V=(A+2C+KH)*(B+2C+KH)*H+1/3K^2H^3推导公式

Question

挖基础土方V=(A+2C+KH)*(B+2C+KH)*H+1/3K^2H^3怎么推导？要过程

Answer 1

如图所示：

基坑体积=中间长方体体积+四周四个三棱柱体积+角落四个四棱锥体积

            V=(a+2c)*(b+2c)*H+2*1/2*kH*H*(a+2c)+2*1/2*kH*H*(b+2c)+4*1/3*kH*kH*H

              =H[(a+2c)*(b+2c)+kH*(a+2c)+kH*(b+2c)]+k²H³+1/3k²H³

              =H[(a+2c)*(b+2c)+kH*(a+2c)+kH*(b+2c)+(kH)²]+1/3k²H³

              =H{(a+2c)*[(b+2c)+kH]+kH*[(b+2c)+kH]}+1/3k²H³

              =H*(a+2c+kH)*(b+2c+kH)+1/3k²H³

Answer 2

就是梯形，圆锥，体得综合计算