恒荷载内力计算

四恒荷载内力计算(一)恒荷载计算1. 屋面框架梁线荷载标准值20厚水泥混凝土找平0.02x20=0.46kN/m240120 厚(1%找坡)膨胀珍珠岩(0.08+0.16)?2x7=0.546kN/m2四层作法防水层0.36kN/m2100mm 厚钢筋混凝土楼板 0.1x25=2.56kN/m220mm厚石灰砂浆抹底0.02x17=0.34kN/m2屋面恒荷载4.08 kN/m2边框架梁自重0.3x0.8x25=6kN/m边框架梁粉刷 2x(0.8-0.1)x0.02x17=0.48kN/m中框架梁自重 0.3x0.6x25=4.5kN/m2中框架梁粉刷 2x(0.6-0.1)x0.03x17=0.34kN/m则作用于屋面框架梁上线荷载标准值为：g5AB1=6.48kN/mg5BC1=4.85kN/mg5AB2=4.08x3.9=15.91kN/mg5BC2=4.08x3=12.24kN/m2. 楼面框架梁线荷载标准值20mm厚水泥砂浆找平0.02x20=0.46kN/m2100mm厚钢筋混凝土楼板0.1x25=2.5kN/m220mm厚石灰砂浆抹底0.02x17=0.34kN/m2水磨石面层0.65 kN/m2楼面恒荷载3.89 kN/m2边框架梁自重及粉刷6.48kN/m中框架梁自重及粉刷4.85kN/m边跨填充墙自重0.24x3.6x18=15.55kN/m填充墙粉刷 2x0.02x2x17=2.45kN/m则作用于楼面框架梁上线荷载标准值为：gAB1=6.48+15.55+2.45=24.48kN/mgBC1=4.85kN/mgAB2=3.89x3.9=15.17kN/mgBC2=3.89x3=11.67kN/m3. 屋面框架节点集中荷载标准值纵向框架梁自重0.3x0.8x7.8x25=46.8kN纵向框架梁粉刷 2x(0.8-0.1)x0.02x7.8x17=3.71kN纵向框架梁传来的屋面恒荷载2x(3.9/2)2x4.08=31.02kN次梁自重及粉刷 0.6x0.2x25x7.2/2+2x0.02x(0.6-0.1)x7.2/2=10.87kN次梁传来的屋面恒荷载(1-2x0.272+0.273)x4.08x3.9x7.2/2=50.06kN1m 高女儿墙自重及粉刷 1x7.8x0.24x18+2x1x7.8x0.02x17=39kN则顶层边节点集中荷载为：G5A=181.46kN纵向框架梁自重及粉刷46.8+3.71=50.51kN纵向框架梁传来的屋面恒荷载 31.02+(1-2x0.192+0.193)x4.08x7.8x3/2=75.64kN次梁自重、粉刷及传来的屋面恒荷载10.87+50.06=60.93kN则顶层中节点集中荷载为：G5B=187.08kN4. 楼面框架节点集中荷载标准值纵向框架梁自重及粉刷51.51kN纵向框架梁传来的楼面恒荷载2x(3.9/2)2x3.89=29.44kN次梁自重及粉刷10.87kN次梁传来的楼面恒荷载(1-2x0.272+0.273)x3.89x3.9x7.2/2=47.73kN钢窗自重 2x2.3x1.8x0.4=3.31kN墙体自重(3.6x7.8-2x2.3x1.8)x0.24x18=85.54kN墙面粉刷 2x(3.6x7.8-2x2.3x1.8)x0.02x1.7=13.46kN框架柱自重 0.602x3.6x25=32.4kN柱面粉刷 4x0.6x0.02x17=0.82kN中间层边柱节点集中荷载为：GA=274.08kN纵向框架梁自重及粉刷50.51kN纵向框架梁传来的楼面恒荷载 29.44+(1-2x0.192+0.1923)x3.89x7.8x3/2=71.98kN次梁粉刷、自重及传来的楼面恒荷载10.87+47.73=58.6kN木门自重 2x1.0x2.6x0.2=1.04Kn墙体自重(3.6x7.8-2x1.0x2.6)x0.24x18=98.84kN墙面粉刷 2x0.02x()x17=15.56kN框架主自重及粉刷32.4+0.82=33.22kN中间层中柱节点集中荷载为：GB=329.75kN(二)恒荷载作用下内力计算1.计算简图计算简图2.荷载等效3.9 =0.272 x 7.2顶层边跨 g = (1 - 2x 0.272 + 0.273)x 15.91 + 6.48 = 20.38kN/m 5边顶层中跨 g；中=5x 12.24 + 4.85 = 12.5kN/m中间层边跨 g = (1 - 2 x 0.272 + 0.273)x 15.17 + 24.48 = 37.74kN/m 边中间层中跨 g中=8x 11.67 + 4.68 = 11.97kN/m荷载等效后的计算简图如下3.固端弯矩计算1顶层边跨 M = x 20.38 x 7.22 = 88.04kN - m5AB 121顶层中跨 M5bc = 3 X 12.5x 1.52 = 9.38kN -m1中间层边跨 MAB =仍 x 37.74x 7.22 = 163.04kN - m1中间层中跨 M5BC = 3x 11.97x 1.52 = 8.98kN-m4.