第五章竖向荷载作用下横向框架内力分析.docx
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第五章竖向荷载作用下横向框架内力分析.docx
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第五章竖向荷载作用下横向框架内力分析
第五章竖向荷载作用下横向框架内力分析.
第五章竖向荷载作用下横向框架内力分析.
内力计算竖向荷载作用下横向框架(KJ-3)第五章
由于结构基本对称,在竖向荷载作用下的框架侧移可略去不计。
其内力分析采用,弯矩分配法,在竖向荷载作用下梁端可以考虑塑性内力重分布,取弯矩调幅系数0.8楼面的竖向荷载分别按恒载及满跨活载计算。
5.1竖向恒载作用下内力计算5.1.1恒荷载计算:
,如图所示。
)计算单元:
计算单元宽度为(13.9m
0072
0003
0012
0072
00723900
直接传给框架的楼面荷载如图中水平阴影所示,计算单元范围内的楼面荷载则直接通过次梁以集中力的形式传给横向框架梁,作用在各结点上。
由于纵向框架梁与柱轴线不重合,因此在框架结点上还作用有集中力矩。
3
(2)荷载计算
F3P3P2F2F1P1
M2M1q1D
Cq1A
①均布荷载:
在上图中=4.125/m代表横梁自重。
q1②顶层:
A、D柱集中力=(2.256+2.187+4.1×1.35)×3.9=38.92KN
C柱集中力=(2.187+4.1×2.55)×3.9=49.30KN
F1处集中力=(1+4.1×2.7)×3.9=47.10KN
F2处集中力=(1+4.1×2.4)×3.9=42.28KN
F3处集中力=(1+4.1×2.85)×3.9=49.47KN
附加节点弯矩:
38.92×0.18=7mkN?
③1~4层:
A、D柱集中力=(3.8×3.15+2.187+3.9×1.35)×3.9+3.6×5.625=96.0KN
C柱集中力=(3.8×3.15+2.187+3.9×2.55)×3.9+3.6×6.75=118.30KN
F1处集中力=(1+3.9×2.7)×3.9=44.97KN
F2处集中力=(3.8×3.15+1+3.9×2.4)×3.9=87.09KN
F3处集中力=(1+3.9×2.85)×3.9=47.25KN
附加节点弯矩:
96.0×0.18=17.28mkN?
即,5层边柱附加弯矩:
38.92/2×0.42+96/2×0.18=16.81m?
kN4层边柱附加弯矩:
96/2×0.42+96/2×0.18=28.8mkN?
2-3层边柱附加弯矩:
96/2×1.0+96/2×0.18=56.64m?
kN1层边柱附加弯矩:
96×0.18=17.28m?
kN
4
活荷载计算5.1.22kN/m2.0活荷载布置:
办公室:
2kN/m2.5走廊、楼梯、卫生间:
2
kN/m0.5不上人屋面:
活载作用在次梁上,次梁作用在主梁上,故考虑框架时,活载按集中力布置。
活荷载作用下框架梁梁上的荷载分布如下:
P3P1P2F3F1F2CDAq1q1
屋面:
P1=0.5×3.9×1.35=2.63KN;F1=0.5×3.9×2.7=5.27KN
F2=0.5×3.9×2.4=4.68KNP2=0.5×3.9×2.55=4.97KN
F3=0.5×3.9×2.85=5.56KNP3=0.5×3.9×1.35=2.63KN
露面:
P1=2×3.9×1.35=10.53KN;F1=2×3.9×2.7=21.06KN
F2=2×3.9×1.35+2.5×3.9×1.05=20.77KNP2=2.5×3.9×1.05+2×3.9×1.5=21.94KN
F3=2×3.9×2.85=22.23KNP3=2×3.9×1.35=10.53KN
一层:
P2=2.5×1.95×2.55+2×1.95×1.5+2.5×1.95×1.05=23.4KN
F3=2.5×1.95×2.85+2×1.95×2.85=25.01KN
P3=2.5×1.95×1.35+2×1.95×1.35=11.85KN
5
2.634.975.562.635.294.6810.5320.7721.9422.2310.5321.0610.5321.9422.2321.0610.5320.7710.5321.9422.2310.5321.0620.7720.7711.8510.5321.0625.0123.4
49.4749.342.2838.9238.9247.1716.814.1254.12547.2587.09969644.97118.317.2828.84.1254.12544.9787.09969647.25118.317.2856.644.1254.12587.0944.97969647.25118.356.6417.284.1254.12587.0947.259696118.344.9717.2817.284.1254.125
活荷载满跨布置图(单)位:
kN
单(恒荷载布置图单位)位:
kN
4.974.682.635.29
2.635.564.97
21.9421.0620.7710.5310.5321.9422.2310.5322.2321.9421.9420.7710.5321.0610.5322.2321.9421.9421.0620.7710.5320.7723.410.5321.0611.8525.0123.4
6
75004.125270030002100270027002700300021.0620.7722.23
单(①工况-活载各层隔跨布置位:
)kN
单(②工况活载各层隔跨布置-)位:
kN
5.1.3恒载作用下固端弯矩计算
均布荷载:
4.125
5700
×4.125—×7.52/12=—4.125==-19.34MMm?
kN左左/12=5.72-11.17mkN?
