Cantilever Beam

ABSTRACT
This study investigates the deflection and stress distribution in a long, slender cantilever beam of
uniform rectangular cross section made of linear elastic material properties that are homogeneous
and isotropic. The deflection of a cantilever beam is essentially a three dimensional problem. An
elastic stretching in one direction is accompanied by a compression in perpendicular directions.
In this project ,static and Modal analysis is a process to determine the stress ,strain and deformation.
vibration characteristics(naturalfrequencies and mode shapes)of a structure or a machine component while
it is being designed. It has become a major alternative to provide a helpful contribution in understanding
control of many vibration phenomena which encountered in practice.
In this work we compared the stress and natural frequency for different material having same I, C and T
cross-sectional beam.The cantilever beam is designed and analyzed in ANSYS.The cantilever beamwhich
is fixed at one end is vibrated to obtain the natural frequency, mode shapes and deflection with different
sections and materials.

I
LIST OF CONTENTS
Contents Page No.
CHAPTER 1 01-06
Introduction
1.1 Beam 01
1.2 Classification of Beams 02
1.3 Moment of Inertia 02
1.4 Stresses in Beams 02
1.5 General Shapes 04
1.6 Thin Walled Shapes 04
1.7 Cantilever Beam 05
1.8 Application 05
1.9 Advantages and Disadvantages 06
CHAPTER 2 08-09
Literature Review
2.1 Abstract 08
2.2 Introduction 08
2.3 Literature Review 08
2.4 Conclusion 09
CHAPTER 3 10-12
Introduction to CAD
3.1 Overview 10
3.2 Advantages 12
CHAPTER 4 13-15
Introduction CREO
4.1 Introduction 13
4.2 Advantages of CREO Software 14
4.3 CREO Parametric Modules 15

II
4.4 3D Models 15
CHAPTER 5 17-22
Introduction to FEM
5.1 Introduction 17
5.2 Introduction to ANSYS 18
5.3 Structural Analysis 19
5.4 Loads In a Structural Analysis 21
5.5 Modal Analysis 21
5.6 Uses of Modal Analysis 22
5.7 Random Vibration Analysis 22
CHAPTER 6 23-33
Structural Analysis of Cantilever Beam
6.1 Condition 1 I-Section 23
6.1.1 Material Steel 23
6.1.2 Material Stainless Steel 26
6.1.3 Material Iron 28
6.2 Condition 2 C-Section 29
6.3 Condition 3 T-Section 33
CHAPTER 7 34-37
Modal Analysis of Cantilever Beam
7.1 Condition 1 34
7.1.2 Material Stainless Steel 37
RESULT TABLES 39
CONCLUSION 41
REFERENCES 42

III
LIST OF FIGURES
Fig No Name Page No
1.1 Beam 01
4.1 Frames 3D Models 15-16
6.1 I-Section Models 23-24
6.4 I-Section Steel Material Structural Analysis 25-26
6.7 I-Section Stainless Steel Material Structural Analysis 27-28
6.10 I-Section Iron Material Structural Analysis 28-29
6.13 C-Section Models 29-30
6.16 C-Section Steel Material Structural Analysis 31-32
6.19 T-Section Steel Material Structural Analysis 33
7.1 I-Section Models 34-35
7.3 I-Section Steel Material Modal Analysis 36-37
7.5 I-Section Stainless Steel Material Modal Analysis 37-38

IV
LIST OF TABLES
Table No. Name of the Table Page No.
1 Static analysis results 39
2 Model analysis results 40

1
CHAPTER 1
INTRODUCTION
1.1 BEAM
A beam is a structural element that is capable of withstanding load primarily by resisting
against bending. The bending force induced into the material of the beam as a result of the external
loads, own weight, span and external reactions to these loads is called a bending moment. Beams
are characterized by their profile (shape of cross-section), their length, and their material.
Beams are traditionally descriptions of building or civil engineering structural elements, but
smaller structures such as truck or automobile frames, machine frames, and other mechanical or
structural systems contain beam structures that are designed and analyzed in a similar fashion.
Figure 1.1 BEAM
A statically determinate beam, bending (sagging) under a uniformly distributed load
Overview
Historically beams were squared timbers but are also metal, stone, or combinations of wood and
metal such as a flitch beam. Beams generally carry vertical gravitational forces but can also be
used to carry horizontal loads (e.g., loads due to an earthquake or wind or in tension to resist rafter
thrust as a tie beam or (usually) compression as a collar beam). The loads carried by a beam are
transferred to columns, walls, or girders, which then transfer the force to adjacent
structural compression members. In light frame construction joists may rest on beams.

2
In carpentry a beam is called a plate as in a sill plate or wall plate, beam as in a summer
beam or dragon beam.
1.2 CLASSIFICATION OF BEAMS BASED ON SUPPORTS
In engineering, beams are of several types:
1. Simply supported - a beam supported on the ends which are free to rotate and have no
moment resistance.
2. Fixed - a beam supported on both ends and restrained from rotation.
3. Over hanging - a simple beam extending beyond its support on one end.
4. Double overhanging - a simple beam with both ends extending beyond its supports on
both ends.
5. Continuous - a beam extending over more than two supports.
6. Cantilever - a projecting beam fixed only at one end.
7. Trussed - a beam strengthened by adding a cable or rod to form a truss.
1.3 Area moment of inertia
In the beam equation I is used to represent the second moment of area. It is commonly known as
the moment of inertia, and is the sum, about the neutral axis, of dA*r^2, where r is the distance
from the neutral axis, and dA is a small patch of area. Therefore, it encompasses not just how much
area the beam section has overall, but how far each bit of area is from the axis, squared. The greater
I is, the stiffer the beam in bending, for a given material.
1.4 Stress in beams
Internally, beams experience compressive, tensile and shear stresses as a result of the loads
applied to them. Typically, under gravity loads, the original length of the beam is slightly reduced
to enclose a smaller radius arc at the top of the beam, resulting in compression, while the same
original beam length at the bottom of the beam is slightly stretched to enclose a larger radius arc,
and so is under tension. The same original length of the middle of the beam, generally halfway
between the top and bottom, is the same as the radial arc of bending, and so it is under neither

