【《某5层宿舍楼建筑结构的荷载计算和内力计算案例》4800字】

某5层宿舍楼建筑结构的荷载计算和内力计算案例目录TOC\o"1-3"\h\u2971某5层宿舍楼建筑结构的荷载计算和内力计算案例 111106第1章荷载计算 1212081.1恒荷载计算： 1286811.2活荷载计算 597051.3风荷载计算 617249第2章内力计算 8141812.1风荷载作用下内力计算 864042.2恒荷载作用下的内力计算 1546922.3活荷载作用下的内力计算 25第1章荷载计算1.1恒荷载计算：（1）梁：自重+粉刷=1\*GB3①A~D轴纵向框架梁：自重：0.3×0.2×25=1.50kN/m粉刷：2×(0.3-0.12)×0.02×17=0.12kN/m1.62kN/m=2\*GB3②1~8轴AB段及CD段横向框架梁：自重：0.55×0.2×25=2.75kN/m粉刷：2×(0.55-0.12)×0.02×17=0.29kN/m3.04kN/m=3\*GB3③1~8轴BC段横向框架梁：自重：0.2×0.4×25=2.00kN/m粉刷：2×(0.4-0.12)×0.02×17=0.19kN/m2.19kN/m（2）柱：自重+粉刷自重：0.4×0.4×25=4kN/m粉刷：(0.4-0.12)×2×17×0.02=0.19kN/m4.19kN/m（3）墙体：自重+粉刷自重：0.25×7=1.75kN/m2粉刷：17×0.02=0.34kN/m22.09kN/m2（4）门、窗：=1\*GB3①铁门：0.45kN/m20.45kN/m2=2\*GB3②塑钢窗：0.1kN/m20.1kN/m2（5）屋面框架梁线荷载标准值顶层梁线荷载作用简图（图4-1）=1\*GB3①屋面恒载标准值计算：由3.1（2）楼面、屋面做法一览表中的用料做法所列楼面、屋面的做法一览表名称用料做法厚度（mm）使用部位防滑地砖楼面8~10后防滑地砖，干水泥擦缝10楼面20厚1:3水泥砂浆结合层，表面撒水泥粉2060厚LC7.5轻骨料混凝土60名称用料做法厚度（mm）使用部位防水屋面高聚物改性沥青防水卷材3屋面聚苯保温板1001:8水泥膨胀珍珠岩2%找坡，最薄处不小于201001:3水泥砂浆找平层20屋面恒荷载标准值的计算为：0.2×0.1+0.1×7+0.1×25+0.02×20+0.0021=3.63kN/m2屋面恒荷：3.63kN/m2=2\*GB3②因此，作用在顶层框架梁上的线荷载为：g1WAB=g1WCD=3.04kN/mg1WBC=2.19kN/mg2WAB=g2WCD=1/2×3.63×1/2×3.6×[1-2×(1.8/7.6)²+(1.8/7.6)³]×2=5.89kN/mg2WBC=3.63×1.5×5/8×2=6.81kN/m（6）楼面框架梁线荷载标准值中间层梁线荷载作用简图（图4-2）=1\*GB3①楼面恒载标准值计算：由3.1（2）楼面、屋面做法一览表与《楼地面建筑构造-12J304》中的用料做法所列，防滑地砖面层重量为1.20kN/m2楼面、屋面的做法一览表（表3-1）名称用料做法厚度（mm）使用部位防滑地砖楼面8~10后防滑地砖，干水泥擦缝10楼面20厚1:3水泥砂浆结合层，表面撒水泥粉2060厚LC7.5轻骨料混凝土60名称用料做法厚度（mm）使用部位防水屋面高聚物改性沥青防水卷材3屋面聚苯保温板1001:8水泥膨胀珍珠岩2%找坡，最薄处不小于201001:3水泥砂浆找平层20120mm厚混凝土楼板：0.12×25＝3kN/m2楼面恒荷：4.20kN/m2=2\*GB3②因此，作用在中间层框架梁上的线荷载为：g1AB=g1CD=3.04+2.09×(3.3-0.55)=8.79kN/mg1BC=2.19kN/mg2AB=g2CD=0.5×4.2×1/2×3.6×[1-2×(1.8/7.6)²+(1.8/7.6)³]×2=6.81kN/mg2BC=4.2×1/2×5/8×2=7.88kN/m（7）屋面框架节点集中荷载标准值顶层节点集中荷载作用简图（图4-3）=1\*GB3①边柱:纵向梁自重：1.62×3.6＝5.83kN女儿墙自重：1.2×2.09×3.6=9.03kN板自重荷载：3.63×1/2×3.6×5/8×2=8.17kN顶层边节点集中荷载：gWA=gWD=23.02kN=2\*GB3②中柱:纵向梁自重：1.62×3.6＝5.83kN板自重传荷载:8.17+0.5×3.63×1.8×[1-2×