两路组团S31-1地块小学石材包柱桁架计算书

同济大学3D3S软件PAGE1两路组团S31-1地块小学石材包柱桁架计算书.1设计依据《钢结构设计标准》(GB50017-2017)《冷弯薄壁型钢结构技术规范》(GB50018-2002)《建筑结构荷载规范》(GB50009-2012)《建筑抗震设计规范》(GB50011-2010)(2016年版)《建筑地基基础设计规范》(GB50007-2011)《钢管混凝土结构技术规范》(GB50936-2014)《钢管混凝土结构设计规程》(CECS28:2012)《矩形钢管混凝土结构技术规程》(CECS159-2004)《钢结构焊接规范》(GB50661-2011)《钢结构高强度螺栓连接技术规程》(JGJ82-2011)2计算简图计算简图(圆表示支座，数字为节点号)3荷载与组合结构重要性系数：1.103.1荷载工况荷载工况汇总表工况号荷载类型荷载说明0恒1风(1)杆件导荷载列表(力：kN；分布力：kN/m；弯矩：kN.m；分布弯矩：kN.m/m)序号荷载类型工况导荷方式体型系数面荷载值(基本风压)1恒0双向杆件--2.002风1双向杆件1.600.483.2节点荷载3.3单元荷载1)工况号:0*输入的面荷载:序号荷载类型导荷方式体型系数面荷载值(基本风压)kN/m21恒载双向杆件--2.00面荷载分布图:面荷载序号1分布图（红线表示荷载分配到的单元）3.4面荷载3.5其它荷载(1).风总信息基本风压：0.48(kN/m2)地面粗糙度：B风压高度变化修正系数η：1.00风荷载计算用阻尼比：0.02风荷载参数高度(m)μz（修正前）ημzβz2.251.001.001.001.27(2).地震作用规范：《建筑抗震设计规范》（GB50011-2010）（2016年版）地震烈度：7度(0.1g)水平地震影响系数最大值：0.040计算振型数：9建筑结构阻尼比：0.040特征周期值：0.25地震影响：多遇地震场地类别：Ⅰ1类地震分组：第一组周期折减系数：1.00地震力计算方法：振型分解法振型号周期（秒）各振型质量参与系数10.116035.71%0.47%0.00%20.090434.06%0.00%0.00%30.086714.81%0.20%0.00%40.08280.24%1.38%0.00%50.04440.33%0.06%0.00%60.03810.11%32.74%0.00%70.03620.04%0.04%0.00%80.03462.68%0.55%0.06%90.03350.12%10.82%0.19%(3).温度作用无温度作用。3.6荷载组合(1)1.30恒载+1.50风载工况1(2)1.20恒载+1.30水平地震(3)1.00恒载+1.50风载工况1(4)1.00恒载+1.30水平地震4内力位移计算结果4.1内力4.1.1最不利内力各效应组合下最大支座反力设计值(单位：kN、kN.m)节点号控制组合号组合序号N1N2N3M1M2M3N1最大42-0.11.86.00.00.00.0N2最大22-0.12.17.10.00.00.0N3最大11-0.21.97.40.00.00.01合力最大11-0.21.97.40.00.00.0N1最小21-0.21.46.50.00.00.0N2最小41-0.21.15.40.00.00.0N3最小41-0.21.15.40.00.00.0N1最大220.2-1.46.50.00.00.0N2最大420.2-1.15.40.00.00.0N3最大110.2-1.97.40.00.00.09合力最大110.2-1.97.40.00.00.0N1最小410.1-1.86.00.00.00.0N2最小210.2-2.17.10.00.00.0N3最小420.2-1.15.40.00.00.0N1最大420.00.12.50.00.00.0N2最大21-0.60.93.10.00.00.0N3最大11-0.40.63.30.00.00.013合力最大11-0.40.63.30.00.00.0N1最小21-0.60.93.10.00.00.0N2最小420.00.12.50.00.00.0N3最小420.00.12.50.00.00.0N1最大220.12.910.30.00.00.0N2最大110.03.410.90.00.00.0N3最大110.03.410.90.00.00.014合力最大110.03.410.90.00.00.0N1最小41-0.02.88.10.00.00.0N2最小420.12.48.60.00.00.0N3最小41-0.02.88.10.00.00.0N1最大220.6-0.93.10.00.00.0N2最大41-0.0-0.02.50.00.00.0N3最大110.4-0.53.30.00.00.035合力最大110.4-0.53.30.00.00.0N1最小41-0.0-0.02.50.00.00.0N2最小220.6-0.93.10.00.00.0N3最小41-0.0-0.02.50.00.00.0N1最大220.1-3.39.70.00.00.0N2最大41-0.1-2.48.60.00.00.0N3最大110.0-3.410.80.00.00.036合力最大110.0-3.410.80.00.00.0N1最小41-0.1-2.48.60.00.00.0N2最小110.0-3.410.80.00.00.0N3最小420.1-2.88.10.00.00.0N1最大410.21.76.10.00.00.0N2最大11-0.02.17.90.00.00.0N3最大11-0.02.17.90.00.00.039合力最大11-0.02.17.90.00.00.0N1最小22-0.31.87.30.00.00.0N2最小42-0.31.56.10.00.00.0N3最小42-0.31.56.10.00.00.0N1最大210.02.07.30.00.00.