1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
75
DISPLACEMENT ANALYSIS OF CANTILEVER BEAM USING FEM
PACKAGE
JN Mahto1
, SC Roy2
, J Kushwaha3
, RS Prasad4
1,2
Department of Mechanical Engineering, BIT, Sindri
3
Department of Mechanical Engineering, KIET, Ghaziabad
4
Department of Mechanical Engineering, RKGIT, Ghaziabad
ABSTRACT
In the present investigation, efforts have been made to characterize behaviour of beam
under longitudinal stress. Specimens were modelled and analysed with the extensive use of
FEM package (Autodesk Inventor). Analysis was done by setting maximum load value as
1100 N. The value of displacement and stress computed for the cantilever beam through FEM
package were tabulated and graphs were drawn to observe pattern. Dimensions of specimen
were initially selected as length 500mm, width as 50mm and thickness as 12mm. By keeping
length of specimen fixed the thickness of specimen, width of specimen and force applied to
the specimen were varied to observe its effect on the behaviour of the beam. Aluminum,
Copper and Steel were selected as three different materials for analysis.
Keywords: Displacement Analysis; FEM Package; Structural Analysis; Mode-I Vibration.
1. INTRODUCTION
It is very important if it is known that how a beam under a load will behave when its
cross section varies in a particular fashion. Also it is important to know the effect of change
in the load applied to a beam. In the earlier work done it was found that cantilever beam
when subjected to a cyclic transverse load frequency for the mode of vibration decreases as
the poisons ratio of the material increases. Modal parameters such as natural frequencies,
mode shapes, were key information in determining the dynamic performance of the structure.
Also, it was found that stress, strain energy, displacement gets affected if property of material
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ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4, Issue 3, May - June (2013), pp. 75-78
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
76
changes. However, the accuracy of these quantities depends on the accuracy of the modal
parameters used in the analysis. For this reason the present investigation was made so that the
behavior of beam under longitudinal load can be observed. FEM packages are adequately
available to simulate and analyze. The data obtained can be further analyzed in order to know
behavior of structure.
2. LITERATURE REVIEW
Frequency response of the vibration is very sensitive to the inhomogenity present in
the structure and can be used to determine location of crack and crack growth rate in a
structure under vibration [1,2].
Frequency response of a material is not only utilized to know about construction materials,
but it has also been utilized to develop sensors. A cantilever sensor can be operated in two
different modes: the static mode, where the cantilever deflection is monitored, and the
dynamic mode, where the cantilever resonance is monitored. The deflection of a cantilever
can be due to number of processes such as molecular adsorption, thermal effects, electric and
magnetic fields, and fluid flow. Cantilevers shorter than 10 µm in length with sub-attogram
sensitivity were demonstrated in 2004 [3,4,5], enabling the detection of single virus particles
of femtogram mass [6].
3. FEM ANALYSIS
Three materials are selected as steel, copper, aluminium because of their different
value of Young’s Modulus (E). The value of Young’s Modulus of the three materials are,
ESteel=210e09, ECu=117.2e09, EAl=68.95e09. Density (ρ) and poison’s ratio (υ) of the
materials were taken as ρSteel=7800 kg/m3
, ρCu=8960 kg/m3
, ρAl=2700 kg/m3
and υSteel=0.3,
υCu=0.36, υAl=0.33.
For the analysis of aluminium bar as a cantilever beam, a rectangular bar with
dimensions 500m*50mm*12mm was modelled and material of model was defined as
aluminium by taking value of Young’s Modulus of Elasticity as 68.95e09 N/m2
, density as
2700 kg/m3
and poison’s ratio of aluminium as 0.33. The size of elements taken was 0.011,
number of elements as 225 and number of nodes as 552.
The maximum force value selected was 1100N for which the maximum displacement
was observed in each case. In case of aluminium, total mass of model calculated as 0.81 kg.
At the force 1000N, width 50mm and thickness 12mm the displacement value under
longitudinal load was 4.75e-04inch.
In case of the analysis of the rectangular bar of copper, value of Young’s Modulus of
Elasticity was 117.2e09 N/m2
, density as 8960 kg/m3
and poison’s ratio as 0.36. Through
analysis the total mass of model was calculated as 2.688 kg. At the force 1000N, width 50mm
and thickness 12mm the displacement value under longitudinal load was 2.79e-04inch.
For the analysis of the rectangular bar of steel, value of Young’s Modulus of
Elasticity was taken as 210e09 N/m2
, density as 7800 kg/m3
and poison’s ratio of steel as 0.3.
Total mass of model was observed as 2.34 kg. At the force 1000N, width 50mm and
thickness 12mm the displacement value under longitudinal load was 1.56e-04inch.

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
77
Fig. 1. Variation in the displacement value with the change in material
Fig. 2. Variation in the displacement value with the change in material
4. RESULTS AND DISCUSSIONS
The value for maximum displacement of cantilever beam along its length when
subjected to the longitudinal load for the three materials were computed using FEM package.
The graphs were drawn with the data obtained using FEM package for displacement is as
shown in Fig. 1. The effect of material change on the stress value of beam is as shown in Fig.
2.
Fig. 3. Frequency Value of Materials at Mode-I

4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 3, May - June (2013) © IAEME
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5. CONCLUSIONS
From Fig. 1 it was observed that displacement value of a rectangular bar under
cantilever beam condition increases when poisons ratio varies from 0.3 to 0.33and then
decreases when poison’s ratio varies from 0.33 to 0.36. From Fig. 2 it can also be observed
that as the poison’s value increases the value of stress increases when subjected to
longitudinal load. But, from Fig. 3 it can be observed that value of poison’s ratio varies from
0.3 for steel to 0.36 for copper where as the value of frequency at mode-I of vibration varies
from 4.1943 Hz for steel to 2.8583 Hz for copper [7].
REFERENCES
[1] Prasad RS, Roy SC, Tyagi KP, Analysis and Comparison of Pattern of Crack Growth
Rate along Vibrating Cantilever Beam using FEM Package, International Journal of
Applied Engineering Research, Vol. 5(12), pp 2091-2095, 2010.
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[3] Ilic B, Craighead HG, Krylov S, Senaratne W, Ober C, Neuzil P, Attogram Detection
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