2/124.125×5.74.125×7.52MM==19.34=m?
kN右右/12=11.17mkN?
集中力作用下:
①47.142.28210027002700
49.41
27003000
M=-70.212)/7.525.4×4.82+42.28××2.147.1=-(×2.7mkN?
左75.89M2×5.4)=××=(47.1×4.82.72+42.282.1mkN?
右M=-49.47×3×2.72/5.72=-33.3mkN?
左7
=37/5.72×32=49.47×2.7MmkN?
右②
47.2544.9787.09
=-91.832)/7.52+87.09×5.4×2.1×=-(44.97×2.74.82MmkN?
左125.73)=×2.1×5.42=(44.97×4.8×2.72+87.09Mm?
kN右M2=-31.81×2.72/5.7=-47.25×3m?
kN左=35.34M32/5.72=47.25×2.7×mkN?
右
故竖向恒载作用下,待分配弯矩为:
=70.21+19.34-16.81=72.74MmkN?
A5=91.83+19.34-28.8=82.37MmkN?
A4M=M=91.83+19.34-56.64=54.53mkN?
A2A3M=91.83+19.34-17.28=93.89mkN?
A1M=-(75.89+19.34)=-95.23m?
kN左c5M=(33.3+11.17)=44.47m?
kN右c5=-(125.73+19.34)=-145.07M=M=M=MmkN?
左C1C3左C2左C4左=M=(31.81+11.17)=42.98=MM=MmkN?
右C4右右C3C1C2右=-(35.34+11.7+7)=-54.04MmkN?
D5=-(35.34+11.7+17.28)=-64.32=M=MM=MmkN?
D1D2D4D3活荷载作用下固端弯矩计算5.1.4①8
5.274.68
210027002700
5.56
/7.52=-7.81+4.68×5.4×2.12)×=-(5.272.7×4.82MmkN?
左8.37)=+4.68×2.1×5.42=(5.27×4.8×2.72Mm?
kN右M2=-3.743×2.72/5.7=-5.56×mkN?
左=M32/5.724.16=5.56×2.7×mkN?
右②
21002700270027003000
M/7.52)2=-32.082+20.77×5.4×2.14.8=-(21.06×2.7×mkN?
左35.71M)=×+20.772.1×5.42=(21.06×4.8×2.72m?
kN右M=-14.962.72/5.72×=-22.23×3mkN?
左=16.63M/5.723=22.23×2.7×2mkN?
右③25.0127003000
M=-16.84/5.72.7223=-25.01××mkN?
左=18.71M/5.722××=25.012.73mkN?
右9
5.2弯矩分配
由于结构基本对称,在竖向荷载作用下的框架侧移可忽略不计,其内力分析采用弯矩分配法,在竖荷载作用下,楼面竖向荷载分别按恒载满布置,活载满跨布置,活载不利布置1,活载不利布置2计算。
恒荷载作用下KJ-2梁内力计算(弯矩分配)(单位:
kN?
