Chapter 3
Rayleigh-Ritz Method
As discussed in Chapter 2, one can solve axially loaded bars of arbitrary cross-section and material
composition along the length using the lumped mass-spring model. As shown in Figure 12 of Exercise
2.4, one can approach th

STRESS
The state of stress at any point in a loaded body is dened completely in terms of the
nine components of stress: xx , yy , zz , xy , yx , yz , zy , zx , and xz , where the rst
three are the normal components and the latter six are the components of

Chapter 5
Finite Element Modeling for Bar Elements Using the MPE Principle
In this Chapter, we will systematically construct the finite element model for the bar element.
5.1 Strain energy for a bar element
Let us recall from Chapter 4 that the strain and

Chapter 1
Introduction
1.1
What is the finite element method
The finite element method (FEM) is a numerical technique for solving problems which are described
by partial differential equations or can be formulated as functional minimization. A domain of i

Chapter 4
Shape Functions
In the finite element method, continuous models are approximated using information at a finite
number of discrete locations. Dividing the structure into discrete elements is called discretization.
Interpolation within the element

Chapter 6
Finite Element Formulation for Trusses
We know that each element in the truss (see Figure 2a) can only take either a tensile or compressive axial
force. In that respect, truss elements are identical to bar elements. So, all the analysis done in

Chapter 2
The Principle of Minimum Potential Energy
The objective of this chapter is to explain the principle of minimum potential energy and its application in
the elastic analysis of structures. Two fundamental notions of the finite element method viz.

STRESS
The state of stress at any point in a loaded body is dened completely in terms of the
nine components of stress: xx , yy , zz , xy , yx , yz , zy , zx , and xz , where the rst
three are the normal components and the latter six are the components of

Chapter 7
Finite Element Formulations for Beams and Frames
Beams and frames can take axial, transverse (i.e., perpendicular to the axis), and moment loads. Unlike
truss elements, they undergo bending. In this chapter, we will obtain element stiffness matr

NARAYANA ENGINEERING COLLEGE
(Affiliated to JNTUA-Ananthapuramu)
I-B.TECH I SEM UNIT TEST-I
Subject : ENGINEERING DRAWING
Date : 13-09-2016
Time : 09.00 AM TO 12.00 PM
Branch: CSE
Max .Marks : 70
1. Construct a regular Square, Pentagon, Hexagon, Heptagon,