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.
It is well known that if a load on a column is eccentric, its strength is considerably less than when the resultant line of pressure passes through the axis of the column. The theoretical demonstration of the amount of this eccentricity depends on assumptions which may or may not be found in practice. The following formula is given without proof or demonstration, in Taylor and Thompson's treatise on Concrete:
Let e = Eccentricity of load; b = Breadth of column; / = Average unit-pressure;
/' = Total unit-pressure of outer fibre nearest to line of vertical pressure
Then, f' = f (1 + 6e/b).. .(45)
As an illustration of this formula, if the eccentricity on a 12-inch column were 2 inches, we should have b = 12, and e = 2. Substituting these values in Equation 45, we should have f' = 2f, which means that the maximum pressure would equal twice the average pressure. In the extreme case, where the line of pressure came to the outside of the column, or when e = 1/2b, we should have that the maximum pressure on the edge of the column would equal four times the average pressure.
Any refinements in such a calculation, however, are frequently overshadowed by the uncertainty of the actual location of the center of pressure. A column which supports two equally loaded beams on each side, is probably loaded more symmetrically than a column which supports merely the end of a beam on one side of it. The best that can be done is arbitrarily to lower the unit-stress on a column which is probably loaded somewhat eccentrically.