(1.8/7.6)²+(1.8/7.6)³]×2×3.6=29.37kN顶层中节点集中荷载：gWC=gWB=35.2kN（8）楼面框架节点集中荷载标准值中间层节点集中荷载作用简图（图4-4）=1\*GB3①边柱:纵向梁自重：1.62×3.6＝5.83kN墙自重：2.09×[(3.3-0.3)×3.6-1.8×1.5]=16.929kN窗自重：0.1×1.8×1.5=0.27kN框架柱自重：4.19×3.3＝13.83kN板自重传荷载：0.5×3.6×4.2×1.8×[1-2×(1.8/3.6)²+(1.8/3.6)³]×2=17.01kN中间层边节点集中荷载：gA=gD=53.87kN=2\*GB3②中柱:纵向梁自重：1.62×3.6＝5.83kN墙自重：2.09×[(3.3-0.3)×3.6-1×2.6]=17.14kN门自重：0.45×2.6×1=1.17kN框架柱自重：4.19×3.3＝13.83kN板自重传荷载：17.01+0.5×3/2×4.2×[1-2×(1/2×3/3.6)²+(1/2×3/3.6)³]×2×3.6=33.46kN中间层中节点集中荷载：gB=gC=71.43kN1.2活荷载计算根据《建筑结构荷载规范》GB50009-2012。屋面活荷载标准值2.0，室内取2.5，走廊取3.5。所以活荷载计算值如下：PWAB=PWCD=0.5×2×1/2×3.6×[1-2×(1.8/7.6)²+(1.8/7.6)³]×2=3.24kN/mPWBC=2×1.5×5/8×2=3.75kN/mPAB=PCD=0.5×2.5×1/2×3.6×[1-2×(1.8/7.6)²+(1.8/7.6)³]×2=4.05kN/mPBC=3.5×1.5×5/8×2=6.56kN/mPWA=PWD=0.5×1.8×5/8×2=1.13kNPWB=PWC=1.13+0.5×2×1.8×[1-2×(1.8/3.6)²+(1.8/3.6)³]×2×3.6=9.23kNPA=PD=0.5×3.6×2.5×1.8×5/8×2=10.125kNPB=PC=10.125+0.5×3.5×1.8×[1-2×(1.8/3.6)²+(1.8/3.6)³]×2×3.6=24.3kN1.3风荷载计算根据建筑结构荷载规范，风荷载由下式计算：（公式4-1）。XX市根据50年最大风速查得基本风压为0.55kN/m²；因结构层高小于30m且高宽比小于1.5，故风振系数取1；地面粗糙度类别为B类，根据插值法可得风压高度变化系数如下；根据建筑结构荷载规范风荷载第34条，体形系数取1.3。A为各层节点受风面积；Pw为各层节点受风载作用形成的集中荷载值。风荷载计算表（表4-1）层次Z(m)()A()P()51.01.316.951.170.557.926.6241.01.313.651.090.5511.889.2531.01.310.351.010.5511.888.5721.01.37.051.000.5511.888.5711.01.33.751.000.5511.888.57风荷载作用简图（图4-5）第2章内力计算2.1风荷载作用下内力计算（1）框架刚度计算：计算风荷载作用的影响时，考虑到现浇楼板产生的作用，计算框架梁惯性矩的时候，取边跨框架梁惯性矩，中跨框架梁惯性矩。框架梁、柱的线刚度如表5-1、5-2所示。i=EI/L，C30混凝土E=30kN/mm²。梁的线刚度计算（表5-1）截面跨度L(mm)I0×1010(mm4)边框架中框架b×h(mm)I×1010(mm4)i×107(kN×mm)相对线刚度I×1010(mm4)i×107(kN×mm)相对线刚度20036000.450.685.671.890.907.502.5030020076000.280.421.660.550.562.210.7455020030000.110.171.700.570.222.200.73400柱的线刚度计算（表5-2）柱号截面b×h(mm)柱高(mm)I0×1010(mm4)ic×107(kN×mm)相对线刚度Z140033000.211.910.64400横向框架柱侧向刚度D值计算表（表5-3）层次柱类型KαcD=(αc×ic×12)/h2(kN/mm)根数底层边框边柱0.870.306.314边框中柱1.750.479.894中框边柱1.530.439.0526中框中柱2.680.5711.9926∑D611.84二至五层边框边柱0.440.183.794边框中柱0.880.306.304中框边柱0.900.316.5026中框中柱1.580.449.326∑D451.16（2）风荷载作用下的位移验算风荷载作用下框架剪力以及侧移计算表（表5-10）层号h(m)Vi(KN)53.306.62451.160.015643.3015.87451.160.035633.3024.44451.160.054623.3033.01451.160.073613.7541.58611.840.0686.82均符合的要求。