2024年2月9日发(作者：)

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0.02×20=0.46kN/m2

40～120厚（1%找坡）膨胀珍珠岩(0.08+0.16)÷2×7=0.546kN/m2

四层作法防水层 0.36kN/m2

100mm厚钢筋混凝土楼板 0.1×25=2.56kN/m2

20mm厚石灰砂浆抹底 0.02×17=0.34kN/m2

屋面恒荷载 4.08 kN/m2

边框架梁自重 0.3×0.8×25=6kN/m

边框架梁粉刷 2×(0.8-0.1)×0.02×17=0.48kN/m

中框架梁自重 0.3×0.6×25=4.5kN/m2

边框架梁粉刷 2×(0.6-0.1)×0.03×17=0.34kN/m

则作用于屋面框架梁上线荷载标准值为：

g5AB1=6.48kN/m

g5BC1=4.85kN/m

g5AB2=4.08×3.9=15.91kN/m

g5BC2=4.08×3=12.24kN/m

2．楼面框架梁线荷载标准值

20mm厚水泥砂浆找平 0.02×20=0.46kN/m2

100mm厚钢筋混凝土楼板 0.1×25=2.5kN/m2

20mm厚石灰砂浆抹底 0.02×17=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 0.24×3.6×18=15.55kN/m

填充墙粉刷 2×0.02×2×17=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/m

gBC1=4.85kN/m

gAB2=3.89×3.9=15.17kN/m

gBC2=3.89×3=11.67kN/m

3．屋面框架节点集中荷载标准值

纵向框架梁自重 0.3×0.8×7.8×25=46.8kN

纵向框架梁粉刷 2×(0.8-0.1)×0.02×7.8×17=3.71kN

纵向框架梁传来的屋面恒荷载 2×(3.9/2)2×4.08=31.02kN

次梁自重及粉刷 0.6×0.2×25×7.2/2+2×0.02×(0.6-0.1)×7.2/2=10.87kN

次梁传来的屋面恒荷载 (1-2×0.272+0.273)×4.08×3.9×7.2/2=50.06kN

1m高女儿墙自重及粉刷 1×7.8×0.24×18+2×1×7.8×0.02×17=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+(1-2×0.192+0.193)×4.08×7.8×3/2=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=187.08kN

4．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 2×(3.9/2)2×3.89=29.44kN

次梁自重及粉刷 10.87kN

次梁传来的楼面恒荷载 (1-2×0.272+0.273)×3.89×3.9×7.2/2=47.73kN

钢窗自重 2×2.3×1.8×0.4=3.31kN

墙体自重 (3.6×7.8-2×2.3×1.8)×0.24×18=85.54kN

墙面粉刷 2×(3.6×7.8-2×2.3×1.8)×0.02×1.7=13.46kN

框架柱自重 0.602×3.6×25=32.4kN

柱面粉刷4×0.6×0.02×17=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+(1-2×0.192+0.1923)×3.89×7.8×3/2=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 2×1.0×2.6×0.2=1.04Kn

墙体自重 (3.6×7.8-2×1.0×2.6)×0.24×18=98.84kN

墙面粉刷 2×0.02×()×17=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

G5Agg5AB2G5Bg5BC2G5CG5D5AB1gAB25BC1GAgGBggGCGDBC2gAB1BC1计算简图

2．荷载等效

13.90.27

27.2顶层边跨

g'5边(120.2720.273)15.916.4820.38kN/m

5顶层中跨

g'5中12.244.8512.5kN/m

8中间层边跨

g'边(120.2720.273)15.1724.4837.74kN/m

5中间层中跨

g'中11.674.6811.97kN/m

8荷载等效后的计算简图如下

g'5边g'5中g'边g'中

3．固端弯矩计算

120.387.2288.04kNm

121顶层中跨

M5BC12.51.529.38kNm

31中间层边跨

MAB37.747.22163.04kNm

121中间层中跨

M5BC11.971.528.98kNm

3

顶层边跨

M5AB4．分层计算弯矩（取半结构计算）

1）顶层

分配系数计算如下

3.564120.569

3.5640.93.041411210.5690.431

213.5640.442

3.5640.93.043.623.62230.223

3.5640.93.043.62251212310.4420.2230.335

内力计算过程如下（单位：kN∙m）

1-4

0.431

37.95

9.88

0.62

48.45

M图见下页（单位：kN∙m）

1-2

0.569

-88.04

50.09

-22.92

13.04

-1.44

0.82

-48.45

→

←

→

←

→

2-1

0.442

88.04

25.05

-45.84

6.52

-2.88

0.41

-0.18

71.12

2-5

0.335

-34.74

-2.19

-0.14

-37.07

2-3

0.223

-9.38

-23.13

-1.45

-0.09

-34.05

48.4548.45(1)71.1234.05(3)(2)37.07(4)16.152）中间层

分配系数计算如下

40.93.031360.301

40.93.0243.5612.36(5)341313610.3010.3010.398

40.93.00.251

40.93.0243.5623.643.56430.331

40.93.0243.5623.6424734142474310.2510.2510.3310.167

内力计算过程如下（单位：kN∙m）

3-6

0.301

49.08

9.29

0.31

58.68

M图见下页（单位：kN∙m）

3-1

0.301

49.08

9.29

0.31

58.68

3-4

0.398

-163.04

64.88

-30.87

12.29

-1.02

0.40

-117.36

→

←

→

←

→

4-3

0.331

163.04

32.44

-61.73

6.15

-2.04

0.20

-0.07

137.99

4-2

0.251

-46.81

-1.54

-0.05

-48.4

4-7

0.251

-46.81

-1.54

-0.05

-48.4

4-5

0.167

-8.98

-31.15

-1.03

-0.03

-41.19

19.56(1)(2)16.13137.9941.19(4)(5)48.448.4117.36(3)58.6858.68(6)19.5616.13(7)

