中南大学2010级矩阵位移法正式报告

1、矩阵位移法正式报告班 级土木10班姓 名学 号指导老师殷勇日 期2012-10-261作图示刚架的、图，已知各杆截面均为矩形，柱截面宽0.4m,高0.4m, 大跨梁截面宽0.35m,高0.85m，小跨梁截面宽0.35m,高0.6m，各杆E=3.0×104 MPa。10分解:对节点和单元进行编号,选定整体坐标系和局部坐标系。输入数据运行程序得到输出文件如下：* * * 10级 第一题* * * The Input Data The General Information E NM NJ NS NLC 3.000E+07 16 13 9 1 The Information of Memb

2、ersmember start end A I 1 1 4 1.600000E-01 2.133330E-03 2 4 5 2.975000E-01 1.791200E-02 3 2 5 1.600000E-01 2.133000E-03 4 5 6 2.100000E-01 6.300000E-03 5 3 6 1.600000E-01 2.133330E-03 6 4 7 1.600000E-01 2.133330E-03 7 7 8 2.975000E-01 1.791200E-02 8 5 8 1.600000E-01 2.133330E-03 9 8 9 2.100000E-01 6

3、.300000E-03 10 6 9 1.600000E-01 2.133330E-03 11 7 10 1.600000E-01 2.133330E-03 12 10 11 2.975000E-01 1.791200E-02 13 11 12 2.975000E-01 1.791200E-02 14 8 12 1.600000E-01 2.133330E-03 15 12 13 2.100000E-01 6.300000E-03 16 9 13 1.600000E-01 2.133330E-03 The Joint Coordinatesjoint X Y 1 .000000 .000000

4、 2 7.600000 .000000 3 11.400000 .000000 4 .000000 4.500000 5 7.600000 4.500000 6 11.400000 4.500000 7 .000000 7.700000 8 7.600000 7.700000 9 11.400000 7.700000 10 .000000 10.900000 11 3.800000 10.900000 12 7.600000 10.900000 13 11.400000 10.900000 The Information of Supports IS VS 11 .000000 12 .000

5、000 13 .000000 21 .000000 22 .000000 23 .000000 31 .000000 32 .000000 33 .000000 ( NA= 348 ) ( NW= 1149 ) Loading Case 1 The Loadings at Joints NLJ= 4 ILJ PX PY PM 7 100.0000 .0000 .00000 10 100.0000 .0000 .00000 11 .0000 .0000 -15.00000 12 .0000 .0000 -15.00000 The Loadings at Members NLM= 7 ILM IT

6、L PV DST 1 3 20.0000 4.500000 2 4 -36.0000 7.600000 2 2 -26.0000 3.800000 4 4 -36.0000 3.800000 4 2 -26.0000 2.700000 7 4 -36.0000 7.600000 9 4 -36.0000 3.800000 The Results of Calculation The Joint Displacementsjoint u v phi 1 7.105574E-21 -1.638200E-20 -1.781344E-20 2 9.610094E-21 -4.106568E-20 -2

7、.156767E-20 3 7.784332E-21 -2.983231E-20 -1.882232E-20 4 1.131958E-02 -1.535812E-04 -1.283838E-03 5 1.131729E-02 -3.849908E-04 3.870654E-05 6 1.130494E-02 -2.796780E-04 -9.193907E-04 7 1.608429E-02 -2.069972E-04 -9.277576E-04 8 1.601002E-02 -5.147194E-04 6.589307E-05 9 1.599418E-02 -3.701334E-04 -4.

8、819466E-04 10 1.845188E-02 -1.982725E-04 -1.263062E-04 11 1.841610E-02 -3.424305E-04 -8.179513E-06 12 1.838032E-02 -5.043550E-04 -1.356570E-04 13 1.836156E-02 -3.892225E-04 -1.683584E-04 The Terminal Forcesmember N(st) Q(st) M(st) N(en) Q(en) M(en) 1 163.820 116.056 211.884 -163.820 -26.056 107.866

9、2 2.682 83.696 -146.726 -2.682 215.904 -355.664 3 410.657 96.101 215.677 -410.657 -96.101 216.778 4 20.489 .160 -42.823 -20.489 162.640 -245.089 5 298.323 77.843 188.223 -298.323 -77.843 162.072 6 80.124 28.738 38.859 -80.124 -28.738 53.103 7 87.225 93.211 -62.614 -87.225 180.389 -268.662 8 194.593

