ASSESSMENT 2008 Home
Last Update: Tim Lovett, 3 April | 8 May 2008 | 5 Aug 2008
|1. Form Design of a C Frame:
|2. Simple Cantilever1: Comparing FEA against formula
|3. Simple Cantilever2: Gravity, Scale, Slenderness
|4. Universal Beam Cantilever: I, Beam
|5. Beam Lab and quiz.
|6. Design Analysis of a Clamp.
|7. Bolt Head Design
|8. Combined Project - Class or
Solid Edge FEA Hints:
- Forces may need to be applied over an area to avoid stress
concentration due to point loads. To make an area you may have to
create a surface.
- To change UNITS, change the default SE units. File >
File Properties > Units (and probably > Advanced Units
- Select material: Tools > Material Table.
Choose appropriate material from the list.
- Custom material: In the Material Table type your own
material in the box and enter your own values, then click Add to
- Find Mass of a part in SE: (You must have a material
first). Inspect > Physical Properties
Task 1: Form Design of a C Frame (FEA)
Design of a “C” frame. The shape of the part is
entirely 2 dimensional and suitable for profile cutting.
The force is applied as a PRESSURE over each face (10mmx10mm), at a
pressure of 20MPa. It should be compressive (pushing the jaws apart)
Material is 10mm “Steel”.
||The profile of the part must not intrude into the 50mm
radius or the 10mm flat face.
You can make it as large as you like and any shape - but we are trying
to minimize weight!.
The mounting must be 40mm long and horizontal, and at least 50mm from
the jaws. (i.e. behind the centre of the inner hole of diam 100mm)
||The force should be applied as a pressure load over the
of the flat face. We do not use a point force due to excessive stress
produced by the force concentration.
Remember to refine the mesh to check your results more thoroughly.
PART A: DESIGN FOR STRESS:
Design for minimum weight, assuming max stress of 200Mpa. You can
modify the external radius and shape, as well as drill holes/carve out
material. The material must remain as a flat plate – i.e. A
that can be made by laser profile cutting, or a single Solid Edge
protrusion sketch. Determine the weight using SolidEdge.
PART B: DESIGN FOR
Design for minimum weight, assuming max stress of 200Mpa, and not more
than 0.25mm displacement on the part. You can modify the external
radius and shape, as well as drill holes/carve out material. The
material must remain as a flat plate – i.e. A shape that can
made by laser profile cutting, or a single Solid Edge protrusion
sketch. Weigh in SolidEdge.
PART C: ADDITIONAL
1. Determine the
force applied to the
clamp faces in kN. Convert this to kg and tonnes to get a better feel
for the magnitude of loading.
2. Make a new
material called BisPlate80.
It has a higher yield stress but the same E. Notice they
show “Yield Stress”, instead they give a
Stress” which is a little higher than yield, so pick the
proof stress given. Change the model to this material and compare the
FEA results. Repeat using a higher strength steel, Hardox 400.
3. What is the effect
of using higher
strength steels in each design? (Stress-based and deflection-based
4. What is the
difference between Yield Stress and Proof Stress?
5. What is happens if
all of the lowest
stress area is cut out as a large slot? Explain in terms of
stress, tensile and compressive stresses in a bending situation.
Task 2: Simple Cantilever 1: Comparing FEA
against formula results
1. Model a Cantilever.
Find force to give stress of 100MPa in a cantilever beam. The force is
applied vertically on the end face. Use Solid Edge to model a
cantilever beam (Or do it directly within Visual Nastran) that you will
use as a loaded member. You must choose your own dimensions
within the parameters shown below;
Do not model a wall – just the beam itself. For a
cross-section, you can measure “I” using Solid Edge
(area properties) which will be needed when you go to calculate the
problem. Try it out on a simple rectangular section first, which can
easily be done by hand calculation.
2. Calculate the problem.
hand calculations (calculator, Excel etc) to work out the maximum
stress and deflection for your problem. (See cantilever beam in bending
|Example Calculations: Assume a force (F) of
500N, a cantilever with
length (L) of 1.5m. The beam is 50mm wide x 100mm deep. Find the stress.
