CIVE 7351 Behavior of Steel Structures Fall Semester 2018 Project #5 PLATE GIRDERS

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1 CIVE 7351 Behavior of Steel Structures Fall Semester 2018 Project #5 Due: Monday, November 5, 2018, 4:35 p.m. PLATE GIRDERS A local fabricator has installed a crane system for their plant. They have asked you to minimize the cost of the crane rail, given the following criteria: Given: The crane consists of two rails spaced 8 feet apart. Use two parallel plate girders for the crane rails (you will be designing one of the plate girders; the other is identical by symmetry). The crane has a large cross beam that spans between the two rails, and the crane hook assembly hangs from the cross beam. The cross beam sits on top of the crane rail, and the two wheels on each end of the cross beam each cause a concentrated load spaced 8 feet apart along the crane rail plate girder (so the plate girder has two concentrated loads that move along the length of the girder together, spaced 8 feet apart). The crane rail plate girder has three spans between supports: 93, 110, and 93, respectively. Use either A572/50 or A572/65 steel for the flange plates, web plates, or stiffener plates. The crane rail should be non-hybrid at any given cross-section, but you may vary the grade of steel as you progress along the length of the crane rail. The grade of steel of the stiffener at a given cross section does not need to match the grade of steel of the flange and web plates at that cross section, but you will have to consider how to handle that difference in yield stress in each design equation. The crane rail is braced out-of-plane at the following locations measured along the length from the left end of the crane rail plate girder: 0 (end support), 31, 62, 93 (first interior support), 120.5, 148, 175.5, 203 (second interior support), 234, 265, and 286 (end support). Use E70 SMAW electrodes for all welds. Use lb = 16 inches for all concentrated load checks as per Chapter J. You should check local web yielding, local web crippling, and compression buckling of the web at all supports due to the reactions, and at any location along the length due to the concentrated load of the crane. Unfactored Dead Loads: Girder self-weight. Note that you do not have to vary this self-weight along the crane rail; rather, you may take an average of the self-weight from the different sections along the crane rail and use that as a uniform dead load kips/foot hangs off the bottom of the girder along its entire length due to mechanical equipment that is hung in the building. Crane dead load: Two loads on the plate girder crane rail that peak at 55 kips each, spaced at 8 feet apart. You must account for the moment and shear envelopes created by this load moving over the crane rail (use PHIL300 or any other software that generates moment and shear envelopes due to moving loads).

2 Unfactored Live Load: Crane live load: Two loads on the plate girder crane rail that peak at 70 kips each, spaced at 8 feet apart. This value already includes the effect of impact. You must account for the moment and shear envelopes created by this load moving over the crane rail (use PHIL300 or any other software that generates moment and shear envelopes due to moving loads). Objective: o Minimize the cost of the plate girder design while maximizing the number of allowable cycles for fatigue, meeting all appropriate AISC specification provisions. The project will be judged on the basis of the cost (minimized) and the number of allowable cycles (maximized). Design: The web and two flange plates along the entire length. You must have two or more changes in either the steel grade or the cross-section (or both) from the end of the crane rail to its centerline (i.e., design an optimal crane rail, within reason). If there is a change of cross section within an unbraced length for the lateral-torsional buckling calculation, use the cross section that gives you the lower lateral-torsional buckling moment strength. It is thus recommended that you change section sizes at the conservative inflection point (based on moment envelopes) or in the positive moment region if possible. Otherwise, the lateraltorsional buckling calculations in the negative moment region become ambiguous. Also, take into account the fact that it is unwieldy to deliver a plate girder by truck that is longer than 80' or so. Note that an easy way to change the cross section is by changing the width of the flanges. Do not vary the depth or thickness of the web plate along the length of the crane rail. All transverse and bearing stiffeners. Vary the transverse stiffeners along the length to optimize (within reason) your shear design. All fillet welds (you do not need to design the butt welds when you have a change in crosssection, but you must account for their cost -- a butt weld penetrates all the way through the flange and web plates -- butt welds are thus simply designed to use a filler metal with a larger yield stress than the yield stress of the materials being joined). For your final design, determine the number of cycles that this plate girder assembly can withstand based on fatigue. Check all relevant fatigue details of the plate girder: base metal, stiffener attachments, welds. Submit: A written introduction describing in words your entire analysis and design approach and your basic results. This should not be detailed (no equations required); it should be relatively brief (less than one page, double-spaced) and very well written. Put this document in the form of a memo to the owner, who will be interested in the quality, clarity, and simplicity of your design concept and approach.

