锥坡体积面积计算e

备注：1.Ho的两种算法：a.（根据涵洞设计手册）Ho=H-0.5(αo+βo)t；b.Ho=H-sqrt(αo*βo)t

2.交角的示意图：3.锥坡基础周长应考虑禁边宽度e与基础宽度Bo的影响，即基础周长为 其中(m+n)H即是a+b。对于斜交可以根据e与Bo的值重新计算椭圆的外锥a，b值及内锥ao，bo值，

ExzyD△H△H2=t2+(Ht/a(b))2

△a(b)2=t2+(a(b)t/H)2tHHobaao(bo)a(b)△a(b)

a15a等分点1/10等分n值0.1距E点距离z1.5曲线纵向y值0.050126a等分点x1.5右斜横轴纵坐标9.19E-17曲线纵坐标-0.05013曲线长度1.500837

曲线点至锥顶斜距离l

b2/100.23

0.202041

3

1.84E-16-0.202041.50767310.68775-1.8E-16-0.202041.507673

10

3/100.34.50.460608

4.52.76E-16-0.460611.52212210.85228-2.8E-16-0.460611.522122

α4/100.46

0.834849

6

3.68E-16-0.834851.54598111.12191-3.7E-16-0.834851.545981

90°

5/106/10

0.50.67.591.3397462

7.594.59E-165.51E-16-1.33975-21.5826941.638882

7/100.710.52.858572

10.56.43E-16-2.858571.728336

14.1862614.3178214.5344414.832415.2069115.6524816.16323

11.5321712.150313.11368-4.6E-16-5.5E-16-6.4E-16-1.33975-2-2.858571.5826941.6388821.728336

表面积10.60956左斜横轴纵坐标-9.2E-17曲线纵坐标-0.05013曲线长度1.500837砌体内锥体

ao

14.81972

a等分点1/10等分n值0.1距E点距离z1.481972曲线纵向y值0.049417a等分点x1.481972右斜横轴纵坐标9.08E-17曲线纵坐标-0.04942

bo2/100.22.9639440.1991842.9639441.82E-16-0.1991.8585793/10

0.34.4459170.4540944.4459172.72E-16-0.45409

α4/100.45.92780.8230425.92783.63E-16-0.8230490°

5/106/10

0.50.67.4098618.18331.3207991.9717167.4098618.18334.54E-165.45E-16-1.3208-1.97172

7/100.710.373812.81814510.373816.35E-16-2.81815

曲线长度

曲线点至锥顶斜距离l

1.4819721.45211.5037361.5272081.5633311.6186211.70665913.9934614.1240914.3391614.6349515.0066915.44815.95571

10.33310.4154310.575510.8378211.2369811.8384312.77588体积可以按内锥与外锥表面积的平均值*t计算，结果相当精确＝

可通过下列数据在CAD中以Pline命令绘制正斜交的锥坡平面图(x,y)1.5,-0.05012562338003-1.5,-0.05012562338004右后台3,-0.202041028867288左后台-3,-0.202041028867288

4.5,-0.460607985830543-4.5,-0.4606079858305446,-0.83484861008832-6,-0.834848610088327.5,-1.33974596215561-7.5,-1.339745962155619,-2-9,-210.5,-2.85857157145715-10.5,-2.8585715714571512,-4-12,-413.5,-5.1101055933-13.5,-5.110105593313.875,-6.200326160733-13.875,-6.20032616073414.25,-6.8775010008008-14.25,-6.877501000800814.625,-7.7779513956711-14.625,-7.777951395671114.7,-8.01002512578676-14.7,-8.0100251257867614.85,-8.5320203341-14.85,-8.532020334114.925,-9.00125078222809-14.925,-9.0012507822280914.955,-9.22598449627931-14.955,-9.2259844962793114.97,-9.36786077482883-14.97,-9.3678607748288414.985,-9.552822187784-14.985,-9.55282218778414.9925,-9.683811792477-14.9925,-9.68381179247814.997,-9.80001000025002-14.997,-9.8000100002500214.9985,-9.85858217934081-14.9985,-9.8585821793408214.99925,-9.90000125000781-14.99925,-9.9000012500078114.99985,-9.95527875225365-14.99985,-9.9552787522536515,-10-15,-10

表面积

通过对正斜交两种方案对比，正斜交的底面积一样大，且斜交锥坡左右大小均一样！！但斜交锥坡的基础周长与正交不同大，且左右不等。

区域为应填数据，黄色填充区域为重要计算结果，粉红色填充区域为绘图坐标

内锥均高内锥横轴内锥纵轴外锥体积砌体体积内锥体积Ho(m)aoboV外(m3)V砌(m3)V内(m3)9.86919714.819729.858579392.699115.209377.44

Kπ；b.Ho=H-sqrt(αo*βo)t[(mn)H2eBo]4宽度Bo的影响，即基础周长为（正交情况）

的外锥a，b值及内锥ao，bo值，按照下述方法即可求出内外锥基础长度，取平均值即可计算基础体积。

无论正斜交：椭圆面积＝πab取a、b计算后的均值锥坡底面积S＝πab/4锥体体积＝S·H/3

t2+(a(b)t/H)2

锥坡的放样

弧度1.570796锥坡高度H8/109/109.25/10

0.80.90.9251213.513.87545.11016.2003291213.513.875

7.35E-168.27E-168.5E-16

-4-5.11-6.20033

1.8849032.2233340.673321

10砌体厚度t0.1

9.5/109.75/109.8/10

0.950.9750.9814.2514.62514.76.8775017.7779518.010025

14.2514.62514.78.73E-168.96E-169E-16-6.8775-7.77795-8.010030.7740720.9754160.2432顺桥向锥坡线斜长l9.9/109.95/10

0.990.99514.8514.9258.53269.00125114.8514.9259.1E-169.14E-16-8.533-9.001250.5984060.41869614.142149.97/10

0.99714.9559.22598414.9559.16E-16-9.225980.226727

16.733217.3565517.5200817.6865117.8557617.417.9586317.9931418.0069714.7516618.149535.6939656.652168.5324312.1579585.326809-7.4E-16-8.3E-16-8.5E-16-8.7E-16-9E-16-9E-16-9.1E-16

-4-5.11-6.20033-6.8775-7.77795-8.01003-8.533

1.8849032.2233340.6733210.7740720.9754160.24320.598406

3.7501622.03671-9.1E-16-9.2E-16-9.00125-9.225980.4186960.226727

弧度8/100.811.855783.94343111.855787.26E-16-3.943431.5707969/10

0.913.337755.56132413.337758.17E-16-5.56132高度Ho9.25/10

0.92513.708246.112313.708248.4E-16-6.1129.8691979.5/10

0.9514.078746.78023814.078748.62E-16-6.78024砌体厚度t0.19.75/109.8/10

0.9750.9814.4492314.523337.6679557.674614.4492314.523338.85E-168.9E-16-7.66795-7.675顺桥向锥坡线斜长l9.9/109.95/10

0.990.99514.6715314.745628.4678558.87395414.6715314.745628.99E-169.03E-16-8.46785-8.8739513.949659.97/10

0.99714.775269.09550914.775269.05E-16-9.09551

1.8607822.1940410.62420.7635110.9619280.2404920.5900230.4128040.22352916.5211817.1395217.3017117.4667717.6346317.6685317.7366517.7708717.7845914.3699517.677185.5451866.4780178.3086142.1012875.1868243.6515491.98313715.21117m3

781

7875225365

交锥坡左右大小均一样！！

9.98/10

0.99814.979.367861

14.979.17E-16-9.367860.1426679.99/10

0.99914.9859.552814.9859.18E-16-9.55290.18549.995/100.999514.99259.68381214.99259.18E-16-9.683810.13112.998/100.999814.9979.8000114.9979.19E-16-9.800010.1162859.999/100.999914.99859.85858214.99859.19E-16-9.858580.0585919.9995/109.9999/1010/10合计0.999950.99999114.9992514.9998515可根据该9.9000019.95527910行数据放样14.9992514.9998515

9.19E-169.19E-169.19E-16通过此计算曲线

-9.9-9.95528-10

0.0414260.0552810.04472119.82104

18.013918.0208218.0242918.0263718.0270618.0274118.0276918.02776

1.2832241.6712241.1812121.0478680.5280670.3733840.4982810.403113154.1054-9.2E-16-9.2E-16-9.2E-16-9.2E-16-9.2E-16-9.2E-16-9.2E-16-9.2E-16通过此计算曲线-9.36786-9.5529-9.68381-9.80001-9.85858-9.9-9.95528-10

0.1426670.18540.1311280.1162850.0585910.0414260.0552810.04472119.82104

9.98/109.99/10

0.9980.99914.7900814.80499.2353799.417814.7900814.80499.06E-169.07E-16-9.23538-9.417.995/100.999514.812319.54686214.812319.07E-16-9.546869.998/100.999814.816769.66141714.816769.08E-16-9.661429.999/100.999914.818249.71916114.818249.08E-16-9.719169.9995/109.9999/1010/10合计0.999950.99999114.81814.8195714.819729.7599949.814499.85857914.81814.8195714.81972

9.08E-169.08E-169.08E-16通过此计算曲线-9.75999-9.81449-9.85858

0.1406530.1830220.1292750.11410.0577630.040840.0544990.044019.56718

17.8052

150.118

0.485170.392506

17.7914617.7983317.8017617.8038317.8045117.8048617.805131.2494661.6272561.1501331.0202960.5141730.363559

备注根据该两行数据放样

算曲线相对坐标

外锥周长外锥表面积

算曲线相对坐标

外锥周长

备注

算曲线相对坐标

内锥周长内锥表面积