3
compression nor tension, and defines the neutral axis (dotted line in the beam figure). The beam,
or flexural member, is frequently encountered in structures and machines, and its elementary stress
analysis constitutes one of the more interesting facets of mechanics of materials. A beam is a
member subjected to loads applied transverse to the long dimension, causing the member to bend.
For example, a simply-supported beam loaded at its third-points will deform into the exaggerated
bent shape shown Before proceeding with a more detailed discussion of the stress analysis of
beams, it is useful to classify some of the various types of beams and loadings encountered in
practice. Beams are frequently classified on the basis of supports or reactions. A beam supported
by pins, rollers, or smooth surfaces at the ends is called a simple beam. A simple support will
develop a reaction normal to the beam, but will not produce a moment at the reaction. If either, or
both ends of a beam projects beyond the supports, it is called a simple beam with overhang. A
beam with more than simple supports is a continuous beam. A simple beam, a beam with overhang,
and a continuous beam. A cantilever beam is one in which one end is built into a wall or other
support so that the built-in end cannot move transversely or rotate. The built-in end is said to be
fixed if no rotation occurs and restrained if a limited amount of rotation occurs. The cantilever
beam, a beam fixed (or restrained) at the left end and simply supported near the other end (which
has an overhang) and a beam fixed (or restrained) at both ends, respectively. Cantilever beams and
simple beams have two reactions (two forces or one force and a couple) and these reactions can be
obtained from a free-body diagram of the beam by applying the equations of equilibrium. Such
beams are said to be statically determinate since the reactions can be obtained from the equations
of equilibrium. Continuous and other beams with only transverse loads, with more than two
reaction components are called statically indeterminate since there are not enough equations of
equilibrium to determine the reactions. Above the supports, the beam is exposed to shear stress.
There are some reinforced concrete beams in which the concrete is entirely in compression with
tensile forces taken by steel tendons. These beams are known as concrete beams, and are fabricated
to produce a compression more than the expected tension under loading conditions. High strength
steel tendons are stretched while the beam is cast over them. Then, when the concrete has cured,
the tendons are slowly released and the beam is immediately under eccentric axial loads. This
eccentric loading creates an internal moment, and, in turn, increases the moment carrying capacity
of the beam. They are commonly used on highway bridges.

4
The primary tool for structural analysis of beams is the Euler–Bernoulli beam equation. Other
mathematical methods for determining the deflection of beams include "method of virtual work"
and the "slope deflection method". Engineers are interested in determining deflections because the
beam may be in direct contact with a brittle material such as glass. Beam deflections are also
minimized for aesthetic reasons. A visibly sagging beam, even if structurally safe, is unsightly and
to be avoided. A stiffer beam (high modulus of elasticity and high second moment of area)
produces less deflection.
Mathematical methods for determining the beam forces (internal forces of the beam and the forces
that are imposed on the beam support) include the "moment distribution method", the force
or flexibility method and the direct stiffness method.
1.5 Generalshapes
Most beams in reinforced concrete buildings have rectangular cross sections, but a more efficient
cross section for a beam is an I or H section which is typically seen in steel construction. Because
of the parallel axis theorem and the fact that most of the material is away from the neutral axis, the
second moment of area of the beam increases, which in turn increases the stiffness.
An I-beam is only the most efficient shape in one direction of bending: up and down looking at
the profile as an I. If the beam is bent side to side, it functions as an H where it is less efficient.
The most efficient shape for both directions in 2D is a box (a square shell) however the most
efficient shape for bending in any direction is a cylindrical shell or tube. But, for unidirectional
bending, the I or wide flange beam is superior.
Efficiency means that for the same cross sectional area (volume of beam per length) subjected to
the same loading conditions, the beam deflects less.
Other shapes, like L (angles), C (channels) or tubes, are also used in construction when there are
special require elements.