（3）风荷载作用下的柱端弯矩计算（Vi=总剪力×Di/ΣD；根据建筑结构抗震规范查得反弯点高度y值如下）风荷载作用下的柱剪力及弯矩计算表（表5-11）层次总剪力(kN)柱别Di(kN/mm)ΣD(kN/mm)h(m)56.62边柱9.05451.160.130.423.3-0.18-0.24中柱11.990.180.45-0.27-0.33415.87边柱9.05451.160.310.473.3-0.48-0.54中柱11.990.420.50-0.69-0.69324.44边柱9.05451.160.490.503.3-0.81-0.81中柱11.990.650.50-1.07-1.07233.01边柱9.05451.160.660.503.3-1.09-1.09中柱11.990.880.50-1.45-1.45141.58边柱6.5611.840.440.553.3-0.80-0.65中柱9.300.630.55-1.14-0.94（4）风荷载作用下的梁端弯矩以及剪力计算风荷载作用下梁端弯矩剪力计算表（表5-12）层次柱别M下M上线刚度之比边跨梁端弯矩中跨梁端弯矩M地震作用下梁端剪力边跨梁跨中弯矩左梁右梁VAVB左VB右5边柱-0.18-0.2400.24-0.06-0.035中柱-0.27-0.331.010.170.16-0.06-0.114边柱-0.48-0.5401.00-0.13-0.325中柱-0.69-0.691.010.350.34-0.13-0.233边柱-0.81-0.8101.29-0.21-0.375中柱-1.07-1.071.010.540.53-0.21-0.352边柱-1.09-1.0901.90-0.28-0.585中柱-1.45-1.451.010.730.72-0.28-0.481边柱-0.80-0.6501.01-0.19-0.27中柱-1.14-0.941.010.470.46-0.19-0.31（5）风荷载作用下的柱轴力计算风荷载作用下的柱轴力计算表（表5-13）层号柱别M下

(kN·m)M上

(kN·m)地震作用下梁端剪力(kN)柱轴力(kN)VAVB左VB右NANB5边柱-0.18-0.24-0.06-0.06中柱-0.27-0.33-0.06-0.11-0.054边柱-0.48-0.54-0.13-0.19中柱-0.69-0.69-0.13-0.23-0.103边柱-0.81-0.81-0.21-0.40中柱-1.07-1.07-0.21-0.35-0.142边柱-1.09-1.09-0.28-0.68中柱-1.45-1.45-0.28-0.48-0.201边柱-0.80-0.65-0.19-0.87中柱-1.14-0.94-0.19-0.31-0.12（6）风荷载作用下的内力图风荷载作用下的弯矩图kN·m（图5-6）风荷载作用下的剪力图kN（图5-7）风荷载作用下的轴力图kN（图5-8）2.2恒荷载作用下的内力计算（1）计算弯矩的分配系数该框架为对称结构，所以取框架的一半进行计算=1\*GB3①节点A1、A2、A3、A4：SA1A0=SA2A1=SA3A2=SA4A3=4i=4×0.64=2.56；SA1A2=SA2A3=SA3A4=SA4A5=4i=4×0.64=2.56；SA1B1=SA2B2=SA3B3=SA4B4=4i=4×0.74=2.96；ΣS=2.56+2.56+2.96=8.08；μA1A0=μA2A1=μA3A2=μA4A3=S÷ΣS=2.56÷8.08=0.32；μA1A2=μA2A3=μA3A4=μA4A5=S÷ΣS=2.56÷8.08=0.32；μA1B1=μA2B2=μA3B3=μA4B4=S÷ΣS=2.96÷8.08=0.37；=2\*GB3②节点B1、B2、B3、B4：SB1D1=SB2D2=SB3D3=SB4D4=i=2×0.73=1.