Create a cover sheet for your assignment to include the following information;
• Assignment Number
• Due date (refer to the Assignment Schedule in Course Spec)
• Date submitted
Number of hours spent on studying for and completing the assignment for:
• Task 1
• Task 2
• Task 3
• Task 4
Brief list of things that you learnt from this assignment
• Task 1
• Task 2
• Task 3
• Task 4
Brief list of things that you remain uncertain about
• Task 1
• Task 2
• Task 3
• Task 4
Note that the last three items (hours, what you learnt and what you are uncertain about) are an essential part of the assignment. The last two force you to reflect for a moment and think- what was this really all about?
Note that I am not spelling out exactly what views to record in your submission. You are expected to adequately document all aspects of your investigations and to demonstrate curiosity and perseverance in getting to grips with the underlying phenomena and with effectively communicating your understanding. Show all theoretical calculations as required, otherwise marks will be deducted.
Task 1 – Relevant to Chapter 3 Weighting 5%
To use Strand7 or any other analysis package ‘responsibly’ you should check the results of the computer analysis against results from a manual analysis (or an alternative computer analysis). This chapter leads you through the development of a 3D model of a typical floor grillage, while at the same time creating 2D models of a typical joist and bearer extracted from the 3D assembly. Significant differences (up to 28%) are found between the 2D and 3D results.
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This chapter is not about demonstrating that 3D modelling is better or more exact than 2D modelling. It is about understanding the approximations made in both forms of analysis that lead to their results being different.
Again you will learn by ‘doing’ – this time a comparison of a 2D to a 3D analysis. You will demonstrate that you have gone through the investigation by recording screen shots and discussion. The overall objective is to set up Strand7 2D and 3D models of the timber floor shown in figure 3.1 – exactly as presented in the study book. Your record of progress should be as follows (be sure to give each screen shot a suitable title).
a) Work through page 35 and then reproduce the view at the top of page 36. Annotate to clearly identify all nodal restraints. Add the joists to the model as described pages 36 and 37. Create a plan view of the bearer and joist assembly with the beams shown as single lines only. Work through pages 37 to 39 and reproduce the view shown at the top of page 40 to confirm correct alignment and offsets. (15 marks)
b) Add loads to your model (page 40) and produce a view that will show (as clearly as possible) the loading that has been applied. Add the 2D models of the central bearer and central joist (page 41). (5 marks)
c) Analyse the model and reproduce the deflected shape view shown on page 41. Develop the
view as shown at the bottom of page 41. (10 marks)
d) Set up a table to compare BM’s and deflections from the 3D and 2D analyses. (10 marks)
e) Provide a brief ‘dot point’ discussion of the differences between 3D and 2D analyses and the reasons for these differences.
Task 2 – Relevant to Chapter 4 Weighting 9%
It is expected that you will find this chapter intellectually challenging. The deliverables relate again to undertaking and recording Strand analyses but if you focus just on this then your study may be of little benefit to you. Buckling and second order effects are generally poorly understood – but confidence in these areas can significantly improve your design abilities and particularly your understanding of the design rules in AS4100. You are encouraged to read the fairly lengthy ‘theoretical discussions’ in this chapter and then attempt to relate these to your analysis investigations.
Q1 Develop four models of the self-weight loaded strut of figure 4.1 with different levels of subdivision as illustrated at the top of page 60. The strut length is 9000 mm, and start the axial load from 40 kN, use section C350 114.3 x 3.6 CHS, 9.83kg/m. Undertake appropriate analyses and use screen shots to record investigations addressing the following questions.
a) Does the level of subdivision affect the accuracy of a first order analysis? Explain why?
b) Does the level of subdivision affect the accuracy of a buckling analysis? Why?