3）底层

分配系数计算如下

40.93.0310.307

40.93.042.8143.5642.81360.32

40.93.042.8143.56341313610.3070.320.373

40.93.00.248

40.93.042.8143.5623.642.81470.259

40.93.042.8143.5623.643.56430.328

40.93.042.8143.5623.64234142474310.2480.2590.3280.165

内力计算过程如下（单位：kN∙m）

3-6

0.32

52.17

9.68

0.30

62.15

3-1

0.307

50.05

9.29

0.29

59.63

3-4

0.373

-163.04

60.82

-30.26

11.29

-0.93

0.34

121.78

→

←

→

←

→

4-3

0.328

163.04

30.41

-60.51

5.65

-1,85

0.17

-0.06

136.85

4-2

0.248

-45.75

-1.40

-0.04

-47.19

4-7

0.259

-47.78

-1.47

-0.04

-49.29

4-5

0.165

-8.98

-30.43

-0.93

-0.03

-40.37

M图如下（单位：kN∙m）

19.88(1)(2)15.73136.8540.37(4)(5)47.1949.29121.78(3)62.1559.63(6)31.0824.65(7)5．不平衡弯矩分配

计算过程见如下（单位：kN∙m），方框内为原不平衡弯矩

左梁 上柱

下柱 右梁

16.15

19.56

19.56

19.56

5.40

7.78

7.69

7.13

11.13 19.56 -11.13 -10.73 -16.13 3.60

9.43 -12.36 -5.21

8.81 19.56 -14.21 -8.98 -16.13 4.76

10.68 -16.13 -8.03

7.78 19.56 -15.57 -8.03 -16.13 5.38

10.54 -16.13 -8.13

4.18 2.66

8.01 19.88 -15.70 -7.73 -15.73 5.32

13.56 5.29 -16.13 -12.13

-6.26 -7.30

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：kN∙m，括号内为调幅后的弯矩值）

6．跨中弯矩计算

159.5878.25M5AB20.287.2262.94kNm

8211M5BC4.853.0212.243.0230.4515.81kNm

8121131.57147.72M4AB37.747.22244.56-139.65104.91kNm

8211M4BC4.683.0211.673.0236.4314.0236.4322.41kNm

812132.92148.67M3AB244.56103.77kNm

2M3BC14.0235.8121.79kNm

M2AB244.56133.06148.67103.77kNm

2M2BC14.0235.8721.85kNm

M1AB244.56129.08142.14108.95kNm

2M1BC14.0237.7123.69kNm

7．剪力计算

59.5868.253.911V5AB[6.487.215.91(7.2)]2.59130.1862.5kN

7.2222

V5BA130.18-62.567.68kN1(4.853.012.241.5)16.46kN

2131.57147.223.911V4AB[24.487.215.17(7.2)]2.24255.97.2222125.71kN

V5BC

V4BA255.9125.71130.19kNV4BCV3BCV2BCV1BCV3AB1(4.683.011.671.5)15.77kN

2132.92-148.671255.9125.76kN

7.22V3BA255.9125.76130.14kN

V2AB133.06-148.521255.9125.8kN

7.22V2BA255.9125.8130.1kN

59.5862.9459.58(66.51)78.2530.45(25.88)15.8147.8(14.23)142.47(125.56)(50.64)(75.53)(111.83)131.5767.4964.08104.9136.43(30.97)53.6122.4157.38(20.17)148.67(126.37)(125.89)(112.98)132.9766.4666.46103.7735.81(30.44)56.4321.7956.43(19.61)(124.52)(113.10)133.0666.6966.69(126.25)148.5335.87(30.49)21.8556.1356.53103.77(19.67)142.14(120.82)(124.52)(109.72)129.0855.8973.19108.9537.71(32.05)59.3223.6945.11(21.32)(130.74)31.0824.65M图（单位：kN∙m）

V1AB129.08-142.141255.9126.14kN

7.22

V1BA255.9126.14129.76kN

8．轴力计算

N5At181.4662.5243.96kN

N5Ab243.9632.40.82277.18kN

N4At243.96274.08125.71643.75kN

N4Ab643.7533.22676.97kN

N3At643.75274.08125.761043.59kN

N3Ab1043.5933.221076.81kN

N2At1043.59274.08125.81443.47kNN2Ab1443.4733.221476.69kN

N1At1443.47274.08126.141843.69kNN1Ab1843.69(0.6525.3250.6545.30.02171843.6956.871900.56kN

N5Bt187.0867.6816.46271.22kNN5Bb271.2233.22304.44kN

N4Bt271.22329.75130.1915.77746.93kN

N4Bb746.9333.22780.15kN

N3Bt746.93345.52130.141222.59kNN3Bb1222.5933.221255.81kN

N2Bt1222.59345.52130.11698.21kN

N2Bb1698.2133.221731.43kN

N1Bt1698.21345.52129.762173.49kN

N1Bb2173.4956.872230.36kN

框架结构的剪力图和轴力图如下（单位：kN）

62.5067.68125.7116.46271.22243.9615.77130.19125.7615.77130.14125.8015.77130.10126.1415.77129.76304.44746.93227.18643.75780.151222.59676.971043.591255.811698.211076.811443.471731.432173.491476.691843.692230.36V N

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

1900.56

10．梁端柱边剪力与弯矩

V (kN)

M (kN∙m)

60.19

-32.58

118.02

-76.42

118.07

-77.56

118.11

-77.67

117.77

-71.44

-65.37 13.55

46.90 -21.82

-122.50 14.02

88.81 -26.76

-122.45 14.02

89.64 -26.23

-122.41 14.02

89.53 -26.28

-121.39 13.84

81.37 -27.55