LECTURE 8 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 1 Trusses Part 2 Methods of Sections and Energy Approach Castigliano s theorum Review Lecture 7 Trusses Part 1 1 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 sign conventions A To determine member forces tension METHOD OF JOINTS joint 1 Draw a free body diagram of the entire truss 2 Determine support reactions using the equations of static equilibrium member force FX 0 FY 0 MXY 0 tension 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 5 Write and solve equations of static equilibrium for diagram drawn in step 4 6 Move to an adjacent joint and repeat steps 4 5 until entire truss is solved C D C A T T B FAD FDB FBE FEC C FAB Pcos60 2sin60 FBC C P 2 CCW P 2 PIN R1x ROLLER R1y R1y FDE Pcos60 sin60 Moment Sign Conventions P each member is of unit length compression FAD P 2sin60 E T T joint CW supports Solving Sample Problem 1 with MDSolids C D C A T T T E C T B P P 2 go to modules trusses click on new truss create grid x direction 0 5 y direction 0 866 to get correct geometry members of unit length number of spaces 5 for both create truss add supports add loads hit compute to redo same truss hit edit P 2 Trusses Method of Sections Sample Problem 2 H I K J L 4kN 2m A 3m B 15kN C 10kN D E 5kN F G Trusses Method of Sections Sample Problem 2 Find FJC H I K J L 4kN 2m A 3m B 15kN C 10kN D E 5kN 1 Draw a free body diagram of the entire truss 2 Determine support reactions using the eqs of static equilibrium F G Trusses Method of Sections Sample Problem 2 Find FJC H I K J L 4kN 2m A 21 28kN 3m B 15kN C 10kN 3 Identify members to be analyzed D E F G 4kN 5kN 8 72kN 4 Cut a section of through the members of interest maximum three Trusses Method of Sections Sample Problem 2 Find FJC 5 Isolate smaller part of truss and draw free body diagram 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 Using Castigliano s Theorum for Solving Deflections in Truss Problems
View Full Document
Unlocking...