Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 28:Method of Joints

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 2 Lecture 28 Objective to understand the method of joints for establishing forces in truss members

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 3 Recall 2D Rigid Body Equilibrium Support Reactions AyAy AxAx CyCy

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 4 Method of Joints Joint Equilibrium  FBD at a joint  Particle equilibrium concepts  Solve for member forces

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 5 Method of Joints (cont.) Joint Forces  Tension pulls on joint + convention  Compression pushes on joint - convention  Newton’s 3 rd Law T pull on member C push on member

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 6 Method of Joints Equilibrium Equations Two-Force Member  Coplanar and concurrent force system  What does this mean? Necessary for Equilibrium Automatically Satisfied

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 7 Procedure for Method of Joints 1. Find Support Reactions  Typically required but not always necessary 2. Draw FBD at Truss Joint  Select joint with 1 known force and at most 2 unknowns  Assume forces are tensile (positive scalar) unless obvious by inspection 3. Apply Equations of Equilibrium 4. Repeat for all Joints

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 8 Joint Free Body Diagrams

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 9 Coordinate Axes Orientation

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 10 Coordinate Axes Orientation (cont.) Resolve F CB Find Support Reactions

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 11 Coordinate Axes Orientation (cont.) Resolve F CB Find Support Reactions Resolve F CD

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 12 Example Determine the force in each member. Indicate whether the member is in tension (T) or compression (C).

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 13 Example (cont.) Where to Start?  Examine joints # Known Forces? # Unknown Forces? F BA F BC 500N

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 14 Example (cont.) Joint B

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 15 Example (cont.) Joint C

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 16 Example (cont.) Joint A

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 17 Example (cont.) Support Reactions  More than 2 unknowns at each joint then determine reactions first  For this case not necessary but to show equivalence AyAy AxAx CyCy

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 18 Example (cont.) Results Summary

ENGI 1313 Statics I – Lecture 28© 2007 S. Kenny, Ph.D., P.Eng. 19 References Hibbeler (2007) mech_1