0N2最大110.02.17.90.00.00.0N3最大110.02.17.90.00.00.047合力最大110.02.17.90.00.00.0N1最小42-0.01.56.10.00.00.0N2最小42-0.01.56.10.00.00.0N3最小42-0.01.56.10.00.00.0N1最大210.3-1.87.40.00.00.0N2最大410.3-1.46.10.00.00.0N3最大110.0-2.17.90.00.00.055合力最大110.0-2.17.90.00.00.0N1最小42-0.3-1.76.10.00.00.0N2最小110.0-2.17.90.00.00.0N3最小42-0.3-1.76.10.00.00.0N1最大410.0-1.46.10.00.00.0N2最大410.0-1.46.10.00.00.0N3最大11-0.0-2.17.90.00.00.057合力最大11-0.0-2.17.90.00.00.0N1最小22-0.0-2.07.30.00.00.0N2最小11-0.0-2.17.90.00.00.0N3最小42-0.0-1.76.10.00.00.0各效应组合下最大支座反力标准值(单位：kN、kN.m)节点号控制组合号组合序号N1N2N3M1M2M3N1最大22-0.11.75.90.00.00.0N2最大22-0.11.75.90.00.00.0N3最大22-0.11.75.90.00.00.01合力最大22-0.11.75.90.00.00.0N1最小21-0.11.25.50.00.00.0N2最小21-0.11.25.50.00.00.0N3最小21-0.11.25.50.00.00.0N1最大220.2-1.25.50.00.00.0N2最大220.2-1.25.50.00.00.0N3最大210.1-1.85.90.00.00.09合力最大210.1-1.85.90.00.00.0N1最小210.1-1.85.90.00.00.0N2最小210.1-1.85.90.00.00.0N3最小220.2-1.25.50.00.00.0N1最大22-0.10.22.50.00.00.0N2最大21-0.50.72.60.00.00.0N3最大21-0.50.72.60.00.00.013合力最大21-0.50.72.60.00.00.0N1最小21-0.50.72.60.00.00.0N2最小22-0.10.22.50.00.00.0N3最小22-0.10.22.50.00.00.0N1最大220.02.48.60.00.00.0N2最大21-0.02.88.10.00.00.0N3最大220.02.48.60.00.00.014合力最大24-0.02.78.50.00.00.0N1最小21-0.02.88.10.00.00.0N2最小220.02.48.60.00.00.0N3最小21-0.02.88.10.00.00.0N1最大220.5-0.72.60.00.00.0N2最大210.0-0.12.50.00.00.0N3最大220.5-0.72.60.00.00.035合力最大220.5-0.72.60.00.00.0N1最小210.0-0.12.50.00.00.0N2最小220.5-0.72.60.00.00.0N3最小210.0-0.12.50.00.00.0N1最大220.1-2.88.10.00.00.0N2最大21-0.0-2.48.50.00.00.0N3最大21-0.0-2.48.50.00.00.036合力最大23-0.0-2.78.50.00.00.0N1最小21-0.0-2.48.50.00.00.0N2最小220.1-2.88.10.00.00.0N3最小220.1-2.88.10.00.00.0N1最大210.21.76.10.00.00.0N2最大210.21.76.10.00.00.0N3最大210.21.76.10.00.00.039合力最大210.21.76.10.00.00.0N1最小22-0.21.56.10.00.00.0N2最小22-0.21.56.10.00.00.0N3最小22-0.21.56.10.00.00.0N1最大210.01.76.10.00.00.0N2最大210.01.76.10.00.00.0N3最大210.01.76.10.00.00.047合力最大210.01.76.10.00.00.0N1最小22-0.01.56.10.00.00.0N2最小22-0.01.56.10.00.00.0N3最小22-0.01.56.10.00.00.0N1最大210.2-1.56.10.00.00.0N2最大210.2-1.56.10.00.00.0N3最大210.2-1.56.10.00.00.055合力最大22-0.2-1.76.10.00.00.0N1最小22-0.2-1.76.10.00.00.0N2最小22-0.2-1.76.10.00.00.0N3最小22-0.2-1.76.10.00.00.0N1最大210.0-1.56.10.00.00.0N2最大210.0-1.56.10.00.00.0N3最大210.0-1.56.10.00.00.057合力最大22-0.0-1.76.10.00.00.0N1最小22-0.0-1.76.10.00.00.0N2最小22-0.0-1.76.10.00.00.0N3最小22-0.0-1.76.10.00.00.04.1.2内力包络及统计按轴力N最大显示构件颜色(kN)轴力N最大的前10个单元的内力(单位：m,kN,kN.m)序号单元号组合号组合序位置轴力N剪力Q2剪力Q3扭矩M弯矩M2弯矩M3110110.6567.2-0.00.00.00.0-0.0216110.0005.9-0.00.0-0.0-0.0-0.0381111.3175.2-0.0-0.0-0.0-0.0-0.0494110