Buckling of Mild Steel FINAL
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Transcript of Buckling of Mild Steel FINAL
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Buckling of Mild Steel
TEAM
BY: Michael Ridolfi
Edward Van MeterMatt McKellar
Neema Kalilli
Dale Mace
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In 1757 Euler derived theformula for maximum axialload a specimen can carrywithout plastically deforming.
The sample was modeled asan ideal column that isperfectly straight and free ofany initial stress.
The original formula ONLYtook into consideration axialloading, but not lateral. It waslater shown to provideapproximately the sameresults.
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Modern History of Buckling
1940s
Known phenomena
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Buckling lab uses a materialsYoungs modulus and momentof inertia, with an appliedforce, to find the criticalloading value.
Three samples made up of thesame material will be used withvarying lengths and constrainttypes.
This information gathered willhelp also aid in determiningthe deflection.
The machine that will be usedis the TQ-STR12
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TQ-STR12 Used to test:
Euler buckling loads. Relationships between strut
length and collapse load. Relationships between end
conditions for collapse load Nature of deflection and
deflected shapes.
Hardware Magnetic deflection
scale. Digital force display.
Screw compressor for strut
experiments.
Load cell for measuring
applied load.
Software Computer simulation of
experiment. Expands scope of
experiment beyond limits
of hardware.
Displays theoretical
buckling.
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A36 Mild Steel
Density = 7800 kg/m^3 Ultimate Strength = 400-550 MPa Poisson's Ratio = 0.260 Youngs Modulus = 200 GPa Shear Modulus = 79.3 Gpa
Member types Plates, sheets (type we are testing) Bars, structural shapes
General Properties Standard low carbon steel No advanced alloying Maintain ultimate strength to about 650F Typically welded, bolted, riveted. Very common structural steel
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Most common hot-rolledand mild steel.
How it is made, carbon, rolltype
How it interacts withmachine
Element Content
Iron 98.0%
Manganese 1.03%
Carbon 0.25-0.29%
Silicon 0.28%Copper 0.20%
Sulfur 0.05%
Phosphorous 0.04%
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Cut
Design, measure, mark sheet material atdifferent lengths.
Make specimen cuts using metal press.
Drill
Mark holes with diameters that will fitthe bending machine.
Drill holes using drill press
Fit
Make final measurements ensuringconsistent width and shape.
Fit specimens individually into TQ-STR12to check they fit properly.
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Problems during production: Width consistency.
Proper width, not too thick, not too thin.
Holes had to be as center as possible
Samples had to be similar to prior aluminum
samples for a proper comparison to be made.
We had to ensure the lengths were appropriate
for buckling machine to gather conclusive results.
Sample Length (L) Width (W) Thickness (T)
A 0.51 m 0.018 m 0.0014 m
B 0.48 m 0.019 m 0.0014 m
C 0.44 m 0.018 m 0.0014 m
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We selected a material and made careful measurements to ensure
the experiment parameters were met. This included proper sheet
thickness and width. Also, with steel being stronger than aluminum,
the samples had to be longer than prior aluminum specimens.
Calculated and theoretical results for deflection and critical
loading were compared and that was then compared to loadings
with different end orientation.
The samples are inserted into the TQ-STR12 machine with the
following methods:
Pinned on both ends
Fixed on both ends
Fixed and Pinned
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Measure thickness,width, length, of
specimen
Attach specimen tothe TQ-STR12.
Choose end state forlink. i.e. FF, PP, FP
Turn nob at the top ofthe specimen,
applying a load untilthe values begin to
fall again.
Record value andcompare to
theoretical values.Repeat for next
sample.
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PP, n=1 Pcr (N)
Sample Measured Theoretical Error (%)
A 26 32.537 20.090
B 35 41.361 15.379
C 42 47.226 11.06615.512
Discussion
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Note: Scales change
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PF, n=1.414 Pcr (N)
Sample Measured Theoretical Error (%)
A 58 70.386 17.597
B 74 90.077 17.848
C 82 103.585 20.83818.761
Discussion
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FF, n=2 Pcr (N)
Sample Measured Theoretical Error (%)
A 121 152.849 20.837
B 154 197.042 21.844
C 181 228.366 20.741
21.141
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FF, n=2 Pcr (N)
Sample Measured Theoretical Error (%)
A 121 152.849 20.837
B 154 197.042 21.844
C 181 228.366 20.74121.141
Discussion
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The most notable and similarly obvious trend in the data is how
the critical loading is strongly correlated to the length of the
member. The shorter the member, the larger the critical
loading.
The next observation is that the members with one fixed end
had a critical loading of about 2x that of the pinned-pinned
end fixture. Similarly, the fixed-fixed end condition provided
another magnitude 2x that of fixed-pinned. There is a very
strong correlation between more fixed positions and larger
critical loading.
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Members are not quite as uniform in width as we would haveliked.
Very slight variation in hole placement.
Members had some imperfections from production such asscrapes, dings, and very very slight deformation.
Machine had some uncertaintyvalues.
Hand measurements had someslight uncertainty.
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Buckling measurements are made onalmost any project including mechanical,structural, and civil engineering.
Mechanical: submarine hauls undercompressive forces from sea water
Structural: underground tunnels with c
shape supports Civil: every building ever made.
Basically, buckling is a typical designconstraint in construction of buildings andmost designs that cause compressivestresses.
Buckling is a important quality to take intoconsideration because failure typicallyresults in a catastrophic failure of themember and possible the entire structure.
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World Trade Center After intense fires that, at
their hottest, were measuredat 1800F the members began
to weaken. At 1100F, mild steel looses
of its total strength!
The second tower hit lasted
twice as long as the firstbecause there was haft thefloors loading the membersabove the fires.
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Future contributions:
Material sciences to produce stiffer materials
Test different cross sections.
What will this lead to
Found information
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http://en.wikipedia.org/wiki/Buckling http://en.wikipedia.org/wiki/A36_steel
http://publish.ucc.ie/boolean/2010/00/dePaor/11/en
http://www.tqstructures.com/STR12/buckling-of-struts.htm
http://en.wikipedia.org/wiki/Bucklinghttp://en.wikipedia.org/wiki/A36_steelhttp://publish.ucc.ie/boolean/2010/00/dePaor/11/enhttp://publish.ucc.ie/boolean/2010/00/dePaor/11/enhttp://www.tqstructures.com/STR12/buckling-of-struts.htmhttp://www.tqstructures.com/STR12/buckling-of-struts.htmhttp://www.tqstructures.com/STR12/buckling-of-struts.htmhttp://www.tqstructures.com/STR12/buckling-of-struts.htmhttp://www.tqstructures.com/STR12/buckling-of-struts.htmhttp://www.tqstructures.com/STR12/buckling-of-struts.htmhttp://www.tqstructures.com/STR12/buckling-of-struts.htmhttp://www.tqstructures.com/STR12/buckling-of-struts.htmhttp://www.tqstructures.com/STR12/buckling-of-struts.htmhttp://publish.ucc.ie/boolean/2010/00/dePaor/11/enhttp://publish.ucc.ie/boolean/2010/00/dePaor/11/enhttp://publish.ucc.ie/boolean/2010/00/dePaor/11/enhttp://en.wikipedia.org/wiki/A36_steelhttp://en.wikipedia.org/wiki/A36_steelhttp://en.wikipedia.org/wiki/Bucklinghttp://en.wikipedia.org/wiki/Buckling -
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