5
1.6 Thin walled beams
A thin walled beam is a very useful type of beam (structure). The cross section of thin walled
beams is made up from thin panels connected among them to create closed or open cross sections
of a beam (structure). Typical closed sections include round, square, and rectangular tubes. Open
sections include I-beams, T-beams, L-beams, and so on. Thin walled beams exist because their
bending stiffness per unit cross sectional area is much higher than that for solid cross sections such
a rod or bar. In this way, stiff beams can be achieved with minimum weight. Thin walled beams
are particularly useful when the material is a composite laminates. Pioneer work on composite
laminates thin walled beams was done by Librescu.
1.7 CANTILEVER BEAM
A cantilever is a rigid structural element, such as a beam or a plate, anchored at only one end to a
(usually vertical) support from which it is protruding. Cantilevers can also be constructed with
trusses or slabs. When subjected to a structural load, the cantilever carries the load to the support
where it is forced against by a moment and shear stress.
Cantilever construction allows for overhanging structures without external bracing, in contrast to
constructions supported at both ends with loads applied between the supports, such as a simply
supported beam found in a post and lintel system.For a simple rectangular cantilever, the thickness,
length, and width of the beam determine the geometric shape. Each of these parameters affects
how a cantilever moves and bends. For example, a short cantilever is stiffer than a long cantilever
of the same material, width and thickness (see figure right). In macroapplications, short cantilevers
are used for balconies and longer cantilevers are used for diving boards. In microapplications, a
short cantilever (~ 10 microns) works best as a latch or a needle. A longer cantilever (~100
microns) works best as a transducer or sensor. However, there are applications where a long
cantilever (e.g. a 1.2 mm neural probe) requires the same rigidity as a 10 micron needle. In this
case, the other cantilever dimensions (width, thickness) and possibly the material would be
adjusted to provide the rigidity needed.

6
1.8 APPLICATIONS
In bridges, towers, and buildings Cantilevers are widely found in construction, notably in cantilever
bridges and balconies (see corbel). In cantilever bridges the cantilevers are usually built as pairs, with
each cantilever used to support one end of a central section. The Forth Bridge in Scotland is an example
of a cantilever truss bridge. A cantilever in a traditionally timber framed building is called
a jetty or forebay. In the southern United States a historic barn type is the cantilever barn of log
construction.
Temporary cantilevers are often used in construction. The partially constructed structure creates a
cantilever, but the completed structure does not act as a cantilever. This is very helpful when
temporary supports, or falsework, cannot be used to support the structure while it is being built
(e.g., over a busy roadway or river, or in a deep valley). So some truss arch bridges (see Navajo
Bridge) are built from each side as cantilevers until the spans reach each other and are then jacked
apart to stress them in compression before final joining. Nearly all cable-stayed bridges are built
using cantilevers as this is one of their chief advantages. Many box girder bridges are
built segmentally, or in short pieces. This type of construction lends itself well to balanced
cantilever construction where the bridge is built in both directions from a single support.
These structures are highly based on torque and rotational equilibrium.
In an architectural application, Frank Lloyd Wright's Fallingwater used cantilevers to project large
balconies. The East Stand at Elland Road Stadium in Leeds was, when completed, the largest
cantilever stand in the world[2] holding 17,000 spectators. The roof built over the stands at Old
Trafford Football Ground uses a cantilever so that no supports will block views of the field. The
old, now demolished Miami Stadium had a similar roof over the spectator area. The largest
cantilever in Europe is located at St James' Park in Newcastle-Upon-Tyne, the home stadium
of Newcastle United F.C.
Less obvious examples of cantilevers are free-standing (vertical) radio towers without guy-wires,
and chimneys, which resist being blown over by the wind through cantilever action at their base.

7
1.9 ADVANTAGES AND DISADVANTAGES
Advantages
 Does not require a support on the opposite side (probably the main reason you would
ever have a cantilever beam).
 Creates a negative bending moment, which can help to counteract a positive bending
moment created elsewhere. This is particular helpful in cantilevers with a backspan
where a uniform load on the backspan creates positive bending, but a uniform load on
the cantilever creates negative bending.
Disadvantages
 Large deflections
 Generally results in larger moments
 You either need to have a fixed support, or have a backspan and check for uplift of the
far support.

8
CHAPTER 2
LITERATURE REVIEW
A Review of Vibration of a cantileverBeam
Prof. Vyankatesh S. Kulkarni Department of Mechanical Engineering, Solapur University
/BIT/Barshi/India
2.1 Abstract :
Estimating damping in structure made of different materials (steel, brass, aluminum) and processes
still remains as one of the biggest challengers. All materials posses certain amount of internal
damping, which manifested as dissipation of energy from the system. This energy in a vibratory
system is either dissipated into heat or radiated away from the system. Material damping or internal
damping contributes to about 10-15% of total system damping. Cantilever beams of required size
& shape are prepared for experimental purpose & damping ratio is investigated. Damping ratio is
determined by half-power bandwidth method. It is observed that damping ratio is higher for steel
than brass than aluminum.
2.2 Introduction :
A wealth of literature exists in the area of vibrations of beams but while going through the literature
regarding material damping of cantilever beams it has been figured out that still a lot of work has
to be done regarding it. Usually whenever study of various materials has been done the focus of
researchers has been damping, mode shapes, resonant frequency, etc. but material damping has
not been paid much attention.
2.3 Literature Review:
1. H H Yoo and S H Shin [4] Vibration analysis of a rotating cantilever beam is an important and
peculiar subject of study in mechanical engineering. There are many engineering examples which
can be idealized as rotating cantilever beams such as turbine blades or turbo engine blades and
helicopter blades .For the proper design of the structures their vibration characteristics which are
natural frequencies and mode shapes should be well identified. Compared to the vibration
characteristics of non rotating structures those of rotating structures often vary significantly. The
variation results from the stretching induced by the centrifugal inertia force due to the rotational

9
motion. The stretching causes the increment of the bending stiffness of the structure which
naturally results in the variation of natural frequencies and mode shapes. The equations of motion
of a rotating cantilever beam are derived based on a new dynamic modeling method. With the
coupling effect ignored the analysis results are consistent with the results obtained by the
conventional modelling method. A modal formulation method is also introduced in this study to
calculate the tuned angular speed of a rotating beam at which resonance occurs. 2. Mousa Rezaee
and Reza Hassannejad [14] derived a new analytical method for vibration analysis of a cracked
simply supported beam is investigated.
2.4 Conclusion:
The main objective of the present work is to study the vibration damping characteristics of three
materials i.e. steel, brass and aluminum. On the basis of present study following conclusions are
drawn: From the review it is evident that material damping is higher for steel in comparison with
brass and aluminum. The increase in material damping could be correlated to the stiffness of
materials. The damping ratio increases with decrease in thickness for each material. The natural
frequency decreases with decreases in thickness for each material. But it is viceversa in case of
length. The damping of specimen made up of aluminum was found to be lowest than either steel
or brass.