10、113.908 181.709 -194.593 -113.908 182.797 9 26.255 29.750 -2.866 -26.255 107.050 -144.002 10 135.683 57.354 83.017 -135.683 -57.354 100.515 11 -13.087 15.963 9.512 13.087 -15.963 41.570 12 84.037 -13.087 -41.570 -84.037 13.087 -8.161 13 84.037 -13.087 -6.839 -84.037 13.087 -42.892 14 -15.547 52.938

11、88.732 15.547 -52.938 80.670 15 31.099 -28.634 -52.777 -31.099 28.634 -56.030 16 28.634 31.099 43.487 -28.634 -31.099 56.030 ( NA= 348 ) ( NW= 1177 )根据上述输出结果，可做出内力图如下u 轴力图：u 剪力图：u 弯矩图：2、计算图示桁架各杆的轴力。已知A=2400mm2,E=2.0×105 MPa。5分解：对节点和单元进行编号,选定整体坐标系和局部坐标系。输入数据运行程序得到输出文件如下：* * * 10级 第二题 * * * The I

12、nput Data The General Information E NM NJ NS NLC 2.000E+08 14 9 4 1 The Information of Membersmember start end A I 1 1 2 2.400000E-03 1.000000E-09 2 2 3 2.400000E-03 1.000000E-09 3 3 4 2.400000E-03 1.000000E-09 4 4 5 2.400000E-03 1.000000E-09 5 8 1 2.400000E-03 1.000000E-09 6 6 1 2.400000E-03 1.0000

13、00E-09 7 6 2 2.400000E-03 1.000000E-09 8 6 3 2.400000E-03 1.000000E-09 9 7 3 2.400000E-03 1.000000E-09 10 7 4 2.400000E-03 1.000000E-09 11 7 5 2.400000E-03 1.000000E-09 12 9 5 2.400000E-03 1.000000E-09 13 8 6 2.400000E-03 1.000000E-09 14 9 7 2.400000E-03 1.000000E-09 The Joint Coordinatesjoint X Y 1

14、 .000000 6.000000 2 2.000000 6.000000 3 4.000000 6.000000 4 6.000000 6.000000 5 8.000000 6.000000 6 2.000000 3.000000 7 6.000000 3.000000 8 .000000 .000000 9 8.000000 .000000 The Information of Supports IS VS 81 .000000 82 .000000 91 .000000 92 .000000 ( NA= 270 ) ( NW= 907 ) Loading Case 1 The Load

15、ings at Joints NLJ= 5 ILJ PX PY PM 1 .0000 -50.0000 .00000 2 .0000 -50.0000 .00000 3 .0000 -50.0000 .00000 4 .0000 -50.0000 .00000 5 -10.0000 -50.0000 .00000 The Loadings at Members NLM= 0 The Results of Calculation The Joint Displacementsjoint u v phi 1 -1.052374E-04 -9.374990E-04 -7.026841E-05 2 -

16、1.746815E-04 -1.193733E-03 1.087896E-04 3 -2.441257E-04 -8.137547E-04 -3.230387E-05 4 -3.552365E-04 -1.302885E-03 -1.022932E-04 5 -4.663472E-04 -9.374989E-04 1.412278E-04 6 3.860341E-04 -8.812339E-04 1.226815E-04 7 -7.938891E-04 -9.903867E-04 -6.211697E-05 8 -3.833336E-21 -1.325000E-20 -2.257486E-04

17、 9 2.833336E-21 -1.175000E-20 3.510741E-04 The Terminal Forcesmember N(st) Q(st) M(st) N(en) Q(en) M(en) 1 16.667 .000 .000 -16.667 .000 .000 2 16.667 .000 .000 -16.667 .000 .000 3 26.667 .000 .000 -26.667 .000 .000 4 26.667 .000 .000 -26.667 .000 .000 5 75.000 .000 .000 -75.000 .000 .000 6 -30.046

18、.000 .000 30.046 .000 .000 7 50.000 .000 .000 -50.000 .000 .000 8 39.060 .000 .000 -39.060 .000 .000 9 21.033 .000 .000 -21.033 .000 .000 10 50.000 .000 .000 -50.000 .000 .000 11 -30.046 .000 .000 30.046 .000 .000 12 75.000 .000 .000 -75.000 .000 .000 13 69.106 .000 .000 -69.106 .000 .000 14 51.079

