In 1930, Hardy Cross published a paper called 'Analysis of Continuous Frames by Distributing Fixed-End Moments' in which he described the moment distribution method, which would change the way engineers in the field performed structural analysis. The method was later made obsolete by computer solving algorithms employing the Newton–Raphson method or other numerical methods that eliminate the need to solve nonlinear systems of equations by hand. Before the method was introduced, solving complex pipe systems for distribution was extremely difficult due to the nonlinear relationship between head loss and flow.
The introduction of the Hardy Cross method for analyzing pipe flow networks revolutionized municipal water supply design. The Hardy Cross method is an adaptation of the Moment distribution method, which was also developed by Hardy Cross as a way to determine the forces in statically indeterminate structures. The method was first published in November 1936 by its namesake, Hardy Cross, a structural engineering professor at the University of Illinois at Urbana–Champaign.
The Hardy Cross method is an iterative method for determining the flow in pipe network systems where the inputs and outputs are known, but the flow inside the network is unknown. Method for determining flow in pipe network systems An example pipe flow network