10
CHAPTER 3
INTRODUCTION TO CAD
3.1 OVERVIEW:
Today’s industries cannot survive worldwide competition unless they introduce new products with
better quality (quality, Q), at lower cost (cost, C), and with shorter lead time (delivery, D).
Accordingly, they have tried to use the computer’s huge memory capacity, fast processing speed,
and user-friendly interactive graphics capabilities to automate and tie together otherwise
cumbersome and separate engineering or production tasks, thus reducing the time and cost of
product development and production. Computer-aided design (CAD), computer-aided
manufacturing (CAM), and computer-aided engineering (CAE) are the technologies used for this
purpose during the product cycle. Thus, to understand the role of CAD, CAM, and CAB, we need
to examine the various activities and functions that must be accomplished in the design and
manufacture of a product. These activities and functions are referred to as the product cycle. The
product cycle described by Zeid [1991] is presented here with minor modificationsThroughout the
history of our industrial society, many inventions have been patented and whole new technologies
have evolved. Perhaps the single development that has impacted manufacturing more quickly and
significantly than any previous technology is the digital computer.
Computers are being used increasingly for both design and detailing of engineering components
in the drawing office. Computer-aided design (CAD) is defined as the application of computers
and graphics software to aid or enhance the product design from conceptualization to
documentation. CAD is most commonly associated with the use of an interactive computer
graphics system, referred to as a CAD system. Computer-aided design systems are powerful tools
and in the mechanical design and geometric modeling of products and components.
Once the conceptual design has been developed, the analysis subprocess begins with analysis and
optimization of the design. An analysis model is derived first because the analysis subprocess is

11
applied to the model rather than the design itself. Despite the rapid growth in the power and
availability of computers in engineering, the abstraction of analysis models will still be with us for
the foreseeable future. The analysis model is obtained by removing from the, design unnecessary
details, reducing dimensions, and recognizing and employing symmetry. Dimensional reduction,
for example, implies that a thin sheet of material is represented by an equivalent surface with a
thickness attribute or that a long slender region is represented by a line having cross-sectional
properties. Bodies with symmetries in their geometry and loading are usually analyzed by
considering a portion of the model. In fact, you have already practiced this abstraction process
naturally when you analyzed a structure in an elementary mechanics class. Recall that you always
start with sketching the structure in a simple shape before performing the actual analysis. Typical
of the analysis are stress analysis to verify the strength of the design, interference checking to
detect collision between components while they are moving in an assembly, and kinematic analysis
to check whether the machine to be used will provide the required motions. The quality of the
results obtained from these activities is directly related to and limited by the quality of the analysis
model chosen.
Designers generally use drawings to represent the object which they are designing, and to
communicate the design to others. Of course they will also use other forms of representation —
symbolic and mathematical models, and perhaps three-dimensional physical models — but the
drawing is arguably the most flexible and convenient of the forms of representation available.
Drawings are useful above all, obviously, for representing the geometrical form of the designed
object, and for representing its appearance. Hence the importance in computer-aided design (CAD)
of the production of visual images by computer, that is computer graphics. In the process of design,
technical drawings are used. Drawings explain the design and also establish the link between
design and manufacture. During the stage of design and detailing depend on the designers’ skill
and experience. Changes in previous designs take a long time because the drawings have to be
produced again. Computer-aided drawing is a technique where engineering drawings are produced
with the assistance of a computer and, as with manual drawing, is only the graphical means of
representing a design. Computer aided design, however, is a technique where the attributes of the
computer and those of the designer are blended together into a problem-solving team. When the
term CAD is used to mean computer-aided design it normally refers to a graphical system where

12
components and assemblies can be modelled in three dimensions. The term design, however, also
covers those functions attributed to the areas of modelling and analysis. The acronym CADD is
more commonly used nowadays and stands for computer-aided draughting and design; a CADD
package is one which is able to provide all draughting facilities and some or all of those required
for the design process. Two-dimensional (2D) computer drawing is the representation of an object
in the single-view format which shows two of the three object dimensions or the mutiview format
where each view reveals two dimensions. In both cases, the database includes just two values for
each represented coordinate of the object. It can also be a pictorial representation if the database
contains X, Y coordinates only.
3.2 Advantages:
There are several good reasons for using a CAD system to support the engineering design function:
• To increase the productivity
• To improve the quality of the design
• To uniform design standards
• To create a manufacturing data base
• To eliminate inaccuracies caused by hand-copying of drawings and inconsistency between
• Drawings

13
CHAPTER 4
INTRODUCTION TO CREO
4.1 Introduction:
PTC CREO, formerly known as Pro/ENGINEER, is 3D modeling software used in mechanical
engineering, design, manufacturing, and in CAD drafting service firms. It was one of the first 3D
CAD modeling applications that used a rule-based parametric system. Using parameters,
dimensions and features to capture the behavior of the product, it can optimize the development
product as well as the design itself.
The name was changed in 2010 from Pro/ENGINEER Wildfire to CREO. It was announced by
the company who developed it, Parametric Technology Company (PTC), during the launch of its
suite of design products that includes applications such as assembly modeling, 2D orthographic
views for technical drawing, finite element analysis and more.
PTC CREO says it can offer a more efficient design experience than other modeling software
because of its unique features including the integration of parametric and direct modeling in one
platform. The complete suite of applications spans the spectrum of product development, giving
designers options to use in each step of the process. The software also has a more user friendly
interface that provides a better experience for designers. It also has collaborative capacities that
make it easy to share designs and make changes.
There are countless benefits to using PTC CREO. We’ll take a look at them in this two-part series.
First up, the biggest advantage is increased productivity because of its efficient and flexible design
capabilities. It was designed to be easier to use and have features that allow for design processes
to move more quickly, making a designer’s productivity level increase.
Part of the reason productivity can be increased is because the package offers tools for all phases
of development, from the beginning stages to the hands-on creation and manufacturing. Late stage
changes are common in the design process, but PTC CREO can handle it. Changes can be made
that are reflected in other parts of the process.

14
The collaborative capability of the software also makes it easier and faster to use. One of the
reasons it can process information more quickly is because of the interface between MCAD and
ECAD designs. Designs can be altered and highlighted between the electrical and mechanical
designers working on the project.
The time saved by using PTC CREO isn’t the only advantage. It has many ways of saving costs.
For instance, the cost of creating a new product can be lowered because the development process
is shortened due to the automation of the generation of associative manufacturing and service
deliverables.
PTC also offers comprehensive training on how to use the software. This can save businesses by
eliminating the need to hire new employees. Their training program is available online and in-
person, but materials are available to access anytime.
A unique feature is that the software is available in 10 languages. PTC knows they have people
from all over the world using their software, so they offer it in multiple languages so nearly anyone
who wants to use it is able to do so.
4.2 ADVANTAGES OF CREO PARAMETRIC SOFTWARE
 Optimized for model-based enterprises
 Increased engineer productivity
 Better enabled concept design
 Increased engineering capabilities
 Increased manufacturing capabilities
 Better simulation
 Design capabilities for additive manufacturing
4.3 CREO parametric modules:
 Sketcher

15
 Part modeling
 Assembly
 Drafting
4.4 3D models
I-section
I-Figure 4.1 3D MODEL OF I-SECTION

16
C-Section
Figure 4.2 MODEL OF C- SECTION
T –section
Figure 4.3 MODEL OF T-SECTION

17
CHAPTER 5
INTRODUCTION TO FEM
5.1 Introduction:
The Basic concept in FEA is that the body or structure may be divided into smaller elements of
finite dimensions called “Finite Elements”. The original body or the structure is then considered
as an assemblage of these elements connected at a finite number of joints called “Nodes” or “Nodal
Points”. Simple functions are chosen to approximate the displacements over each finite element.
Such assumed functions are called “shape functions”. This will represent the displacement with in
the element in terms of the displacement at the nodes of the element.
The Finite Element Method is a mathematical tool for solving ordinary and partial differential
equations. Because it is a numerical tool, it has the ability to solve the complex problems that can
be represented in differential equations form. The applications of FEM are limitless as regards the
solution of practical design problems.
Due to high cost of computing power of years gone by, FEA has a history of being used to
solve complex and cost critical problems. Classical methods alone usually cannot provide adequate
information to determine the safe working limits of a major civil engineering construction or an
automobile or an aircraft. In the recent years, FEA has been universally used to solve structural
engineering problems. The departments, which are heavily relied on this technology, are the
automotive and aerospace industry. Due to the need to meet the extreme demands for faster,
stronger, efficient and lightweight automobiles and aircraft, manufacturers have to rely on this
technique to stay competitive.
FEA has been used routinely in high volume production and manufacturing industries for many
years, as to get a product design wrong would be detrimental. For example, if a large manufacturer
had to recall one model alone due to a hand brake design fault, they would end up having to replace
up to few millions of hand brakes. This will cause a heavier loss to the company.
The finite element method is a very important tool for those involved in engineering design; it is
now used routinely to solve problems in the following areas.
Structural analysis
• Thermal analysis
• Vibrations and Dynamics

18
• Buckling analysis
• Acoustics
• Fluid flow simulations
• Crash simulations
• Mold flow simulations
Nowadays, even the most simple of products rely on the finite element method for design
evaluation. This is because contemporary design problems usually can not be solved as accurately
& cheaply using any other method that is currently available. Physical testing was the norm in the
years gone by, but now it is simply too expensive and time consuming also.
5.2 INTRODUCTIONTO ANSYS
The ANSYS program is self contained general purpose finite element program developed
and maintained by Swason Analysis Systems Inc. The program contain many routines, all inter
related, and all for main purpose of achieving a solution to an an engineering problem by finite
element method.
ANSYS finite element analysis software enables engineers to perform the following tasks:
• Build computer models or transfer CAD models of structures, products, components, or
systems.
• Apply operating loads or other design performance conditions
• Study physical responses,such as stress levels, temperature distributions, or
electromagnetic fields
• Optimize a design early in the development process to reduce production costs.
• Do prototype testing in environments where it otherwise would be undesirable or
impossible
The ANSYS program has a compressive graphical user interface (GUI) that gives users easy,
interactive access to program functions, commands, documentation, and reference material. An
intuitive menu system helps users navigate through the ANSYS Program. Users can input data
using a mouse, a keyboard, or a combination of both. A graphical user interface is available
throughout the program, to guide new users through the learning process and provide more

