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ENGI 1313 Mechanics I . Lecture 28: Method of Joints. Lecture 28 Objective. to understand the method of joints for establishing forces in truss members. Recall 2D Rigid Body Equilibrium. Support Reactions. A x. A y. C y. Method of Joints. Joint Equilibrium FBD at a joint
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ENGI 1313 Mechanics I Lecture 28: Method of Joints
Lecture 28 Objective • to understand the method of joints for establishing forces in truss members
Recall 2D Rigid Body Equilibrium • Support Reactions Ax Ay Cy
Method of Joints • Joint Equilibrium • FBD at a joint • Particle equilibrium concepts • Solve for member forces
Method of Joints (cont.) • Joint Forces • Tension pulls on joint • + convention • Compression pushes on joint • - convention • Newton’s 3rd Law • T pull on member • C push on member
Method of Joints Equilibrium Equations • Two-Force Member • Coplanar and concurrent force system • What does this mean? Automatically Satisfied Necessary for Equilibrium
Procedure for Method of Joints • Find Support Reactions • Typically required but not always necessary • 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 • Apply Equations of Equilibrium • Repeat for all Joints
Find Support Reactions Coordinate Axes Orientation (cont.) Resolve FCB
Find Support Reactions Coordinate Axes Orientation (cont.) Resolve FCB Resolve FCD
Example 28-01 • Determine the force in each member. Indicate whether the member is in tension (T) or compression (C).
500N FBC FBA Example 28-01 (cont.) • Where to Start? • Examine joints • # Known Forces? • # Unknown Forces?
Example 28-01 (cont.) • Joint B
Example 28-01 (cont.) • Joint C
Example 28-01 (cont.) • Joint A
Example 28-01 (cont.) • Support Reactions • More than 2 unknowns at each joint then determine reactions first • For this case not necessary but to show equivalence Ax Ay Cy
Example 28-01 (cont.) • Results Summary
References • Hibbeler (2007) • http://wps.prenhall.com/esm_hibbeler_engmech_1