MSU ME 424 - Tapered Beam (35 pages)

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Tapered Beam



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Tapered Beam

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Pages:
35
School:
Michigan State University
Course:
Me 424 -

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Application of the Finite Element Method Using MARC and Mentat 4 1 Chapter 4 Tapered Beam Keywords elastic beam 2D elasticity plane stress convergence deformed geometry Modeling Procedures ruled surface convert 4 1 Problem Statement and Objectives A tapered beam subjected to a tip bending load will be analyzed in order to predict the distributions of stress and displacement in the beam The geometrical material and loading specifications for the beam are given in Figure 4 1 The geometry of the beam is the same as the structure in Chapter 3 The thickness of the beam is 2h inches where h is described by the equation h 4 0 6 x 0 03x 2 Geometry Length L 10 Width b 1 uniform Thickness 2h a function of x Material Steel Yield Strength 36 ksi Modulus of Elasticity 29 Msi Poisson s Ratio 0 3 Density 0 0088 slugs in3 Loading Tip Load P 10 000 lbs P x 2h L Figure 4 1 Geometry material and loading specifications for a tapered beam 4 2 Analysis Assumptions Because the beam is thin in the width out of plane direction a state of plane stress can be assumed The length to thickness ratio of the beam is difficult to assess due to the severe taper By almost any measure however the length to thickness ratio of the beam is less than eight Application of the Finite Element Method Using MARC and Mentat 4 2 Hence it is unclear whether thin beam theory will accurately predict the response of the beam Therefore both a 2D plane stress elasticity analysis and a thin elastic beam analysis will be performed 4 3 Mathematical Idealization Based on the assumptions above two different models will be developed and compared The first model is a beam analysis In this model the main axis of the bar is discretized using straight twonoded 1D thin beam finite elements having a uniform cross sectional shape within each element Thus the geometry is idealized as having a piecewise constant cross section as shown in Figure 4 2 The uniform thickness within each element is taken to be equal to the actual



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