Intro to Engineering Pract & Prin II for Electrical & Computer Engineering
Intro to Engineering Pract & Prin II for Electrical & Computer Engineering ENGR 1202
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Learning Activity 5 Design and Build a Model Truss Bridge Overview of the Activity In this learning activity we will design build and testa model truss bridge We will analyze the Owner s needs then formulate specific design requirements We will develop a truss configuration analyze the struc tu re design each individual member and connection then develop plans and specifications Finally we will build the bridge and test it to verify that it can carry load safely Why In Learning Activity 1 we played the role of the Constructor and built a model bridge that had been designed by someone else In Learning Activity 5 we will assume the role of the Design Professional and design a new bridge with the same span length but with adifferent loading and a very different geometric configuration In doing so we will learn a process that can be used to design a bridge with practically any span length loading or configuration This project provides an opportunity to apply everything we have seen in the previous four learning activi ties We will see how the various elements of the engineering design process fit togetherihow scientific principles mathematic tools engineering concepts experimental data and practical considerations contribute to the final product We ll see how the truss configuration is tailored to the Owner s needs how the structural model is derived from the truss configuration how structural analysis results and experimental data contribute to the design of structural members how the size and shape of connections are determined how constructabil ity considerations affect the final design and how engineering computations are translated into the drawings and schedules required for construction Finally we will build the bridge we designedia great way to check the validity of the design and the accuracy of the plans and specifications b 3 E 2 m b h I S q lt 5 Learning Objectives As a result of this learning activity you will be able to do the following Explain how designbuild project delivery differs from designbid build project delivery Explain how the factor ofsafety is used in design I Explain how scientific principles mathematic tools engineering concepts experimental data and practical considerations contribute to the engineering design process I Design a model truss bridge to meet a set of design requirements I Build a model truss bridge consistent with a set of plans and specifications Key Terms To successfully complete this learning activity you must understand the following key terms and concepts from previous learning activities truss deck truss internal force right triangle member through truss tension hypotenuse top chord gusset plate compression Pythagorean theorem bottom chord joint strength Owner diagonal reaction factor of safety Design Professional deck load static determinacy Constructor abutment equilibrium stability plans amp specifications If you need to refresh your memory on any of these terms see the Glossary in Appendix D Information Using the Factor of Safety in Design When we analyzed a structure in Learning Activity 3 we used the following definition for the factor of safety Strength Factor of Safety lntemal Member Force To use this equation we first determined the internal force in each member by doing a structural analysis and the strength of each member by using our experimental data from Learning Activity 2 Then we used these numbers to calculate a unique factor of safety for every member in the structure In short we used known values of internal force and strength to calculate unknown factors of safety When we design a structure we need to select members that are strong enough to carry load safely Thus in design the unknown quantity in the equation above is the strength The known quantities are the internal forces and the factor of safety As before the internal member forces are determined by a structural analysis but in design we will simply specify the factor of safety We might use a design code as the basis for deciding what the factor of safety should be or we might simply use our experience and judgment In either case we will choose a value that appropriately reflects the level of safety required for our structure Since strength is the unknown quantity it makes sense to algebraically rearrange the equation above by multiplying both sides by the internal member force The result is Strength Factor of SafetyXlntemaI Member Force To use this equation for design purposes we will change the quotequal sign to a quotgreater than or equal sign like this Strength 2 Factor of Safetylnternal Member Force The product on the righthand side of this expressionithe factor of safety times the internal member forceiis called the required strength This expression tells us that the actual strength of a member must be greater than or equal to its required strength We use 2 because it s always OK for a member to be quottoo strong Indeed as we saw in Learning Activity 3 sometimes it makes good economic sense for some members in a structure to be stronger than they really need to be We will use the expression above as the basis for determining the size of each structural member in our design DesignBuild Proiect Delivery As we discussed in Learning Activity 4 most public works projects in the United Sates use designbid build project delivery In this system 1 the Design Professional develops a complete design and provides it to the Owner 2 the Owner advertises the project 3 construction contractors submit bids and 4 the Owner awards the construction contract to the lowest responsive responsible bidder Owners typically use design bidbuild project delivery because the competitive bidding process tends to keep the construction cost low However this system has some significant disadvantages as well I In designbidbuild project delivery the Design Professional often has only minimal involvement in the construction phase of the project Thus the designer is not able to ensure that that structure is built as intended I The Constructor is never involved in the design process Thus constructability issues may not be fully considered in the design b 3 E 2 m b h I S q lt 5 I The period of time required for advertising collecting contractors bids and awarding the construction contract can be quite substantial At this point in the process the design is complete and construction activity has not yet begun Thus this entire period is essentially nonproductive For these reasons and others an alternative system called designbuild project delivery is becoming increasingly popular In a designbuild project a single firm contracts with the Owner to do an entire pro jecti both