c) When does the presence of a ‘beam load’ affect the predicted axial buckling load for this member? Explain why? (10 marks)
d) Does the level of subdivision affect the accuracy of a second order analysis? Investigate first with the original axial load of 40 kN and then increase this to 100 kN in 10 kN intervals without increasing the beam load. Explain the results. (10 marks)Q2 Develop the beam model illustrated in figure 4.13. Note that the ‘dummy’ beams may be of the same section as the main beam 310UB46.2 of length 8000 mm. Use this model to investigate and document the accuracy of this model in predicting beam buckling loads in comparison to the methods defined in AS4100 1998:
a) Apply the loads and restraints as shown in the middle of page 66 and undertake a buckling analysis. Record the buckling shape and compare the Strand7 prediction to the prediction of the AS4100 formula for Mo. (10 marks)
b) Add a midspan top flange restraint (page 67) and again compare the Strand7 prediction of buckling moment to the value of Mo. (15 marks)
c) Modify your model to correspond to the fourth beam of figure 4.15, apply two concentrated loads at the top flange at the quarter points of the beam and compare the Strand7 prediction of maximum moment at buckling to the value of Mo. (15 marks)
d) Carry out a 2nd order analysis for the above case c) show the results and comment.
e) For those who want a challenge attempt to recreate the graph at the bottom of page 69.
(Additional 5 marks)
Task 3 – Relevant to Chapter 5 Weighting 11%
Some of you may be finding the ‘spoon feeding approach’ a bit tedious – but I think it is also the quickest way to getting through the course material.
Remember that I am not all that interested in your submission except as confirmation that you have been systematic in applying various modelling, analysis, manual checking and interpretation and recording procedures. You do not learn by ‘writing the assignment’ but by using Strand7 AND making comparisons between results.
This will represent the hardest chapter so far. There are only a few new mechanical tricks to learn but more importantly the intention is to help you to develop an appreciation for the importance of ‘aspect ratios’ and appropriate mesh subdivision. In the text this is done by extensive comparative analysis summarised in Table 5.1. You are required to ‘reproduce’ a subset of these results and record your results in as simple and informative fashion as possible. You may choose to deviate substantially from the ordering of analyses presented below if you think that it will better achieve the objectives.
Q1. Column modelling
a) Follow the instructions of chapter 5.1.1 (pages 83 to 87) to develop a 60 x Quad 8 plate element model of a 9000 mm long 410UB59.7 column axially loaded between pinned ends. (Note that your model will be identical to that developed in the text except that it is 9000 rather than 6000 long – and thus all numerical results will be different. This change will be made in the first step of chapter 5.1.1 by making 15 x 533.3 increment extrusions rather than 15 x 600.) Provide appropriate screen shots to define your model. Undertake a buckling analysis and provide screen shots of the first four buckling modes. (15 marks)
b) Use manual calculations to determine the major axis Euler column buckling load and the torsional buckling load Noz. Refer to page 87 of the text for the equation for Noz and note that r1 is the polar radius of gyration of the section. Compare the results of the numerical analysis to your manual results. (15 marks)
c) Section 4.10 illustrates a method of axial column design based on explicit modelling of geometric imperfections plus second order analysis. Study Sec 5.3 and model the same column introducing the initial imperfection in the form of Perry Robertson out of straightness. Use the AISC Design Capacity Tables to determine the value of Nc. Undertakea second order analysis with Nc and display the total fibre stress (Rainbow icon/Beam/Contour/Stress/Total Fibre). Comment on the magnitude of the maximum recorded stress. (40 marks)
d) Next select all plate elements and – Top menu item Tools / Subdivide / A = 1, B = 1 / Targets Plate Quad4 Note that with A = B = 1, this does not make more plate elements but rather converts from the Quad8 elements initially created back to the simple Quad4 elements. Record a screen shot of the model. Re run the buckling analysis and compare the Quad4 results to the earlier Quad8 results record screen shots of the first four buckling modes. (10 marks)
e) Again select all plate elements and – Top menu item Tools / Subdivide / A = 1, B = 2 / Targets Plate Quad8. This will change back to Quad8 elements and at the same time will double the number of plate elements along the length. Analyse record and compare to previous results. (10 marks)
f) Consider each of the dot point items of 5.1.3 and briefly indicate whether your modelling investigations confirm the correctness of these conclusions and recommendations with regard to column modelling and design.
