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)


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)


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)


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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Buckling of Mild Steel FINAL

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