ENSC2004 - Lecture 6

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ENSC2004 - Lecture 5
Trusses & Method of Joints - Slides

Simple Trusses

• A truss is a structure composed of slender members joined together at their end points
  • If a truss lies in a single plane, it is called a planar truss

• A simple truss is a planar truss which begins with a triangular element and is expanded by adding two members and a joint

  

• The relationship between # of members and # of joints: $\text{M}=2\text{J}-3$

Analysis and Design Assumptions

• When designing truss, necessary to determine forces in each member
  • This is known as force analysis of a truss
• When doing this, we have two assumptions:
  1. All loads are applied at the joints
     • Weight of members is neglected as weight is small
  2. The members are joined together by smooth pins
• With these assumptions, the members act as two-force members
  • They are loaded in either tension or compression

Using our equations of equilibrium, we can solve for the forces acting upon members in a simple truss!

Zero-Force Member

• If a joint has only two non-collinear members and there is no external load or support reaction at that joint, then those two members are zero-force members
• In a THREE member joint: If TWO of those members ARE parallel AND there are no other external loads (or reactions) at the joint THEN the member that is not parallel is a zero force member

• They can be excluded from your analysis

Zero-force members are used to increase stability and rigidity of the truss, and to provide support for various different loading conditions

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Determinacy - Slides

External Determinacy

• If a truss has more external supports than is necessary to ensure equilibrium, the truss as a whole is statically indeterminate
  • The extra support is referred to as external redundancy

Internal Determinacy

• If a truss has more internal members than is necessary to ensure stability, the truss as a whole is statically indeterminate
  • The extra member is referred to as redundant member

Determinacy

• For a truss that is externally statically determinate, we will have 3 unknown reaction forces
  • We have $m$ unknown internal forces
    • $m$ is the # of members
  • Total unknowns: $3+m$
• At each joint ($j$) we have two equations of equilibrium
  • $\Sigma Fx=\Sigma Fy=0$
  • Number of equations: $2\times j$
• Therefore, a truss is statically determinate when: $3+m=2j$

Stability

• If $m+3<2j$ the truss will be unstable
  e.g. if we remove the diagonal member in the system below:

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ENSC2004 - Lecture 7