ISSN: 2277-3754
ISO 9001:2008 Certified
International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 6, December 2012
Development of a Beam Deflection Apparatus
from Locally Sourced Material
Buliaminu Kareem
Department of Mechanical Engineering, Federal University of Technology, Akure, Nigeria
Abstract— Continued hike in cost of laboratory equipment
calls for seeking an alternative way of manufacturing such
equipment using indigenously sourced material. The most critical
laboratory equipment useful in material testing is Beam
Deflection Apparatus (BDA) which is useful in the determination
of elastic modulus of engineering materials and among others. It
was designed to comprise a spring, dial gauge, beam support and
measuring scale. The spring permitted the horizontal movement,
while the deflection of beam was measured by the dial gauge with
the scale measuring the length of the expansion. The assembled
apparatus comprised leaf spring, bolts, load hanger, T-leg and
spring support with one side fixed. Test experiments were carried
out on the apparatus, in the areas of young’s modulus of material
determination under a given loading system. The results from the
test showed that the apparatus performance is adequate. This has
supported the efficacy of the apparatus as a replacement to the
imported ones in the institutional laboratories.
Index Terms—Mechanical Test, Beam Deflector, Elastic
Modulus, Laboratory.
I. INTRODUCTION
The beam theory is one of the basic knowledge to be
acquired for all industrial engineers. The beam deflection is
capable of measuring support reaction, shearing force,
bending moment, deflection, deflection angle, young modulus
of various materials [1-2]. In the same way, the apparatus
allow deeper understanding of the significance of the beam
theory through comparative examination between obtained
experimental values and the theoretical values. The
production of beam deflection apparatus, is to enable one
especially students, study beam deflection under various load
and fixing conditions. There are different sizes and product
codes of this apparatus from different countries (such as
United States of America, Canada, England etc.). There were
product codes such as beam deflection apparatus SAN 313,
Benkelmen Beam Deflection Apparatus, deflection of beam
apparatus, Norwood Instruments, HSM1 Beam Deflection
Apparatus, SM104 Beam Apparatus, etc.[3-8].
A. Beam Deflection Apparatus San 313
This apparatus is of dimension (420 X 420 X 1200) mm
and net weight 26kg. It consists of a rigid main support on
which the hardened knife edge and cantilever supports for the
test beams can be easily positioned. The standard equipment
includes three test beam of the same material having suitable
cross sectional dimensions. This apparatus is produced by
both Delta Analytical Instruments (U.S.A) and society Delta
Lab. (France) [9,10].
B. Benkelmen Beam Deflection Apparatus
The beam theory is one of the basic knowledge to be
acquired for all industrial engineers. The beam deflection
apparatus is a newly developed epoch making small model
experimentation apparatus This apparatus consists of a
Benkelman beam (B.B) which measures static pavement
deflection. The BB consists of a slender beam 3.6m long
pivoted at a distance of 2.44m from the tip. By suitable
planning the prove between the dual wheels of a loaded truck,
it is possible to measure the rebound and residual deflections
of the pavement structure. The over long thickness required
for strengthening of a given road stretch is derived from the
BB deflection record and other necessary design parameters
[11,12}.
C. Deflection of Beam Apparatus (Norwood Instrument
The apparatus consist of a twin beam support fitted with a
scale to which the various supports are attached. The beam is
loaded by a double ended hook and stirrup passing through
the support beams [11].
D. HSM1 Beam Deflection Apparatus
This apparatus has features such as rigid base and supports,
choice of end conditions. It can be used for verification of
beam deflection formula, deflection and slope of beams and
cantilevers, verification of both area moment theories [12].
E. SM104 Beam Apparatus
The SM104 beam apparatus was tested to industrial
standards and can be used for class demonstrations, student
experiments, projects and research. Its dimensions 1870 X
320 X 580mm and Net weight 43kg. It is very simple to
design and fabricate [8,11]. The modification of this design
will be adopted in this study because of its simplicity and
availability of local material substitution.
