(8 × 63 × 2,410)/182 = (8 × 216 × 2,410)/324
= 12,853 lbs.
The safe working load = say, 1,285 lbs.
On the strength of posts of medium length.—When a post is less than 30, but over 5, diameters in length, and therefore tending to fail by crushing as well as by bending, the resistance to crushing is a considerable proportion of the strength. This must, in consequence, be allowed for in any calculation for the breaking weight.
To find the weight that would break a square or rectangular post of between 5 and 30 diameters in length:
Multiply the area of the cross section of the post in square inches by the weight in pounds that would crush a short prism of 1 inch square (Table II.), and divide the product by 1·1 added to the square of the length in feet, divided by 2·9 times the square of the least thickness in inches.
The formula is as follows:
W = DS/(1·1 + L2/T2 2·9)
where D = the constant for the resistance to crushing.
S = the area of the cross section of the post in square inches.
1·1 is a modification introduced in order that the result
may be in accord with the result of experiments.
L = the length of the post in feet.
T = the least thickness in inches.
2·9 = the constant for the resistance to bending, and which
is taken at that figure for all timbers (Table II.).
Example.—Find the breaking weight of a post of Dantzic oak 10 feet long and 6 inches square.
The constant for Dantzic oak (Table II.) is 7,731.
W = (7,731 × 36)/(1·1 + 100/(2·9 × 36))
= 278,316/2·05
= 135,763 lbs.