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Structures Lab 2
Lauren Mooney
10508554
4.Use any set of the experiment data (attached at the end, but don’t mix them up) and
do the calculations.
Plot the stress cr at buckling against (K/Leff )2 (the inverse of the squared slenderness
ratio), experimental and theoretical on the same plot.
(20 marks)
Effective Width Thickness
Specimen Length
"b"
"t"
No
"Leff" (m) (m)
(m)
Cross
Section
Area
"A" (m2)
Second
moment
of Area
"I" (m4)
Radius of
gyration
"K" (m)
(K/Leff)2
Theoretical Theoretical Experiment
Load "Pcr" Stress "cr" load "Pcr"
(N)
(N)
(N/m2)
Experiment
Stress "cr"
(N/m2)
1
0.715
0.0254 0.00297 7.5438x10-5 5.545x10-11
8.573x10-4
1.41x10-6
224.8
2.98x106
217.5
2.88x106
2
0.662
0.0254 0.00294 7.4676x10-5 5.379x10-11
8.487x10-4
1.64x10-6
254.4
3.41x106
286.0
3.83x106
3
0.615
0.0254 0.00289 7.3406x10-5 5.109x10-11
8.343x10-4
1.84x10-6
280.0
3.81x106
270.5
3.68x106
4
0.710
0.0254 0.00246 6.2484x10-5 3.151x10-11
7.101x10-4
1.00x10-6
129.6
2.07x106
138.0
2.21x106
5
0.661
0.0254 0.00245 6.2230x10-5 3.113x10-11
7.073x10-4
1.14x10-6
147.7
2.37x106
173.0
2.78x106
6
0.612
0.0254 0.00244 6.1976x10-5 3.0748x10-11
7.043x10-4
1.32x10-6
170.2
2.75x106
183.0
2.95x106
7
0.712
0.0254 0.00181 4.5974x10-5 1.255x10-11
5.225x10-4
5.38x10-7
51.3
1.12x106
50.0
1.09x106
8
0.659
0.0254 0.00182 4.6228x10-5 1.276x10-11
5.254x10-4
6.36x10-7
60.9
1.32x106
65.0
1.41x106
9
0.618
0.0254 0.00185 4.6990x10-5 1.340x10-11
5.340x10-4
7.47x10-7
72.7
1.55x106
87.7
1.87x106
10
0.563
0.0254 0.00184 4.6736x10-5 1.319x10-11
5.312x10-4
8.90x10-7
86.2
1.84x106
90.0
1.93x106
Stress/Pa
Theoretical And ExperimentalStress Against (K/Leff)^2
4500000
4000000
3500000
3000000
2500000
2000000
1500000
1000000
500000
0
0
0.0000002 0.0000004 0.0000006 0.0000008 0.000001 0.0000012 0.0000014 0.0000016 0.0000018 0.000002
(K/Leff)^2
Theoretical Stress "scr" (N/m2)
Experiment Stress "scr" (N/m2)
Linear (Theoretical Stress "scr" (N/m2))
Linear (Experiment Stress "scr" (N/m2))
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5.
Compare the experimental results with the theoretical predictions.
(Reasons are not needed, they are required in the next question)
(20 marks)
As you can see in the graph, the line of best fit for both theoretical and experimental stresses
have similar gradients which indicates the as the (K/Leff)2 increases both Stresses also
increase at a similar rate to each other. However the line of best fit for experimental results is
slightly higher than the best fit for theoretical stresses indicating that the values for
experimental stresses are higher than values for theoretical
As you can see for the blue theoretical value lines, the plotted points are all along the line of
best fit where as the yellow plotted points are quite sporadic in that they could be a lot higher
or lower than the line of best fit.
6.There are many probable sources of error which affects the experimental results. List
(a) One source which makes the experimental result higher than the theoretical
prediction.
The outcome of experimental values could be larger than theoretical if increment of the weights
used were too large. (eg. If a weight of 1Kg was added when a load of 0.25Kg would result in
the column buckling). This is because the column will not buckle until Pcr is achieved which
means if P>Pcr it will also buckling allowing the value of Pcr to be misjudged to be higher than
theoretical.
(b) Two sources which make the experimental result lower than the theoretical
prediction.
One source that would make the experimental result lower than the theoretical is if in the
beginning there may have been a small force applied to the column before any weights are
added.
Another source would be if the material was already deformed before the column undergoes
the compression. This may lead the material to buckle prematurely which will therefore make
the experimental results smaller than the theoretical.
(c) Two sources which may affect the experimental results randomly (sometimes higher,
sometimes lower).
Human error could be the cause of the experimental results to produce a higher or lower value
compared to the theoretical value. This involves misreading the lengths of columns.
7. Is there any major merit in plotting cr ~ (K/Leff)2 rather than Pcr ~ I/Leff2 to show the
buckling behaviour of columns under axial compression? Give reasons. (12 marks)
After plotting this graph, you can see a similar trend in that both graphs show lines of a similar
positive gradient. Although they show similar results in terms of trend, I believe that the graph
of cr ~ (K/Leff)2 as it takes into consideration of more factors than the graph of Pcr ~ I/Leff2 (ie,
cross sectional and second moment area) and therefore provides a better presentation of the
information calculated.
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8. Application of buckling theory to structural failure analysis
(33 marks)
A pin-jointed truss structure is loaded by three forces as shown below. The bars are made of
the same material of Young’s modulus E=210GPa and a permissible stress =200MPa. All
the bars have a solid circular cross-section of a radius r= 0.01 m. The length of the diagonal
bars is a = 0.5m. Assuming bars under compression can be considered as simply supported
columns (therefore Euler formula for buckling load Pcr = 2EI / L2can be used). Determine the
maximum value of load W which will not cause the failure of the structure.
2W
6W
B
a
A
45
D
a
a
45
45
C
a
45
E
3W
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N