Task 4 – Relevant to Chapter 6 Weighting 15%
Chapter 6 covers a fair bit of territory including the preliminary general discussion of mechanical/ structural design issues. Task deliverables will be kept to a minimum but you are encouraged to ‘study’ the entire chapter.
Q1. Linear analysis of a stiffened plate assembly
a) Develop models of the stiffened plate assembly shown in figure 6.6 using both alternative A and alternative B – with one difference – reverse the direction of the applied 10 kN loads. Initially use Quad4 elements. Note that the restraints are as shown in the figure below. Undertake linear static analysis and reproduce views similar to those of figure 6.7. (Figure 6.7 actually uses Quad8 elements so expect your results to be different.) (10 marks)
b) Convert Quad4 elements to Quad8 (Tools / Subdivide / A = 1, B = 1 Targets Quad8). Note that this creates new mid element nodes. Subdivide the beams by 2 so that they are hooked to the new mid element nodes. Apply Top menu item, Tools / Clean / Mesh and set the Tolerance to Absolute = 2 mm. (What this does is to look at all nodes and if it finds any that are closer than 2 mm apart then it pulls the two together. You need to be careful in doing this because if it finds close nodes then it will change the geometry of the model slightly. If the zip tolerance is set to a large value then it may grossly distort the original geometry. It is a good idea to use Clean Mesh because sometimes when subdividing elements, arithmetic rounding errors can lead to nodes that are very close together – and that will look like a single node on screen – but that are not connected.) (10 marks)
c) Undertake a linear static analysis display and print deflected shape plot and compare to the previous analysis. Compare the results with an unstiffened plate with the same loading and boundary conditions. (10 marks)
d) Subdivide the main horizontal plates 3 x 2 / Target = Quad8 as indicated in figure 6.7. Subdivide the stiffeners 3×1 (i.e. do not subdivide them in the 75 mm length dimension as this will lead to long thin elements with bad aspect ratios and consequently poor performance). Subdivide the beams by 2 so that they again connect to each of the subdivided plate nodes. Again apply Clean Mesh. (10 marks)
e) Undertake a linear static analysis display and print deflected shape plot and compare to the previous analysis. (10 marks)
Q2. Buckling analysis of a stiffened plate assembly
a) Take the last (most subdivided) model as developed and undertake a buckling analysis. Display and print the buckled shape similar to figure 6.10. (5 marks)
b) Undertake a linear analysis for a load corresponding to the first buckling mode. (You will probably have got a first mode buckling load factor of around 5.5 so you can either change each of the 10 kN loads to 55 kN and analyse for this – or you can got to Top menu item Results / Linear load case combinations / Add and input 5.5 as at right. The combination load case will then exist as a load case in the post processing environment.) (10 marks)
Q3. Nonlinear analysis of a stiffened plate assembly
a) Modify the last model by the addition of new stiffeners, modified restraints and a new ‘axial’ load set consisting of three 10 kN loads acting down the length of the panel as shown below. Undertake a buckling analysis. (Firstly you will need to undertake a linear analysis to establish the ‘initial conditions’. Make sure you do this for the ‘axial’ load case and assign this for ‘initial conditions’.)
I expect that you will find that the nonlinear analysis will not converge beyond about 50% of increment 4 corresponding to a load factor of about 35. On the face of it this could make sense because a load factor of 30 corresponds to the first buckling load and normally second order analysis will not converge beyond the buckling load factor – but in this case I want you to try
Only use a “plate and plate assembly” for this model
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Show plate free edges icon
harder. Nonlinear analyses may not converge because you are beyond the buckling load and there is simply no solution beyond this point. They may also not converge either because there is nothing to kick in the nonlinear displaced shape – or – because the mesh subdivision is too coarse to model the complexity of the nonlinear response.
On figure 6.16, I suggest the use of push pull ‘imperfection loads’ to kick in the ‘dimpling’ shape corresponding to buckling as a means of assisting Strand to find a solution. But I think the main problem with the current model is the coarse mesh. (15 marks)
c) So – subdivide the model 2 x 2 Target = Quad8 except for the stiffeners that should be subdivided 2×1 as: