Analysis: Formulas
Support hangers are typically placed near heavy load devices, or when a run of pipe changes in direction [1]. Since there are multiple sensors and devices attached to the system, a hanger will be placed before and after each special load to provide support as per industrial piping design.
With the tentative placements of the hangers, analysis of forces and moments were done to justify the hangers’ location. Provided below are the calculations derived from the following equations:
where ΣM and ΣF are the summation of moments and forces that equate to zero. Due to the multiple loads integrated throughout the pipe run, several equations for a continuous beam were used to analyze the moment of forces. The first theory (2) is the equation used to determine the moment between two fixed ends,
where LHM and RHM signify the left hand and right hand moment analysis between two fixed ends: a is the distance between the start of both the section and distribution load, b is the distance between the start of the section and end of the distribution load, c is the distance between the start and end of the distributed load, and d is the distance between the end of the section and equivalent load location.
The second theory is used for sections along the pipe run with a single concentrated load and no support. The analysis for a concentrated load between two fixed ends is calculated with the following:
where P is the concentrated load and L is the length of the pipe run. In contrast to the prior equation, the third theory details the moment of a beam due to a single distributed load between two fixed supports as follows:
where w represents the weight of the load. The final theory is used for a section where there is a load between one fixed end and one free end of a pipe run. The analysis for the specific section is determined by the following:
Analysis: Calculations
Handwritten Calculations: