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To satisfy the required design content of Finite Element Analysis, MENG 421, students design a set of trusses that are analyzed with Ansys. A comprehensive report details the effort.
The Bridge Design Problem
The problem is to design seven different bridge trusses using Ansys. Each truss is supported at the ends and there are three, 33-kip loads on the other three lower nodes. The problem is introduced in Assignment 5. Four of the trusses are designed by taking different locations and numbers of upper nodes. The remaining three are as follows. The fifth truss must be of the K design; see your statics book for examples. The sixth truss has two pairs of tension-only members. These six trusses will be pinned at the left end and have a roller at the right end. The seventh truss will be identical to one of the first five trusses (don't consider the tension-only truss for this). This duplicate truss will have pins at both ends. Try to group two or three designs that subtly change one feature such as upper-node height or slope of the sides.
Your Truss Plan showing the design of each of your seven trusses and including the original Trussw is due at the beginning of Assignment 5. Copies of this Truss Plan will be included in each of several submissions in the coming weeks. It may be necessary to change this plan if you discover problems with a particular design.
Start by making six copies of the file trussw.a that you ran in Assignment 5. Name the copies Truss1.a, Truss2.a, etc. Edit each of the six files and put your name, date, and file name on the TITLE line. Change the upper nodes and elements according to your Truss Plan. Run each truss with Ansys and check that the plot matches the shape on your Truss Plan. An incorrectly programmed point will be obvious from the Ansys figure. When the figure look OK, capture and print it as you did in Assignment 5. Copy the mass, deflection, and stresses into the bottom of the appropriate Ansys code. Make a copy of the single-pinned truss you are going to double-pin and name it Truss7. Change the support at the right end so it is pinned (UX=0). Now you are ready to optimize six of the seven trusses by changing the areas. Don't try to optimize the tension-only truss.
Then, except for the tension-only truss, change the cross-sectional areas of all the elements for each of the other six trusses so that the stresses are all within 5% of the design stress of 16 ksi. Do not change the lower node locations or the loads. Compare the relative merits of your truss designs.
The First SubmissionThe design work will be submitted in stages. The first submission is your one-page Truss Plan that is due at the beginning of Assignment 5 For this firstsubmission, turn in one page showing all your trusses. Arrange the trusses in two columns with similar trusses side by side. Draw the trusses on engineering data paper using a pencil. After this first submission, your truss plan will be made with Word and you will import your truss shapes from graphics made by Ansys.
Make sure to include the types of trusses discussed in class, such as the K truss, one double-pinned truss, and a truss with four tension-only elements. There should not be quadrilateral regions, only triangles. Use my trussw as one of your trusses, but it doesn't count as one of the required seven trusses. Put circles at each node to distinguish pinned joints from crossing elements. Clearly show the supports, whether pin (a triangle) or roller (triangle and ball), and the three loads. Make two trusses the same, but for one, use pins at both ends while for the other use a pin at one end and a roller at the other. Don't double-pin the K truss. There must be one truss with two pairs of tension-only members using ET Link10.
Under each truss give the number of pins, elements, and reactions with the symbols P, E, and R. Compare the number of pins with the number of elements and reaction forces using the formula described in class (and derived in your report). Each pair of tension-only elements counts as only one element since only one can be working at a time. Don't use zero-force elements except as a prop. Then, don't count them as elements. Don't go on without my approving of your truss designs.
Here are some points to think about:
- For the initial design:
- Compare twice number of nodes (N) to number of elements (E) plus number of reactions (R). Derive this equation and explain its meaning for the three possibilities.
- Sketch all trusses on one page including supports and loads. Give values for N, E, R and 2N and E+R (3 or 4). Put both values of FOM when you have them.
- Clearly show pinned joints with a small circle to distinguish them from crossing members that are not pinned.
- For variations, consider upper nodes over lower, upper nodes between lower, and K truss.
- Keep bottom nodes and loads the same as in trussw.a, except for cross-sectional area, which must be changed to increase FOM.
- Make two trusses the same except for the supports. One truss has pins at both ends and the other has a pin at one end and a roller at the other. Compare the stress distribution for these two trusses. All other trusses will have a pin at one end and a roller at the other.
- Use four tension-only elements for one truss. Make it otherwise the same as another truss. That is, four tension-only elements replace two regular elements. Choose a design that has quadrilateral regions that can be spanned with two, tension-only elements to form an X. (See trussten.a)
- Use element type Link1 except for the tension-only elements, which are type Link10.
