msi10 plastic analysis

Faculty : Civil And EnvironmentEngineering

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Department : Structure And MaterialEngineering

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Title :PLASTIC ANALYSIS

Effective DateAmendmentDate

1.0 OBJECTIVE1.1 To find the form factor1.2 To investigate the load deflection relationship for a beam to the point of

plastic collapse

2.0 LEARNING OUTCOME2.1 Able to apply the structural knowledge in practical application.2.2 To improve the technical efficiency through the laboratory work.2.3 Able to communicate effectively in team work.2.4 Able to recognize the problem, solving and getting the solution through

experimental work

3.0 INTRODUCTIONDuring the design process for beams it would not be unreasonable for one toassume that no part of the beam should experience a stress greater than thatallowable for the working material. However, it can be found that a beam willwithstand much larger forces before collapse than simple elastic theory predict.

Prepared by:Name: Ahmad Zurisman bin Mohd AliSingnature:Date:


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4.0 THEORYWhen a beam is bent around the neutral axis, the stress through the beam sectionvaries with the distance from the neutral axis, form the greatest att the extremefibres ( y= maximum) to zero at the neutral axis ( y = 0)

If the beam is subjected to an increasing bending moment, the stress will build upthrough the section to a maximum at the extreme fibres. This means that althoughthe outer parts of the beam may well have yielded and are behaving plastically,the inner parts may still be behaving elastically and resisting load.If the bending moment continues to increse, the plastic portion will move furtherinto the beam leaving a smaller elastic core. This called the partially plasticcondition. The beam will continue to resist the bending moment although with anincresing rate of deflection as the plastic portion moves further toward the neutralaxis. ( See diagram below )

Neutral axis

y (max)

y

Neutral axis

y

y

Plastic portion


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Eventually the elastic portion will far enough into the beam andthe beam willbe fully plastic. It will form a plastic hinge and be unable ti resist any furtherbending moment ( shown below)

The ratio of the fully plastic bending to the just plastic moment is call FORMFACTOR. The form factor is entirely dependent on the shape of the beam and not on thesize, material or fixing condition.

For cantilever beam

Yield stress bdWL

y4 .equation 1

For the simply supported beam

Maximum bending moment, 4WLM p .. equation 2

Bending moment at yield of the extreme fibre yIM yy Experiment form factor = yp MM where the text book value is 1.5

Neutral axis

y

y

y


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5.0 PROCEDUREExperiment (Simply Supported Beam)

1. Tke the specimen beam and measure the cross section, calculate thesecond moment of area for the spesimen.

2. ensure the clamp plates are removed and place the specimen beam acrossthe chucks of the unit

3. Push the roller mechanism outwards to its stop.4. Put the pin through the load cell fork and wind the load cell down until the

pin just touches the specimen beam, zero both the load cell and theindicator.

5. Wind the load cell down to cause a measured deflection of 3mm and takea reading of the force required.

6. Continue to wind the load cell down in 3 mm step until there is no or verylittle increse in load for each increment of deflection.

7. Enter ypur result into Table 1.

6.0 APPARATUSSketch the apparatus used un this experiment and named the essential components


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7.0 RESULT

Deflection(mm)

Force ( N )

0369121518212427303336

Table 1 : Result for experiment ( Simply Supported Beam)

8.0 DISCUSSIONExperiment 1

1. Plot the graph Force vs Deflection and from your result comment on theshape of the resulting plot.

2. From Table 1, note the collapse load, and using the bending momentdiagram calculate the plastic moment ( Mp).

3. Using yield stress of 325 Mpa* Calculate the bending moment (My) to justcause yielding of the extreme fibres.

4. Calculate the form factor (Mp/My) . Compare to the text book value5. Discuss the advantages of considering the extra available strength duet o

the plastic beam theory when designing structures.

msi10 plastic analysis

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