FARIZ ASWAN AHMAD ZAKWAN

2.1 Introduction

A truss comprises straight bars joined together at their ends in the form of rivets or welds.

A typical truss consists of three straight bars that form a triangle. Roof trusses are often used as part of an industrial building frame. Figure 2.1 shows some of the common types of trusses used. Trusses also being used for bridge trusses as shown in Figure 2.2 Trusses can be classified as simple truss, compound truss and complex

truss.

Learning Outcome: • At the end of this chapter, students should be able to:

Solve the axial forces in members by using Method of section, joint and graphical method.

Figure 2.1

Figure 2.2

All ideal trusses when analysed are subjected to the following assumptions: All external forces are applied at the joints Members are connected by frictionless hinges or pins Stress in each member is constant along its length

The objective of analyzing the trusses is to determine the reactions and member forces.

Three methods to analyze member forces of the trusses Method of joints Method of sections Graphical method: Maxwell’s diagram

2.2 Method of jointsThe first method to analyze a truss assumes that all

members are in tension.A tension member is when a member experiences pull

forces at both ends of the bar (the force tends to elongate the member). Denoted by positive (+) sign.

A compression member is when a member experiences push forces at both ends (the force tends to shorten the member). Designed as negative (-) sign.

Tension (+) Compression (-)

P1 P1 P2 P2

In the method of joints, a cut is made around a joint and the cut portion is isolated as FBD.

If the truss is in equilibrium, then each of its joints must also be in equilibrium.

Using the equations of equilibrium:

ΣFx = 0, ΣFy = 0 the unknown member forces are solved

2.2.1 Simple guidelines

1. Draw FBD2. Solve the reactions3. Select a joint with a minimum number of unknowns

(not more than 2) and analyse using ΣFx = 0, ΣFy = 0

4. Proceed to other joints, concentrating on joints that have a minimum number of unknowns

5. Check member forces at unused joint (ΣFx = 0, ΣFy = 0)

6. Tabulate the member forces (tension (+) and compression (-))

Example 2.1: Determine the reactions of the truss as shown in Figure 2.1.Using the method of joints, determine the force in each

member of the truss.

20kN 25kN

15kN2m 2m

1.5m

A

E

C D

B

2.3 Method of sections The method of sections is an effective method in

finding forces in all members of a truss where only a few members of a truss are to be found.

This method consists of passing an imaginary section through the truss, thus cutting it into two parts.

In the method of section, a larger portion of the truss will be chosen as a free body, composed of several joints and members, provided that the desired force is one of the external forces acting on that portion

Simple guidelines:-1. Pass a section through a maximum of three members

of the truss, one of which is the desired member (that is divide the truss into two completely separate parts)

2. For one part of the truss only, take moments, about the point where the two members intersect and solve for the member force (ΣM = 0)

3. Solve the other two unknowns by using equilibrium equations for forces (ΣFx = 0, ΣFy = 0)

Example 2.2Find the member forces in members CD, GD and GF

as shown below.

2.4 Graphical methodSimple guidelines:-

1. Solve the reactions at the supports by solving equations of equilibrium for the entire truss

2. Move clockwise around the outside of the truss, draw to scale the force polygon for the entire truss

3. Take each joint in turn, draw a force polygon by treating successively joints acted upon by only two unknown forces

4. Measure the magnitude of the force in each member from the Maxwell diagram

5. Note that work proceed from one end of the truss to the other.

Note: equipment – set square is required.