ES220 Statics

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ES220 Statics

• Exam III Review Notes

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Analysis of Structures

• Trusses
• Designed to support loads
• Consist entirely of two-force members
• Frames
• Designed to support loads
• Include one or more multi-force members
• Machines
• Designed to transmit and/or modify forces
• Include one or more multi-force members

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Two-Force Members

• Pinned at both ends (both joints)
• No applied forces between joints
• No applied moments
• Line of action of forces is directed along a line
  drawn between the two joints

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Trusses

• Consist entirely of straight two-force members,
  connected at joints

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Trusses

• Example on board decompose truss into two-force
  members and joints, and show how forces meet at
  joints

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Trusses Method of Joints

• Typically used to find forces in all or several
  of the members
• Each joint is a particle
• Particle equilibrium in 2D
• For each joint, we have 2 equations, therefore,
  we can solve for 2 unknowns
• Must start process at a joint with only 2 unknown
  forces

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Trusses Method of Joints

• Find a joint with only two unknown forces
• First, may need to draw an FBD of the entire
  truss and find support reactions
• Draw FBD of selected joint
• Draw each force along the direction of the member
• Draw in tension (away from joint)
• Find angle of force from truss geometry
• Resolve angled forces into x, y components

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Trusses Method of Joints

• Apply equilibrium, to solve for 2 unknown forces
• A sign the force is tension (T)
• A sign the force is compression (C)
• Find the next joint that has only 2 unknown
  forces and repeat the process
• Typically this is adjacent to the prior joint
• Repeat with additional joints until all member
  forces are known.
• Remember to specify (T) or (C) for each force!

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Special Cases
Zero Force Members
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Trusses Method of Joints

• Example

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Trusses Method of Joints

• Example

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Trusses Method of Sections

• Typically used when only 1 or a few member forces
  are needed
• Since a section consists of multiple joints and
  multiple members, it is a rigid body
• Rigid body equilibrium in 2D
• For each section, have 3 equations, therefore,
  can solve for 3 unknown forces

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Trusses Method of Sections

• Identify the member(s) for which we will
  determine the forces
• Can determine up to 3 forces for each section
• Create a separable section by cutting through the
  member(s)
• May need to cut additional members to cut loose a
  section
• Decide which portion of the truss to keep

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Trusses Method of Sections

• Draw a free body diagram of the section
• Replace cut members with forces directed along
  the direction of the cut members
• Draw unknown forces in tension (pointed away from
  the joint)
• Include externally applied forces and support
  reactions
• First, you may need to draw an FBD of the entire
  truss to find support reactions
• Include dimensions needed to sum moments

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Trusses Method of Sections

• Determine angles from truss geometry
• Resolve angled forces into x, y components
• Apply equilibrium,to solve for 3 unknown forces
• A sign the force is tension (T)
• A sign the force is compression (C)

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Trusses Method of Sections
Special Case Finding only one force

• Cut the member for which you are finding the
  force
• If possible, choose the other cuts such that the
  extra unknown forces (but not the force you need)
  pass through a single joint
• Sum the moment about that joint

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Trusses Method of Sections

• Example

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Frames

• Contain at least one multi-force member
• Objective Find some or all forces acting on
  members and/or find support reactions

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Frames Method of Analysis

• Draw a FBD of the entire frame, showing applied
  loads and support reactions

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Frames Method of Analysis

• Draw a FBD for each member of the frame
• Find any two-force members
• Pinned at both ends, no applied moments or loads
• Draw forces directed along line connecting the
  two joints

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Frames Method of Analysis

• Multi-force members
• Pin connections x and y reaction forces
• Where two members connect, draw forces equal and
  opposite

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Frames Method of Analysis

• Draw forces on connecting members equal and
  opposite
• Draw forces due to two-force members in the known
  direction

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Frames Method of Analysis

• FBD of entire frame is a rigid body
• A multi-force member is a rigid body
• For each rigid body, can solve for three
  unknowns, using 2D equilibrium
• Using 2 or more of these rigid bodies, can find
  all the desired forces and reactions

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Frames Method of Analysis

• Example

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Machines

• Transmits or modifies forces
• Contain one or more multi-force members

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Machines Method of Analysis

• Similar to method for frames

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Machines
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Machines
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Machines
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Machines