3. Pin Jointed Trusses, Methods of Joints

Question 1

What is the definition of a truss?

Answer 1

• A truss is a structure consisting of straight members (bars) connected at joints

Question 2

Why do we use trusses?

Answer 2

Generally they are applied to many structures to save material and reduce weight.

Question 3

What are some assumptions we use to model trusses?

Answer 3

• Pin-jointed trusses are simplified models of reality, that are convenient for analysis.
• We (currently) only consider them in 2D (planer trusses)
• Each structural member can be modelled as a bar
• All bars are considered to be connected by pins
• It is assumed the bars are free to rotate without any friction
• All external forces and reactions are applied only in the joints. (i.e. no in the middle of the bar)
• We only consider small deformations, so we can consider the inital undeformed geometry for loading analysis
• Depending on the specific application the weight of the structure can be neglected (e.g. bridge vs lightweight bike)

Question 4

Why is it so important that bars can rotate freely without any friction?

Answer 4

No friction means that there are only axial forces (tensile and compressive) acting on the bar, but no moments.

Question 5

What are the two types of supports for trusses?

Consider the axial forces on each.

Answer 5

• Pinned (Pin support)
• Rolling / sliding (roller / slider support)

Question 6

What are the two aims of truss analysis?

Answer 6

• Evaluate strength (i.e. which bars will fail first?)
• Evaluate truss deformation

Question 7

State the two methods of truss analysis.

Answer 7

1. Methods of Joints
2. Methods of Sections

Question 8

What is the steps to solve forces on bars (using methods of joints) for a three bar truss?

Consider solving this question if you want

Answer 8

1. Draw a Free Body Diagram and determine external reactions
   
   • Solve the vertical equilibrium equation
   • Solve the horizontal equilibrium equation
   • Solve the rotational equilibrium equation
2. Once you have solved all the external forces, you can use the methods of joints by drawing a Free Body Diagram for at one of the joints. Solving the two unkown forces outwards from the joint
   
   • Solve the angle using pythagoras theorem
   • Solve the vertical equilibrium equation
   • Solve the horizontal equilibrium equation
   • Solve the rotational equilibrium equation
3. We can then move to another joint and do the same thing to find the remaining unkown force(s), using prior results to find all forces acting on the bars and then summarise it into one Free Body Diagram.

Question 9

What is a limitation of using Methods of Joints?

Answer 9

It works well if there are only a few bars. If there are too many, it can get long and complicated, especially if we only care about a few forces in a few bars. Therefore it would be easier to use Methods of Sections.