MIT 16 01  Slender Structures (27 pages)
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Slender Structures
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 Pages:
 27
 School:
 Massachusetts Institute of Technology
 Course:
 16 01  Unified Engineering I, II, III, & IV
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Lecture M1 Slender one dimensional Structures Reading Crandall Dahl and Lardner 3 1 7 2 This semester we are going to utilize the principles we learnt last semester i e the 3 great principles and their embodiment in the 15 continuum equations of elasticity in order to be able to analyze simple structural members These members are Rods Beams Shafts and Columns The key feature of all these structures is that one dimension is longer than the others i e they are one dimensional Understanding how these structural members carry loads and undergo deformations will also take us a step nearer being able to design and analyze structures typically found in aerospace applications Slender wings behave much like beams rockets for launch vehicles carry axial compressive loads like columns gas turbine engines and helicopter rotors have shafts to transmit the torque between the components andspace structures consist of trusses containing rods You should also be aware that real aerospace structures are more complicated than these simple idealizations but at the same time a good understanding of these idealizations is an important starting point for further progress There is a basic logical set of steps that we will follow for each in turn 1 We will make general modeling assumptions for the particular class of structural member In general these will be on a Geometry b Loading Stress State c Deformation Strain State 2 We will make problem specific modeling assumptions on the boundary conditions that apply idealized supports such as pins clamps rollers that we encountered with truss structures last semester a b On stresses On displacements Applied at specified locations in structure 3 We will apply an appropriate solution method a b Exact analytical Unified 16 20 Approximate often numerical 16 21 Such as energy methods finite elements finite difference use computers Let us see how this works Rods bars The first 1 D structure that we will analyzes is that of a rod or bar such as we
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