Structural_Analysis-I,_Unit load.pptx

Course Title: Structural Analysis
Course Code: RCI4C003
– I
Lecture PPT of Module – III
4th Semester, B. Tech
Civil Engineering
By
Dr. Kishor Chandra
Professor and Head
Department of Civil
Panda
Engineering
GCEK, Bhawanipatna, Odisha

Dr. Kishor Chandra Panda
Professor and Head
Department of Civil Engineering
GCEK, Bhawanipatna, Odisha
Deflection of Pin - Jointed
Truss by Unit Load Method

Introduction
A truss consists of the number of members connected at the
joint called as pin-jointed truss.
It is assumed that pin-jointed truss carry axial force only.
A truss which satisfies the equation (m = 2j – 3) is known



as perfect
A perfect
truss.
truss is one which has just sufficient members to

keep the truss in equilibrium under any external force
acting at
Truss is
way that
its joints.
a structural member that is assembled in such a
forces are applied only on the ends.

GCEK,
Bhawanipatna
2

Classification of Truss
Statically
determinate
plane truss
Statically
indeterminate
plane truss
Statically
determinate
space truss
Statically
indeterminate
space truss
Plane Truss
Space Truss
Perfect Truss
Truss
Imperfect
Truss
Simple Truss
Compound
Truss
Complex
Truss
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Bhawanipatna
3

Zero Force Members used for analysis of the Truss
• The zero force members may be directly used, during the
analysis of the truss.
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4

Deflection of pin-jointed plane truss by unit load method
 Unit load method can be used for finding deflection of a single joint at a time.
Deflection of the truss can be find out by
Where, ∆ = Displacement at the point in the direction of unit load applied
P´ = Stress due to unit load
e = Strain due to applied load
 In the case of a pin-jointed plane frames, there is only one type of stress, i.e.
direct stress. This stress may be different in different
all points in a member.
 Hence,
members but is constant at
Where, ∑ is to cover all the members
A = Cross sectional area of members
L = Length of the member
P´ = Stress due to unit load =
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Where, k = Force in the member due to unit load
e = Strain due to given load
Where, P = force in the member due to given loading
 Displacement at a point in the direction of unit load is
∆
• The method needs analysis of the truss twice, once with the given
loading to get ‘P’terms, and second time with unit load to get ‘k’terms.
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Bhawanipatna
6

Sign Convention
If the force in the member of the truss is tensile in nature, the arrow
mark should be away from the joint.

If the force in the member of the truss is compressive in nature, the
arrow mark should be towards the joint.

Use tensile force in the member of the truss positive (+) and

compressive force negative (-)
In the analysis of each joint, use write arrow mark positive and left

arrow mark negative. Also, upward arrow mark positive and
downward arrow mark negative.
Clockwise moment positive and anticlockwise moment negative.

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Bhawanipatna
7

Procedure for calculating truss deflection
First, calculate the real forces in the member of the truss either by
method of joints or by method of sections due to externally applied
forces. (P)

Then, calculate forces in the member of the truss consider the
the
the

virtual load system such that only a unit load is considered at
joint in the horizontal or in the vertical direction where
deflection is required. (k)
The length of the truss member is calculated from the geometry. (L)




The area of the truss member is known in the problem. (A)
Modulus of Elasticity is known in the problem, (E)
Displacement at the joint is calculated in the direction of unit
is
∆
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Structural_Analysis-I,_Unit load.pptx

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