分层计算弯矩（取半结构计算）1）顶层分配系数计算如下竺三= 0.5693.56 x 4 + 0.9 x 3.0 x 4气=1-% = 1 - 0.569 = 0.4313.56 x 43.56 x 4 + 0.9 x 3.0 x 4 + 3.6 x 23.6 x 2= 0.442=0.2233.56 x 4 + 0.9 x 3.0 x 4 + 3.6 x 21 - % - %3 = 1 - 0.442 - 0.223 = 0.3351-40.4311-20.5692-10.4422-50.3352-30.223-88.0488.04-9.3837.9550.09一25.05-22.92-45.84-34.74-23.139.8813.04一6.52-1.44-2.88-2.19-1.450.620.82一0.41-0.18-0.14-0.0948.45-48.4571.12-37.07-34.05内力计算过程如下（单位：kNm）M图见下页（单位：kNm）71.122）中间层分配系数计算如下4 x 0.9 X3.0 = 0.30136 4 x 0.9 x 3.0 x 2 + 4 x 3.56旦34 = 1 一旦31 一旦36 = 1 0.301 - 0.301 = 0.3984 x 0.9 x 3.0470.2514 x 0.9 x 3.0 x 2 + 4 x 3.56 + 2 x 3.6=0.3314 x 0.9 x 3.0 x 2 + 4 x 3.56 + 2 x 3.64 x 3.56旦1旦一旦一旦1 0.251 0.251 0.331 0.167 34424743内力计算过程如下（单位：kNm）3-60.3013-10.3013-40.3984-30.3314-20.2514-70.2514-50.167-163.04163.04-8.9849.0849.0864.88一32.44-30.87-61.73-46.81-46.81-31.159.299.2912.29一6.15-1.02-2.04-1.54-1.54-1.030.310.310.40一0.20-0.07-0.05-0.05-0.0358.6858.68-117.36137.99-48.4-48.4-41.19M图见下页（单位：kNm）19.56T1)(邛6.13117.36(3)58.68 -58.68y/48137.9941.19 项2 19.5616.13 7 3）底层分配系数计算如下4 x .9 x3.0= 0.3074 x 0.9 x 3.0 + 4 x 2.81 + 4 x 3.56=0.324 x 0.9 x 3.0 + 4 x 2.81 + 4 x 3.564 x 2.81旦34 = 1 -四罚一四 = 1 - 0.307 - 0.32 = 0.3734 x 0.9 x 3.04 x 0.9 x 3.0 + 4 x 2.81 + 4 x 3.56 + 2 x 3.64 x 2.81=0.2484 x 0.9 x 3.0 + 4 x 2.81 + 4 x 3.56 + 2 x 3.64 x 3.56=0.259=0.3284 x 0.9 x 3.0 + 4 x 2.81 + 4 x 3.56 + 2 x 3.6=1-旦42 -旦们一旦牝=1 0.248 - 0.259 - 0.328 = 0.165内力计算过程如下（单位：kNm）3-60.323-10.3073-40.3734-30.3284-20.2484-70.2594-50.165-163.04163.04-8.9852.1750.0560.82一30.41-30.26-60.51-45.75-47.78-30.439.689.2911.29一5.65-0.93-1,85-1.40-1.47-0.930.300.290.34一0.17-0.06-0.04-0.04-0.0362.1559.63121.78136.85-47.19-49.29-40.37M图如下（单位：kNm）19.88(1)(2)6.73121.7862.15 59.63136.85二 40.37(4) (5)47.19 |49.29I(6) 31.08Z24.65 (7)Z Z Z5.不平衡弯矩分配计算过程见如下（单位：kNm）,方框内为原不平衡弯矩左梁上柱下柱右梁7.1311.1319.56-11.135.40-10.73-16.133.60-5.219.4316.15-12.368.8119.56-14.21-8.98-16.134.7619.567.7810.68-16.13-8.037.7819.56-15.57-8.03-16.135.3819.567.6910.54-16.13-8.138.0119.88-15.70-7.73-15.735.3219.5613.565.29-16.13-12.13-6.26 -7.304.18 2.66不平衡弯矩调整之后即可得出恒荷载作用下框架弯矩图，见第29页（单位:kNm, 括号内为调幅后的弯矩值）6.跨中弯矩计算159.58 + 78.25M = x 20.28 x 7.22 一2= 62.94kN - m11M5BC = 8 x 4.85 x 3.02 + 12 x 12.24 x 3.02 一 30.45 = 15.81kN - m1131.57 +147.72 一M4AB =耳 x 37.74 x 7.22 一2= 244.56 -139.65 = 104.91kN - m11M4BC =月 x 4.68 x 3.02 + & x 11.67 x 3.02 一 36.43 = 14.02 一 36.43 = 22.41kN - mM3ABc” u, 132.92 +148.67244.56= 103.77kN - mM3bc = 14.02 - 35.81 = 21.79kN - mM2AB=244.56 - 133.06 +148.67 = 103.77kN - mM2BC=14.02 - 35.87 = -21.85kN - mM1AB=244.56 - 129.08 十1424 = 108.95kN - mM1bc = 14.02 - 37.71 = -23.69kN - m7.