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Deflection and Supporting Force Analysis of a Slender Beam under Combined Transverse and Tensile Axial Loads

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Technical Report

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Defence Science and Technology Group Fishermans Bend Victoria Australia

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This report describes the deflection and supporting force analysis of a static pressure pipe that is to be used in the Defence Science and Technology Group Transonic Wind Tunnel test facility. The static pressure pipe was modelled as a slender propped cantilever beam fixed at one end and roller-supported at the other that is subjected to combined transverse and tensile axial loading. An analytical solution to this problem has been derived from first principles using Euler-Bernoulli beam theory, and a closed-form expression for the beam deflection as a function of the axial tension load is provided. The analytical solution was checked by performing a separate nonlinear finite element analysis using beam elements. The value of the peak deflection and its position along the beam axis was determined as a function of the applied axial tension load by solving a nonlinear equation using the bisection method. The analytical functions and numerical solution methods described in this report have been implemented for general use in a spreadsheet, and the source code for these is provided. They can be used to study other slender beam configurations that may be of interest. A modal finite element analysis of a further idealised beam configuration was also conducted to provide estimates of the natural frequencies and associated mode shapes for the beam.

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