Measuring the Tension and Compression of an Aluminum Cantilever Beam

Name:
Instructor:
California State University, Sacramento.
Department of Civil Engineering
CE 113, Structural Laboratory.
Measuring the tension and compression of an aluminum cantilever beam and verifying the flexural bending stress equation.
Tuesday Lab.
Group 1.
Executive Summary
The strength of any structural establishment on earth is on its ability to slightly adjust in relation to the natural or artificial forces. It is as a result of this that there is every reason for the knowledge of the flexural ability of these structures through determination of flexural bending stress .In order to construct any structure, the material used, and subsequently, the flexural bending stress of this material, is important so as to determine the extent to which the structure can move or be bent. This can be determined through the performance of a simple stress-strain test on the material, through application of a considerable amount of load on the material, that doesn’t exceed its maximum stress value.
This plays a very important role, since it ensures that the maximum flexural strength of the material is known, without causing its breakage or snapping, which usually occurs after exceeding the stress value. Putting this into practical ,real-life application, exceeding the stress value of the material making up a structure like say, a suspension bridge, can result to its collapse, resulting to a lot of losses, both economically, and maybe in form of human lives as well.
This experiment was carried out in order to determine the two main features of strength for the aluminum cantilever beam; the compression, and the tension. This would in turn help in the determination and verification of the flexural stress equation. The first step was to fix one end of the beam firmly to a strong support. Secondly, a load, in this case, a container, was freely hung on the other end of the beam, and the load was increased gradually by the use of small load of around 1.5 pounds. Both the quarter and half bridge were used, and the process repeated again.
Introduction:
As earlier mentioned, the objective of this experiment is to determine the stress and strain of an aluminum cantilever beam and then compare the findings of the experimental and theoretical values of flexural bending .In order to achieve the objectives, the setup was made by connection of the aluminum cantilever beam to the strain indicator. This was to complete the first part of the experiment, which centered on the determination of the tension within the beam.
N.B:
There was no use of full bridge in this experiment. Only the half and quarter bridge were applicable. It is important to understand clearly, how these two are connected to the strain indicator, as their respective setup consists of distinct and different wire connections.
Then, in order to determine the compression of the same, it was the bottom of the aluminum cantilever beam that was connected. A container was then hooked onto the aluminum beam, and loads put in t incrementally. The setup was in suspension, in such a way that there was a combination of both tensional and compression forces acting on it, at the top and bottom respectively.
With the setup now complete, it was then important to calculate the loads at each time of increment sp as to be able to determine the load at which the beam would not hold anymore. It is at this load that the beam becomes permanently deformed. The derivation below comes in handy:
Aplying Hooke’s Law, ɛ = σ/E………………………………..(1)
But σ/E = y/ƿ,therefore , σ = (y/ ƿ).(E)…………………………(2)
M = EI/ ƿ which can still be put as ƿ = EI/M……………………(3)
Replacing Æ¿ = E/f,the equation becomes; (E/f) = (EI/M),
This gives; f = (M/I)……………………………………………..(4)
Where;
Ç· is the radius of curvature, M is the bending moment, F is the flexural stress. I is the moment of inertia.
Equation (4) is the bending stress equation.From the experimental setup,the following initials are important;
P for the maximum load,L is the distance between the bucket hook and the strain gauge, E is the modulus of elasticity, B is the base of the beam,E(Al) is the modulus of elasticity of aluminium,and h is the height of the beam.
Substituting for the maximum load in equation (4) ;
P = [EE (AL) I]/ [YL] where y=h/2 and I= [bh3]/12
Relating from equation (1) and (4);
E = [(PL) (H/2)]/ [(E (al) (bh3/12)………………………………………………………… (5)
Approach
This section explains in details how the experiment was carried out.
An alumin...