F. Beam Column
Much research has been done on metal beams and their
behavior under Compressive loads. In many cases, members
are subjected to both a bending moment and a compressive or
tensile load. When the magnitude of one is relatively small, its
effect is neglected and the section is designed as a beam, an
axially loaded column, or a tensile member. However in some
cases magnitudes are relatively large and cannot be easily
neglected. Therefore combined loads have to be accounted
for in design. In the case where members are subjected to
compressive loads and bending moments, they are referred to
as beam-columns. They therefore provide a link between
columns under pure axial loads, and a beam under pure
bending loads. Since axial load is involved, stability related
factors such as buckling have to be considered. When a
343
ISSN: 2277-3754
ISO 9001:2008 Certified
International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 6, December 2012
member is subjected to small loads, its shape remains the operate the apparatus at a convenient working height. The
same, but as the load increases the deflection of the member size of the individual components, sub-system and the entire
increases as well, the member could suddenly become apparatus were designed to ensure portability, easy
unstable. Such a phenomenon is called the buckling accessibility for maintenance and operation.
phenomenon. Usually the buckling of a column can lead to
B. Design Specification and Analysis
The main frame of the apparatus consist of an upper cross
catastrophic failures in many structures. Therefore special
attention has to be taken in order to make sure that such member carrying graduated scale and two lower members
members can safely support combined loads without bolted tee-legs to form a rigid assembly.
becoming unstable. Though many high precision systems
Spring: It slides freely on the main support beam when
[13,14] had been developed in literature but the beam load is applied. Springs based on the principle of long slander
deflection apparatus is important in allowing deeper beams of rectangular section subjected to bending. They are
understanding of the significance of beam theory and practice used as cantilever springs (fixed at one end), or as simple
in developing economy [15-17].
beams (fixed at both ends). The leaf springs can be used either
independently or in sets (laminated leaf springs). Single
II. MATERIAL AND METHODS
springs are used for the following reasons: suitable for low
To satisfy operational requirement and design purposed and medium load forces; linear working characteristics;
standard values were used in developing the design relatively low spring constant; considerable length
consideration, specification analysis and drawing. The design requirements; and minimum space needed with low
was then used in the fabrication of the apparatus. The production costs. The maximum bending moment
occurs
designed and fabrication of parts included the dial gauge
support, load hanger, spring support, Tee-legs, etc. with all at the centre and is resisted by all N plates equally.
these in place, the beam deflection apparatus was assembled
by bolting and welding.
WL
A. Design Consideration
/4
This is concerned with the detailed design of the beam
deflection apparatus. This includes design specification and
choice of material used in the constructing of the apparatus. In
W
W
/2
/2
the production of apparatus, cost, maintenance, portability,
efficiency and other characteristics were considered. The
beam deflection apparatus is laboratory equipment widely
W
used in construction industry and tertiary institutions. Some of
the design consideration includes:
Reliability: This is the acceptability of the apparatus over
a period of time. It is the possibility of the apparatus to
t
perform without failure under a given condition for a specific
period. Thus, from the design stage, the possibility of
operating the apparatus for a long period of time without
W
/2
L
excessive failure of component parts or breakdown of
operation was considered.
Ergonomics: This can be defined as the study of working
R
condition. It is important in the design of equipment to enable
C
people work more efficiently. It is the study of objects,
systems and the environment for their safe and efficient use by
people concerned and those within the operational
environment. It deals with human comfort obtained in the use
of a given product. The apparatus was designed in such a way
o
that the operator can operate it safely, easily and effectively
by putting the following factors into consideration; personnel
Fig. 1 Design Configuration of Beam Deflector
protection, and stability. Personnel protection entails
Resisting moment of each plate,
designing for consideration for safety of the personnel such as
minimizing excessive noise, guarding moving parts that can
(1)
course injury and ensuring the comfort of the operator.