.4175.10.0-0.1-0.00.00.0586110.4175.1-0.0-0.10.00.0-0.0679111.3174.9-0.0-0.0-0.0-0.0-0.0728210.0004.3-0.0-0.20.00.10.0876110.0004.00.0-0.00.0-0.00.09112110.0003.9-0.0-0.1-0.00.0-0.01074110.0003.90.0-0.00.0-0.00.0按轴力N最小显示构件颜色(kN)轴力N最小的前10个单元的内力(单位：m,kN,kN.m)序号单元号组合号组合序位置轴力N剪力Q2剪力Q3扭矩M弯矩M2弯矩M3141110.469-6.1-0.00.0-0.0-0.00.0235111.125-5.9-0.00.0-0.00.00.0378110.000-5.10.00.0-0.0-0.0-0.0480110.000-4.90.00.0-0.0-0.0-0.0597110.583-4.70.0-0.1-0.0-0.0-0.0689110.583-4.7-0.0-0.10.0-0.00.0775111.353-4.0-0.00.00.0-0.00.0877211.353-4.0-0.00.00.0-0.00.09115111.125-4.0-0.0-0.1-0.0-0.00.01088111.000-3.8-0.0-0.1-0.0-0.00.0按弯矩M2最大显示构件颜色(kN.m)弯矩M2最大的前10个单元的内力(单位：m,kN,kN.m)序号单元号组合号组合序位置轴力N剪力Q2剪力Q3扭矩M弯矩M2弯矩M3164110.0001.5-0.0-0.6-0.00.30.0263110.0001.2-0.0-0.6-0.00.3-0.0362110.0001.2-0.0-0.50.00.3-0.0465110.0001.0-0.0-0.50.00.3-0.0531110.000-2.9-0.1-0.20.00.1-0.166110.0002.7-0.1-0.3-0.00.1-0.0722110.000-1.3-0.1-0.3-0.00.1-0.1828110.0004.2-0.1-0.20.00.1-0.0934110.000-0.00.2-0.3-0.00.10.0109110.0000.10.2-0.3-0.00.10.0按弯矩M2最小显示构件颜色(kN.m)弯矩M2最小的前10个单元的内力(单位：m,kN,kN.m)序号单元号组合号组合序位置轴力N剪力Q2剪力Q3扭矩M弯矩M2弯矩M3163111.125-1.5-0.0-0.6-0.0-0.3-0.0264111.125-1.2-0.0-0.6-0.0-0.30.0365111.125-0.3-0.0-0.50.0-0.30.0462111.1250.8-0.0-0.50.0-0.30.0528111.1253.1-0.1-0.20.0-0.10.1622111.125-2.7-0.1-0.3-0.0-0.10.076111.1251.3-0.1-0.3-0.0-0.10.1831111.125-3.8-0.1-0.20.0-0.10.0939111.1250.2-0.2-0.1-0.0-0.00.11040111.125-2.3-0.2-0.1-0.0-0.00.1按弯矩M3最大显示构件颜色(kN.m)弯矩M3最大的前10个单元的内力(单位：m,kN,kN.m)序号单元号组合号组合序位置轴力N剪力Q2剪力Q3扭矩M弯矩M2弯矩M31109110.000-0.22.50.10.0-0.00.82105110.000-0.12.50.00.0-0.00.83111110.000-0.22.40.0-0.0-0.00.74102110.571-0.7-1.3-0.00.0-0.00.65106110.5710.7-1.30.00.0-0.00.66107110.0000.41.80.1-0.0-0.00.57103110.000-0.51.80.0-0.0-0.00.58104110.686-0.0-0.7-0.0-0.0-0.00.49108110.6860.0-0.70.0-0.00.00.410110110.686-0.0-0.7-0.00.0-0.00.4按弯矩M3最小显示构件颜色(kN.m)弯矩M3最小的前10个单元的内力(单位：m,kN,kN.m)序号单元号组合号组合序位置轴力N剪力Q2剪力Q3扭矩M弯矩M2弯矩M31111110.561-0.22.40.0-0.00.0-0.62109110.561-0.22.50.10.00.0-0.63105110.561-0.12.50.00.00.0-0.6417210.3230.02.20.2-0.0-0.0-0.4529220.323-0.02.2-0.2-0.00.0-0.46107110.5610.41.40.1-0.00.0-0.37103110.561-0.51.40.0-0.00.0-0.3825110.0000.0-5.20.1-0.3-0.0-0.3913110.0000.0-5.20.2-0.3-0.0-0.31031210.000-2.3-0.2-0.2-0.00.1-0.24.2位移4.2.1组合位移最大正位移组合1:Uz(mm)最大负位移组合2:Uz(mm)5设计验算结果本工程有1种材料：Q235：弹性模量：2.06*105N/mm2；泊松比：0.30；线膨胀系数：1.20*10-5；质量密度：7850kg/m3。5.1设计验算结果图及统计表根据计算分析模型，进行规范检验，检验结果表明，结构能够满足承载力计算要求，应力比最大值为0.18。