19
experienced users with multiple windows, pull-down menus, dialog boxes, tool bar and online
documentation.
5.3 STRUCTURALANALYSIS
Static analysis calculates the effects of steady loading conditions on a structure, while ignoring
inertia and damping effects, such as those caused by time-varying loads. A static analysis,
however, includes steady inertia loads (such as gravity and rotational velocity), and time-varying
loads that can be approximated as static equivalent loads (such as the static equivalent wind and
seismic loads commonly defined in many building codes). In order to conduct the analysis, both
the geometry of the structure and the actions and support conditions are idealised by means of an
adequate mathematical model, which must also roughly reflect the stiffness conditions of the cross-
sections, members, joints and interaction with the ground. The structural models must allow to
consider the effects of movements and deformations in those structures or part thereof, where
second-order effects increase the effects of the actions significantly. In certain cases, the model
must incorporate the following into its stiffness conditions:
- the non-linear response of the material outside the elastic analysis;
- the effects of shear lag in sections with wide flanges;
- the effects of local buckling in compressed sheet panels;
- the effects of the catenary (using a reduced modulus of elasticity, for example) and of
displacement on structures with cables;
- the shear deformability of certain structural members;
- the stiffness of the joints;
- interaction between the ground and the structure.
Where it is necessary to conduct dynamic analyses, the structural models must also consider the
properties of mass, stiffness, resistance and damping of each structural member, as well as the
mass of other, non-structural, members. Where it is appropriate to perform a quasi-static
approximation of the structure's dynamic effects in accordance with the codes or regulations in
force, such effects may be included in the static values of the actions, or dynamic amplification
factors equivalent to such static actions could even be applied. In some cases (e.g. vibrations
caused by wind or earthquake), the effects of the actions may be obtained from linear elastic

20
analyses using the modal superposition method. Structural analyses for fire require specific models
that are considered. In some cases, the results of the structural analysis may undergo marked
variations regarding to possible fluctuations in some model parameters or in the design hypotheses
adopted. In such cases, the Designer shall perform a sensitivity analysis that allows to limit the
probable range of fluctuations in the structural response.
The content of this subsection only applies directly to linear members subjected to torsion where
the distance between points where there is no moment is equal to orgreater than 2.5 times its depth,
and the width is less than or equal to four times its depth, and the directrix is straight or curved.
The response of linear members to torsion, where the effects of distortion on the members may be
discounted, is the sum of two mechanisms: a) uniform or Saint-Venant torsion that only generates
shear stresses in the crosssection and the stiffness of which is characterised by the torsion modulus
It of the cross-section; b) non-uniform or warping torsion that generates both direct and shear stress
in the different sheet panels of the cross-section. Its stiffness remains characterised by its warping
modulus, Iw. The response of a member to torsion may be obtained through an elastic analysis that
incorporates the general equations for mixed torsion, depending on the static torsional magnitudes
of the cross-sections, It and Iw, the material deformation modulus, E and G, the connecting factors
for rotation and warping at the ends of the member, and the distribution of torsion action along it.
Alternatively, the structural analysis for torsion may be approached through finite elements models
for the part. It may be permitted for the effects of warping stress to be discounted in a suitably
approximate way, to analyse just the uniform torsion in members in the following cases: a)
members that have freedom to warp at their extremities and which are required solely for moment
at such extremities; b) members in which the warping module of the cross-section, Iw, is of
negligible or small magnitude in comparison with the torsion module, It. This is the case for the
following: – solid sections (round, square, rectangular, etc.); – open cross-sections made up of
rectangles that are sheared at a given point (angles, cross-shaped sections, single T units, etc.); –
closed cross-sections (tubes, single-cell or multi-cell boxes with no distortion, etc.). Additionally,
by way of simplification, it may be permitted for the effects of uniform torsion to be discounted,
and only analyse the warping stress, in the case of beams with thin-walled open sections such as
double T, U, H, Z sections, etc.

21
5.4 LOADS IN A STRUCTURALANALYSIS
Static analysis is used to determine the displacements, stresses, strains, and forces in
structures or components caused by loads that do not induce significant inertia and damping
effects. Steady loading and response conditions are assumed; that is, the loads and the structure's
response are assumed to vary slowly with respect to time. The kinds of loading that can be applied
in a static analysis include:
• Externally applied forces and pressures
• Steady-state inertial forces (such as gravity or rotational velocity)
• Imposed (non-zero) displacements
• Temperatures (for thermal strain)
• Fluences (for nuclear swelling)
5.5 MODAL ANALYSIS
Any physical system can vibrate. The frequencies at which vibration naturally occurs, and the
modal shapes which the vibrating system assumes are properties of the system, and can be
determined analytically using Modal Analysis.
Modal analysis is the procedure of determining a structure's dynamic characteristics;
namely, resonant frequencies, damping values, and the associated pattern of structural deformation
called mode shapes. It also can be a starting point for another, more detailed, dynamic analysis,
such as a transient dynamic analysis, a harmonic response analysis, or a spectrum analysis.
Modal analysis in the ANSYS family of products is a linear analysis. Any nonlinearities,
such as plasticity and contact (gap) elements, are ignored even if they are defined. Modal analysis
can be done through several mode extraction methods: subspace, Block Lanczos, Power
Dynamics, Reduced, Unsymmetrical and Damped. The damped method allows you to include
damping in the structure. Theoretical modal analysis was developed during the 19th century. At
that stage, the analytical approaches were used to solve differential equations to determine the
modal parameters. During the last century, the theoretical modal analysis for the complex and large
systems made great progress with the fast development of the discretization technique (finite
element method) and computer techniques. Since then, numerical rather than analytical methods
have been commonly used in the modal analysis, called numerical modal analysis.

