LECTURE 9 3 11 MECHANICS OF MATERIALS F03 INSTRUCTOR Professor Christine Ortiz OFFICE 13 4022 PHONE 452 3084 WWW http web mit edu cortiz www Review Trusses Part 2 Trusses Part 3 Energy Approach Castigliano s theorum Review Lecture 8 Trusses Part 2 2 TRUSSES Defined statically determinate and statically indeterminate STATICALLY 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 of a 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 truss 2 Determine support reactions using the equations of static equilibrium 3 Identify members to be analyzed 4 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 FBD of Isolated Part of Truss FIND FJC FJCx K L H J I K L FIJ 4kN 4kN FJC 2m A 21 28kN 3m B 15kN C 10kN D E 5kN F FCD G D E F 4kN 5kN 8 72kN cut through member of interest FJCy FJC Fy 0 FJC 6 71 kN G 4kN 8 72kN Free Body Diagrams Review H I 3m B C 15kN 21 28kN L 4kN T 2m A K J C T D 10kN E G F 4kN 5kN 8 72kN cut through member of interest K FIJ L sign conventions tension 4kN joint FJC FCD compression D E 5kN F member force joint sign conventions G 4kN 8 72kN joint member force joint Elastic Strain Energy for Solving Deflections in Truss Problems Castigliano s Theorum for Solving Deflections in Truss Problems Castigliano s Theorum for Solving Deflections in Truss Problems 1 3 1m 2 4 6 B E C A 1m D 5 10kN FIND DISPLACEMENT OF JOINT E Castigliano s Theorum for Solving Deflections in Truss Problems 2Q A T 1 T 3 1m C 2Q C 4 6 B Q 1m C D T 2 5 C E Q MAKE TABLE OF VALUES FOR EACH TRUSS MEMBER SUM COLUMN 4 FROM PREVIOUS CHART CREATED Q dUTOTAL dQ n i 1 PiLi dPi AiEi dQ Thermal Expansion of Solid Materials T T Linear Coefficient of Thermal Expansion T Linear Coefficient of Thermal Expansion Values for Various Materials Material L 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 1 Lo y Ao x Lo Ao Thermal Expansion Sample Problem 1 R Lo Ao Pc Lo y Ao Lo Ao x R R Thermal Expansion Sample Problem 1
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