A Realistic and Continuous Wood Column Formula

Strength tests were conducted on hundreds of full-size wood studs and small columns to develop a more definite relation between compressive stress and slenderness ratio. These experiments, together with a simple rational analysis relating crushing, buckling, and slenderness ratio, led to a new and basic third-degree formula applicable to all lengths of columns. The slenderness ratio is carried to the third power, instead of the second power as in the Euler equation. This formula proved to be in close agreement with strength test data, and it is accurate and relatively easily computed. It may also be applicable to columns of steel, aluminum, and concrete. The tests showed greatly increased strength for square-end columns over those with pinned or pointed ends (to the extent of 300 percent) although this full-increase is not entirely dependable. The complete continuity of the formula makes it adequate without need for associated equations or correction curves, since it extends from the region of direct crushing of a short stub column, through the reversed curve representing an intermediate-length column, to the section of long columns, where it is very similar to the Euler buckling curve. It can be used to represent ultimate strength curves of various species of wood, and can also be applied to safe and allowable design stresses, using different selected factors of safety for direct compression and/or for Young’s modulus of elasticity.

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