Cone pyramid

A HOLLOW PYRAMID

What is the best shape to build a hollow structure of masonry or unreinforced concrete where the compressive stresses, due to self load, minimise the resulting tensile stresses? I think it is a cone.

In a homogeneous concrete cube subjected to increasing compressive stress in one direction, failure occurs by tensile failure in the other two directions.

A masonry cone, such as a Church steeple, is subject to compressive stresses down the slope and circumferential stresses due to the tendency of the blocks to fall inwards.

Ignoring other requirements, the structurally most economical solution is to equalise the compressive stresses in two directions at right angles, which results in a tensile stress in only one direction at right angles to both.

The optimum slope of the cone is given in the attached calculations.