A cast iron column of thirty diameters in length, is fractured by bending; when the length is less than this ratio—by bending and splitting off of wedge shaped pieces. But by casting the column hollow, and swelling it in the middle, its strength is greatly increased.
Barlow's formula for finding the weight that can be sustained by any beam, acting as a pillar or strut, before bending, is:—
, whence
now, having the weight given, and assuming the dimensions of the cross-section—we shall have
and
in the above formulæ,