下图为模型总体应力比分布图：杆件应力比分布图按“强度应力比”显示构件颜色“强度应力比”最大的前10个单元的验算结果（所在组合号／情况号）序号单元号强度绕2轴整体稳定绕3轴整体稳定沿2轴抗剪应力比沿3轴抗剪应力比绕2轴长细比绕3轴长细比结果1340.125(1/1)0.1060.1060.0050.0075757满足290.123(1/1)0.1040.1040.0050.0075757满足3800.112(1/1)0.1790.1770.0000.001134134满足4780.110(1/1)0.1810.1800.0000.001134134满足51090.098(1/1)0.1260.1260.0290.0012816满足6150.097(1/1)0.0820.0820.0010.0035757满足71050.096(1/1)0.1240.1240.0290.0012816满足8270.095(1/1)0.0810.0810.0010.0035757满足9210.094(1/1)0.0800.0800.0010.0035757满足101110.090(1/1)0.1160.1160.0280.0022816满足按“强度应力比”统计结果表范围>1.001.00~0.900.90~0.700.70~0.500.50~0.00单元数0000116百分比0.0%0.0%0.0%0.0%100.0%按“绕2轴应力比”显示构件颜色“绕2轴整体稳定应力比”最大的前10个单元的验算结果（所在组合号／情况号）序号单元号强度绕2轴整体稳定绕3轴整体稳定沿2轴抗剪应力比沿3轴抗剪应力比绕2轴长细比绕3轴长细比结果1780.1100.181(1/1)0.1800.0000.001134134满足2800.1120.179(1/1)0.1770.0000.001134134满足3750.0650.142(1/1)0.1410.0000.001138138满足4770.0610.138(1/1)0.1380.0000.001138138满足51090.0980.126(1/1)0.1260.0290.0012816满足61050.0960.124(1/1)0.1240.0290.0012816满足71110.0900.116(1/1)0.1160.0280.0022816满足8340.1250.106(1/1)0.1060.0050.0075757满足990.1230.104(1/1)0.1040.0050.0075757满足10730.0480.104(1/1)0.1040.0000.000127127满足按“绕2轴整体稳定应力比”统计结果表范围>1.001.00~0.900.90~0.700.70~0.500.50~0.00单元数0000116百分比0.0%0.0%0.0%0.0%100.0%按“绕3轴应力比”显示构件颜色“绕3轴整体稳定应力比”最大的前10个单元的验算结果（所在组合号／情况号）序号单元号强度绕2轴整体稳定绕3轴整体稳定沿2轴抗剪应力比沿3轴抗剪应力比绕2轴长细比绕3轴长细比结果1780.1100.1810.180(1/1)0.0000.001134134满足2800.1120.1790.177(1/1)0.0000.001134134满足3750.0650.1420.141(1/1)0.0000.001138138满足4770.0610.1380.138(1/1)0.0000.001138138满足51090.0980.1260.126(1/1)0.0290.0012816满足61050.0960.1240.124(1/1)0.0290.0012816满足71110.0900.1160.116(1/1)0.0280.0022816满足8340.1250.1060.106(1/1)0.0050.0075757满足9730.0480.1040.104(1/1)0.0000.000127127满足1090.1230.1040.104(1/1)0.0050.0075757满足按“绕3轴整体稳定应力比”统计结果表范围>1.001.00~0.900.90~0.700.70~0.500.50~0.00单元数0000116百分比0.0%0.0%0.0%0.0%100.0%5.2设计验算结果表设计验算结果表(强度和整体稳定)单元号强度绕2轴整体稳定绕3轴整体稳定沿2轴抗剪应力比沿3轴抗剪应力比绕2轴长细比绕3轴长细比结果10.0070.0090.0090.0020.0003822满足20.0090.0110.0110.0020.0003822满足30.0090.0120.0120.0020.0003822满足40.0090.0110.0110.0020.0003822满足50.0070.0070.0070.0020.0003822满足60.0470.0180.0370.0020.0065733满足70.0250.0320.0320.0330.00632满足80.0340.0260.0260.0050.00277满足90.1230.1040.1040.0050.0075757满足100.0240.0000.0000.0000.0005733满足110.0210.0260.0260.0070.002169满足120.0140.0140.0140.0050.0004928满足130.0400.0520.0520.0610.00432满足140.0170.0140.0140.0020.00477满足150.0970.0820.0820.0010.0035757满足160.0190.0000.0000.0000.0005733满足170.0480.0610.0610.0210.002169满足180.0080.0100.0100.0010.0014928满足190.0260.0330.0330.0360.00432满足200.0270.0230.0230.0040.00677满足210.0940.0800.0800.0010.0035757满足220.0470.0350.0520.0010.0065733满足230.0190.0250.0250.0070.002169满足240.0080.0110.