- For the calculations:
- Put comments in your code to easily identify each truss element for later optimization. Also, it is important that you define elements in symmetric pairs. That is, define a far left and far right element one after the other. They will have the same stress and so will only need one REAL statement for the pair. You should not need more than six REAL statements. As you know, Ansys numbers your elements in the order you define them.
- Check for zero-force or near zero-force members. These will have a stress less that 1% of the design value. Don't increase the area of these elements.
- Calculate the Figure of merit (FOM) as:1e7 / (weight * highest stress)where the absolute value of the stress is used. The higher the FOM, the lighter the bridge for a given allowable stress. Put the value near the top of the original Ansys code.
- Notice that initially the stresses in the elements are very different from one to the next. Except for the tension-only truss, optimize each truss by making all stresses the same, equal to a design stress. However, don't increase the area of elements with stress less than 1% of the design.
- To optimize the first truss, truss1.a, make a copy called trussop1.a. Change the title line in the copy to the new name. Don't make a copy of the graphic since it will look the same as the one for the unoptimized truss.
- Increase the FOM for each truss by changing the areas of the elements. Increase the areas of those elements with stress greater than design stress and decrease the area of those with stress less than design stress so they all have the design stress.
- Put both the original and the optimized values of FOM as comments at the top of each optimized Ansys program.
- The higher the FOM the better. There is not a maximum value.
- See the file: trusswop.a to see how to optimize trussw.a.
- You can't make meaningful comparisons between the before and after weights. Some of the original elements were above the design stress and so the original bridge would fail.
- Remember that your bridges are models that are only 40 inches long. If increasing the area of some elements increases the total weight, this is not a disadvantage. It simply means that your original design would not hold up the required load, i.e., the bridge would fail.
- For the report:
- Reports must be printed, e.g., use Word on the PC. See Assignment 5: for setting up Word on a PC and setting up the title page and major headings.
- Use a serif typeface such as Times New Roman except for the section headings, which should be a sans serif such as Arial. Check the typefaces for this web page.
- Discuss other factors not considered: beauty, height, durability, match nearby bridge, wind, rain.
- Draw the shear and bending moment diagrams for one of your trusses. Point out that the maximum stress is located at the midpoint. Normal stress is much more important than shear stress. Therefore, point out that bridge should be tall in center where moment is maximum and zero height at ends where the moment is zero.
- Compare roof and road trusses and discuss zero-force members. Try not to include zero-force members or use small area.
- Report must have standard parts: Abstract, Table of Contents, Introduction, Objective, Procedure, Results, Discussion, Conclusions, References, and Appendix. Start Roman numerals with Introduction and end with Conclusions. That is, don't number Abstract, Table of Contents, References, or Appendix.
- Change /Title line of each Ansys file to reflect file name of truss so title will properly show in plot, e.g., truss1, truss2, etc.
- Copy the mass, node deflections, and element stresses from the Ansys output and paste them to the end of each truss program.
- Assemble your data in the Appendix by truss. For each truss put the original Ansys listing first, followed by the optimized listing, followed by the truss graphic. Turn the graphics all the same way so the top is along the binding edge.
- In the body of the report, include a table listing each truss with its weight, initial and final FOM, and highest stress. Use no more than three significant figures.
- On the page after the table, put your Truss Plan. Mark with a slash the element having largest absolute stress. Mark with two slashes the element having he next largest stress. Give the original and final FOM below each truss on the Truss Plan.
- As you write your report with Microsoft Word, misspelled words are marked with a wave underline. Right-click a misspelled word and choose the correct spelling.
- Watch out for these problems:
- its is the possessive form
- it's means it is
- Principal means main (both have an a)
- Principle means rule (both have an e)
- Don't use @ when you mean at.
- Don't use the expression and/or; choose one or the other
- Don't use varying when you mean various.
- Bind the final report
- Make sure that all graphics face the same way, with the top at the binding side (rotate graphics counter clockwise)
- Don't use a ring binder or a plastic strip down the spine
- If the report is stapled, make sure the staple ends aren't sticking out to poke fingers
- The pages should not fall out when the report is opened
- The title and your name must be visible on the outside
Also see the following web sites:
UF Civil Engineering pages The Bridge Site
Bridge Engineering Home Page Bridge Pros DOT Highway Structures Model Bridge Software The Bridges of Porto Bridge LRFD How Bridges Work Georgia Tech Civil Engineering Virtual Library Steel bridges Links to Bridge Pages, 2 San Francisco Bridges
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Last revised: October 3, 2003 -- Copyright © 1997-2003