框架結(jié)構(gòu)——豎向荷載例題

1、2022-5-32豎向荷載下豎向荷載下分層法分層法 計算例題計算例題3.8 kN/m3.4 kN/m2.8 kN/m右圖括號中為梁、柱線剛度的相對值3600440075005600(4.21)(7.11)(7.63)(10.21)(4.21)(1.79)(4.84)(3.64)ABCDEFGHI(9.53)(12.77)2022-5-33注：內(nèi)力及位移正負(fù)號規(guī)定 本題中，桿端彎矩以順時針為正，剪力以使隔離體產(chǎn)生順時針轉(zhuǎn)動趨勢為正，軸力以受壓為正；桿端轉(zhuǎn)角以順時針為正，側(cè)移或相對側(cè)移以向右為正。豎向荷載下豎向荷載下分層法分層法 計算例題計算例題2022-5-34VMVNMN內(nèi)力符號規(guī)定位移符號規(guī)

2、定豎向荷載下豎向荷載下分層法分層法 計算例題計算例題2022-5-35F頂層計算簡圖(0.94.21)(7.11)(4.84)(3.64)ABCDEFGHI(9.53)(12.77)(0.94.21)(0.91.79)3.8 kN/m3.4 kN/m底層計算簡圖(7.63)(10.21)(0.94.21)(0.91.79)DEGHI2.8 kN/m(0.94.21)豎向荷載下豎向荷載下分層法分層法 計算例題計算例題2022-5-3青海大學(xué)6計算節(jié)點彎矩分配系數(shù)節(jié)點 G：GH7.630.6687.630.9 4.21(7.63)(10.21)(0.94.21)(0.91.79)DEGHI(0.9

3、4.21)FGD0.9 4.210.3327.630.9 4.21節(jié)點 H：HG7.630.3537.630.9 4.21 10.21HE0.9 4.210.1757.630.9 4.21 10.21HI10.210.4727.630.9 4.21 10.21節(jié)點 I：IH10.210.86410.21 0.9 1.79IF0.9 1.790.13610.21 0.9 1.792022-5-37計算節(jié)點彎矩分配系數(shù)節(jié)點 D：DG0.9 4.210.1860.9 4.21 9.537.11DE9.530.4660.9 4.21 9.537.11(0.94.21)(7.11)(4.84)(3.64

4、)ABCDEFGHI(9.53)(12.77)(0.94.21)(0.91.79)DA7.110.3480.9 4.21 9.537.112022-5-38計算節(jié)點彎矩分配系數(shù)節(jié)點 E：ED9.530.3089.530.9 4.21 12.774.84EH0.9 4.210.1239.530.9 4.21 12.774.84(0.94.21)(7.11)(4.84)(3.64)ABCDEFGHI(9.53)(12.77)(0.94.21)(0.91.79)EF12.770.4139.530.9 4.21 12.774.84EB4.840.1569.530.9 4.21 12.774.84202

5、2-5-39計算節(jié)點彎矩分配系數(shù)節(jié)點 F：FI0.9 1.790.0890.9 1.79 12.773.64FE12.770.7090.9 1.79 12.773.64(0.94.21)(7.11)(4.84)(3.64)ABCDEFGHI(9.53)(12.77)(0.94.21)(0.91.79)FC3.640.2020.9 1.79 12.773.642022-5-310計算桿件固端彎矩：頂層2FGH2.8 7.5kN m13.13kN m12M 2FJK12qlM qJKFJKMFKJMl2FKJ12qlM2FHG2.8 7.5kN m13.13kN m12M2FHI2.8 5.6kN

6、 m7.32 kN m12M 2FIH2.8 5.6kN m7.32 kN m12MDEGHIF2.8 kN/m750056002022-5-311計算桿件固端彎矩：底層2FDE3.8 7.5kN m17.81kN m12M 2FED3.8 7.5kN m17.81kN m12M2FEF3.4 5.6kN m8.89 kN m12M 2FFE3.4 5.6kN m8.89 kN m12M75005600ABCDEFGHI3.8 kN/m3.4 kN/mDEGHIF0.332 0.668下柱下柱右梁右梁0.864 0.1360.353 0.175 0.472左梁左梁下柱下柱右梁右梁下柱下柱左梁左

7、梁計算各節(jié)點彎矩：頂層計算各節(jié)點彎矩：頂層-13.1313.13-7.327.328.774.36-1.00-6.324.38-3.16-1.23-2.49-3.32-1.250.410.844.77-4.771.59-1.661.430.230.77-0.77-0.260.420.72-0.20-0.40-0.54-1.4315.05-13.62-0.48計算各節(jié)點彎矩：底層計算各節(jié)點彎矩：底層0.186 0.348 0.466下柱下柱右梁右梁上柱上柱0.308 0.123 0.156 0.413上柱上柱右梁右梁左梁左梁下柱下柱0.709 0.202 0.089下柱下柱上柱上柱左梁左梁-17

8、.8117.81-8.898.896.203.31-3.158.30-0.79-6.304.15-1.22-3.06-1.55-4.10-1.53-2.050.530.290.716.733.60-10.330.360.191.450.73-0.601.99-0.13-0.3418.92-0.17-0.46-1.35-1.72-15.85-0.863.37ABCDEFGHI-0.70-1.800.41-1.39-0.20-0.451.20ABCEFGHI6.733.374.7715.050.7710.3318.9215.851.9913.621.720.860.701.395.975.191.

