Simple Trusses: Method of Joints, Zero-Force Members, and Truss Analysis, Exams of Engineering Physics

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SIMPLE TRUSSES, THE

METHOD OF JOINTS,

& ZERO-FORCE MEMBERS

Objectives:

Students will be able to:

a) Define a simple truss.

b) Determine the forces in

members of a simple truss.

c) Identify zero-force members.

APPLICATIONS

(continued)

Trusses are also used in a variety of

structures like cranes and the frames

of aircraft or the space station.

How can you design a light weight

structure satisfying load, safety, cost

specifications, is simple to

manufacture, and allows easy

inspection over its lifetime?

SIMPLE TRUSSES

If a truss, along with the imposed load, lies in a single plane

(as shown at the top right), then it is called a planar truss.

A truss is a structure composed of slender members joined together at

their end points.

A simple truss is a planar truss which begins

with a triangular element and can be expanded

by adding two members and a joint. For these

trusses, the number of members (M) and the

number of joints (J) are related by the equation

M = 2 J – 3.

8

Introduction

• For the equilibrium of structures made of several

connected parts, the internal forces as well the external

forces are considered.

• In the interaction between connected parts, Newton’s

3

rd

Law states that the forces of action and reaction

between bodies in contact have the same magnitude,

same line of action, and opposite sense.

• Three categories of engineering structures are

considered:

a) Frames : contain at least one multi-force member,

i.e., member acted upon by 3 or more forces.

b) Trusses : formed from two-force members , i.e.,

straight members with end point connections

10

With these two assumptions, the members act as

two-force members. They are loaded in either

tension or compression. Often compressive

members are made thicker to prevent buckling.

2 -

Consider parts of the column

External Forces

Internal Forces (to the column AB)

From 2 to 1

From 1 to 2

Load

reaction

A

y

=

10

0N

A

y

= 10

0N

100 N

100 N

100 N

A

B

FBD

Joints Under Special Loading Conditions

6 -

• Forces in opposite members intersecting in

two straight lines at a joint are equal.

• The forces in two opposite members are

equal when a load is aligned with a third

member. The third member force is equal

to the load (including zero load).

• The forces in two members connected at a

joint are equal if the members are aligned

and zero otherwise.

• Recognition of joints under special loading

conditions simplifies a truss analysis.

14

THE METHOD OF JOINTS

When using the method of joints to solve for the forces in truss

members, the equilibrium of a joint (pin) is considered. All

forces acting at the joint are shown in a FBD. This includes all

external forces (including support reactions) as well as the forces

acting in the members. Equations of equilibrium ( å

F

X

= 0 and

å

F

Y

= 0) are used to solve for the unknown forces acting at the

joints.

A free-body diagram of Joint B

4. Repeat steps 2 and 3 at each joint in succession until all the

required forces are determined.

ZERO-FORCE MEMBERS

You can easily prove these results by

applying the equations of

equilibrium to joints D and A.

If a joint has only two non-collinear

members and there is no external

load or support reaction at that joint,

then those two members are zero-

force members. In this example

members DE, DC, AF, and AB are

zero force members.

Zero-force members can be

removed (as shown in the

figure) when analyzing the

truss.

rigidity of the truss, and to provide

support for various different loading

conditions.

EXAMPLE

1. Check if there are any zero-force members.
2. First analyze pin D and then pin A
3. Note that member BD is zero-force member. F

BD

= 0

4. Why, for this problem, you do not have to find the external

reactions before solving the problem?

Given

: Loads as shown on the truss

Find:

The forces in each member

of the truss.

Plan: