Trusses are structures commonly seen in bridges, roofs, etc.
Members: Individual pieces of a truss.
Joints: Connection points of members, usually using a pin.
Tension vs Compression:
Tension: Forces pull on member ends.
Compression: Forces push on member ends.
Method of Joints
Equilibrium Concept: If the whole truss is in equilibrium, so is each member and joint.
Goal: Write equilibrium equations to solve for forces at each member.
Starting Point: Begin at a joint with at least one known force and a maximum of two unknowns.
Solving Trusses
Steps:
Isolate the Joint: Start with a joint with known forces and up to two unknowns.
Assume Force Direction: Decide if the force is towards or away from the joint. A wrong assumption results in a negative value, indicating the opposite direction.
Determine Tension or Compression:
If the calculated force is coming towards the pin, it's in compression.
If the force is going away from the pin, it's in tension.
Force Components: Break forces into x and y components.
Equilibrium Equations: Write equations for both x and y direction forces.
Example Problem 1
Starting Point: Joint D
Assumptions: Forces away from pin
Equations:
Y-axis: Solve for member DC, result indicates tension.
X-axis: Result is negative, indicating compression.
Next Joint: Point C, using known forces from D.
Assumptions: CE towards pin C, CB away.
Equations:
Y-axis: Correct assumptions, in compression.
X-axis: Correct assumptions, in tension.
Further Analysis: Point B, Point E
Use force directions found in previous steps, adjust for direction.
Example Problem 2
Objective: Determine force in members
Starting Point: Joint D
Find angles: Use trigonometry.
Assumptions: Force DE towards pin D, DC away.
Equations:
X-axis: Solve, indicating compression.
Y-axis: Solve, indicating tension.
Next Joint: Point C, assume forces and solve.
Point E Analysis: Determine angles, write equilibrium equations.
Example Problem 3
Objective: Max force P that can be applied
Constraints: Max tension = 5 kN, max compression = 3 kN
Angles: Use trigonometry for angles in the truss.
Starting Point: Point C
Assumptions: Forces towards pin C
Equations: Write forces in terms of P.
Further Analysis: Points D and A
Solve equations to ensure forces do not exceed given constraints.
Conclusion
Method of Joints: Effective for solving truss forces.
Key Skills: Breaking forces into components, writing equilibrium equations, using trigonometry for angles.
Practical Application: Understanding constraints in tension and compression limits for safety in truss design.