46；ΣS=8.08+1.46=9.54；μB1B0=μB2B1=μB3B2=μB4B3=S÷ΣS=2.56÷9.54=0.27；μB1B2=μB2B3=μB3B4=μB4B5=S÷ΣS=2.56÷9.54=0.27；μB1A1=μB2A2=μB3A3=μB4A4=S÷ΣS=2.96÷9.54=0.31；μB1D1=μB2D2=μB3D3=μB4D4=S÷ΣS=1.46÷9.54=0.15；=3\*GB3③节点A5：μA5A4=S÷ΣS=2.56÷(2.56+2.96)=0.46；μA5B5=S÷ΣS=2.96÷(2.56+2.96)=0.54；=4\*GB3④节点B5：μB5B4=S÷ΣS=2.56÷(2.56+2.96+1.46)=0.37；μB5A5=S÷ΣS=2.96÷(2.56+2.96+1.46)=0.42；μB5D5=S÷ΣS=1.46÷(2.56+2.96+1.46)=0.21；（2）计算杆件端部弯矩计算杆件固端弯矩的候一律以顺时针的方向为正方向。=1\*GB3①五层横梁固端弯矩横梁的自重作用：MA5B5=-MB5A5=-ql2/12=-3.04×7.62÷12=-14.63kN·m；MB5D5=-ql2/3=-2.19×1.52÷3=-1.64kN·m；MD5B5=MB5D5/2=(-1.64)÷2=-0.82kN·m；板传来的恒荷载作用：MA5B5=-MB5A5=-ql2(1-2a2/l2+a3/l3)/12=-5.89×7.62×(1-2×1.82÷7.62+1.83÷7.63)÷12=-25.55kN·m；MB5D5=-5ql2/96=-5×6.81×1.52÷96=-0.80kN·m；MD5B5=-ql2/32=-6.81×1.52÷32=-0.48kN·m；=2\*GB3②二到四层横梁固端弯矩横梁的自重作用：MAB=-MBA=-ql2/12=-3.04×7.62÷12=-14.63kN·m；MBD=-ql2/3=-2.19×1.52÷3=-1.64kN·m；MDB=MBD/2=(-1.64)÷2=-0.82kN·m；板传来的恒荷载作用：MAB=-MBA=-ql2(1-2a2/l2+a3/l3)/12=-6.81×7.62×(1-2×1.82÷7.62+1.83÷7.63)÷12=-29.54kN·m；MB5D5=-5ql2/96=-5×7.88×1.52÷96=-0.92kN·m；MD5B5=-ql2/32=-7.88×1.52÷32=-0.55kN·m；=3\*GB3③梁端弯矩顶层：MFAB=-14.63-25.55=-40.18kN·mMFBA=14.63+25.55=40.18kN·mMFBD=-1.64-0.80=-2.44kN·mMFDB=-0.82-0.48=-1.30kN·m二到四层：MFAB=-14.63-29.54=-44.17kN·mMFBA=14.63+29.54=44.17kN·mMFBD=-1.64-0.92=-2.56kN·mMFDB=-0.82-0.55=-1.37kN·m=4\*GB3④梁端附加弯矩考虑到集中荷载引起的偏心弯矩作用，偏心距e=0.1m顶层：MAe=23.02×0.1=2.30kN·mMBe=-35.20×0.1=-3.52kN·m二到四层：MAe=53.87×0.1=5.39kN·mMBe=-71.43×0.1=-7.14kN·m=5\*GB3⑤节点不平衡弯矩顶层：MFA=-40.18+2.30=-37.88kN·mMFB=40.18-2.44-3.52=34.22kN·m二到四层：MFA=-44.17+5.39=-38.68kN·mMFB=44.17-2.56-7.14=34.47kN·m（3）计算框架内力=1\*GB3①进行恒载作用的弯矩分配：AB上柱下柱右梁左梁上柱下柱右梁0.460.540.420.370.21不平衡弯矩-37.8834.22梁端弯矩-40.1840.18-2.4417.4220.4610.23-4.667.72-8.36-16.71-11.54-8.360.290.350.180.1725.43-27.73-1.48-1.31-0.7432.40-17.34-11.540.320.320.370.310.270.270.15不平衡弯矩-38.6834.47梁端弯矩-44.1744.17-2.568.716.19-5.35-10.69-9.31-9.31-5.1715.4315.4317.858