混凝土分層法彎矩分配法計(jì)算題（課堂PPT）

1、122.3 豎向荷載作用下框架內(nèi)力分析的近似方法豎向荷載作用下框架內(nèi)力分析的近似方法 q 【例題3.1】某三跨五層鋼筋混凝土框架，各層框架梁所受豎向荷載設(shè)計(jì)值（恒載）如圖3.8a所示，各桿件相對(duì)線剛度示于圖中。試用分層法計(jì)算各桿件的彎矩。36003600360036003800(i=0.448)(i=0.448)6000Ai=0.471i=0.498BCD6000i=0.471i=0.498i=1i=1i=1i=16000q=40.2kN/mi=0.498i=0.498i=0.498(i=0.448)(i=0.448)i=1i=1i=0.498(i=0.448)(i=0.448)i=0.498

2、i=0.498(i=0.448)i=1(i=0.448)i=1i=1i=1q=40.2kN/mq=40.2kN/mq=40.2kN/mq=32.8kN/m32.3豎向荷載作用下框架內(nèi)力分析的近似方法豎向荷載作用下框架內(nèi)力分析的近似方法 【解】求解步驟如下：（1）將原框架分為5個(gè)敞口框架，除底層外的各柱線剛度均乘以折減系數(shù)0.9，如圖3.8括號(hào)內(nèi)數(shù)值；（2）求節(jié)點(diǎn)分配系數(shù)及桿端固端彎矩；（3）用彎矩分配法計(jì)算每一敞口框架的桿端彎矩，利用對(duì)稱性取半跨，底層柱彎矩傳遞系數(shù)仍取l/2，其余各柱彎矩傳遞系數(shù)取l/3具體計(jì)算過(guò)程見(jiàn)圖3.9；（4）將分層法所得彎矩圖疊加，并將A、D軸線各節(jié)點(diǎn)不平衡彎矩作一次

3、分配，B、C軸線各節(jié)點(diǎn)不平衡彎矩相差不大，不再分配。框架最終彎矩圖示于圖3.10。4等截面直桿的勁度系數(shù)和傳遞系數(shù)5(b)(a)q=40.2kN/mq=40.2kN/mq=40.2kN/mq=40.2kN/mq=32.8kN/mi=1DCAB(i=0.498)(i=0.498)(i=0.498)(i=0.498)i=0.471i=0.498i=0.498i=0.498i=0.498(i=0.498)(i=0.498)(i=0.498)(i=0.498)i=0.471i=0.498i=0.498i=0.498i=0.498q=32.8kN/mq=40.2kN/mq=40.2kN/mq=40.2k

4、N/mq=40.2kN/mi=1i=1i=1i=1i=1i=1i=1i=1i=16000600060003800360036003600360036003600360036003800(i=0.448)(i=0.448)6000Ai=0.471i=0.498BCD6000i=0.471i=0.498i=1i=1i=1i=16000q=40.2kN/mi=0.498i=0.498i=0.498(i=0.448)(i=0.448)i=1i=1i=0.498(i=0.448)(i=0.448)i=0.498i=0.498(i=0.448)i=1(i=0.448)i=1i=1i=1q=40.2kN/m

5、q=40.2kN/mq=40.2kN/mq=32.8kN/m611.02.88.539.733.133.1+116.1107.9q=32.8kN/m頂層7+8.7-8.7-7.8-17.4-8.7+11.0+33.1+2.7+6.0-33.1-2.8+116.5-8.5-107.9-39.7+3.0-1.5-0.7-0.8+0.80.6910.3090+30.4+68.0-98.4下柱右梁上柱0.5130.23000.257+34.0+98.4-98.4-49.2左梁上柱下柱右梁頂層8頂層11.02.88.539.733.133.1107.9q=32.8kN/m+116.59+9.5-2.0+

6、10.3+31.0-58.9+27.9-2.2-6.0+140.4-6.6-127.9-53.0q=40.2kN/m四層10四層-2.10.1870.417+31.8+120.6左梁上柱0.209-120.6右梁下柱-60.3+10.1+30.2+0.1+30.2+0.1+1.6+1.6-60.3+0.2+3.5-0.4-6.7-5.9-6.2-0.3-2.1+140.1 -6.2+1.8-0.8-13.3-0.3-5.9-127.6-0.4-6.6-53.3+0.4+6.60.2360.236+28.5 +28.5下柱上柱+10.10.528-120.6+63.7右梁0.1871110.12

7、.110.130.260.330.22.16.2140.16.2127.653.3四層12+15.6+9.90.234上柱+28.2+1.5+29.8+0.1+31.2+0.1+1.60.245+29.5下柱-0.4-61.1+0.2-6.5+3.40.521+62.8-120.6右梁-2.1+6.5-60.3+0.4-53.4-3.2下柱-6.1-6.4-0.30.195-13.0+1.7-0.7+140.0-0.3-6.2-5.80.413左梁+31.4+120.60.185上柱-127.5-0.4-6.5-120.60.207右梁底層1341.38.38.33.215.661.131.2

8、127.96.439.98.3140.441.360.340.1127.6140.18.341.38.360.3(36.1)41.3127.6140.18.39.041.2(36.1)(40.1)107.933.1(72.0)60.343.2127.9140.410.6(40.1)116.5彎矩圖142.3豎向荷載作用下框架內(nèi)力分析的近似方法豎向荷載作用下框架內(nèi)力分析的近似方法 2.3.2 彎矩二次分配法 q 計(jì)算要點(diǎn)q 計(jì)算時(shí)，先對(duì)各節(jié)點(diǎn)不平衡彎矩進(jìn)行第一次分配，并向遠(yuǎn)端傳遞（傳遞系數(shù)均取1/2）；q 再將因傳遞彎矩而產(chǎn)生的新的不平衡彎矩進(jìn)行第二次分配，整個(gè)彎矩分配和傳遞過(guò)程即告結(jié)束，此即彎

9、矩二次分配法。q 計(jì)算例題【例題3 2】某三跨五層鋼筋混凝土框架，各層框架梁所受豎向荷載設(shè)計(jì)值（恒載）如圖3.11所示，各桿件相對(duì)剛度示于圖中，試用二次彎矩分配法計(jì)算各桿件的彎矩。153600i=0.498i=0.4983800i=0.471i=0.471600060002700ACBDq=40.2kN/mq=40.2kN/mi=1.24i=1i=0.498i=0.498i=1i=1.24i=0.498i=0.498i=1i=1.2436003600q=32.8kN/mq=40.2kN/mq=40.2kN/mi=1i=1.24i=0.498i=0.498i=1i=1.24360016解：計(jì)算步

10、驟如下 q 因框架結(jié)構(gòu)和作用荷載均對(duì)稱，僅取半跨進(jìn)行分析，這時(shí)中跨梁的相對(duì)線剛度應(yīng)乘以修正系數(shù)2，根據(jù)各桿件的線剛度計(jì)算各節(jié)點(diǎn)桿端彎矩分配系數(shù)。q 計(jì)算豎向荷載作用下各跨梁的固端彎矩，并將各節(jié)點(diǎn)不平衡彎矩進(jìn)行第一次分配。 q 將所有桿端的分配彎矩向遠(yuǎn)端傳遞，傳遞系數(shù)均取1/2。 q 將各節(jié)點(diǎn)因傳遞彎矩而產(chǎn)生的新的不平衡彎矩進(jìn)行第二次分配，使各節(jié)點(diǎn)處于平衡狀態(tài)。q 將各桿端的固端彎矩，分配彎矩和傳遞彎矩相加，即得各桿端彎矩。17上柱 下柱 右梁0.6680.332右梁下柱右梁下柱右梁下柱右梁下柱上柱上柱上柱上柱上柱右梁下柱下柱 右梁上柱下柱 右梁上柱下柱 右梁上柱下柱 右梁上柱左梁左梁左梁左梁左

11、梁0.235 0.2930.4720.250 0.5000.3830.2370.1900.239 0.5080.3860.2400.1820.1900.2500.2530.192-98.465.7-18.62.3-49.049.01.215.132.7-85.3-6.6-18.460.3-120.630.115.1-3.341.9-84.7-6.0-18.460.3-120.630.115.1-3.042.2-76.11.8-18.661.3-120.628.80.829.643.2-3.316.430.130.115.1-3.042.230.515.10.946.5-29.7-2.2-9.2

12、-18.3-29.7-2.2-9.2-18.3-24.4-22.8-2.8-50.0-33.2-5.6-9.2-18.4-19.9-23.0-6.9-49.8-31.8-4.1-9.2-18.5-21.4-3.9-17.5-24.4-23.1-5.2-52.783.0-11.232.9-37.198.4120.6-36.830.2-4.5109.5120.6-37.130.7-8.3105.90.2500.5000.2500.2500.5000.25042.2-3.015.130.142.2-3.015.130.1-120.660.3-18.4-6.0-84.7109.5-4.530.2-36

13、.8-50.0-2.8-22.8-18.3-9.2-2.2-29.7-18.3-9.2-2.2-29.7-24.4120.6109.5-4.530.2-36.8-50.0-2.8-22.8-18.3-9.2-2.2-29.7-18.3-9.2-2.2-29.7-24.4120.60.190 0.190 0.2370.3830.190 0.190 0.2370.38314.8-10.71829.729.729.729.752.752.7105.9105.950.050.0109.5109.550.050.0109.5109.5109.5109.550.050.029.729.731.831.810.710.776.184.784.783.514.846.542.242.243.221.429.829.829.733.233.221.429.829.829.714.846.542.242.276.