列表计算两铰拱的内力

1、列表计算两铰拱的内力郭昊宁 1533104 1153310415本文将从一道实例题运用Excel表格列表计算三铰拱的内力。例题1：两铰拱及其所受荷载如图所示拱的轴线为抛物线方程，=甘。-x) 试计算反力并绘制内力图。F =10kNpf=4mAl=16m题目分析：该题为超静定问题，可利用力法求解水平力Fh，再利用求三铰拱内力时的公式 硝|_0 -sin fsFh 即可求出剪力、轴力、弯矩，再利用Excel即可绘制相应的剪力 图、轴力图和弯矩图：具体步骤：画出对应简支梁弯矩图解力法方程解得Fh利用公式求剪力、轴力、弯矩利用坐标变换公式在两铰拱上绘制弯矩图。由于第一部分存在积分电脑难以完成，所以用力

2、法计算水平推力Fh部分人工手写完成。再利用手写得出的水平推力编程让电脑自动运算即可得出相应剪力、轴力、弯矩。其他荷载同样可以采用本方法思路。注：坐标变换公式为X=x0-f*sin 6Y=y0+f*con 6X0,y0为拱轴线坐标，f为剪力、轴力、弯矩，。为拱上点的切线与x轴夹角。X，Y为所得的坐标值斜绑剪力Fq0弯0夹角正弦余弦Fh=2850/512=5弯5矩M剪力Fq轴力Fn0017.500.78540.707110.7071075.5664062501.367257253-9.23934446510.93750.8757.57.50.718830.65850.7525775.5664062

3、5-2.2814941411.978821045-9.12793217621.750.757.5150.64350.60.85.56640625-5.2587890632.66015625-8.95312532.43750.6257.522.50.55860.530.8479985.56640625-8.9318847663.409797868-8.695295109430.57.5300.463650.447210.8944275.56640625-13.300781254.218831379-8.33284707253.43750.375-2.527.50.358770.351120.93

4、63295.56640625-8.365478516-4.295318664-4.33417998263.750.25-2.5250.244980.24254 0.9701435.56640625-4.125976563-3.775408069-4.79386821473.93750.125-2.522.50.124350.124030.9922785.56640625-0.582275391-3.171122414-5.213334938840-2.5200015.566406252.265625-2.5-5.5664062593.9375-0.13-2.517.5-0.1244-0.124

5、0.9922785.566406254.417724609-1.79026697-5.833508611103.75-0.25-2.515-0.245-0.24250.9701435.566406255.874023438-1.075304431-6.006546339113.4375-0.38-2.512.5-0.3588 -0.35110.9363295.566406256.634521484-0.386327224-6.08979719123-0.5-2.510-0.4636 -0.44720.8944275.566406256.699218750.253304576-6.0967790

6、95132.4375-0.63-2.57.5-0.5586-0.530.8479985.566406256.0681152340.830193652-6.045300409141.75-0.75-2.55-0.6435-0.60.85.566406254.7412109381.33984375-5.953125150.9375-0.88-2.52.5-0.7188 -0.65850.7525775.566406252.7185058591.784062428-5.835409137160-1-2.50-0.7854-0.70710.7071075.5664062502.168276653-5.

7、703810559现将表格数据公布如下:x表1剪力x剪力y轴力x轴力y弯矩x弯矩y-0.1933593750.1933593752.177734375-2 0.7393874451.235342923.003595133-1.3523230091.150237440.765800068匚 1.680781252.1756253.790625-0.63752.3155273441.329296875P 2.6385621493.0158005624.53616573-0.0203651693.4733889461.680077687Q 3.622656253.75468

8、755.24218750.5156254.5948290211.8103419595.3016374142.6331335625.5072773972.0847602745.2937315612.654215838P 6.1831341913.0174632356.3875612752.1997549026.100069633.349721478Q 7.0786658653.3081730777.2155448722.2131410267.0072222373.87972210183.582.1445312584.2265625P 8.9555889423.5822115388.7588141

9、032.0080128219.054795134.37586104Q 9.9478400743.5413602949.514399511.80759803910.142465994.31986397810.972870293.3651541110.287243151.53681506811.23295364.058709605P 12.022656253.045312511.091145831299598173.599196341Q 13.088000352.57830056211.931999060.72869850213.321609462.95207514314.160781251.96437512.8093750.162514.284472662.129296875P 15.234962671.20602876113.71911873-0.52636430715.1790