22
5.6 USES OF MODAL ANALYSIS
Modal analysis is used to determine the natural frequencies and mode shapes of a structure. The
natural frequencies and mode shapes are important parameters in the design of a structure for
dynamic loading conditions. They are also required to do a spectrum analysis or a mode
superposition harmonic or transient analysis. Another useful feature is modal cyclic symmetry,
which allows reviewing the mode shapes of a cyclically symmetric structure by modeling just a
sector of it.
5.7 RANDOM VIBRATION ANALYSIS
A Random Vibration Analysis is a form of Spectrum Analysis.
•The spectrum is a graph of spectral value versus frequency that captures the intensity and
frequency content of time-history loads.
•Random vibration analysis is probabilistic in nature, because both input and output quantities
represent only the probability that they take on certain values
Random Vibration Analysis uses Power spectral density to quantify the loading.
• (PSD) is a statistical measure defined as the limiting mean-square value of a random variable. It
is used in random vibration analyses in which the instantaneous magnitudes of the response can
be specified only by probability distribution functions that show the probability of the magnitude
taking a particular value.

23
CHAPTER 6
STRUCTURAL ANALYSIS OF CANTILEVER BEAM
6.1 CONDITION 1-I-SECTION
6.1.1 Material - STEEL
Save Creo Model as .iges format
→→Ansys → Workbench→ Select analysis system → static structural → double click
→→Select geometry → right click → import geometry → select browse →open part → ok
→→ select mesh on work bench → right click →edit
Figure 6.1 I-SECTION STEEL MATERIAL
Double click on geometry → select geometries → edit material
MATERIAL PROPERTIES OF STEEL
Density : 7850 kg/m3
Young’s modulus : 205000 Mpa
Poisson’s ratio : 0.3

24
Select mesh on left side part tree → right click → generate mesh →
Figure 6.2 I-SECTION STEEL MATERIAL
Select static structural right click → insert → select pressure –0.096MPa
Figure 6.3 I-SECTION OF STEEL MATERIAL
Select displacement → select required area → click on apply →
Select solution right click → solve →
Solution- right click → insert → deformation → total
Solution right click → insert → strain → equivant (von-mises) →
Solution right click → insert → stress → equivant (von-mises) →
Right click on deformation → evaluate all result

25
TOTAL DEFORMATION
Figure 6.4 TOTAL DEFORMATION OF STEEL MATERIAL
VON-MISES STRESS
Figure 6.5 VON-MISES STRESS OF STEEL MATERIAL
VON-MISES STRAIN

26
Figure 6.6 VON-MISES STRAIN OF STEEL MATERIAL
6.1.2 MATERIAL- STAINLESS STEEL
Density : 5030 Kg/m3
Poisions ration : 294426 Mpa
Youngs modulus : 0.275
TOTAL DEFORMATION
Figure 6.7 TOTAL DEFORMATION OF STAINLESS STEEL

27
VON-MISES STRESS
Figure 6.8 VON-MISES STRESS OF STAINLESS STEEL
VON-MISES STRAIN
Figure 6.9 VON-MISES STRAIN OF STAINLESS STEEL

28
6.1.3 MATERIAL- Iron
6.4.1 MATERIAL PROPERTIES OF IRON
Density : 7874 Kg/m3
Young’s Modulus : 20400 Mpa
Poisons ratio : 0.29
TOTAL DEFORMATION
Figure 6.10 TOTAL DEFORMATION OF IRON MATERIAL
VON-MISES STRESS
Figure 6.11 VON-MISES STRESS IRON MATERIAL

29
VON-MISES STRAIN
Figure 6.12 VON-MISES STRAIN OF IRON MATERIAL
6.2 CONDITION 2-C-SECTION
Imported model
Figure 6.13 MATERIAL STEEL

30
Meshedmodel
Figure 6.14 MESHOD MODEL OF A STEEL MATERIAL
Force &displacement
Figure 6.15 FORCE & DISPLACEMENT OF A STEEL MATERIAL

31
TOTAL DEFORMATION
Figure 6.16 TOTAL DEFORMATION OF A STEEL MATERIAL
VON-MISES STRESS
Figure 6.17 VON-MISES STRESS OF A STEEL MATERIAL

32
VON-MISES STRAIN
Figure 6.18 VON-MISES STRAIN OF A STEEL MATERIAL

33
6.3 CONDITION 1-T-SECTION
TOTAL DEFORMATION
Figure:6.19 TOTAL DEFORMATION OF STEEL MATERIAL
VON-MISES STRESS
Figure:6.20 VON-MISES STRESS OF STEEL MATERIAL

