩求出，见下表：表5-10左地震作用下梁端弯矩计算节点号上柱弯矩KN·m下柱弯矩KN·m左梁线刚度KN·m右梁线刚度KN·m左梁弯矩KN·m右梁弯矩KN·mA-40517.7709.3×0517.77A-3173.61721.9309.3×0891.54A-2481.28619.5809.3×01100.86A-1929.37510.9109.3×01440.28B-40838.669.3×6.17×503.20331.46B-3209.661277.19.3×6.17×892.60594.70B-2547.331409.169.3×6.17×1173.89782.60B-1939.44922.589.3×6.17×1119.38742.64C-40838.666.17×9.3×331.46503.20C-3209.661277.16.17×9.3×594.70892.60C-2547.331409.166.17×9.3×782.601173.89C-1939.44922.586.17×9.3×742.641119.38D-40517.779.3×0517.770D-3173.61721.939.3×0891.540D-2481.28619.589.3×01100.860D-1929.37510.919.3×01440.280注：1、所求弯矩以使梁顺时针转动为正。2、节点号如“A-3”表示：A号轴线第三层节点，其他类似。图5-10左震作用下弯矩图（KN·m）图5-10左震作用下弯矩图（KN·m）5）剪力计算利用杆件平衡求解杆端剪力。计算简图如下：图5-10图5-10列力矩平衡方程：MA=0VV因此，计算结果如下表所示：表5-11左地震作用下梁端剪力梁类型层数梁长m梁固端弯矩KN·m梁端剪力KN左右左右A~B轴边跨46517.77503.2-170.16-170.1636891.54892.6-298.02-298.02261100.861173.89-379.13-379.13161440.281119.38-426.61-426.61D~C轴边跨46503.2517.77-170.16-170.1636892.6891.54-298.02-298.02261173.891100.86-379.125-379.125161119.381440.28-426.61-426.61中跨43.3331.46503.2-254.14-254.1433.3594.7892.6-450.70-450.7023.3782.61173.89-592.88-592.8813.3742.641119.38-564.25-564.25则柱端剪力见下表：表5-12左地震作用下轴线处柱端剪力柱类型层数柱高m柱固端弯矩KN·m柱端剪力KN上下上下A轴柱44.5-517.77-173.61153.64153.6434.5-721.93-481.28267.38267.3824.5-619.58-929.37344.21344.2114.5-510.91-1541.85456.17456.17D轴柱44.5-517.77-173.61153.64153.6434.5-721.93-481.28267.38267.3824.5-619.58-929.37344.21344.2114.5-510.91-1541.85456.17456.17B轴柱44.5-838.66-209.66232.96232.9634.5-1277.1-547.33401.43401.4324.5-1409.16-939.44521.91521.9114.5-922.58-1721.76587.63587.63C轴柱44.5-838.66-209.66232.96232.9634.5-1277.1-547.33401.43401.4324.5-1409.16-547.33521.91521.9114.5-922.58-1721.76587.63587.63图5-11左震作用下剪力图（KN）图5-11左震作用下剪力图（KN）轴力计算柱轴力计算如下：表5-13左震作用下柱中轴力柱类型层数邻梁剪力（KN）柱中轴力（KN）左右A轴柱40−170.16−170.1630−298.02−468.1820−379.13−847.3110−426.61−1273.92D轴柱4−170.160170.163−298.020468.182−379.130847.311−426.6101273.92B轴柱4−170.16−254.14−83.983−298.02−450.70−236.662−379.13−592.88−450.411−426.61−564.25−588.05C轴柱4−254.14−170.1683.983−450.70−298.02236.662−592.88−379.13450.411−564.25−426.61588.05图5-12左震作用下轴力图（KN）图5-12左震作用下轴力图（KN）2、风荷载作用内力风荷载内力计算同水平地震