中南大學2010級矩陣位移法正式報告

1、矩陣位移法正式報告班 級土木10班姓 名學 號指導老師殷勇日 期2012-10-261作圖示剛架的、圖，已知各桿截面均為矩形，柱截面寬0.4m,高0.4m, 大跨梁截面寬0.35m,高0.85m，小跨梁截面寬0.35m,高0.6m，各桿E=3.0×104 MPa。10分解:對節(jié)點和單元進行編號,選定整體坐標系和局部坐標系。輸入數(shù)據(jù)運行程序得到輸出文件如下：* * * 10級 第一題* * * 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 )根據(jù)上述輸出結果，可做出內力圖如下u 軸力圖：u 剪力圖：u 彎矩圖：2、計算圖示桁架各桿的軸力。已知A=2400mm2,E=2.0×105 MPa。5分解：對節(jié)點和單元進行編號,選定整體坐標系和局部坐標系。輸入數(shù)據(jù)運行程序得到輸出文件如下：* * * 10級 第二題 * * * 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 )可得每根桿軸力如圖：3作圖示連續(xù)梁的、圖，已知各梁截面面積A=6.5,慣性矩I=5.50，各桿E=3.45×104MPa。5分解：對節(jié)點和單元進行編號,選定整體坐標系和局部坐標系。輸入數(shù)據(jù)運行程序得到輸出文件如下：* * * 10級 第三題* * * 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 剪力圖：u 彎矩圖：土木工程2009級矩陣位移法上機題1作圖示剛架的、圖，已知各桿截面均為矩形，柱截

24、面寬0.4m,高0.4m, 大跨梁截面寬0.35m,高0.85m，小跨梁截面寬0.35m,高0.6m，各桿E=3.0×104 MPa。解：首先進行單元劃分及結點編號，如下圖所示 結果輸出部分顯示如下：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簡略畫出下圖：n 軸力圖n 剪力圖n 彎矩圖第二題計算圖示桁架各桿的軸力。已知A=2400mm2,E=2.0×105 MPa。5分解:首先進行單元劃分及結點編號。如下頁圖所示結果輸出部分顯示如下：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