34
CHAPTER 7
MODAL ANALYSIS OFCANTILEVER BEAM
7.1 CONDITION 1-I-SECTION
7.1.1 MATERIAL- STEEL

Save CREO Model as .IGES format
→→ANSYS → Workbench→ Select analysis system → model → double click
→→Select geometry → right click → import geometry → select browse →open part → OK
→→Select modal → right click →select edit → another window will be open
Figure 7.1 I- SECTION MODEL OF STEEL MATERIAL
Density : 7850kg/m3
Young’s modulus : 205000Mpa
Poisson’s ratio : 0.3
Select mesh on left side part tree → right click → generate mesh →

35
Figure 7.2 I-SECTION MODEL OF STEEL MATERIAL
Select displacement → select required area → click on apply → Select solution right click →
solve →
Solution right click → insert → deformation → total deformation → mode 1
Solution right click → insert → deformation → total deformation2 → mode 2
Solution right click → insert → deformation → total deformation 3→ mode 3
Right click on deformation → evaluate all result

36
TOTAL DEFORMATION 1:
Figure 7.3 TOTAL DEFORMATION OF STEEL MATERIAL
TOTAL DEFORMATION 2
Figure 7.4 TOTAL DEFORMATION 2 OF STEEL MATERIAL

37
TOTAL DEFORMATION 3
Figure 7.5 TOTAL DEFORMATION 3 OF STEEL MATERIAL
7.1.2 MATERIAL– STAINLESS STEEL
TOTAL DEFORMATION 1
Figure 7.6 TOTAL DEFORMATION 1 OF STAINLESS STEEL

38
TOTAL DEFORMATION 2
TOTAL DEFORMATION 3

39
RESULT TABLES
7.2 Static analysis results
7.2.1 I-Section
Material Deformation(mm) Stress (N/mm2) Strain
Steel 2.4219 77.836 0.00038918
Stainless steel 2.5099 78.313 0.00040577
Cast iron 4.4028 76.871 0.00069883
7.2.2 C-Section
Steel 10.361 169.52 0.00084759
Stainless steel 10.778 170.35 0.00088267
Cast iron 18.696 167.77 0.0015251
7.2.3 T-Section
Steel 4.7314 207.08 0.0010354
Stainless steel 4.9027 208.22 0.0010789
Cast iron 8.6034 204.75 0.0018614

40
7.3 Modal analysis results
7.3.1 I-Section
Material Total Deformation
1(mm)
Total Deformation
2(mm)
Total Deformation
3(mm)
Steel 9.2158 11.7 9.06
Stainless steel 9.2752 11.8 9.12
Cast iron 9.6225 12.23 9.466
7.3.2 C-section
1(mm)
Total Deformation
2(mm)
Total Deformation
3(mm)
Steel 9.9427 14.092 11.479
Stainless steel 10.012 14.192 11.553
Cast iron 10.37 14.691 11.987
7.3.3 T-Section
1(mm)
Total Deformation
2(mm)
Total Deformation
3(mm)
Steel 13.151 13.465 10.829
Stainless steel 13.053 13.37 10.76
Cast iron 13.599 13.941 11.236

41
CONCLUSION
In this work we compared the stress and natural frequency for different material having same I, C and T
cross-sectional beam.The cantilever beam is designed and analyzed in ANSYS.The cantilever beamwhich
is fixed at one end is vibrated to obtain the natural frequency, mode shapes and deflection with different
sections and materials.
By observing the static analysis the deformation and stress values are less for I-section cantilever
beam at cast iron material than steel and stainless steel.
By observing the modal analysis results the deformation and frequency values are less for I-section
cantilever beam more for T-section.
So it can be conclude the cast iron material is better material for cantilever beam in this type I-
section model.

42
REFERENCES
[1] Chandradeep Kumar, Anjani Kumar Singh, Nitesh Kumar, Ajit Kumar, "Model Analysis and
Harmonic Analysis of Cantilever Beam by ANSYS" Global journal for research analysis, 2014,
Volume-3, Issue-9, PP:51- 55.
[2] Yuan, F.G. and R.E. Miller. A higher order finite element for laminated composite beams.
Computers & Structures, 14 (1990): 125-150.
[3] Dipak Kr. Maiti& P. K. Sinha. Bending and free vibration analysis of shear deformable
laminated composite beams by finite element method. Composite Structures, 29 (1994): 421- 431
[4]. DaDeppo, D. Introduction to Structural Mechanics and Analysis. Upper Saddle River, NJ:
Prentice-Hall, 1999.
[5]. Beer, F. P., and E. R. Johnston. Vector Mechanics for Engineers, Statics and Dynamics, 6th
ed. New York: McGraw-Hill, 1997.
[6[ Teboub Y, Hajela P. Free vibration of generally layered composite beams using symbolic
computations. Composite Structures, 33 (1995): 123– 34.
[7] Banerjee, J.R. Free vibration of axially loaded composite Timoshenko beams using the
dynamic stiffness matrix method. Computers & Structures, 69 (1998): 197-208 [6] Bassiouni AS,
Gad-Elrab RM, Elmahdy TH. Dynamic analysis for laminated composite beams. Composite
Structures, 44 (1999): 81–7.
[8]. Budynas, R. Advanced Strength and Applied Stress Analysis. 2d ed. New York: McGraw-
Hill, 1998.
[9] Love, A. E. H. A Treatise on the Mathematical Theory of Elasticity. New York: Dover
Publications, 1944

Cantilever Beam

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Cantilever Beam

Similar to Cantilever Beam (20)

Recently uploaded

Recently uploaded (20)

Cantilever Beam