Stability involves designing to ensure rigidity and stability of
Now,
the apparatus. The height of the beam deflection apparatus
Or
was carefully chosen and considered during the design and
construction of the apparatus. This allows the operator to
344
ISSN: 2277-3754
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International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 6, December 2012
Maximum bending moment =
=
=100N/m
Let E = 200GN/
Or
(2)
Strain energy = U =
Where, b = width of each plate
t= thickness of each plate
a = overlap at each end
N = Number of plates in the spring
L = the spring span length
=
δ=
E = Young’s modulus of elasticity
Refer to the Fig. 1
=
(3)
δ=
,
.δ=
2
Also
Or,
=
=
(4)
.:δ=
Or. δ =
(5)
Strain energy, U =
=
X total length of leaves
X total length of leaves
=
X total length of leaves
=
total length of leaves
=
total length of leaves =
U=
x volume of spring
=25N/m
Deflection of the spring
=Bending stress
Neglecting
X total length of leaves spring
volume of spring
(6)
From the design;
Number of leave spring used = 1
Length of spring = 1000mm
Width of spring = 50mm
Thickness of spring = 9.5mm
The apparatus was designed to carry a maximum load of
1000N
= 43.7mm
Dial Gauge: The dial gauge is mounted on magnetic
carrier which slide across the upper cross member. It is used
to measure all beam deflection. The dial gauge is 0.25mm in
0.1mm division. Since the deflection of the spring is 43.7mm,
the dial gauge for the apparatus is above 43.7mm because of
safety reasons.
Scale: This is suitably marked or graduated scale that is
secured to the main support beams so that test beam supports
the load and the dial gauge may be quickly and accurately
located. It is IM to B54372.
Dial Gauge Support: It is mounted in the main support
beam and can be readily moved to the selected point where
the deflection is to be measured. It holds the dial gauge firmly
in position.
Slope Indication: This is used for measuring slopes. It is
used in fixing moments for a built-in beam experiment and it
is placed so that it is symmetrical.
Slope Indicator Clamp: It is used to hold the slope
indicator to the test beam. It is placed over the outer support
bar of the slope indicator.
Build in Support: It is a rigid pillar at one end of the
heavy steel base of the bench mounted (Beam deflection
apparatus) it is positioned on the rigid main support beam; it is
used for test beams.
Test Beam: They are made of different materials like
wood, aluminum, mild steel and brass. The test beams are
usually straight steel beams that must be free of corrosion or
major blemishes.
Load Hanger: They are fitted with cursor, which
register on the scale thus ensuring easy accurate positioning,
loads weights are applied to the load hangers during
experiment. The load on each hanger is identical.
Load Rail: It is a heavy steel base on which all weights of
most of the component of the apparatus hang on.
Load Link: This holds the load hangers on which loads are
placed.
Spring Support: Mounted on the main frame to permit
horizontal movement of the spring.
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Volume 2, Issue 6, December 2012
Tee-Legs: The two members of the main frame of the
D. Construction Process
Some of the processes used during construction are
beam deflection apparatus are bolted to the T-legs to form
marking out, welding, turning etc. Drilling machine, lathe
rigid assembly and balance.
Stirrup: The stirrup is used to hold and suspend the load machine, welding machine, hack saw blade etc. were used
during the construction. The member bolted to the T-legs is of
link.
Beam Clamp: It is used to hold the beam in position. It is length 1,501mm (after being cut to size). The T-legs were cut
to the size of the base length 304mm and height 390mm. A
made up of mild steel iron.
40mm diameter round pipe of length 1240mm was welded to
C. Material Selection
Generally engineering materials includes, metal and the side of the T-legs for rigidity. Holes were drilled at the
non-metals which differ in their chemical, physical and base of the T-legs with a pillar drill to allow the two stands to
mechanical properties and therefore determine their usage. be bolted and welded to the base of the T-legs. Other
Before any material can be selected for use in the construction assembling works were done in the workshop like the fixing
of this apparatus. The following factors have to be of the dial gauge and the spring support.
