ANALYSIS OF STRUCTURES

Chapter Objectives Determine the forces in the members of a truss using the method of joints and the method of sections

Roof Trusses

Definition Load Transferred Load not Transferred Load Transferred

Truss Types Trusses are categorised into 3 groups depending on the shape of the top chord Triangular Roof Trusses Crescent roof Trusses Other Types

Triangular Roof Trusses Simple Triangular geometric shape Web Bracing Straight Top Chord

Triangular Roof Trusses

Crescent Roof Trusses Top Chord is manufactured with a curved top chord The Harbour bridge is a good example

Other Types Top Chords may be parallel – such as floor joist trusses Or they may be nearly parallel – such as bridges

Roof Truss Members

Roof Truss Panel Points

Roof Truss Stress Types

Parallel Chord Trusses Top Chord & Bottom Chord are parallel Used as Rafters Advantages Lighter Larger Spans Allow for easy access for services Disadvantages Cannot be site modified Generally Deeper

Parallel Chord Trusses

Transfer of Loads Click to show load flow on correctly installed trusses Tensile Load to Counteract Compressive Load Compression Load Internal Wall Min 12 Clear No load in this Area

Transfer of Loads Click to show load flow on incorrectly installed trusses Bottom Chord is not designed to take horizontal load and will fail Bottom Chord bearing on Internal Wall Load transmits Horizontally to wall.

Trusses Method of Joints Method of Sections

The Method of Joints For truss, we need to know the force in each members Forces in the members are internal forces Resultant of internal force in each member has to equal to zero (equilibrium condition) For external force members, equations of equilibrium can be applied

The Method of Joints Procedure for Analysis Draw the FBD with at least 1 known and 2 unknown forces Find the external reactions at the truss support Choose the joint has the less unknown forces Apply equilibrium equations Use known force to analyze the unknown forces

Example 1 Determine the force in each member of the truss and indicate whether the members are in tension or compression.

Example 2 Determine the force members HC,CG and DF of the truss. State if the members are in tension or compression. Use joint method of analysis

The Method of Sections Consider the truss and section a-a as shown Member forces are equal and opposite to those acting on the other part – Newton’s Law

The Method of Sections Free-Body Diagram Procedure for Analysis Free-Body Diagram Choose the section that at least cut almost if not all the required internal forces. Determine the truss’s external reactions Use equilibrium equations to solve member forces at the cut session Draw FBD of the sectioned truss which has the least number of forces acting on it Find the sense of an unknown member force

The Method of Sections Equations of Equilibrium Procedure for Analysis Equations of Equilibrium Summed moments about a point Find the 3rd unknown force from moment equation

Example 3 Determine the force in members GE, GC, and BC of the truss using sectional method of analysis. Indicate whether the members are in tension or compression.

Example 3

Example 4 Determine the force in members DE, EB, and AB of the truss using sectional method of analysis. Indicate whether the members are in tension or compression

Example 4