1. Engineering Mechanics: Statics
Chapter 4: Structures

2. Statically Determinate Structure
Do not have more supporting constraints than are necessary to maintain equilibrium
This chapter focus on trusses, frames and machines
Truss = A framework composed of members joined at their ends to form a rigid structure
When the members lie in a single plane = a plane truss

3. Simple Trusses Basic element of a plane truss = triangle
Three bars joined by pins at their ends constitute a “rigid” frame (noncollapsible)
Structures built from a basic triangle are known as simple trusses
Truss members = Two-force members

4. Simple Trusses Assumptions Two approaches for force analysis
All external forces are applied at the joints. (If consider weight, apply half of the magnitude at each end)
The members are joined together by pin connections
Two approaches for force analysis
Method of joints
Method of sections

5. Method of Joints Used to find the forces in the truss members
Analysis steps
Draw FBD of a joint
Use and to find the member forces
Begin analysis with a joint where
at least one known load exists
Not more than two unknown forces are present

6. Method of Joints Special conditions Zero-force member
(a) Three members – two collinear + one noncollinear
(b) Two noncollinear members
Two pairs of collinear members – forces in each pair equal and opposite
Choice of reference axis

7. Problem 4/20
A snow load transfers the forces shown to the upper joints of a Howe roof truss. Neglect any horizontal reactions at the supports and solve for the forces in all members
Problem 4/21

8. Method of Sections Take advantage of moment equation of equilibrium
Not necessary to proceed with the calculation from joint to joint until the member in question has been reached
Procedures
1. Determine external reactions by considering whole truss (R1 & R2)
2. An imaginary section (dashed line) is passed through the truss
3. To determine BC use
To determine FE use
To determine BE use

9. Sample Problem 4/4
Calculate the force in member CD and member DJ of the roof truss illustrated. Neglect any Horizontal components of force at the supports

10. Frames and Machines
Structures which contain one or more multi-force members
Frame = Structure designed to support loads
Machine = Structure which transforms input actions (forces or couples) to output actions

11. Problem 4/71 Determine the force supported by the roller at E.
Ans E = 150 N

12. Problem 4/80
The elements of a floor jack are shown in the figure. The figure CDFE is a parallelogram. Calculate the force in the hydraulic cylinder AB corresponding to the 10-kN load supported as shown. What is the force in link EF?