0110.0020.0014928满足250.0420.0540.0540.0610.00332满足260.0250.0210.0210.0030.00577满足270.0950.0810.0810.0010.0035757满足280.0540.0210.0320.0020.0055733满足290.0470.0610.0610.0210.003169满足300.0080.0110.0110.0010.0014928满足310.0530.0440.0590.0020.0055733满足320.0180.0230.0230.0330.00332满足330.0200.0150.0150.0030.00377满足340.1250.1060.1060.0050.0075757满足350.0190.0290.0270.0000.0005733满足360.0220.0280.0280.0070.003169满足370.0140.0190.0180.0050.0004928满足380.0240.0190.0050.0020.0015733满足390.0270.0260.0150.0020.0025733满足400.0270.0370.0250.0020.0025733满足410.0200.0310.0280.0000.0005733满足420.0210.0210.0210.0010.001136136满足430.0180.0160.0160.0010.001136136满足440.0170.0150.0150.0010.001136136满足450.0180.0160.0160.0010.001136136满足460.0060.0070.0070.0040.0003822满足470.0130.0160.0160.0050.0005632满足480.0060.0070.0070.0040.0003822满足490.0080.0100.0100.0030.0003822满足500.0090.0110.0110.0020.0005632满足510.0080.0110.0110.0030.0003822满足520.0080.0110.0110.0030.0003822满足530.0010.0020.0020.0010.0005632满足540.0080.0100.0100.0030.0003822满足550.0080.0100.0100.0030.0003822满足560.0090.0120.0120.0020.0005632满足570.0080.0110.0110.0030.0003822满足580.0210.0220.0220.0010.001136136满足590.0060.0070.0070.0040.0003822满足600.0130.0160.0160.0050.0005632满足610.0060.0080.0080.0040.0003822满足620.0610.0150.0710.0000.0115733满足630.0630.0240.0810.0000.0125733满足640.0630.0220.0800.0000.0125733满足650.0610.0190.0760.0000.0115733满足660.0320.0000.0000.0000.000127127满足670.0490.1010.1020.0000.000127127满足680.0450.0000.0000.0000.000127127满足690.0470.1030.1040.0000.000127127满足700.0440.0000.0000.0000.000127127满足710.0500.1010.1010.0000.000127127满足720.0440.0000.0000.0000.000127127满足730.0480.1040.1040.0000.000127127满足740.0520.0000.0000.0000.001138138满足750.0650.1420.1410.0000.001138138满足760.0530.0000.0000.0000.001138138满足770.0610.1380.1380.0000.001138138满足780.1100.1810.1800.0000.001134134满足790.0790.0010.0010.0000.001134134满足800.1120.1790.1770.0000.001134134满足810.0790.0000.0000.0000.001134134满足820.0140.0200.0110.0020.0015029满足830.0140.0130.0100.0010.0015029满足840.0140.0210.0180.0010.0015029满足850.0190.0140.0040.0020.0015029满足860.0230.0000.0000.0000.0025029满足870.0180.0030.0030.0000.0025029满足880.0180.0260.0240.0000.0025029满足890.0220.0310.0300.0000.0025029满足900.0150.0210.0120.0020.0015029满足910.0140.0120.0120.0010.0015029满足920.0140.0190.0190.0010.0015029满足930.0190.0140.0030.0020.0015029满足940.0230.0000.0000.0000.0025029满足950.0180.0040.0040.0000.0025029满足960.0180.0260.0240.0000.0025029满足970.0220.0310.0290.0000.0025029满足980.0190.0060.0060.0010.0015733满足990.0130.0130.0130.0010.0015733