9、831.880.970.86D彎矩圖qJKJKMKJM0llVrV梁端剪力的計算qJJKMxMxlVxV梁跨中彎矩的計算uNlNlVrV柱軸力的計算JKKJMJKMuVlV0h柱剪力的計算豎向荷載作用下豎向荷載作用下 彎矩二次分配法彎矩二次分配法 計算步驟 (1) 計算各節(jié)點彎矩分配系數(shù)； (2) 計算框架梁的固端彎矩；(3) 計算各節(jié)點不平衡彎矩，并對所有節(jié)點的不平衡彎矩同時進(jìn)行第一次分配（其間不進(jìn)行彎矩傳遞)； (4) 將所有桿端的分配彎矩同時向其遠(yuǎn)端傳遞（對于剛接框架，傳遞系數(shù)均取1/2）;(5) 將各節(jié)點因傳遞彎矩而產(chǎn)生的新的不平衡彎矩進(jìn)行第二次分配，使各節(jié)點處于平衡狀態(tài); (6) 將

10、各桿端的固端彎矩、分配彎矩和傳遞彎矩疊加，即得各桿端彎矩。 計算例題3.8 kN/m3.4 kN/m2.8 kN/m右圖括號中為梁、柱線剛度的相對值3600440075005600(4.21)(7.11)(7.63)(10.21)(4.21)(1.79)(4.84)(3.64)ABCDEFGHI(9.53)(12.77)豎向荷載作用下豎向荷載作用下 彎矩二次分配法彎矩二次分配法計算節(jié)點彎矩分配系數(shù)節(jié)點 G：GH7.630.6447.634.21GD4.210.3567.634.21節(jié)點 I：IH10.210.85110.21 1.79IF1.790.14910.21 1.79(4.21)(7.

11、11)(7.63)(10.21)(4.21)(1.79)(4.84)(3.64)ABCDEFGHI(9.53)(12.77)節(jié)點 H：(4.21)(7.11)(7.63)(10.21)(4.21)(1.79)(4.84)(3.64)ABCDEFGHI(9.53)(12.77)HG7.630.3467.634.21 10.21HE4.210.1917.634.21 10.21HI10.210.4637.634.21 10.21節(jié)點 D：(4.21)(7.11)(7.63)(10.21)(4.21)(1.79)(4.84)(3.64)ABCDEFGHI(9.53)(12.77)DG4.210.20

12、24.21 9.537.11DE9.530.4574.21 9.537.11DA7.110.3414.21 9.537.11節(jié)點 E：(4.21)(7.11)(7.63)(10.21)(4.21)(1.79)(4.84)(3.64)ABCDEFGHI(9.53)(12.77)ED9.530.3049.534.21 12.774.84EH4.210.1349.534.21 12.774.84EF12.770.4079.534.21 12.774.84EB4.840.1559.534.21 12.774.84節(jié)點 F：(4.21)(7.11)(7.63)(10.21)(4.21)(1.79)(4.

13、84)(3.64)ABCDEFGHI(9.53)(12.77)FI1.790.0981.79 12.773.64FE12.770.7021.79 12.773.64FC3.640.2001.79 12.773.64計算框架梁固端彎矩2FGH2.8 7.5kN m13.13kN m12M 2FHG2.8 7.5kN m13.13kN m12M2FHI2.8 5.6kN m7.32 kN m12M 2FIH2.8 5.6kN m7.32 kN m12M3.8 kN/m3.4 kN/m2.8 kN/m75005600ABCDEFGHI2FDE3.8 7.5kN m17.81kN m12M 2FED3

14、.8 7.5kN m17.81kN m12M2FEF3.4 5.6kN m8.89 kN m12M 2FFE3.4 5.6kN m8.89 kN m12M3.8 kN/m3.4 kN/m2.8 kN/m75005600ABCDEFGHI0.202 0.341 0.4570.304 0.134 0.155 0.4070.702 0.200 0.098上柱上柱0.346下柱下柱右梁右梁左梁左梁0.356 0.644下柱下柱右梁右梁0.851 0.149左梁左梁下柱下柱上柱上柱上柱上柱0.191 0.463梁端不平衡彎矩及其分配梁端不平衡彎矩及其分配-17.8117.81-8.898.89-13.13-7.3213.137.324.678.466.073.608.14-2.01-1.11-2.69-6.23-1.09-2.71-1.20-1.38-3.63-1.78-6.24-0.874.232.34-1.01-0.56-1.35-3.12-0.551.803.044.07-1.36-0.60-0.69-1.82-3.12-0.89-0.44-0.28-0.51-0.18-0.10-0.231.520.27-0.33-0.20-0.45-0.12-0.0