This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
This is also called the centroid of compression. The theoretical determination of this center of gravity is virtually the same as the determination of the center of gravity of the shaded area shown in Figs. 96 and 97. The general method of determining this center of gravity requires the use of differential calculus, and is a very long and tedious calculation. But the final result may be reduced to a surprisingly simple form, as expressed in the following equation: x = kd 4 - q
12 - 4q Assuming, as explained above, the value of q = 2/3, this reduces to: x = .357 kd..(14)
When q equals zero, the value of x equals 333 kd; and, at the other extreme, when q = 1, x = .375 kd.
There is, therefore, a very small range of inaccuracy in adopting the value of q = § for all computations.