What is the Allowable Unit Stress in Timber Columns?

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Timber coloums are seldom used singly. Mostly they are a group of lumber which are stick together to form a single member. The allowable unit stress on timber is calculated by using the following formula

P/A=3.619E/(l/r)²

When the Columns have square or rectangular cross section
P/A=0.30E/(l/d)²

When the Columns have circular cross section
P/A=0.22E(l/d)²

where
P= total allowable load, lb (N)
A= area of column cross section, in² (mm²)
c= allowable unit stress in compression parallel to grain, lb/in² (MPa)
d= dimension of least side of column, in (mm)
l= unsupported length of column between points of lateral support, in (mm)
E= modulus of elasticity, lb/in² (MPa)
r= least radius of gyration of column, in (mm)

Specific Conditions to be kept in mind
1) The allowable unit stress(P/A) may not exceed the allowable compressive stress c.
2) 1/d must not exceed 50.

Note: The allowable unit stresses for bearing on end grain are published by lumber associations.

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