Triaksha's Notes 🍀

Frames and Machines

2 min read

Frames are common types of structures that have at least one multi-force member, where trusses have only two-force members. They’re most often connected by pins at the joints. 

Frames are generally stationary, and are designed to support external loads. They have at least one multi-force member. 

Machines contain moving parts, and are designed to transmit and alter the effect of forces. They also have at least one multi-force member. 

Useful to know, two-force members are members which have no forces along their length besides at their joints, and they’re supported by pins. Their shape isn’t relevant to whether they’re a two-force member or not. 

FBD for Frames and Machines

  1. Isolate each part by drawing outlined shape
  2. Establish x-y axes
  3. Show all forces and/or couple moments, assume unknowns
  4. Usually represent with x, y components
  5. Indicate dimensions

Analysis

  1. Draw FBD
  2. Identify any two-force members, and represent them as having two equal but opposite collinear forces acting at their points of application
  3. Draw forces common to any two contacting members as having equal magnitudes and opposite directions; they’re usually between pins and members
  4. For joints with more than two members or an external force, draw an FBD for the pin
  5. Apply equations of equilibrium to solve for unknowns

Solving the equilibrium equations is simpler considering members that are subjected to forces at only two points, knowing that the resultant forces at each point must be equal in magnitude and act in opposite directions along the line joining them. 

When pulleys and cords are involved, draw the FBDs for:

  • The entire frame including pulleys and cords
  • The frame without pulleys and cords
  • Pulleys alone

Trying to solve problems with frames and machines is needlessly complex without simplification from knowing that connected parts always contain equal and opposite forces.

physics statics

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