满足1000.0130.0190.0180.0010.0015733满足1010.0160.0220.0220.0010.0015733满足1020.0730.0940.0940.0150.0013520满足1030.0700.0900.0900.0210.0012816满足1040.0540.0690.0690.0080.0003520满足1050.0960.1240.1240.0290.0012816满足1060.0730.0880.0880.0150.0003520满足1070.0710.0880.0880.0210.0012816满足1080.0530.0680.0680.0080.0003520满足1090.0980.1260.1260.0290.0012816满足1100.0520.0670.0670.0080.0013520满足1110.0900.1160.1160.0280.0022816满足1120.0190.0000.0000.0000.0015733满足1130.0190.0020.0020.0000.0015733满足1140.0190.0270.0260.0000.0015733满足1150.0190.0270.0260.0000.0015733满足1160.0200.0280.0150.0020.0015733满足最严控制表(强度和整体稳定)强度绕2轴整体稳定绕3轴整体稳定沿2轴抗剪应力比沿3轴抗剪应力比绕2轴长细比绕3轴长细比所在单元34787813647575数值0.1250.1810.1800.0610.012138138附录矩形空心型钢截面示意图普通角钢(等肢)截面示意图此模型位于1~8#桁架柱位置，详见节点图ZS-602：幕墙埋件计算(后锚固结构-特殊倒锥形化学锚栓)埋件受力基本参数V=6750NN=5000NM=1935000N·mm选用锚栓：慧鱼特殊柱锥化学锚栓,FHB-A12x100HDG锚栓排数×列数：2×2；锚栓最外排间距×最外列间距：150mm×200mm；混凝土等级：C40；；锚栓群中锚栓的拉力计算按5.2.2[JGJ145-2013]规定，在轴心拉力和弯矩共同作用下(下图所示)，进行弹性分析时，受力最大锚栓的拉力设计值应按下列规定计算：1：当N/n-My1/Σyi2≥0时：5.2.2-1[JGJ145-2013]Nsdh=N/n+My1/Σyi25.2.2-2[JGJ145-2013]2：当N/n-My1/Σyi2<0时：Nsdh=(NL+M)y1//Σyi/25.2.2-3[JGJ145-2013]在上面公式中：M：弯矩设计值；Nsdh：群锚中受拉力最大锚栓的拉力设计值；y1，yi：锚栓1及i至群锚形心轴的垂直距离；y1/，yi/：锚栓1及i至受压一侧最外排锚栓的垂直距离；L：轴力N作用点至受压一侧最外排锚栓的垂直距离；在本例中：N/n-My1/Σyi2=5000/4-1935000×75/22500=-5200因为：-5200<0所以：Nsdh=(NL+M)y1//Σyi/2=7700N按JGJ102-2003的5.5.7中第七条规定，这里的Nsdh再乘以2[=15400N]就是现场实际拉拔应该达到的值。另外，我们接着分析一下锚栓群受拉区的总拉力：当N/n-My1/Σyi2≥0时：螺栓群中的所有锚栓在组合外力作用下都承受拉力，中性轴在锚栓群形心位置，这种情况下群锚受拉区总拉力为：Nsdg=N+MΣyi/Σyi2=N而当N/n-My1/Σyi2＜0时：最下排的锚栓底部埋板部分为结构受压区，螺栓群的中性轴取最下一排锚栓位置，这种情况下群锚受拉区总拉力为：Nsdg=ΣNsi5.2.3-1[JGJ145-2013]Nsi=Nsdh·yi//y1/5.2.3-2[JGJ145-2013]对上两个公式整理后，得：Nsdg=(NL+M)Σyi//Σyi/2本例中，因为：-5200<0所以：Nsdg=(NL+M)Σyi//Σyi/2=15400N群锚受剪内力计算按5.3.1[JGJ145-2013]的规定，计算钢材破坏或混凝土剪撬破坏时，应按群锚中所有锚栓均承受剪力进行计算，也就是：Vsdh=6750/4=1687.5N锚栓钢材破坏时的受拉承载力计算NRd,s=kNRk,s/γRS,N6.1.2-1[JGJ145-2013]NRk,s=fykAs6.1.2-2[JGJ145-2013]上面公式中：NRd,s：锚栓钢材破坏时的受拉承载力设计值；NRk,s：锚栓钢材破坏时的受拉承载力标准值；k：地震作用下锚固承载力降低系数，按表4.3.9[JGJ145-2013]选取；As：锚栓应力截面面积；fyk：机械锚栓屈服强度标准值；γRS,N：锚栓钢材受拉破坏承载力分项系数,按规范表4.3.10，取：γRS,N=1.2；NRk,s=Asfyk=84.3×640=53952NNRd,s=kNRk,s/γRS,N=1×53952/1.2=44960N≥Nsdh=7700N锚栓钢材受拉破坏承载力满足设计要求！混凝土锥体受拉破坏承载力计算因锚固点位于结构受拉面，而该结构为普通混凝土结构，故锚固区基材应判定为开裂混凝土。混凝土锥体受拉破坏时的受拉承载力设计值NRd,c应按下列公式计算：NRd,c=kNRk,c/γRc,N6.1.3-1[JGJ145-2013]NRk,c=NRk,c0×Ac,N/Ac,N0×ψs,Nψre,Nψec,N6.1.3-2[JGJ145-2013]对于开裂混凝土土：NRk,c0=7.0×fcu,k0.5×hef1.56.1.3-3[JGJ145-2013]对于不开裂混凝土土：NRk,c0=9.8×fcu,k0.5×hef1.56.1.3-4[JGJ145-2013]在上面公式中：NRd,c：混凝土锥体破坏时的受拉承载力设计值；NRk,c：混凝土锥体破坏时的受拉承载力标准值；k：地震作用下锚固承载力降低系数，按表4.3.9[JGJ145-2013]选取；γRc,N：混凝土锥体破坏时的受拉承载力分项系数，按表4.3.10[JGJ145-2013]采用，取1.8；NRk,c0：开裂混凝土单锚栓受拉，理想混凝土锥体破坏时的受拉承载力标准值；fcu,k：混凝土立方体抗压强度标准值，当其在45-60MPa间时，应乘以降低系数0.95；hef：锚栓有效锚固深度；NRk,c0=7.0×fcu,k0.5×hef1.5=7.0×400.5×1001.5=44271.887NAc,N0：混凝土理想锥体破坏投影面面积，按6.1.4[JGJ145-2013]取；scr,N：混凝土锥体破坏情况下，无间距效应和边缘效应，确保每根锚栓受拉承载力标准值的临界间矩。