3 A detailed set of drawings, to scale, of the final crane rail (elevation and each significant section, at a minimum). These may be done on 8.5"x11" graph paper (or similar), or you may use larger paper. Show all important dimensions (including girder cross-section). Identify typical weld size sizes. Look at pictures in books and manuals for examples of how these sketches should look. Summarize all given information, including the applied loading. Lay out the results of your analysis in an organized fashion. Do not submit reams of paper, particularly from analysis or spreadsheet program output. Rather, summarize the analysis results succinctly. Provide neat, detailed, drawings (to scale) on graph paper of your shear and moment diagrams (including their envelopes). This is important. Show on engineering paper all final calculations leading to your design (this is the bulk of the report). You do not need to show why other design alternatives are worse (including using the other grade of steel at a particular location), or how you initiated your preliminary design; just submit a complete final design that indicates good, clean logic. However, your introduction should discuss why you designed the girder as you did (i.e., how and why you varied the grade of steel, etc.). Do not submit all your scratch paper showing your various trials and errors. Remember (from the syllabus): at the end of the report, summarize your design by performing a brief capacity check of your plate girder at one cross section, one transverse stiffener, one bearing stiffener, and one each of the key welds, showing all key equations, including slenderness limits, nominal load and force calculations, and anything else needed to show in summary that you understand completely how to design these girders. Alternately, if your project is laid out clearly, with each part of the design highlighted easily, so that it is obvious where to find everything, then you may skip this capacity check. However, if your project is put together quickly at the end with different contributions from different individuals, then please consider doing this capacity check at the end of the report. Notes: Factor all loads for design, including the crane load. You do not need to check deflections. Plate thicknesses are usually rounded to the nearest 1/8. Salmon et al. or other texts may provide further guidance on this that you may use to represent typical practice. Except for the restriction of having a non-hybrid cross section and a constant depth and thickness of web, you may optimize the cost in any other way you would like. The program PHIL300 is an analysis program (available from the course website) which will calculate the moment and shear envelopes for you (including the dead load). The instructions are attached. Please read the instructions carefully and watch your units. All loads may be entered as positive downward (note that the program plots the negative moment as positive values, and vice versa). Also, you must use a decimal point for all real numbers and you may not use a decimal point for any integers - the program is very sensitive about such things. You can import the *.env files into a spreadsheet to visualize or plot them (if you are going to submit these plots as your M and V diagrams, add written detail to them to make sure they are clear, accurate, and complete). Make an appointment with the TA if

4 you need assistance in running the program. Always verify all results with some quick hand calculations to make sure your analysis is correct. You will have to come up with an initial estimate of the girder size based on hand calculations so that you may enter its moment of inertia in PHIL300 and so that you may include an estimate of its self weight right from the start. If your final girder values are much different from your initial estimates, you should reanalyze and redesign! Fabricated cost: $2.00/lb for A572/50 steel plates for flanges or webs. $2.50/lb for A572/65 steel plates for flanges or webs. $100.00/linear foot for each longitudinal fillet weld (used for flange-web intersection, etc.). $200.00/linear foot for each butt weld (used at changes in flange plate dimensions along the length). $100.00/linear foot for any stiffeners, including their welds. Final thoughts: Plate girder design is a much more subtle, intricate, and complete design problem than appears at first glance (and thus a much more interesting structural engineering problem than it may seem initially). For example, while you may choose your I-section size primarily to achieve a sufficient nominal bending moment capacity, this size in turn has a large effect on how many stiffeners you will need, and the stiffener size. It is a common error, for example, to make your flange widths, bf, too small so as to save material -- the result is that you may need stiffeners that are unrealistically thick (e.g., 2, which is too thick to be practical for a stiffener) because the stiffeners themselves cannot have a width that causes them to extend beyond the beam flange tip. The resulting required redesign of the entire plate girder at that late stage of the design process is... painful. Read Salmon, Johnson, and Malhas, Chapter 11, to get a feel for plate girder design. Salmon et al. provide excellent guidance near the end of Chapter 11 on how to proportion a plate girder. Use it (but use it wisely -- in structural engineering, always think before you strike).

5 PHIL300 Program: User s Manual To execute PHIL300, go into the directory containing the program and type PHIL300. Input data is queried interactively by the program. PHIL300 calculates the moment and shear envelopes for continuous beams up to 300 ft. long and with up to 6 concentrated loads (e.g., up to six axles of trucks). Moments of inertia can change along the beam up to 20 times. The program considers both the dead load and a moving truck load. In actuality, the dead load should be your factored line load, and may include dead, live, snow, etc. Enter all numbers marked (*) as real numbers (with decimal). All others are integers. All values that are obviously integers should not include a decimal point, and all values that are obviously real numbers must include a decimal point. The units must be entered as shown below. Required input data: 1. Number of spans in your beam 2. E for your beam, ksi (*) 3. For each span, the span length, in. (*) 4. The number of changes in I (must be at least 1) 5. For each section, I, in. 4 (*) 6. For each section, the length L, ft. (*) (note feet!) 7. Distance to each support measured from left end, in. (*) (note that the first support will generally be at a zero distance and must be entered as such) 8. The dead loads, kips/in. (*) (positive downward; note kips/in.!) 9. The number of axles in loading vehicle 10. For each axle the load, kips (*) 11. The spacing between axles, ft. (*) Note that the loads to be input are the factored loads. All data is saved for printing and plotting. There is no output to the screen except to let you know how far along the analysis is. The following files are created each time you run the program: BRES = contains all the results; suitable for printing AXIS.ENV = contains the x-axis values for the envelopes MNEG.ENV = contains the negative moment envelope MPOS.ENV = contains the positive moment envelope STRA.ENV = contains the stress range envelope SHPOS.ENV = positive shear envelope SHNEG.ENV = negative shear envelope The last six files are suitable for plotting with any spreadsheet program such as Excel. You will need to import them as ASCII text files. Be sure to rename the files before running the program or an error will occur. If you do not want the plot files, do a global erase for *.ENV. You still must erase or rename the BRES file manually before each new analysis run. This program is not user friendly and may crash if you do not follow all instructions carefully (and it may crash even if you do).