Experiment:09
9.1 Objective:
Parametric analysis of cantilever beam subjected to point load.
9.2 Apparatus:
Beam apparatus
Vernier clipper
Dial indicator
Weight and hanger
Balance
Meter rod
Clamps
9.3 Diagram:
Figure (1)
9.4 Theory:
Beam
A beam is a structural member used for bearing loads. It is typically used for resisting vertical
loads, shear forces and bending moments.
According to its requirement, different beams use in different conditions like fix beam, cantilever
beam etc.
Types of beams
Beams are classified as follow.
According to end support:
Simply Supported Beam
As the name implies, simply supported beam is supported at both ends. One end of the beam is
supported by hinge support and other one by roller support. This support allows to horizontal
movement of beam. It beams type undergoes both shear stress and bending moment.
Continuous Beams
When we talk about types of beams we cannot forgot continuous beam. This beam is similar to
simply supported beam except more than two support are used on it. One end of it is supported by
hinged support and other one is roller support. One or more supports are use between these beams.
It is used in long concrete bridges where length of bridge is too large.
Overhanging Beams
Overhanging beam is combination of simply supported beam and cantilever beam. One or both of
end overhang of this beam. This beam is supported by roller support between two ends. This type of
beam has heritage properties of cantilever and simply supported beam.
Cantilever Beams
Cantilever beams a structure member of which one end is fixed and other is free. This is one of the
famous types of beam use in trusses, bridges and other structure member. This beam carry load
over the span which undergoes both shear stress and bending moment.
Fixed beam
A fixed beam is supported at both free ends and is restrained against rotation and vertical
movement. It is also known as built-in beam. A fixed beam is abeam which is built in such a way
such that their end slopes remain zero.
9.5 Procedure:
1. Measure the width and height of the cross section of the beam with Vernier caliper.
2. Position and fix the support on the beam apparatus to get the cantilever action on its fixed
end
3. Measure this distance L, length of the beam
4. Level the whole apparatus using the levelling screws at the bottom
5. Mount a dial gauge, above the beam at this location ( free end ) such as the knob of the dial
gauge is in contact with beam
6. Apply small load by adding a weight n the hanger
7. Note the deflection in the gauge
8. Keep adding weight with regular increment and note the dial gauge reading for each
successive addition
9. Note the dial gauge reading while un loading the weight one by one
10. Calculate the mean deflection and slope at both locations from this experiment data and
compare with theoretical result.
9.6 Observations and calculations:
Length of the beam = 46 cm
Width of the beam = 2.65 cm
Height of the beam = 0.68 cm
Moment of inertia of the beam = 0.001668 in4
Modulus of elasticity of aluminum = 10 MPsi
Table 1: Summary of results
Sr. Load Deflection(yexp) Deflection Absolute %
# (lb.) (Inches) (yth) difference difference
Loading Unloading Mean
(Inches)
1 0.1 0.003 0.0035 0.00325 0.00118 0.72 72
2 0.2 0.0019 0.0023 0.0021 0.00237 0.1285 12.85
3 0.3 0.0039 0.0042 0.00405 0.003556 0.138 13.8
4 0.4 0.0057 0.0059 0.0058 0.004742 0.22 22
5 0.5 0.0076. 0.00768 0.00768 0.005928 0.29 29
9.7 conclusion:
When we add the increment of the load on the beam as from the table it shows that the deflection in
the beam also increases because the weight stretches the beam down ward. The deflection is also
depending on the composition of the beam material. For harder material the deflection is less and
for soft material like aluminum there will be more deflection.
9.8 references:
1. S. Kumar and S. V. Barai, “Influence of specimen geometry on determination of
double-K fracture parameters of concrete: a comparative study,” International
Journal of Fracture, vol. 149, no. 1, pp. 47–66, 2008. View at Publisher · View at
Google Scholar · View at Scopus
2. B. L. Kari aloo and P. Nallathambi, “Size-effect prediction from effective crack
model for plain concrete,” Materials and Structures, vol. 23, no. 3, pp. 178–185,
1990. View at Publisher · View at Google Scholar ·View at Scopus
3. Z. P. Bazand and P. C. Prat, “Effect of temperature and humidity on fracture energy
of concrete,” ACI Materials Journal, vol. 85, no. 4, pp. 262–271, 1988. View at
Google Scholar · View at Scopus
4. G. Baker, “The effect of exposure to elevated temperatures on the fracture energy of
plain concrete,” Materials and Structures, vol. 29, no. 6, pp. 383–388, 1996. View at
Google Scholar · View at Scopus
