Last Update: Tim Lovett, 3 April | 8 May 2008 | 5 Aug 2008
Assignment  % DUE
1. Form Design of a C Frame:  Stress/Deflection analysis 10% Week 5
2. Simple Cantilever1: Comparing FEA against formula results 6% Week 7
3. Simple Cantilever2: Gravity, Scale, Slenderness effects. 7% Week 8
4. Universal Beam Cantilever: I, Beam Tables, Design.  7% Week 9
5. Beam Lab and quiz. 10% Mid Sem
6. Design Analysis of a Clamp. 20% Week 13
7. Bolt Head Design 20% Week 15
8. Combined Project - Class or student-preferred project 20% Week 17
Total 100%

Solid Edge FEA Hints:

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 area 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 shape that can be made by laser profile cutting, or a single Solid Edge protrusion sketch. Determine the weight using SolidEdge.

PART B: DESIGN FOR DEFLECTION: 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 be made by laser profile cutting, or a single Solid Edge protrusion sketch. Weigh in SolidEdge.

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 don’t show “Yield Stress”, instead they give a “Proof Stress” which is a little higher than yield, so pick the lowest 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 designs).
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 shear stress, tensile and compressive stresses in a bending situation.

Task 2: Simple Cantilever 1: Comparing FEA against formula results 

1. Model a Cantilever. Force: 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;
Width: 20-40mm
Height: 30-60mm
Length: 1000-2000mm

Do not model a wall – just the beam itself. For a complex cross-section, you can measure “I” using Solid Edge draft (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. Use hand calculations (calculator, Excel etc) to work out the maximum stress and deflection for your problem. (See cantilever beam in bending table)

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 on the shape of the cross-section, and for a rectangle it is I = b * d^3/12.  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
                                                      = 750E3/83.33E3
                                                      = 9 MPA

3. Compare results on FEA. Run 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, Slenderness effects 

1. Gravity. 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 each method?

2. Scale: 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 part?

3. Slenderness:  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 Detailing effects.

Cantilever. Use Solid Edge to model a standard beam section.
(200UB – 18.2 kg/m)

1.Calculating Ixx
(a) Draw up the cross-section using the dimensions shown in the beam tables. (One Steel Structural sections). Manufacturer's document;

(Or use this link for a copy of the relevant page: Universal Beam Dimensions)
(b) Measure the 2nd Moment of Area through SE and compare your result to the reference tables. (Get the cross-sectional profile in SE draft, Tools > Area Properties > Click inside the area > Advanced. Read the value for Ixx)

2. Determine and compare Z. 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)

3. Cantilever. 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 the beam be?

4. Design. A 200UB/18.2 beam 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.

 Cantilever.  Using 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.

Cantilever Arrangement.

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

Lab instructions:

6. Design Study 1 - Trigger Clamp (FEA) Back to List

Trigger Clamp. 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.

Consider 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

1. 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.

2. 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

Material. Grade 8.8. (For details see http://www.matweb.com, or go to the bolt grades listed in MEM) 

Loading. This part must be designed to endure >106 cycles. See Fatigue info.

Length. 400mm.

1. Bolt Design: Build a model of a standard M16 bolt. Use the following dimensions below; (More accurate specifications are available in Aust Standards for metric bolts)

bolt head proportions

Bolt under FEA

 Load the bolt in tension. Ignore the thread of the bolt and assume a shank length of at least 50mm - yet try to minimize mesh size.

(a) Calculate the maximum load for the 8.8 bolt. Ensure you have a fine mesh to maintain accuracy.

(b) Re-design the bolt-head to reduce the stress concentration at the shank/head connection. The load must be applied on a flat circular surface under the head with inside diameter of 19mm and outside dimaeter of 25mm diameter. Demonstrate the effect of corner radius and shank relief groove.

(c) Calculate a 10^6 fatigue load for the bolt. (in kg)

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.