19、.000 .000 -51.079 .000 .000 ( NA= 270 ) ( NW= 907 )可得每根杆轴力如图：3作图示连续梁的、图，已知各梁截面面积A=6.5,惯性矩I=5.50，各杆E=3.45×104MPa。5分解：对节点和单元进行编号,选定整体坐标系和局部坐标系。输入数据运行程序得到输出文件如下：* * * 10级 第三题* * * The Input Data The General Information E NM NJ NS NLC 3.450E+07 4 5 6 1 The Information of Membersmember start end A I

20、 1 1 2 6.500000E+00 5.500000E+00 2 2 3 6.500000E+00 5.500000E+00 3 3 4 6.500000E+00 5.500000E+00 4 4 5 6.500000E+00 5.500000E+00 The Joint Coordinatesjoint X Y 1 .000000 .000000 2 40.000000 .000000 3 60.000000 .000000 4 80.000000 .000000 5 120.000000 .000000 The Information of Supports IS VS 11 .000

21、000 12 .000000 13 .000000 22 .000000 42 .000000 52 .000000 ( NA= 66 ) ( NW= 299 ) Loading Case 1 The Loadings at Joints NLJ= 1 ILJ PX PY PM 3 .0000 -320.0000 -100.00000 The Loadings at Members NLM= 4 ILM ITL PV DST 1 4 -10.5000 40.000000 2 4 -10.5000 20.000000 3 4 -10.5000 20.000000 4 4 -10.5000 40.

22、000000 The Results of Calculation The Joint Displacementsjoint u v phi 1 0.000000E+00 3.713942E-21 4.951923E-20 2 0.000000E+00 -2.916827E-20 -5.219418E-05 3 0.000000E+00 -1.405865E-03 1.038816E-06 4 0.000000E+00 -3.431731E-20 4.276883E-05 5 0.000000E+00 6.771635E-21 5.239688E-05 The Terminal Forcesm

23、ember N(st) Q(st) M(st) N(en) Q(en) M(en) 1 .000 172.861 904.808 .000 247.139 -2390.385 2 .000 359.543 2390.385 .000 -149.543 2700.481 3 .000 -170.457 -2800.481 .000 380.457 -2708.654 4 .000 277.716 2708.654 .000 142.284 .000 ( NA= 66 ) ( NW= 315 )u 剪力图：u 弯矩图：土木工程2009级矩阵位移法上机题1作图示刚架的、图，已知各杆截面均为矩形，柱截

24、面宽0.4m,高0.4m, 大跨梁截面宽0.35m,高0.85m，小跨梁截面宽0.35m,高0.6m，各杆E=3.0×104 MPa。解：首先进行单元划分及结点编号，如下图所示 结果输出部分显示如下：member N(st) Q(st) M(st) N(en) Q(en) M(en) 1 754.931 75.762 109.157 -754.931 14.238 29.273 2 640.632 -72.893 -96.161 -640.632 136.893 -239.498 3 -58.656 114.299 66.887 58.656 144.901 -177.054 4 1

25、36.893 640.632 239.498 -136.893 770.568 -707.268 5 41.218 484.722 517.816 -41.218 260.078 -90.991 6 -2.657 30.889 -29.123 2.657 131.911 -142.018 7 1255.290 95.675 116.708 -1255.290 -95.675 189.452 8 260.078 41.218 55.908 -260.078 -41.218 75.991 9 1431.081 39.677 89.077 -1431.081 -39.677 89.469 10 39

26、1.988 38.561 87.413 -391.988 -38.561 86.110简略画出下图：n 轴力图n 剪力图n 弯矩图第二题计算图示桁架各杆的轴力。已知A=2400mm2,E=2.0×105 MPa。5分解:首先进行单元划分及结点编号。如下页图所示结果输出部分显示如下：member N(st) Q(st) M(st) N(en) Q(en) M(en) 1 19.500 .000 .000 -19.500 .000 .000 2 11.518 .000 .000 -11.518 .000 .000 3 -7.731 .000 .000 7.731 .000 .000 4

27、9.375 .000 .000 -9.375 .000 .000 5 5.000 .000 .000 -5.000 .000 .000 6 -5.039 .000 .000 5.039 .000 .000 7 -5.154 .000 .000 5.154 .000 .000 8 1.440 .000 .000 -1.440 .000 .000 9 10.000 .000 .000 -10.000 .000 .000 10 9.375 .000 .000 -9.375 .000 .000 11 -2.577 .000 .000 2.577 .000 .000 12 9.375 .000 .000 -9.375 .000 .000 13 5.000 .000 .000 -5.000 .000 .000 14 -3.599 .000 .000 3.599 .000 .000