Engi 1313 mechanics i
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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

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Engi 1313 mechanics i

ENGI 1313 Mechanics I

Lecture 28:Method of Joints


Lecture 28 objective

Lecture 28 Objective

  • to understand the method of joints for establishing forces in truss members


Recall 2d rigid body equilibrium

Recall 2D Rigid Body Equilibrium

  • Support Reactions

Ax

Ay

Cy


Method of joints

Method of Joints

  • Joint Equilibrium

    • FBD at a joint

    • Particle equilibrium concepts

    • Solve for member forces


Method of joints cont

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

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

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


Joint free body diagrams

Joint Free Body Diagrams


Coordinate axes orientation

Coordinate Axes Orientation


Coordinate axes orientation cont

Find Support Reactions

Coordinate Axes Orientation (cont.)

Resolve FCB


Coordinate axes orientation cont1

Find Support Reactions

Coordinate Axes Orientation (cont.)

Resolve FCB

Resolve FCD


Example 28 01

Example 28-01

  • Determine the force in each member. Indicate whether the member is in tension (T) or compression (C).


Example 28 01 cont

500N

FBC

FBA

Example 28-01 (cont.)

  • Where to Start?

    • Examine joints

      • # Known Forces?

      • # Unknown Forces?


Example 28 01 cont1

Example 28-01 (cont.)

  • Joint B


Example 28 01 cont2

Example 28-01 (cont.)

  • Joint C


Example 28 01 cont3

Example 28-01 (cont.)

  • Joint A


Example 28 01 cont4

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 cont5

Example 28-01 (cont.)

  • Results Summary


References

References

  • Hibbeler (2007)

  • http://wps.prenhall.com/esm_hibbeler_engmech_1


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