Bending Moment M = F
* L = 500 x 1500 = 750000 Nmm (you must use mm)
Section Modulus Z =
b * d^2 / 6 = 50 x 100^2 / 6 = 83.333 e3 mm^3
Note: Z is actually
derived from the Second moment of Area (I) using the equation
Z = I / y , where y = distance from Neutral Plane to furthest extent of
the beam cross-section…often half the depth. Now, I is based
shape of the cross-section, and for a rectangle it is I = b *
Therefore Z = I / y where y = d/2, so…
= b * d^3/12 * 2/d
= b * d^2 / 6
Formula for stress:
Stress s = M / Z
= 9 MPA
3. Compare results on FEA.
FEAMAP to compute your model conditions using FEA. The fixed end of the
cantilever is simply locked to ground (constraint) and the free end has
the force applied. Experiment with the force loading arrangement to see
how it affects results. Check stress and deflection.
4. Use Beam analysis in Solid Edge. (Applications > Engineering
Reference > Beam Designer)
(a) Solve this question using Beam Designer. (Watch out - beam designer
will automatically include gravity! To stop this, use a material of
almost zero density - like 0.001kg/m3)
(b) What are the advantages and limitations of
each method - hand calcs with calculator, hand calcs with Excel, SE Engineering Reference and FEA?
(c) Of the 4 methods above, which one is fundamentally different to the others? What is the difference?
Task 3: Simple Cantilever 2: Gravity, Scale,
Repeat the above
question but without any load except the weight of the beam. To do this
you will need to apply a DISTRIBUTED LOAD along the
length of the beam that is equivalent to the total weight of the beam.
(i.e. a force applied over a surface along the whole length of the
beam). Use the following 3 methods;
(a) Hand calculation by beam table formulae.
(b) Beam analysis in Solid Edge. (Applications > Engineering
Reference > Beam Designer. Very simple, since Beam Designer includes gravity by default)
(c) FEAMAP. (Have to apply a FORCE equal to the weight of the beam and apply it over the entire top face of the beam)
Explain the differences. What are the advantages and limitations of
Repeat the above question (using FEA only) in the following cases:
(Remember to re-calculate mass of course!)
(a) All dimensions of the beam are halved.
(b) All dimensions of the beam are doubled.
What does this tell you about the effect of changing the scale of the
This time make the length of your beam equal to it's depth.
Apply a vertical force on the end of 2000N.
(a) Calculate the bending stress using hand calculations
(b) Calculate the bending stress using FEA
Explain the difference. Which one is more reliable when the beam is
relatively short compared to it's depth?
What is the recommended slenderness (Length to Depth) ratio of a beam
when formulas are to be used?
4. Universal Beam
Cantilever: I, Beam Tables, End
|Cantilever. Use Solid Edge to model a standard beam
(200UB – 18.2 kg/m)
(a) Draw up the cross-section using the dimensions shown in the beam
tables. (One Steel Structural sections).
(Or use this link for a copy of the relevant page: Universal Beam
(b) Measure the 2nd Moment of Area through SE and
your result to the reference tables. (Get the cross-sectional profile
in SE draft, Tools > Area Properties > Click inside the
Advanced. Read the value for Ixx)
2. Determine and
The One Steel table has values for Zxx and Zyy - called the Section
Modulus. This is simply Z=I/y, which gives the very simple definition
of stress as f=M/Z.. Determine the Zxx for this section and compare to
the manufacturer's data. (See relevant page here)
What is the
specified Yield Stress? If the bending stress reaches half
the yield stress limit due to it's own weight, how long would
4. Design. A
is used in the wall of a vacuum chamber
where 99% of a
full vacuum is applied. Ignoring the strength contribution of the
vacuum chamber wall, and assuming the beams are 500mm apart, how long
can the beams span if the stress must not exceed 100MPa.