E. Maintenance
considered: material analysis; material sourcing; and material
For effective condition of the beam deflection apparatus,
costing
Material Analysis: This is the process of assessing the the following steps need to be taken: the steel beam should be
materials to determine the inherent properties posed by that straight and kept free from corrosion or other defect. But in
particular material so as to meet or perform the desired the case of a wood beam they are slightly soiled and oil and
function without difficulty. The material selected for use in should not be saturated by oil or grease; the dial spindle
the manufacturing of beam deflection apparatus must be should not be oiled, but wipe with a clean dry cloth or wiper
suitable for the prevailing condition of service. For the which should be lint free. The spindle should be gently pushed
purpose of this project, analysis was based on the strength, through the instrument and other side wiped. The dial gauge
toughness and hardness of the materials selected. The should be free to move; the clamping screws and nuts should
material used for the construction of this apparatus be free to move, clean the threads with suitable tap or die. The
component includes: mild steel; and plastics. The mild steel general sizes used are M6 and M8 to B.S and ISO standards;
contains 0.05-0.30 percent of carbon and some percentage of and the bright parts and the under sides of base should be free
iron. The mild steel because of its desirable properties such as from corrosion and kept lightly oiled.
F. Installation
ductility was used for the construction of the build in support,
The apparatus was designed for bench mounting. Every
Tee-legs, spring support, etc. A plastic was chosen for the
construction of the meter rule at the side of the cross-bar item of the apparatus was wiped with a soft cloth to remove
because of the dominant role it plays both for industrial and any dust. The apparatus was placed on a firm level bench with
domestic application. Hence, their high specific strength and legs about 150mm to 200mm away from the front of the
stiffness (as a result of low relative density), corrosion bench. A spirit level is placed on the parallel beam and the
resistance, good electrical and thermal insulating properties, leveling screws were adjusted to set the apparatus level in two
low coefficient of friction, toughness and resilience with good places with the main scale facing the test piece. Every safety
vibration damping capacities, ease of fabrication and regulations were observed, such as none flooding the
apparatus with solvent, using a wiper that has been dampened
inexpensiveness compared to other metals on volume basis.
Material Sourcing: The material selected for use should with solvent to clean, allowing the parts to dry and cover with
perform satisfactory under loading conditions. Also, the a thin film of oil. In every warm climate, light or less viscous
material selected for used are those readily available locally. grease is preferentially used in order to retain a protective
film.
This making the project cost effective.
G. Operational Safety
Material Costing: This is one of the factors guiding the
The apparatus is safe and possesses no health hazard when
selection of material which must be relatively cheap in order
to meet up in the competitive market of the product. Any mounted correctly and used properly under adequate
industrial set up has to produce at a minimum cost and at the supervision. The operator should be encouraged to adopt safe
same time improves the quality of the product. The cost of an working practices by wearing protective boots or shoes. In
engineering product can be considered in two ways namely, addition, safety glasses and laboratory coats should be worn at
direct cost and indirect cost. Indirect cost is the cost of the all times in the laboratory. It is advisable that all mounted
overheads such as land, maintenance cost and repair cost apparatus is guarded to prevent persons from walking into it
while direct cost refers to the cost of raw materials, salaries (obstruction) and to prevent a fall of weight onto the feet of
and wages etc. The direct costs are mostly considered because person close to the apparatus. When the apparatus is bench
they are the costs directly related to the price of a specific mounted and requires a weight on a cord to overhang the
product. This type of cost was employed in determining which bench through a pulley, this should not be sited on a main
process is feasible for the manufacturing of the beam access or emergency gangway. When performing experiments
ensure those load hangers are properly engaged with load
deflection apparatus
cords, beams hook etc. as appropriate.
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International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 6, December 2012
The Apparatus: consisted of a twin beam support fitted
H. Servicing Safety
During servicing it is desirable that all personnel should with a scale to which the various support were attached. The
wear eye shields and a filter mask with an organic protection beam was loaded by a double hook and stirrup passing
filter. If the service involves moving weights no matter how through the support beam, the arrangement of this apparatus
small, protective foot wear must be worn. After contact with was described by Fig. 2. A number of different support loads
oil and solvents, hands should be washed with a hand cleanser were used at predetermined points in the experiment.
to remove all traces. All electrical equipments must be
Young’s Modulus Determination: The experimental
disconnected from the supply before servicing. Table I shows set-up comprised 3 triangular stirrup, 2 double ended hooks, 1
bill of materials for the apparatus.