scr,N=3hef=3×100=300mmAc,N0=scr,N26.1.4[JGJ145-2013]=3002=90000mm2Ac,N：混凝土实际锥体破坏投影面积，按6.1.5[JGJ145-2013]取：当N/n-My1/Σyi2≥0时：Ac,N=(min(c1,ccr,N)+s1+min(c1a,ccr,N))×(min(c2,ccr,N)+s2+0.5scr,N)……情况一当N/n-My1/Σyi2<0时：若锚栓共有2排，则：Ac,N=(min(c1a,ccr,N)+min(c1+s1,ccr,N))×(min(c2,ccr,N)+s2+0.5scr,N)……情况二若锚栓共有3-4排(下面公式中参数n为锚栓层数)，则：Ac,N=(min(c1a,ccr,N)+s1×(n-2)/(n-1)+min(ccr,N,c1+s1/(n-1)))×(min(c2,ccr,N)+s2+0.5scr,N)……情况三其中：c1、c1a、c2：方向1及2的边矩；s1、s2：方向1及2的间距；ccr,N：混凝土锥体破坏时的临界边矩，取ccr,N=1.5hef=1.5×100=150mm；c1≤ccr,Nc1a≤ccr,Nc2≤ccr,Ns2≤scr,N所以，本计算为：Ac,N=(min(c1a,ccr,N)+min(c1+s1,ccr,N))×(min(c2,ccr,N)+s2+0.5scr,N)=(150+150)×(150+200+0.5×300)=150000mm2ψs,N：边矩c对受拉承载力的降低影响系数，按6.1.6[JGJ145-2013]采用：ψs,N=0.7+0.3×c/ccr,N≤16.1.6[JGJ145-2013]其中c为边矩，当为多个边矩时，取最小值；ψs,N=0.7+0.3×c/ccr,N≤1=0.7+0.3×200/150=1.1所以，ψs,N取1。ψre,N：表层混凝土因为密集配筋的剥离作用对受拉承载力的降低影响系数，按6.1.7[JGJ145-2013]采用，当锚固区钢筋间距s≥150mm或钢筋直径d≤10mm且s≥100mm时，取1.0；ψre,N=0.5+hef/200≤1=0.5+100/200=1所以，ψre,N取1。ψec,N：荷载偏心eN对受拉承载力的降低影响系数，按6.1.8[JGJ145-2013]采用；ψec,N=1/(1+2eN/scr,N)=1把上面所得到的各项代入，得：NRk,c=NRk,c0×Ac,N/Ac,N0×ψs,Nψre,Nψec,N=44271.887×150000/90000×1×1×1=73786.478NNRd,c=kNRk,c/γRc,N=0.8×73786.478/1.8=32793.99N≥Nsdg=15400N所以，群锚混凝土锥体受拉破坏承载力满足设计要求！混凝土劈裂破坏承载力计算当不满足6.2.14[JGJ145-2013]规定时，混凝土劈裂破坏承载力按下面公式计算：NRd,sp=kNRk,sp/γRsp6.2.15-1[JGJ145-2013]NRk,sp=ψh,spNRk,c6.2.15-2[JGJ145-2013]ψh,sp=(h/hmin)2/36.2.15-3[JGJ145-2013]上面公式中：NRd,sp：混凝土劈裂破坏受拉承载力设计值；NRk,sp：混凝土劈裂破坏受拉承载力标准值；k：地震作用下锚固承载力降低系数，按表4.3.9[JGJ145-2013]选取；NRk,c：混凝土锥体破坏时的受拉承载力标准值；γRsp：混凝土劈裂破坏受拉承载力分项系数，按表4.3.10[JGJ145-2013]取1.8；ψh,sp：构件厚度h对劈裂承载力的影响系数，不应大于(2hef/hmin)2/3；h：基材厚度厚度；hmin：锚栓安装过程中，不产生基材劈裂破坏的最小厚度，取为2hef，且不小于100mm；NRk,c=NRk,c0×Ac,N/Ac,N0×ψs,Nψre,Nψec,N6.1.3-2[JGJ145-2013]其中：NRk,c0=44271.887按6.2.14[JGJ145-2013]：ccr,sp=2hef=200按6.2.15[JGJ145-2013]：scr,sp=2ccr,sp=400当N/n-My1/Σyi2≥0时：Ac,N=(min(c1,ccr,sp)+s1+min(c1a,ccr,sp))×(min(c2,ccr,sp)+s2+0.5scr,sp)……情况一当N/n-My1/Σyi2<0时：若锚栓共有2排，则：Ac,N=(min(c1a,ccr,sp)+min(c1+s1,ccr,sp))×(min(c2,ccr,sp)+s2+0.5scr,sp)……情况二若锚栓共有3-4排(下面公式中参数n为锚栓层数)，则：Ac,N=(min(c1a,ccr,sp)+s1×(n-2)/(n-1)+min(ccr,sp,c1+s1/(n-1)))×(min(c2,ccr,sp)+s2+0.5scr,sp)……情况三其中：c1、c2：方向1及2的边矩；s1、s2：方向1及2的间距；c1≤ccr,spc1a≤ccr,spc2≤ccr,sps2≤scr,sp所以，本计算为：Ac,N=(min(c1a,ccr,sp)+min(c1+s1,ccr,sp))×(min(c2,ccr,sp)+s2+0.5scr,sp)=(200+200)×(200+200+0.5×400)=240000mm2Ac,N0=(scr,sp)2=(400)2=160000mm2ψs,N：边矩c对受拉承载力的降低影响系数，按6.1.6[JGJ145-2013]采用：ψs,N=0.7+0.3×c/ccr,sp≤16.1.6[JGJ145-2013]其中c为边矩，当为多个边矩时，取最小值；ψs,N=0.7+0.3×c/ccr,sp≤1=0.7+0.3×200/200=1≥1所以，ψs,N取1。