Applied Mechanics

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CHAPTER 4
TRUSS
CONTENT OF THE TOPIC:
 Definition of truss
 Types of truss
 Perfect Truss
 Imperfect Truss
 Deficient Truss
 Redundant Truss
 Assumption made for the analysis of truss
 Analysis of truss
 Types of methods of analysis
 Method of joint
 Method of section and
 Graphical method
 Problems on Method of joint and Method of section
Definition of Truss:
A truss is defined as a system of two force members connected in such a way that a rigid
structure is formed. Truss is made up of two force members.
Types of Trusses:

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Perfect Truss:
A perfect truss is that, which is made up of members just sufficient to keep it in
equilibrium, when loaded, without any change in its shape. Such structure satisfies
following equation.
n = 2j-3
where,
n = number of members
j = number of joints
Eg.
Basic Perfect Truss
Here n = 3 and j = 3
3 = (2 x 3) – 3
3= 3
Perfect Truss
Here n = 5 and j = 4
5 = (2 x 4) – 3
5= 5
Deficient Truss:
In such truss the numbers of members are less than (2j-3). Such trusses are unable to carry
any loads. So such trusses are unstable which undergo deformation.
Eg.
Here n = 4 and j = 4
4 = (2 x 4) – 3
4 < 5
Where, δ is lateral displacement
Redundant Truss:
In such truss the numbers of members are more than (2j-3). In such trusses the members are
more than required which is sufficient to carry loads. They don’t undergo any deformation.

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Eg.
Here n = 6 and j = 4
6 = (2 x 4) – 3
6 > 5
Member:
The straight component bars of the trusses joined at the ends by the pins are known as
members.
Two force member:
When a member is subjected to no couples and forces are applied at only two ends of the
member is called as two force member or two point force member.
Arrow away from joints Arrow towards the joints
or or
Arrow facing towards each other Arrow away from each other
Frame:
A frame is structure of combination of two force members and three force members or
multi-force members as shown in Fig. 2.
Figure 2

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Assumption made for the analysis of truss
1) All the members are pin jointed.
2) All the members are assumed to two force members.
3) The truss is loaded at the joints only.
4) The self weight of the truss is considered as negligible in comparison with the other
external forces acting on a truss.
5) The cross section of the members of trusses is uniform.
Analysis of Truss:
To analyze a truss is nothing but a determination of the reactions at the supports and the
forces in the members of the frame.
STEPS FOR MEHOD OF JOINTS AND MEHOD OF SECTION:
Method of Section:
1) When the forces in all members of a truss are to be determined, then the Method of
Joint is useful.
2) Calculate the support reactions for external loading acting on the truss.
3) Then find the forces in the members by joint by joint.
a. Select a joint, in such a way that it will have only two unknown members
(i.e. forces in the two members of a truss have to find).
b. We have to select only two unknowns at every joint because we are
available with only two equations (∑FY = 0 and ∑FX = 0).
c. Initially assume all the unknown forces in the members of a truss as tensile.
After calculation of force, if the calculated value in any of the member is
negative then it reveals that the assumed direction or sense in that member is
wrong; in that case change the sense. (i.e. if assumed direction is tension,
then make it as compression and vice versa, in F.B.D. and calculate the force
in other member by considering the changed sign. Repeat the same
procedure for other joints).
4) Prepare a table showing member, magnitude and sense of force of each member of a
truss.
Method of Section:
1) When the forces in a few members of a truss are to be determined, then the Method
of Section is mostly used.
2) Calculate the support reactions for external loading acting on the truss.
3) In this method, a section line is passed through the members, in which forces are to
be determined.

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4) The section line should be passed in such a way that, it does not cut more than three
members in which forces are unknown because we are available with three
equations ∑M = 0, ∑FY = 0 and ∑FX = 0.
5) If force in the members BC, GC and GF i.e. FBC, FGC, and FGF respectively we want
to calculate. Then pass a section line 1-1 through these members.
6) The part of the truss, on any one side of the section line, is treated as a free body in
equilibrium under the action of external forces on that part and forces in the
members cut by the section line. See Fig. (1) and (2). (We have to select the LEFT
or RIGHT part of the truss in such a way that, it will contain less geometry and
external loads acting on the truss).
Fig.1 Fig.2
7) The unknown forces in the members are then calculated by using the equations of
equilibrium.
∑M = 0, ∑Fy = 0 ∑FX = 0

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PROBLEMS ON ANALYSIS OF PERFECT TRUSSES
1. Find the forces in the members BC, GC and GF for the truss shown in following
Fig.
2. Find the forces in all members for the truss shown in following Fig.

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3. A cantilever truss of span 4.5 m is shown in Figure below. Find the forces in all the
members of the truss.
4. Find the forces in various members of truss as shown below. (May 2007 12 Mks)

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5. Find the forces in the members DE, LE, KN and EF for the truss shown in following
Fig.

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6. V g,,bm
7. Svjdjbu

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