常用求面积、体积公式施工技术.docx
1-3常用求面积、体积公式1-3-1平面图形面积平面图形面积见表1-73。平面图形面积表1-73图形尺寸符号面枳（八）1心(G)正方团a边长d对角援A-,a-A-0.707a在对角奴交点上_<三1.414o三1.44A一K方形城边b一长边d一财角税A=a6d>/d?M在对身段交点匕用形A.1D1.cA高I周长a、b、c财应用A、8、C的边长A-=MfinC=4±±GD三yBDCD=DAT-行S边形际a、b冬边h对边间的距离A=bh=aa611nAC8D-n2tsm在对角蝶交点上序形CE-ABAF=CDa=CD（上底边）A-AB（下底边）h-*A=审AHGr既空3÷6c=÷2V?3a6Kyr率径d一直径P-制图长A/,0.785,-0.07958p-d在测心tM0S形4、b主轴.Jr=a*b在主轴交点GJ1.a形xyVr半径>瓠长a孤，的咐应中心角a-1,-*SGO-'xfe38号090时COw”,=0.6,弓形r一半径，狐长。中心角6弦长hA-MiS）=Cr（S-6）*Wi3*rj0.017Sroh=-，/-十八c"当。=180时GO备OMr图影尺寸符号体枳(V)底面根（八）表面税(三)例或面积(S1)K心(G)n环体堂R-Ii环体平均半径D环体平均直径<1圈环体©面直径r圈环体敛面半径V-2<,Rrj三yrjDrf,S=4<r=<2CW=39.478Rr在环中心上球带体>Y1.R一球半径rvn-底面半径A腰药Ai雄心O至带底0S心O1的距离(3r+3rJ+2)S12>rRS2Rh(rjrJ)=,+yM形由下D中间断面！径d底反径I精高对于推卷线形横银,v=×(2D,+Etf+yrf,)对于B1.形横板：V=W1.(2D'+/)在泊交点上M球体1.。、6、c华Ii1.V-<jfcfr在轴女点上S=226i*6i交乂H柱体A:rBf柱半径A、IIB柱长V-rr,>1-1)在二轴线交点上9影体区a、&-下底边长“、6,一上底边长A一上、下底边距«(X)V=-(2a1.)6(2°*a)6j=-(*(<÷a)(6÷6|)0IbJ物料堆体积计算见表1-75.物料堆体积计算表1-751-3-4-1(B球形薄壳(BQ1-1)图IT圆球形薄壳计算图球面方程式：2+2+z2=R2(对坐标系XYZ,原点在O)式中R半径；X、Y、Z在球壳面上任一点对原点O的坐标。假设C弦长(AC)52a弦长(AB);26弦长(BC);F、GAB,BC的中点；f弓形AKC的高(KO3;hx弓形AEB的高(EF);h1弓形BDC的高(DG);SX弧AEB的长；Sr弧BDC的长；Am弓形AEB的面积(侧面积)；Ay弓形BIX：的面积；24*对应弧AEB的圆心角（弧度）；23一对应弧嬴:的圆心角（弧度）；O'新坐标系xyz的原点（XOY平面平移r2-左后与Z轴的交点）。Sin九嘴.bsn%=gCK=arcsin&-R6Ry=arcsinh=Rii-jR2-a-biAy=>2-2-jR1-a2-b1弧G与嬴:之曲线方程式分别为：X2+z2=(R2-fe2)(AEB)+z2=R2-2(BDC)1.弧长按下式计算：A=SxSy其一次近似值为:A=4Rarcsin=I=4Rr其二次近似值为:a=4Kc8in.sinxtgv=4=41+6点;1-3-4-2椭IB抛物面扁亮（图1-2）图1-2椭圆抛物面扁壳计算图壳面方程式：z=+y2abX、丫、Z在壳面上任一点对原点O的坐标工2a对应弧ADB的弦长；2b对应孤嬴的弦长；m弓形ADB的高；h1弓形BEC的高O假设：SX瓠石的长；Sy弧BEC的长；Am弓形ADB的面积；Ay弓形BEC的面积。1.弧长按下式计算Sa=c1+m1.1.n(+jSy=c2+fan21.n(+)式中c1.=7+41c2=62+4jbm2=T或者：S1,=20x系数KtSy=26x系数Kb式中系数K.、Kb可分别根据?、3的值，查表卜76得到。0262 .壳表面积按下式计算A=SSy3 .侧面积按下式计算Ay=y1-3-4-3棚m抛物面篇充系数计算见图I-2.壳表面积（八）计算公式：A=，Sv=2X系数K“X2bX系数的式中心、Kb一一椭圆抛物面扁壳系数，可按表1-76查得。椭圆抛物面扁壳系数表表1-76电1七包1.2严2。乐RK.或Kb1.aIb系RK.或Kb心或x2asstt2系RK.或Kb2avt2b系BK.或Kb系Ka*k0.0501.00660.0801.01680.1101.03140.U01.05000.1701.07240.0511.00690.0811.01720.1111.03200.1411.05070.1711.07330.0S21.00720.0821.01770.1121.03250.1421.05140.1721.07410.0531.00740.0831.01810.1131.03310.1431.05210.1731.07490.0541.00770.0841.01850.1141.03370.1441.05280.1741.07570.0551.00800.0851.01890.1151.03420.14S1.05350.1751.07650.0561.00830.0861.01940.116103480.1461.05420.1761.07730.0S71.00860.0871.01980.1171.03540.1471.05500.1771.07820.051.00890.08«1.02030.1181.03600.1481.05570.1781.07W0.0591.00920.0891.02070.1191.03660.1491.05640.1791.07980.0601.00950.0901.02120.1201.03720.1S01.05710.1801.08070.0611.00980.0911.02170.1211.03780.1511.05780.1811.08150.0621.01020.项1.02210.1221.03840.1521.05S60.1821.08240.0631.01050.0931.02260.1231.03900.1531.05930.1831.08320.0641.01080.0941.02310.1241.03960.1541.06010.1841.08410.0651.01120.0951.02360.1251.04020.1551.06080.1851.08490.0661.01!50.0961.02410.1261.04080.1561.06160.1861.08580.0671.01180.即1.02460.1271.04150.1571.06230.171.08670.0681.01220.0981.02510.12S1.04210.1581.06310.1H81.08750.0691.01260.0991.02560.1291.04280.1591.06380.1S91.08S40.0701.01290.1001.02610.1301.04340.1601.0M60.1901.08930.0711.01330.1011.02660.B11.04400.1611.06540.1911.09020.0721.01370.1021.02710.1321.04470.1621.06610.1921.09100.0731.01400.1031.02760.1331.04530.1631.06690.1931.09190.0741.01440.1041.02810.1541.04600.1641.06770.1941.092«0.0751.01480.1051.02870.1551.04670.1651.06850.1951.09370.0761.01520.1061.02920.1361.04730.1661.06930.196).09460.0771.01560.1071.02970.1371.04800.1671.07000.1971.09550.0781.01600.1081.03030.1S81.04870.1681.07080.1981.09640.0791.01640.1091.03080.1391.04940.1691.07160.1991.0973查表说明例已知2a=24.0m,2b=1.6.0m.h,=3.0m,hy=2.8m,试求椭圆抛物面扁壳表面枳A。先求出h2a=3.024.0=0.125hy2b=2.816.0=0.175分别查表得系数Ka为1.0402和系数Kb为1.0765.则扁壳
