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MIT 3 11 - Lecture Notes

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LECTURE #9 :3.11 MECHANICS OF MATERIALS F03INSTRUCTOR : Professor Christine OrtizOFFICE : 13-4022 PHONE : 452-3084WWW : http://web.mit.edu/cortiz/www• Review Trusses : Part 2• Trusses Part 3 :Energy Approach (Castigliano’s theorum)ABH10kNJCDEFGIKL15kN 5kN4kN2m3m8.72kN4kN21.28kNABH10kNJCDEFGIKL15kN 5kN4kN2m3m8.72kN4kN21.28kNReview Lecture #8 : Trusses Part 22. TRUSSES : Defined statically determinate and statically indeterminateSTATICALLY DETERMINATE :can solve the problem using just the (1) equations of static equilibrium STATICALLY INDETERMINATE :besides the (1) equations of static equilibrium, you also need(2) compatibility equations (geometrical continuity, e.g. deformations)(3) constitutive equations (material properties, e.g. Hooke’s law)B. To determine member forces:METHOD OF SECTIONS : advantage : force is any member can be found directly from an analysis ofa section of the truss which has cut that member; don’t have to go from joint to joint 1. Draw a free-body diagram of the entire truss2. Determine support reactions using the equations of static equilibrium 3. Identify members to be analyzed4. Cut an imaginary section of through the members of interest (maximum three)5. Isolate smaller part of truss, consider it as a single body in equilibrium, and draw free-body diagram 6. Write and solve equations of static equilibrium for diagram drawn in step 5*EFGKL5kN4kNDFCDFJCFIJ8.72kN4kNFJCyFJCxEFGKL5kN4kNDFCDFJCFIJ8.72kN4kN8.72kN4kNFJCyFJCxFJC⇒ΣFy=0FJC =6.71 kNFBD of Isolated Part of Trusscut through member of interestFIND FJCFree Body Diagrams : ReviewABH10kNJCDEFGIKL15kN 5kN4kN2m3mcut through member of interestEFGKL5kN4kND8.72kN4kN8.72kN4kN21.28kNCTTFCDFJCFIJtensionjoint jointmember forcesign conventionscompressionjoint jointmember forcesign conventionsElastic Strain Energy for Solving Deflections in Truss ProblemsCastigliano’s Theorum for Solving Deflections in Truss ProblemsCastigliano’s Theorum for Solving Deflections in Truss ProblemsABCD1 m1 mE12345610kNFIND DISPLACEMENT OF JOINT ECastigliano’s Theorum for Solving Deflections in Truss ProblemsABCD1 m1 mQEQ2Q2Q(T)(T)(C)(C)(T)(C)123456MAKE TABLE OF VALUES FOR EACH TRUSS MEMBERSUM COLUMN 4 FROM PREVIOUS CHART CREATEDδδδδQ=dUTOTAL= PiLidPidQ AiEidQΣi =1nThermal Expansion of Solid Materials∆T∆TLinear Coefficient of Thermal Expansion∆TLinear Coefficient of Thermal Expansion Values for Various MaterialsMaterial (ααααL(10-6/oF)) Polymers : Nylon (40-80) Rubber (70-110) Polyethylene (80-160) Brass (10.6-11.8) Bronze (9.9-11.6) Steel (5.5-9.9) Rock (3-5) Glass (3-6) Titanium (4.5-6) Concrete (4-8) Tungsten (2.4)Thermal Expansion : Sample Problem #1LoAoxyLoAoThermal Expansion : Sample Problem #1δδδδLoLoAo=xyAoLoAoPc+RRRThermal Expansion : Sample Problem


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MIT 3 11 - Lecture Notes

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