LECTURE #8 :3.11 MECHANICS OF MATERIALS F03INSTRUCTOR : Professor Christine OrtizOFFICE : 13-4022 PHONE : 452-3084WWW : http://web.mit.edu/cortiz/www• Review Trusses : Part 1• Trusses Part 2 : Methods of Sections and Energy Approach (Castigliano’s theorum)Review Lecture #7 : Trusses Part 11. TRUSSES : • definitions : joints, members, supports (e.g. pin, roller) ASSUMPTIONS :• joints are free to rotate, i.e. no moments at joints • all members support either axial tension or compression, i.e. no shear or bending A. To determine member forces:METHOD OF JOINTS :1. Draw a free-body diagram of the entire truss2. Determine support reactions using the equations of static equilibrium :ΣFX=0, ΣFY =0,, ΣMXY=03. 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 tensile5. Write and solve equations of static equilibrium* for diagram drawn in step 46. Move to an adjacent joint and repeat steps 4-5 until entire truss is solvedtensioncompressiontensionjoint jointmember forceR1yR1xsupportsPINROLLERR1yABCDPECTP/2 P/2CTTTCFAD=P/2sin60FAD=FDB=FBE=FECFAB= Pcos60/2sin60=FBCFDE =Pcos60/sin60sign conventionseach member is of unit lengthCCW+CW-Moment Sign Conventions:Solving Sample Problem #1 with MDSolidsABDPECTP/2 P/2CTTTC• go to modules / trusses • click on “new truss”• create grid : x-direction 0.5, y-direction 0.866 (to get correct geometry, members ofunit length) number of spaces =5 for both• create truss• add supports• add loads• hit compute• to redo same truss hit “edit”Trusses : Method of Sections : Sample Problem #2ABH10kNJCDEFGIKL15kN 5kN4kN2m3mTrusses : Method of Sections : Sample Problem #2Find FJCABH10kNJCDEFGIKL15kN 5kN4kN1. Draw a free-body diagram of the entire truss2. Determine support reactions using the eqs of static equilibrium 2m3mTrusses : Method of Sections : Sample Problem # 2 Find FJC3. Identify members to be analyzed4. Cut a section of through the members of interest (maximum three)ABH10kNJCDEFGIKL15kN 5kN4kN2m3m8.72kN4kN21.28kNTrusses : Method of Sections : Sample Problem # 2 Find FJC5. Isolate smaller part of truss and draw free-body diagram EFGKL5kN4kND8.72kN4kNFCDFJCFIJtensionjoint jointmember forcesign conventionscompressionjoint jointmember forcesign conventionsElastic Strain Energy for Solving Deflections in Truss ProblemsCastigliano’s Theorum for Solving Deflections in Truss ProblemsUsing Castigliano’s Theorum for Solving Deflections in Truss
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