Moment-Distribution Constants from Models

An experimental method of determining the moment-distribution constants for beams with variable moments of inertia is presented. The method does not rely on the use of deformeter-type gages or other special instruments. It is based on the concept of a three-dimensional solid whose properties are functions of the loads, slopes, and deflections of the statically indeterminate member which it represents. It is shown that each moment-distribution constant is a function of a ratio, J/Q, which also defines the location of the center of gravity of the solid. This ratio is evaluated experimentally by weighing the solid and by using the principles of statics. Mathematical integration or the approximate summation process are replaced by weighing, which offers simpler computations and more reliable results in comparison with standard methods of analysis. The method can be applied readily to the determination of the moment-distribution constants of arches with constant or variable moments of inertia.

Once the moment-distribution constants are known, the moments can be balanced with little difficulty.