.92-5.77-4.360.15-1.310.190.380.330.330.19-5.96-5.96-6.8942.78-14.75-13.34-7.5418.3314.35-38.370.320.320.370.310.270.270.15不平衡弯矩-38.6834.47梁端弯矩-44.1744.17-2.5612.3812.3814.317.16-4.66-4.667.725.07-5.01-10.02-8.72-8.72-4.85-2.61-2.61-3.02-1.510.170.2117.4914.84-37.890.350.310.310.1740.15-12.90-12.86-7.240.320.320.370.310.270.270.15不平衡弯矩-38.6834.47梁端弯矩-43.8643.86-2.596.196.19-5.35-10.69-9.31-9.31-5.1710.1310.1311.715.86-4.36-3.06-1.13-0.310.250.490.420.420.240.280.280.3239.52-13.25-11.95-7.5215.4516.29-36.930.320.320.370.310.270.270.15不平衡弯矩-38.6834.47梁端弯矩-43.8643.86-2.5912.3812.3814.317.16-4.665.07-3.51-7.02-6.12-6.123.40-0.62-0.62-0.72-0.360.2116.8311.76-33.78-2.06-1.79-1.79-1.0041.58-12.36-7.91-0.195.88-3.96恒荷载作用下的弯矩分配图（图5-9）=2\*GB3②梁端剪力计算：其中VA=gl/2+u-∑Mik/l；VB=-（gl/2+u+∑Mik/l）恒载作用下AB跨梁端剪力计算表（表5-14）层qkN/mgkN/ma(m)L(m)gl/2u=(l-a)×q/2-MABkN·mMBAkN·m∑Mik/lVA-VB55.893.751.87.614.2517.0827.7332.400.6131.2531.4146.813.751.87.614.2519.7538.3742.780.5833.9234.0836.813.751.87.614.2519.7537.8940.150.3033.9634.0426.813.751.87.614.2519.7536.9339.520.3433.9534.0516.813.751.87.614.2519.7533.7841.581.0333.8634.14恒载作用下BC跨梁端剪力计算表（表5-15）层q(kN/m)g(kN/m)l(m)gl/2l×q/4VB=gl/2+l×q/4VC=-(gl/2+l×q/4)56.812.1933.295.118.408.4047.882.1933.295.919.209.2037.882.1933.295.919.209.2027.882.1933.295.919.209.2017.882.1933.295.919.209.20=3\*GB3③跨中弯矩计算：其中M=gl/2×l/4+u×1.05-MAB-VA×l/2恒载作用下AB跨跨中弯矩计算表（表5-16）层q(kN/m)g(kN/m)a(m)l(m)gl/2u=(l-a)×q/2MAB(kN·m)∑Mik/lVAM55.893.751.87.614.2517.08-27.730.6131.25-18.9446.813.751.87.614.2519.75-38.370.5833.92-15.6436.813.751.87.614.2519.75-37.890.3033.96-15.7926.813.751.87.614.2519.75-36.930.3433.95-17.1916.813.751.87.614.2519.75-33.781.0333.86-20.00=4\*GB3④柱轴力计算：恒载作用下柱轴力计算表（表5-17）层边柱A轴、D轴中柱B轴、C轴横梁端部压力纵梁端部压力柱重柱轴力横梁端部压力纵梁端部压力柱重柱轴力5柱顶31.2523.0213.8354.2731.4117.2613.8348.67柱底68.1062.504柱顶33.9253.8713.83156.4334.0871.4313.83168.01柱底170.26181.843柱顶33.9653.8713.83258.0934.0471.4313.83287.31柱底271.92301.142柱顶33.9553.8713.83359.7434.0571.4313.83406.62柱底373.57420.451柱顶33.8653.8713.83461.3334.1471.4313.83526.02柱底475.16539.85（4）框架内力图恒载作用下的框架弯矩图（图5-10）恒载作用下的框架轴力图（图5-11）恒载作用下的框架剪力图（图5-12）2.3活荷载作用下的内力计算（1）杆件端部弯矩计算计算杆件固端弯矩的候一律以顺时针的方向为正方向。