本文格式為Word版，下載可任意編輯——列表計算兩鉸拱的內(nèi)力列表計算兩鉸拱的內(nèi)力

郭昊寧15331041153310415

本文將從一道實例題運用Excel表格列表計算三鉸拱的內(nèi)力。例題1：兩鉸拱及其所受荷載如下圖拱的軸線為拋物線方程

y?4f?x?l?x?l2

A試計算反力并繪制內(nèi)力圖。

P

題目分析：該題為超靜定問題，可利用力法求解水平力Fh，再利用求三鉸拱內(nèi)力時的公式

0?y??M0??M??1?????0??FQ???0cos??sin???FQ??F??0?sin??cos???F??N????H?即可求出剪力、軸力、彎矩，再利用Excel即可繪制相應的剪力圖、軸力圖和彎矩圖。具體步驟：

1.畫出對應簡支梁彎矩圖2.解力法方程3.解得Fh

4.利用公式求剪力、軸力、彎矩

5.利用坐標變換公式在兩鉸拱上繪制彎矩圖。

由于第一部分存在積分電腦難以完成，所以用力法計算水平推力Fh部分人工手寫完成。再利用手寫得出的水平推力編程讓電腦自動運算即可得出相應剪力、軸力、彎矩。

其他荷載同樣可以采用本方法思路。

F=10kNf=4mB

l=16m

注：坐標變換公式為X=x0-f*sinθY=y0+f*conθ

X0,y0為拱軸線坐標，f為剪力、軸力、彎矩，θ為拱上點的切線與x軸夾角。X，Y為所得的坐標值

現(xiàn)將表格數(shù)據(jù)公布如下：

x012345678910111213141516y=x*(16-x)/16斜率K剪力Fq0彎矩M0夾角00.93751.752.437533.43753.753.937543.93753.753.437532.43751.750.9375010.8750.750.6250.50.3750.250.1250-0.13-0.25-0.38-0.5-0.63-0.75-0.88-17.57.57.57.57.5-2.5-2.5-2.5-2.5-2.5-2.5-2.5-2.5-2.5-2.5-2.5-2.507.51522.53027.52522.52023.51512.5107.552.500.78540.718830.64350.55860.463650.358770.244980.124350-0.1244-0.245-0.3588-0.4636-0.5586-0.6435-0.7188-0.7854正弦0.707110.65850.60.530.447210.351120.242540.124030-0.124-0.2425-0.3511-0.4472-0.53-0.6-0.6585-0.7071余弦Fh=2850/512=5.5彎矩M剪力Fq軸力Fn0.7071075.5664062501.367257253-9.2393444650.7525775.56640625-2.2814941411.978821045-9.1279321760.85.56640625-5.2587890632.66015625-8.9531250.8479985.56640625-8.9318847663.409797868-8.6952951090.8944275.56640625-13.300781254.218831379-8.3328470720.9363295.56640625-8.365478516-4.295318664-4.3341799820.9701435.56640625-4.125976563-3.775408069-4.7938682140.9922785.56640625-0.582275391-3.171122414-5.21333493815.566406252.265625-2.5-5.566406250.9922785.566406254.417724609-1.79026697-5.8335086110.9701435.566406255.874023438-1.075304431-6.0065463390.9363295.566406256.634521484-0.386327224-6.089797190.8944275.566406256.699218750.253304576-6.0967790950.8479985.566406256.0681152340.830193652-6.0453004090.85.566406254.7412109381.33984375-5.9531250.7525775.566406252.7185058591.784062428-5.8354091370.7071075.5664062502.168276653-5.703810559表1

剪力x剪力y軸力x軸力y彎矩x彎矩y-0.1933593750.1933593752.177734375-2.177734375000.7393874451.235342923.003595133-1.3523230091.150237440.7658000681.680781252.1756253.790625-0.63752.3155273441.3292968752.6385621493.0158005624.53616573-0.0203651693.4733889461.6800776873.622656253.75468755.24218750.5156254.5948290211.8103419595.3016374142.6331335625.5072773972.0847602745.2937315612.6542158386.1831341913.0174632356.3875612752.1997549026.100069633.3497214787.0786658653.3081730777.2155448722.2131410267.0072222373.87972210183.582.1445312584.22656258.9555889423.5822115388.7588141032.0080128219.054795134.375861049.9478400743.5413602949.514399511.80759803910.142465994.31986397810.972870293.3651541110.287243151.53681506811.23295364.05870960512.022656253.045312511.091145831299598173.59919634113.088000352.57830056211.931999060.72869850213.321609462.95207514314.160781251.96437512.8093750.162514.284472662.12929687515.234962671.20602876113.71911873-0.52636430715.179014861306640630.30664062514.65559896-1.344401042160

表2

表1為運用Fh計算剪力、軸力、彎矩的的過程

表2為將計算出的剪力、軸力、彎矩畫在拱上的坐標變換

以下為Excel繪制的剪力圖、軸力圖、彎矩圖：