Experiment B lab
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Dec 6, 2023
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Experiment B Stresses In a Thin
Walled Pressure Vessel
Lab 2
MAAE2202 section B
Department of Mechanical and Aerospace Engineering
Carleton University
Prepared by: George Grivas (101273448)
(georgegrivas@cmail.carleton.ca)
Lab Performed: November 2nd, 2023
Lab Submitted: November 9th, 2023
Summary
The main objective of this lab was to gain a better understanding about how strain
gauges work and their function. To do this, strain gauges were used on a standard 355
mL soda can and the strain in the hoop as well as the strain in the longitude axis were
recorded. This was done twice, the first time had the soda in its normal state and the
second was after the soda can had been shaken. After all the strain values were
recorded, stress and internal pressure of the can were calculated using data for
aluminium collected from trusted sources. The calculated stress was in two parts that
being the hoop stress and longitude stress, the ratio of these values was recorded and
compared to the actual known property that hoop stress will be twice that of longitude
stress. The lab appears to have been successful as the experimental ratio was close to
that of the actual ratio.
Nomenclature
Theory and Analysis
Stress (
𝜎
)
Defined as F/A, The two kinds of stress are normal and shear where normal describes
force perpendicular to the cross sectional area and where shear describes force parallel
to the cross sectional area. This experiment only focuses on normal stress, more
specifically normal compressive stress. The unit of stress is newtons (N) divided by
metres (m) also known as Pascals (Pa).
In this experiment stress will be calculated from strain alongside the young’s modulus of
aluminium using the derived equations for hoop and longitude stress:
Strain (ϵ)
As force is applied to an object there will always be some sort of deformation this is
where strain is used. Defined as Δl/l
o
. Strain represents the unitless ratio of the change
in length divided by the original length.
Young’s Modulus (E)
The young’s modulus is used in hooke's law which is defined as
𝜎
= ϵE. When hooke’s
law is rearranged E represents the ratio of stress and strain. E is known as a material
elasticity or in other terms its stiffness. The material used in this experiment is
aluminium which has an elasticity of E = 70 GPa [2].
Internal Pressure (P)
Pressure is the force that acts perpendicular to the surface of the soda can, similar to
stress it uses the same units (MPa) as it describes force over area. In this lab the can
will experience a pressure from the fluid inside of it.
Poisson’s ratio (v)
Poisson’s ratio depicts how much an object deforms in both axis relative to each other.
For aluminium this ratio is v = 0.35
Ultimate tensile strength (
𝜎
)
The ultimate tensile strength describes the maximum amount of pulling/stretching of a
material before it eventually fails. For aluminium the ultimate tensile strength is 600 Mpa
Experimental Setup and Procedure
The Procedure went as the lab manual describes.
Soda can dimensions
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=
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%3D
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