剪力计算 59 58 68 253 911V =5 + 6.48 x 7.2 + 15.91x (7.2 一 3-) x - = -2.59 + - x 130.18 = 62.5kN5ab 7.2222V5BA = 130.18 - 62.5 = 67.68kN1V = x (4.85 x 3.0 +12.24 x 1.5) = 16.46kN5BC 2 131 57 147 223 911V4AB =72+ 24.48 x 7.2 +15.17 x (7.2 一 2 ) x 2 = 一2.24 + 2 x 255.9=125.71kNV4BA=255.9 -125.71 = 130.19kNV4BC1 =V3BC = V2BC = V1BC = 2 x (4.68 x 3.0 +11.67 x 1.5) = 15.77kNV3AB132.92-148.67721+ x 255.9 = 125.76kN2V3BA = 255.9 -125.76 = 130.14kNV2AB133.06-148.52 1 + x 255.97.22=125.8kNV2ba = 255.9 -125.8 = 130.1kN59.5878.2(66.51)(50.64)59.58-67.49131.5764.08132.9766.46 -66.46-.,66.69 -133.0666.69-129.0855.89 -73.1931.08I62.9415.81 4(14.23)27.8(75.53)142.47 /.736.43 (30.97_53.61104.91：22.41 5 忠。.17)(125.56)78(125.89)(111.83)148.67(126.37)(112.98)5.81 (30.44”56.43103.7721.79 .5 5.43 (19.61)(124.52)103.77148.53：-56.53(126.25)(113.10)5.87 (30.4921.85 . 56.13 (19.67) 142.14；：7.71 (32.05(124.52)n592108.95(120.82)、一(109.72)24.6523.69 45.11(21.32)(130.74)M图（单位：kNm）V = 129.08-142.14 + 1 x 255.9 = i26.14kN1AB 7.22V1BA= 255.9 126.14 = 129.7608. 轴力计算N5A = 181.46 + 62.5 = 243.96kNN5A = 243.96 + 32.4 + 0.82 = 277.18kN 凡血=243.96 + 274.08 +125.71 = 643.75kNN4A = 643.75 + 33.22 = 676.97kNN3A = 643.75 + 274.08 +125.76 = 1043.59kNN3A = 1043.59 + 33.22 = 1076.81kNN2A =1043.59 + 274.08 +125.8 = 1443.47kNN2A = 1443.47 + 33.22 = 1476.69kNN/ = 1443.47 + 274.08 +126.14 = 1843.69kN“A = 184369+(0.652 x 5.3x 25+0.65 x 4 x 5.3x 0.02x17 = 184369+56.87 = 190056kNN = 187.08 + 67.68 +16.46 = 271.22kNN = 271.22 + 33.22 = 304.44kNN4b = 271.22 + 329.75 +130.19 +15.77 = 746.93kNN4Bb = 746.93 + 33.22 = 780.15kNN3b = 746.93 + 345.52 +130.14 = 1222.59kNN3Bb = 1222.59 + 33.22 = 1255.81kNN2B = 1222.59 + 345.52 +130.1 = 1698.21kNN = 1698.21 + 33.22 = 1731.43kNN1b = 1698.21 + 345.52 +129.76 = 2173.49kN%刖=2173.49 + 56.87 = 2230.36kN框架结构的剪力图和轴力图如下（单位：kN）V, M图（单位：kN）9. 弯矩调幅边跨：端部弯矩值乘以0.85，跨中弯矩值乘以1.2 中跨：端部弯矩值乘以0.85，跨中弯矩值乘以0.9 将调幅后的弯矩值表于框架弯矩图的（）内10. 梁端柱边剪力与弯矩V (kN)M (kNm)60.19-65.3713.55-32.5846.90-21.82118.02-122.5014.02-76.4288.81-26.76118.07-122.4514.02-77.5689.64-26.23118.11-122.4114.02-77.6789.53-26.28117.77-121.3913.84-71.4481.37-27.55