ψec,N=1把上面所得到的各项代入，得：NRk,c=NRk,c0×Ac,N/Ac,N0×ψs,Nψre,Nψec,N=44271.887×240000/160000×1×1×1=66407.83Nψh,sp=(h/2hef)2/3=(400/2/100)2/3=1.587≥(2hef/hmin)2/3=1；所以，ψh,sp=1NRk,sp=ψh,spNRk,c=1×66407.83=66407.83NNRd,sp=kNRk,sp/γRsp=0.8×66407.83/1.8=29514.591N≥Nsdg=15400N当满足6.2.14[JGJ145-2013]规定的两个条件之一时，可不考虑荷载条件下的劈裂破坏，这两条分别是：(1)c≥1.5ccr,sp、h≥2hmin且hmin≥100mm，其中hmin=2hef；(2)采用适合于开裂混凝土的锚栓，按照开裂混凝土计算承载力，且考虑劈裂力时基材裂缝宽度不大于0.3mm；这里的第二条很难定性判断，因此我们仅考虑满足第一条的时候可不考虑计算劈裂，在本例中：c=200mm<1.5ccr,sp=1.5×200=300mm；h=400mm≥max(2hmin=4hef=4×100=400，200)mm；综上所述，本处需要进行混凝土劈裂破坏计算，混凝土劈裂破坏承载力满足设计要求！锚栓钢材受剪破坏承载力计算VRd,s=kVRk,s/γRs,V6.1.14-1[JGJ145-2013]其中：VRd,s：钢材破坏时的受剪承载力设计值；VRk,s：钢材破坏时的受剪承载力标准值，对群锚，锚栓钢材断后伸长率不大于8%时，应乘以0.8的降低系数；k：地震作用下锚固承载力降低系数，按表4.3.9[JGJ145-2013]选取；γRs,V：钢材破坏时的受剪承载力分项系数，按表4.3.10[JGJ145-2013]，取γRs,V=1.2；VRk,s=0.5Asfyk6.1.14-2[JGJ145-2013]=0.5×84.3×640=26976NVRd,s=kVRk,s/γRs,V=1×1×26976/1.2=22480N≥Vsdh=1687.5N所以，锚栓钢材受剪破坏承载力满足设计要求！混凝土楔形体受剪破坏承载力计算按6.2.18[JGJ145-2013]的规定，锚栓边距c≤10hef或c≤60d时，混凝土边缘破坏承载力设计值按如下公式计算：VRd,c=kVRk,c/γRc,V6.2.18-1[JGJ145-2013]VRk,c=VRk,c0×Ac,V/Ac,V0×ψs,Vψh,Vψα,Vψre,Vψec,V6.2.18-2[JGJ145-2013]在上面公式中：VRd,c：构件边缘混凝土破坏时的受剪承载力设计值；VRk,c：构件边缘混凝土破坏时的受剪承载力标准值；k：地震作用下锚固承载力降低系数，按表4.3.9[JGJ145-2013]选取；γRc,V：构件边缘混凝土破坏时的受剪承载力分项系数，按表4.3.10[JGJ145-2013]采用，取1.5；VRk,c0：混凝土理想楔形体破坏时的受剪承载力标准值，按6.2.19[JGJ145-2013]采用；Ac,V0：单锚受剪，混凝土理想楔形体破坏时在侧向的投影面积，按6.1.17[JGJ145-2013]采用；Ac,V：群锚受剪，混凝土理想楔形体破坏时在侧向的投影面积，按6.1.18[JGJ145-2013]采用；ψs,V：边距比c2/c1对受剪承载力的影响系数，按6.1.19[JGJ145-2013]采用；ψh,V：边厚比c1/h对受剪承载力的影响系数，按6.1.20[JGJ145-2013]采用；ψα,V：剪切角度对受剪承载力的影响系数，按6.1.21[JGJ145-2013]采用；ψec,V：偏心荷载对群锚受剪承载力的降低影响系数，按6.1.22[JGJ145-2013]采用；ψre,V：锚固区配筋对受剪承载力的影响系数，按6.1.23[JGJ145-2013]采用；下面依次对上面提到的各参数计算：c1=200mmc2=200mmψs,V=0.7+0.3×c2/1.5c1≤16.1.19[JGJ145-2013]=0.7+0.3×200/1.5/200=0.9<1取：ψs,V=0.9VRk,c0=1.35dαhefβ(fcu,k)0.5c11.5(对开裂混凝土)6.2.19-1[JGJ145-2013]α=0.1(hef/c1)0.56.2.19-3[JGJ145-2013]β=0.1(d/c1)0.26.2.19-4[JGJ145-2013]其中：α、β：系数；d：锚栓杆公称直径(mm)；fcu,k：混凝土立方体抗压强度标准值；hef：锚栓有效锚固深度(mm)；c1：锚栓与混凝土基材边缘的距离(mm)；α=0.1(hef/c1)0.5=0.1×(100/200)0.5=0.071β=0.1(d/c1)0.2=0.1×(12/200)0.2=0.057VRk,c0=1.35dαhefβ(fcu,k)0.5c11.5=1.35×120.071×1000.057×(40)0.5×2001.5=37456.796NAc,V0=4.5c126.1.17[JGJ145-2013]=4.5×2002=180000mm2因为：h≤1.5c1；s2≤3c1；c2≤1.5c1所以：Ac,V=(1.5c1+s2+c2)×h6.1.18-3[JGJ145-2013]=(1.5×200+200+200)×300=210000ψh,V=(1.5c1/h)1/2≥16.1.20[JGJ145-2013]