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

Abstract

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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Document Details

Document Type
Technical Report
Publication Date
May 01, 2016
Accession Number
AD1015137

Entities

People

  • Witold Waldman
  • Xiaobo Yu

Organizations

  • Defence Science and Technology Group

Tags

Communities of Interest

  • Air Platforms
  • Space

DTIC Thesaurus Topics

  • Axial Loads
  • Cantilever Beams
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Programs
  • Equations
  • Finite Element Analysis
  • Fluid Dynamics
  • Frequency
  • Geometry
  • Mechanics
  • Modal Analysis
  • Resonant Frequency
  • Spreadsheet Software
  • Static Pressure
  • Transonic Wind Tunnels
  • Wind Tunnels

Fields of Study

  • Engineering
  • Physics

Readers

  • Structural Dynamics.