分層法題目解答

1、分層法例：某教學樓為四層現(xiàn)澆鋼筋混凝土框架結(jié)構(gòu)。梁的截面尺寸：250mmX600mm,混凝土采用C20;柱的截面尺寸：450mmx450mm,混凝土采用C30。石gJ-mEW"試按分層法計算鋼筋混凝土框架的彎矩，并繪出彎矩圖。屋面和樓面荷載標準值見下表?？蚣芪菝婧蜆敲婧奢d荷載性質(zhì)荷載泰別屋面荷載(kW)樓面荷載仕“向)教室走道需栽使用荷救0.702.002.50雪荷載0.30-地面材料重2.93LJ01.JO恒載疊合層重1.001001.00預制板重12.602.602®解：（1）計算梁、柱線剛度1）梁的線剛度邊跨梁：kb=EbIb/l=25.5X106x（1/12）x0.

2、25X0.63x1.5/5.7=24.16X103kNm（框架梁截面慣性矩增大系數(shù)均采用1.5）中跨梁：kb=EbIb/l=25,5X106x（1/12）x0.25X0.63x2.0/3.00=45.90X103kNm2）柱的線剛度底層柱：kc=EcIc/h=30X106X(1/12)X0.45X0.453/4.55=22.53Xl03kNm其他層柱：kc=EcIc/h=30X106X(1/12)X0.45X0.453/3.60=28.48X103kNmxlC?kNrn/,2AJ6IO125.6345so25,63T飛24J6925.639。25.633z1勿(2)計算分配系數(shù)那a25.6J4

3、5.9025.63"加后72253j6bd玷SO22.53除底層外，各層柱的線剛度應乘以0.9。(3)荷載分析1)屋面梁上線荷載設計值恒載：1.2(2.93+1.00+2.60)X4.5+0.25X0.60X25Xl.2=40.67kN/m活載：1.4X0.7X4.5=4.41kN/m(系數(shù)1.2為考慮梁挑檐及抹灰重的系數(shù))q=45.08kN/m2)樓面梁上線荷載設計值教室恒載：1.2(1.10+1.00+2.60)X4.5+0.25X0.60X25xi.2=30.78kN/m活載:1.4X2.00X4.5X0,9=11.34kN/m（系數(shù)0.9為屋面及樓面活荷載折減系數(shù)）q2=42

4、.12kN/m走道恒載：30.78kN/m活載：1.4X2.50X4,5X0.9=14.18kN/mq3=44.96kN/m。產(chǎn)42,12kN/m仃=時96kN/mq*（J1=45.08kN/m=42.L2kN/m43-44.1川田196kN/m也Ihhhmuh5242.12kN/m用皿196kN/m詼THTTEllJ5.70m7空3m7刷5170m1-1L（4）梁端固端彎矩Mf頂層邊跨梁（教室）：MF=q1l12/12=45.08X5.72/12=122.05kNm中跨梁（走道）：MF=q1l22/3=45.08X（3/2）2/3=33.81kNm其他層邊跨梁（教室）：MF=q2l12/12

5、=41.12X5.72/12=114.04kN.m中跨梁（走道）：MF=q3l22/3=44.96X（3/2）2/3=33.72kNm（5）彎矩分配與傳遞（用彎矩分配法計算）1）屋面層列表計算，如表1表1用彎矩分配法計算框架梁、柱端彎矩（屋面層）（kNm）下柱右梁左梁下柱右梁左梁下柱右梁左梁下柱10.5150.4850.2520.2680.4800.4800.2680.2520.4850.5152ABCD3-122.05+122.05-33.80+33.80-122.05+122.054+62.86+59.19一+29.60-29.60一-59.19-62.865-14.58一-29.70-3

6、1.58-56.57一-28.296+7.65+7.20一+3.60+35.07一+70.15+39.17+36.83一+18.417-4.87一-9.74-10.36-18.56一-9.28-4.47一-8.93-9.488+2.51+2.36+115.81-41.94-73.86+6.60+3.69+3.47+72.34-72.349+73.02-73.02+72.98+42.86-115.82梁調(diào)幅X0.8-58.42+92.65-59.09+58.38-92.66+57.87對上柱傳遞X1/3+24.34-13.98+14.27-24.112）中層列表計算，如表2表2用彎矩分配法計算框

7、架梁、柱端彎矩（34層）（kNm）上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱10.3400.3400.3200.1190.2110.2110.3790.3790.2110.2110.1990.3200.3400.3402ABCD3-114.04+114.04-33.72+33.72-114.04+114.044+38.77+38.77+36.49一+18.25-18.25一-36.29-38.77-38.775-9.81一-19.62-20.80-20.80-37.36一-18.686+3.34+3.34+3.14一+1.57+22.22一+44.44+24.74+24.74+2

8、3.33一+11.677+42.11+42.11-84.22-4.73-5.02-5.02-9.02一-4.51-1.87一-3.73-3.97-3.978+109.51-25.82-25.82-57.88+2.42+1.35+1.35+1.27+85.69-42.74-42.749+57.39+26.09+26.09-109.56梁調(diào)幅X0.8-67.38+87.61-46.30+45.91-87.65+68.55對上柱傳遞X1/3+14.04-8.61+8.61-14.04對下柱傳遞X1/3+14.04-8.61+8.61-14.043）首層列表計算，如表3表3用彎矩分配法計算框架梁、柱端

9、彎矩（首層）（kNm）上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱右梁左梁上柱下柱10.3540.3120.3340.2040.2170.1910.3880.3880.2170.1910.2040.3340.3540.3122ABCD3-114.04+114.04-33.72+33.72-114.04+114.044+40.37+35.58+38.09一+19.04-19.04一-38.09-40.37-35.585-10.13一-20.27-21.56-18.98-38.55一-19.276+3.59+3.16+3.38一+1.69+23.01一+46.03+25.74+22.66+24.20一+12.107+43.96+38.74-82.70-5.04-5.36-4.72-9.58一-4.79-2.02一-4.04-4.28-3.778+109.46-26.92-23.70-58.84+2.64+1.48+1.30+1.39+84.01-44.65-39.359+58.33+27.22+23.96-109.51梁調(diào)幅X0.8-66.16+87.57-47.07+46.66-87.61+67.21對上柱傳遞X1/3+14.65-8.97