LECTURE #7 :3.11 MECHANICS OF MATERIALS F03INSTRUCTOR : Professor Christine OrtizOFFICE : 13-4022 PHONE : 452-3084WWW : http://web.mit.edu/cortiz/www• Review of Composites• Trusses Part 1Review : Lecture #6 Composite Materials• definitions : reinforcing component and “matrix”, anisotropic or isotropic• mechanical properties (E and σb) depend on :1) mechanical properties of each component2) relative amount of each component, i.e. “volume fraction” Vcomponent/Vtotal3) shape and size of reinforcing component4) loading orientation relative to anisotropic component• types of composites :1) Fiber-reinforced a) continuous aligned, b) woven, and c) short fiber chopped2) particulate• rule of mixtures for aligned continous fiber-reinforced composites :FFFF////Ecomposite stiffness parallel to fiber axisE composite stiffness perpendicular to fiber axisvolume fraction of fibers, elastic modulus of fibersvolume fractioff mmfmfm mfffmEvEvEEEvE vEEvEv⊥⊥=+=+===== n of matrix, elastic modulus of matrix1=ffmEvv=+Young’s Modulus of a Aligned Fiber CompositeMDSOLIDS EDUCATIONAL SOFTWARE(*http://www.mdsolids.com/)Introduction to TrussesTobin Memorial Bridge, BostonSchematic of a TrussABCDPEStatically Determinate and IndeterminateMethod of Joints to Determine Member ForcesSample Problem #1 : Find Forces in all MembersABCDPEtensioncompressiontensionjoint jointmember force1) Draw a FBD of entire truss2) Determine magnitude / direction of the support reactions using the eqs of static equilibriumsign conventionsmembers are each of unit lengthABCDPEP/2 P/23. 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 tensileSample Problem #1 : Find Forces in all MembersABCDPEP/2 P/23. 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 tensileSample Problem #1 : Find Forces in all MembersP/2AFABFADFADxFADyFBD of JOINT AABCDPECTP/2 P/2Sample Problem #1 : Find Forces in all MembersMove to Joint D :ABCDPECTP/2 P/2CTTTCSample Problem #1 : Find Forces in all MembersMove to subsequent joints :FAD=P/2sin60=FDB=FBE=FECFAB= Pcos60/2sin60=FBCFDE
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