m)
A轴
C轴
D轴
上柱
下柱
右梁
左梁
上柱
下柱
右梁
左梁
上柱
下柱
0.000
0.415
0.585
0.282
0.000
0.346
0.372
0.650
0.000
0.350
-72.740
95.230
-44.470
54.040
0.000
30.187
42.553
-16.288
-19.985-21.487
-35.126
-18.914
-8.144
21.276
-17.563
-10.743
3.380
4.764
-1.047
-1.285
-1.381
6.983
3.760
33.567
-33.567
99.171
-21.270-84.901
15.154
-15.154
0.293
0.293
0.413
0.210
0.257
0.257
0.276
0.481
0.260
0.260
-82.370
145.070
-42.980
64.320
0.000
24.17424.174
34.022
-21.433-26.228-26.228-28.202
-30.923-16.698-16.698
-10.717
17.011
-15.462
-14.101
3.145
3.145
4.426
-0.325
-0.398
-0.398
-0.428
6.779
3.661
3.661
27.31927.319
-54.638
140.323-26.626-26.626-87.071
26.075
-13.038-13.038
0.293
0.293
0.413
0.210
0.257
0.257
0.276
0.481
0.260
0.260
-54.530
145.070
-42.980
64.320
16.00316.003
22.523
-21.433-26.228-26.228-28.202
-30.923-16.698-16.698
-10.717
11.262
-15.462
-14.101
3.145
3.145
4.426
0.882
1.079
1.079
1.160
6.779
3.661
3.661
19.14819.148
-38.297
135.780-25.149-25.149-85.483
26.075
-13.038-13.038
0.293
0.293
0.413
0.210
0.257
0.257
0.276
0.481
0.260
0.260
-54.530
145.070
-42.980
64.320
16.00316.003
22.523
-21.433-26.228-26.228-28.202
-30.923-16.698-16.698
-10.717
11.262
-15.462
-14.101
3.145
3.145
4.426
0.882
1.079
1.079
1.160
6.779
3.661
3.661
26.075135.780-25.149-25.149-85.483-13.038-13.038-38.29719.14819.148
0.4810.4130.2930.2930.2760.2570.2100.2570.2600.260
64.320145.070-42.980-93.890
38.78127.55527.555-30.923-16.698-16.698-21.433-26.228-26.228-28.202
-14.101-15.462-10.71719.390
4.4263.1453.1456.7793.6613.661-1.085-1.009-1.009-0.825
-13.038-13.038
142.202-27.237-27.237-87.728
26.075-61.400
30.70030.700
活荷载满布作用下kN(单位:
梁内力计算(弯矩分配)KJ-2m?
)10
A轴
C轴
轴D
上柱
下柱
右梁
左梁
上柱
下柱
右梁
左梁
上柱
下柱
0.000
0.415
0.585
0.282
0.000
0.346
0.372
0.650
0.000
0.350
-7.810
8.370
-3.740
4.160
0.000
3.241
4.569
-1.306
-1.602
-1.722
-2.704
-1.456
-0.653
2.284
-1.352
-0.861
0.271
0.382
-0.263
-0.323
-0.347
0.560
0.301
3.512
-3.512
9.086
-1.925
-7.161
1.155
-1.155
0.293
0.293
0.413
0.210
0.257
0.257
0.276
0.481
0.260
0.260
-32.080
35.710
-14.960
16.630
0.000
9.415
9.415
13.250
-4.356
-5.331
-5.331
-5.732
-7.995
-4.317
-4.317
-2.178
6.625
-3.998
-2.866
0.639
0.639
0.900
-0.552
-0.675
-0.675
-0.726
1.378
0.744
0.744
10.05410.054
-20.108
37.427
-6.006
-6.006
-25.416
7.147
-3.573
-3.573
0.293
0.293
0.413
0.210
0.257
0.257
0.276
0.481
0.260
0.260
-32.080
35.710
-14.960
16.630
0.000
9.415
9.415
13.250
-4.356
-5.331
-5.331
-5.732
-7.995
-4.317
-4.317
-2.178
6.625
-3.998
-2.866
0.639
0.639
0.900
-0.552
-0.675
-0.675
-0.726
1.378
0.744
0.744
10.05410.054
-20.108
37.427
-6.006
-6.006
-25.416
7.147
-3.573
-3.573
0.293
0.293
0.413
0.210
0.257
0.257
0.276
0.481
0.260
0.260
-32.080
35.710
-14.960
16.630
0.000
9.415
9.415
13.250
-4.356
-5.331
-5.331
-5.732
-7.995
-4.317
-4.317
-2.178
6.625
-3.998
-2.866
0.639
0.639
0.900
-0.552
-0.675
-0.675
-0.726
1.378
0.744
0.744
-3.57310.05410.05437.4277.147-3.573-25.416-20.108-6.006-6.006
0.2600.4130.2930.2930.2760.2570.2100.2570.4810.260
18.710-16.84035.710-32.080
-4.857
-4.848-4.848-3.962-5.213-8.99513.2509.4159.415-4.857
-2.606-1.981-4.4986.625
0.6771.2530.677-0.588-0.547-0.447-0.5470.8180.5810.581
-4.181
-5.394-5.39437.927-27.1388.362-4.181
-19.992
9.9969.996
11
活荷载隔层隔跨----①作用下KJ-2梁内力计算(弯矩分配)(单位:
kN?
m)
A轴
C轴
D轴
上柱
下柱
右梁
左梁
上柱
下柱
右梁
左梁
上柱
下柱
0.000
0.415
0.585
0.282
0.000
0.346
0.372
0.650
0.000
0.350
-7.810
8.370
0.000
0.000
0.000
3.241
4.569
-2.360
-2.896
-3.114
0.000
0.000
-1.180
2.284
0.000
-1.557
0.490
0.690
-0.644
-0.790
-0.850
1.012
0.545
3.731
-3.731
7.650
-3.686
-3.963
-0.545
0.545
0.293
0.293
0.413
0.210
0.257
0.257
0.276
0.481
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