load hanger, weight, steel beam (normal 25 x 6), 1 dial gauge
Table I Engineering Bill of Measurement and Evaluation
and a tall dial gauge support, and position gauge. The
Material
Size
Qua
Rat
Amount
arrangement is shown in Fig. 2 similar to Fig. 1, where, for
description
ntity
e
the leaf spring, b, width of each plate; T, thickness of each
plate; A, distance of each plate; N, number of plate in the
spring; L, the spring span length; δ, bending stress; and
Mild steel
100mm
1
11,
11, 500
U- channel
x75mm
500
young’s modulus of elasticity (Eqns. 1-6). The results
650mm
x 650mm
1
75mm
x 25mm
2
1,300 x
10mm
1
Bolts and
nuts
Mild
steel Pipe
Dial
gauge
Electrode
14mm
Cutting
disc
m
Grinding
disc
m
Miscellan
eous
Locally
made
Imported
5
2
2
4,000
1,3
1,300
250
100
60
2pc
s
W
W
410
1
18,
500
30
1
25
750
250
250
10,
300
20
10,300
Ø230m
1
cups
1
2,
000
1,5
00
500
500
10
Ø230m
1
500
500
5
7,
200
α
Fig. 2 Experimental Set up
18,500
750
Pkt
1
L/2
L/2
α
2, 600
1,300
Set
Mild steel
Rod
Paint
2,0
obtined using the following parameters: L, 500mm; a,
250mm; W, 40N on each end in step of 10N, is presented as
Fig. 3 from which young’s modulus E is 271kN/m2.
00
Ø50m
Hack saw
blade
Leaf
Spring
3,500
00
17
19
22
m
x
100mm
0.1mm
Division
Gauge
10
3,5
00
Load (N)
10mm
mild
steel
plate
Mild steel
rectangular
bar
Plastic
scale
2,000
15
1,500
7, 200
0
0
N
64,710
$ 431.40
N
500,000
$3333.3
3
10
20
30
40
50
Deflection (mm)
Fig. 3 Relationship between loads and deflections
I. Performance Evaluation
The beam deflection apparatus was used to conduct an
experiment to determine young’s modulus for a metal bar.
III. RESULTS AND DISCUSSION
Fig. 3 shows that results are dependent upon the average
material properties of the beam rather than being influenced
by any localized variation. Four points loading was used in
this test because it gave constant bending moment over a
347
ISSN: 2277-3754
ISO 9001:2008 Certified
International Journal of Engineering and Innovative Technology (IJEIT)
Volume 2, Issue 6, December 2012
relatively long length of the beam under test in the [7] J.A Gilbert, C.L. Carmen, "Chapter 11 – Beam Deflection
Test."MAE/CE 370 – Mechanics of Materials Laboratory
experiment. The young’s modulus elasticity of the iron bar
2
Manual, 2000.
tested was found to be 271kN/m , which indicated that the
material is relatively ductile. It was also clear that as the [8] P.A. Hilton, “H.SM1 Beam Deflection Apparatus” United
Kingdom, H1– tech Education, P. A Hilton Limited Article
modulus of elasticity decreased from material to material, the
Published at http://www.intech.com/products/hsm.htm.,2003.
deflection increased for the same applied load. This was true
for both the theoretical and the experimental data. It will be [9] K. Bramble, “Strength of Materials Engineers” Edge USA:
Engineer Edge Inc., 2005.
economically justifiable if the beam deflection apparatus
could be manufactured and sold locally, in Nigeria (Table I) [10] M.R. Islam, M.A. Mansur, M. Maalej, “Shear strengthening of
as compared to the high cost of the imported item (Table I). N,
RC deep beams using externally bonded FRP system,” Elsevier
Ltd., pp 413-420, 2004.
is the symbol for Nigerian currency. Besides, delay in
importation, high import duty, and high cost of foreign [11] Norwood, “Deflection of Beam Apparatus”, Great Britain:
exchange would lead to high cost of imported item.
Norwood Instrument Limited. New Mill Road, Honley
Huddershield, 1990.
IV. CONCLUSION
The beam material size, support spacing and loading can all
be adjusted to give a wide range of experimental conditions.