To begin this problem, since each beam is equally spaced you only need
to consider a single beam and the equivalent amount of plate that it
has to support.
Since the vacuum is 99% and atmospheric pressure is 101kPa, then the pressure difference is about 100kPa.
To model this in Feamap, ignore the plate altogether and apply an
appropriate PRESSURE on the top flange face of the beam. Now increase
the length of the beam until the stress reaches the maximum of 100MPa.
What is this length?
5. Beam Lab and quiz.
the aluminium beam jig, compare the deflection of various loadings on a
cantilever. Assume the weight of the beam is the starting datum for
measurement. Weights are added and the deflection measured. You must
record all relevant information (beam material, cross-section, length,
mass etc), then calculate the deflection by analytical methods (see bending table), then model the
beam in FEAMAP and check results.
Comment on any differences that might occur between the 3 methods. What
are the sources of error in each of the following; Consider measurement
tolerances, calculation rounding, theoretical approximations of
formulas, variability of material properties like E. (In other words, discuss all the sources of error).
(a) Analytic calculation (by formulas)
(b) FEA analysis (Using SE and FEAMAP)
(c) Experimental measurement
- Take at least 3 measurements for the comparison. (Take care not to overload the beam)
- Hang weights off the end, but try to estimate the more precise line of action of the weight force.
- Measure the deflection at the end of the beam somehow (perhaps
use a ruler to extend the base, or some other solution. You need
to measure the maximum deflection, not somewhere along the
- Since the zero-weight measurement already includes gravity and
you are simply comparing results, so you can ignore gravity in all the
6. Design Study 1 - Trigger Clamp (FEA) Back
The jaws of this clamp are injection moulded in a reasonably strong
(but not fibre reinforced) plastic. One rule for moulded parts
(especially plastics) is to try to keep the wall thickness constant.
Any corners that are stressed should have a generous radius to reduce
the risk of cracking. In a moulded part it is more difficult to make a through-hole
than a blind hole because each half of the mould must touch with zero gap -
otherwise the plastic will seep into the surface and create a thin film
(flash) across the hole.
the end jaw. It is well rounded, but the slot in the arm goes right
through. If it is supposed to be a rigid as possible (for plastic),
what should they have done in this area?
The main jaw has a similar issue, a through hole in the middle of the web.
Download a solid model of the end jaw here; end_jaw.zip
Test the parts using FEA. Assume the steel bar remains rigid and only
the plastic jaws flex. Determine the spring stiffness of each jaw in
N/mm. (You will need to consider a likely candidate for the plastic
itself - the selections in Solid Edge should be adequate. Use
Polycarbonate as a reasonable estimate.
Determine the overall spring stiffness when clamping an object. Apply a
force to the clamping face and constrain the on hole surface.
It is very easy for a designer to test these designs in FEA today
(Actually, even easier in countries where you don't get in trouble for
using pirated software for commercial use). Virtually every engineered
plastic component is solid modelled today - with exception of some
carved objects like toy animals. So they should have known about this.
The solid model is needed for the CNC machining of the mould, so FEA is
just a few clicks away.
Consider what might happen if the jaws were more rigid.
Think about the way the trigger works, consider stress, deflection etc.
Did they do this on purpose? Alternatively, what if ther designer jumped on FEA and chopped out all
the "low stress" area. What is the danger with doing that? So do you think they made a mistake or did they do this on purpose? Explain your answer.
3. Redesign the end jaw to maximize stiffness. You cannot increase the
wall thickness, nor the external dimensions (within a rectangle
bounding the part on the parting plane).
7. Bolt Head Design
8. Combined Project - Class project:
Apply FEA analysis to a selected portion of the current student class
project. The analysis will cover multiple subject disciplines - such as
Free Body Diagrams, kinematics, mechanics and forces in order
to bring the problem into FEA. The student is expected to research some
areas of the study such as material properties, standard component
specifications or FEA methods for specialized cases such as
welds and fasteners.
The student may elect to do FEA analysis on their own project, but this
needs to be checked with the teacher to ensure that it is suitable.