LECTURE 7 3 11 MECHANICS OF MATERIALS F03 INSTRUCTOR Professor Christine Ortiz OFFICE 13 4022 PHONE 452 3084 WWW http web mit edu cortiz www Review of Composites Trusses Part 1 Review Lecture 6 Composite Materials definitions reinforcing component and matrix anisotropic or isotropic mechanical properties E and b depend on 1 mechanical properties of each component 2 relative amount of each component i e volume fraction Vcomponent Vtotal 3 shape and size of reinforcing component 4 loading orientation relative to anisotropic component types of composites 1 Fiber reinforced a continuous aligned b woven and c short fiber chopped 2 particulate F rule of mixtures for aligned continous fiber reinforced composites E v f E f vm Em E E f Em v f Em vm E f E composite stiffness parallel to fiber axis F E composite stiffness perpendicular to fiber axis v f volume fraction of fibers E f elastic modulus of fibers vm volume fraction of matrix E f elastic modulus of matrix 1 v f vm F F Young s Modulus of a Aligned Fiber Composite MDSOLIDS EDUCATIONAL SOFTWARE http www mdsolids com Introduction to Trusses Tobin Memorial Bridge Boston Schematic of a Truss D A E C B P Statically Determinate and Indeterminate Method of Joints to Determine Member Forces Sample Problem 1 Find Forces in all Members sign conventions 1 Draw a FBD of entire truss 2 Determine magnitude direction of tension joint the support reactions using the eqs of static equilibrium member force joint tension compression E D A C B P members are each of unit length Sample Problem 1 Find Forces in all Members 3 Identify a joint where you know the maximum amount of forces e g a support with two members D 4 Draw a free body diagram of the joint and determine whether forces are compressive or A tensile E C B P P 2 P 2 Sample Problem 1 Find Forces in all Members 3 Identify a joint where you know the maximum amount of forces e g a support with two members 4 Draw a free body diagram of the joint and determine whether forces are compressive or tensile D E A C B P P 2 P 2 FAD FADy FADx A FAB P 2 FBD of JOINT A Sample Problem 1 Find Forces in all Members Move to Joint D D E C A T C B P P 2 P 2 Sample Problem 1 Find Forces in all Members C D C A T T T E T B C C P P 2 P 2 Move to subsequent joints FAD P 2sin60 FDB FBE FEC FAB Pcos60 2sin60 FBC FDE Pcos60 sin60
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