=1\*GB3①五层横梁MA5B5=-MB5A5=-ql2(1-2a2/l2+a3/l3)/12=-3.24×7.62×(1-2×1.82÷7.62+1.83÷7.63)÷12=-14.05kN·m；MB5D5=-5ql2/96=-5×3.75×1.52÷96=-0.44kN·m；MD5B5=-ql2/32=-3.75×1.52÷32=-0.26kN·m；=2\*GB3②二到四层横梁MAB=-MBA=-ql2(1-2a2/l2+a3/l3)/12=-4.05×7.62×(1-2×1.82÷7.62+1.83÷7.63)÷12=-17.57kN·m；MB5D5=-5ql2/96=-5×6.56×1.52÷96=-0.77kN·m；MD5B5=-ql2/32=-6.56×1.52÷32=-0.46kN·m；=3\*GB3③梁端弯矩为顶层：MFAB=-14.05kN·mMFBA=14.05kN·mMFBD=-0.44kN·mMFDB=-0.26kN·m二到四层：MFAB=-17.57kN·mMFBA=17.57kN·mMFBD=-0.77kN·mMFDB=-0.46kN·m=4\*GB3④附加弯矩为考虑到集中荷载引起的偏心弯矩作用，偏心距e=0.1m顶层：MAe=1.13×0.1=0.11kN·mMBe=-9.23×0.1=-0.92kN·m二到四层：MAe=10.13×0.1=1.02kN·mMBe=-24.30×0.1=-2.43N·m=5\*GB3⑤节点不平衡弯矩为顶层：MFA=-14.05+0.11=-13.94kN·mMFB=14.05-0.44-0.92=12.69kN·m二到四层：MFA=-17.57+1.02=-16.55kN·mMFB=17.57-0.77-0.24=16.56kN·m（2）计算框架内力=1\*GB3①进行满跨活荷载作用的弯矩分配：AB上柱下柱右梁左梁上柱下柱右梁0.460.540.420.370.21不平衡弯矩-13.9412.69梁端弯矩-14.0514.05-0.446.417.533.77-2.242.12-2.99-5.97-5.26-2.990.360.420.210.308.89-9.09-0.21-0.19-0.1111.85-7.39-3.540.320.320.370.310.270.270.15不平衡弯矩-16.5516.56梁端弯矩-16.3516.35-0.773.212.65-2.57-5.13-4.47-4.47-2.484.244.244.912.46-2.63-2.050.18-0.350.350.690.600.600.33-0.100.10-0.1114.37-6.5-7.12-2.927.536.44-13.770.320.320.370.310.270.270.15不平衡弯矩-16.5516.56梁端弯矩-16.3516.35-0.775.305.306.123.06-2.24-2.242.122.21-2.35-4.69-4.09-4.09-2.27-0.69-0.69-0.80-0.400.300.216.736.82-13.380.150.130.130.0714.47-5.90-5.99-2.970.320.320.370.310.270.270.15不平衡弯矩-16.5516.56梁端弯矩-16.3516.35-0.772.652.65-2.57-5.13-4.47-4.47-2.484.424.425.122.56-2.05-2.35-0.350.050.240.470.410.410.23-0.03-0.02-0.0314.25-6.93-7.23-3.486.697.10-13.590.320.320.370.310.270.270.15不平衡弯矩-16