sprh04

# sprh04 - KEY CONCEPTS FOR MATERIALS AND STRUCTURES Handout...

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Unified Engineering M&S Quiz Handout, 2004 Materials and Structures, SMS KEY CONCEPTS FOR MATERIALS AND STRUCTURES Handout for Spring Term Quizzes Basic modeling process for 1-D structural members (1) Idealize/model – make assumptions on geometry, load/stress and deformations (2) Apply governing equations (e.g. equations of elasticity) (3) Invoke known boundary conditions to derive constitutive relations for structure (load- deformation, load-internal stress etc.) Analytical process for 1-D structural members (1) Idealize/model – assumptions on geometry, load/stress and deformations (2) Draw free body diagram (3) Apply method of sections to obtain internal force/moment resultants (4) Apply structural constitutive relations to relate force/moment resultants to a) internal stresses b) deformations (usually requires integration – invoking boundary conditions) Elastic bending formulae Based on convention for positive bending moments and shear forces: for continuous loading, q, q = dS dx , S = dM Bending of a symmetric cross section about its neutral axis (mid plane for a cross-section with two orthogonal axes of symmetry). s xx =- Mz I M = EI d 2 w 2 xz SQ Ib where s is the axial (bending) stress, M is the bending moment at a particular cross-section, I is the second moment of area about the neutral axis, z is the distance from the neutral axis, E is the Young’s modulus of the material, w is the deflection, x is the axial coordinate along the beam, s is the shear stress at a distance z above the neutral axis, S is the shear force at a particular cross, section, Q is the

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## This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

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sprh04 - KEY CONCEPTS FOR MATERIALS AND STRUCTURES Handout...

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