The beam deflection apparatus is one apparatus that can be
used to understand beam theory which is one of the functional
knowledge highly significant to the industrial engineer. The
cost of materials required for large-scale production is not too
high and can be easily sourced locally. The technical
manpower required can be found locally by training and
re-training of existing technical artisans, technologists and
engineers. The market is large locally and can also be
exported to other African countries. More research should be
embarked on in the process of production of beam deflection
apparatus. The apparatus should be mass-produced to ensure
its availability in the laboratories for students’ experimental
demonstration.
ACKNOWLEDGMENT
The effort of Ibraimoh, a Mechanical Engineering
Postgraduate Diploma Student, is appreciated in the areas of
fabrication and testing of the apparatus.
REFERENCES
[1] A. S. Mohamad, “Thesis on Flexural strengthening of RC
beams using CFRP strips,” UTP Library, Malaysia, 2004.
[2]
A. Spencer, P.A. Hiltion, “Material Testing and Properties”,
U.S.A.
Techquipment
Inc.
Article
Published
at
www.techquip.com. 2003a.
[3] A. Spencer, and P.A. Hiltion, “SM 104 Beam Apparatus”,
USA
Techquiipment
Inc.
Article
Published
at
www.techquip.com, 2003b
[4] C. Riley, K. Muoio, “Beam Deflection Apparatus SAN313”,
USA: Delta Analytical Instrument Inc. France: Societe DELTA
LAB pared activities de centr’ Alp Moiran Articles Published
www.deltalab.com.http://www.deltalab.fr/uk/product.php?pro
did579. 2004.
[5] L. Chilver, C.T.F. Ross, “Strength of Materials and
Structures”, 4th Edition USA and Canada: Elsevier Knouel
Corporation, 1999.
[6] H. C. Luebkenman, D. Petting”Structures Strength of
Materials”, Development in Structural Form, England: Allen
Lame/Penguin Books, 1996.
[12] R.Ehsani, “Shear and flexural strengthening of R/C beams
with carbon fiber sheets, “Journal of structural
Engineering, Vol. 123, No.7 pp. 903-911, 1997.
[13] R.G. Wight, M.A. Erki, C.T, Shyu, R. Tanovic, P. J.
Heffernan, “Development of FRP Short-Span Deployable
Bridge-Experimental Results” Journal of Bridge Engineering,
pp. 489-498, ASCE / Jul/Aug, 2006 .
[14] B. Kareem, “Development of a changeable die forging machine
for small scale forging industries”, J. Eng. Applied Sci., Vol 2,
No. 1, pp 77-80, 2007.
[15] P. Russell, “ Historical evolution of fib instrumentation and
technology”, in Nanofabrication using focused ion and electron
beams (principles and applications), I. Utke, et al. eds. (Oxford
series on Nano manufacturing, pp. 36-42, 2012
[16] R.G. Wight, C.T. Shyu, R. Tanovic, M.A. Erki, P. J.
Heffernan, “Short-span deployable GFRP tapered box Beam
Bridge” Proc., 4th Int. Conf. on Advanced Composite
Materials in Bridges and Structures (CD-ROM), pp. 20–23,
2004a.
[17] R.G. Wight, C.T. Shyu, R. Tanovic, M.A. Erki, and P.J.
Heffernan, “Deployable Tapered Box Beam Bridge: Advanced
Polymer Composites for Structural Applications in
Construction”, L.C. Hollaway, M. K. Chrysanthopoulos, and
S.S.J. Moy, eds., Wood head Publishing, Cambridge, England,
pp. 428-433, 2004b.
AUTHOR BIOGRAPHY
B. Kareem was trained in Nigeria at the Federal
University of Technology, Akure, where he obtained
his B.Eng. (Mechanical Engineering), M.Eng.
(Production Engineering), and Ph.D (Industrial
Engineering) degrees. He served as the Acting Head
of the Department of Mechanical Engineering at the
Federal University of Technology Akure, Nigeria. He
has been the head of the industrial development research group at the
University. His areas of research included industrial systems’ design and
development. He has supervised to completion several M.Eng. and Ph.D
candidates. He has published several research articles in reputable journals
and books of conference proceedings. He was given several academic
honors and awards including the best researcher of the year by his
University. He is a member of many professional bodies including World
Academy of Science, Engineering and Technology (WASET). He is a
reviewer/editor to many reputable academic journals.
348