design and construction Thus in a designbuild project there is no break in continuity between design and construction Coordination between the Design Professional and the Constructor is likely to be more effective because one firm has overall responsibility for the project Eliminating the bidding phase may also speed up the project Indeed with designbuild project delivery it is possible for construction to begin even before the design is completeia procedure called quotfasttracking Of course designbuild project delivery also has its disadvantages Thus the best means of project delivery always depends on the nature of the project The Problem The Need Recently a tractortrailer truck lost its brakes while driving on Grant Road The driver lost control of the vehicle and it collided with one of the end posts on the west end of the Grant Road Bridge Fortunately no one was hurt but the bridge was damaged beyond repair Grant Road is now closed and the Town of Hauptville has initiated a project to replace the structure as quickly as possible Design Requirements The Town of Hauptville is the Owner for this project On behalf of the Owner the Town Engineer has again hired Thayer Associates to provide design services ThayerAssociates has sent a team of engineers to begin working on the needs analysis The engineers meet with the Mayor the Town Council the Town Engineer and other Hauptville residents to work out the functional and aesthetic requirements for the new structure At the meeting the engineers receive the following input The Mayor says quotI don t want another bridge failure in my town I want you to ensure that this new bridge is not as vulnerable to a vehicular collision as the old one was The President of the Town Council adds quotWe didn t plan on having to replace a bridge when we developed this year s budget The cost of this project must be kept as low as possible Another member of the Town Council adds quotThe residents of Hauptville are very upset about the closure of Grant Road We need to get this project completed as soon as possible A member of the Hauptville Historical Society says quotI know money is tight But it would be a terrible mistake to build an ugly bridge just to save some money We at the Historical Society think it s important to the preserve the historic character of the town so if possible we d like the new bridge to be a truss Finally the Town Engineer adds his own input quotI am still very concerned with the everincreasing number of heavy trucks using Grant Road To give us an added margin of safety I d like the new structure to be designed for a 20 highervehicular loading than the AASHTO bridge design code requires Based on this input as well as data gathered from a thorough investigation of the project site the engineers from ThayerAssociates develop the following design requirements The replacement bridge will be constructed on the existing abutments which are 24 meters apart Again our 740 scale model bridge will have a span of 60 centimeters Like the previous bridge the new structure will carry two lanes of traffic However the width of the deck will be increased by 20 to provide more space for largervehicles Our model bridge will have a roadway width of 77 centimetersiZ centimeters wider than the first Grant Road Bridge model b 3 E 2 m b h I S q lt 5 l The bridge will be designed for avehicular loading 20 larger than that required by the AASHTO bridge design code Our model bridge will be designed for a quottraffic load consisting of a 6 kilogram mass placed on the struc ture at midspan the first Grant Road Bridge model was designed for only 5 kilograms I The factor of safety will be 20 I The bridge will be made of steel Again our model will use cardboard from standard manila file folders The bridge configuration will be a deck truss With no portion of the structure extending above the road way the bridge will be invulnerable to avehicular collision I Because of the limited project budget the cost of the new bridge must be kept to a minimum I To get the bridge into service as quickly as possible designbuild project delivery will be used for this project Consistent with this requirement Thayer Associates enters into a partnership with Mahan Con struction Company a local contractor to do the project Your Job You are the Chief Engineerfor Thayer Associates You are the Design Professional for this project Your responsibility is to design a replacement for the Grant Road Bridge that meets all of the Owner s requirements Once the design is complete you will continue to work with Mahan Construction Company to ensure that the bridge is built correctly The Solution The Plan Our plan to design the new Grant Road Bridge consists of the following major activities I Decide on a truss configuration I Create the structural model I Check static determinacy and stability I Calculate reactions I Calculate internal memberforces I Determine member sizes I Check member sizes for constructability I Draw plans I Create a schedule of truss members and a schedule of gusset plates I Build the bridge Decide on a Truss Configuration In general when you design a truss bridge you may use any stable truss configuration that satisfies the project requirements Of course for any given set of project requirements some configurations are bound to be more efficient than others An experienced engineer might be able to choose an efficient configuration based simply on what has worked well for previous projects If you lack experience you might try several different alternative configurations develop a preliminary design for each one and select the configuration that costs the least You might also base your selection on aesthetics or constructability rather than on structural efficiency For this specific project the only constraint on the selection of a truss configuration is that it must be a deck truss Fortunately we do have previous experience with designing this particular bridge type In Learning Activity 4 we used the West Point Bridge Designer software to design aWarren Deck Truss that proved to be quite efficient Let s use this same configuration for our Grant Road Bridge replacement This configuration is also included as Truss 16 in the Gallery of Structural Analysis Results Appendix B By using a configuration that is included in the Gallery we will be able to save considerable effort in our structural analysis Create the Structural Model Having selected a truss configuration we will now model the structure by defining 1 the geometry of the truss 2 the loads and 3 the supports and reactionsijust as we did in Learning Activity 3 We idealize the threedimensional bridge as a pair of identical twodimensional trusses The geometry of one main truss is shown below The dimensions indicate the locations of the member centerines Joints are identified with the letters A through M A 750m 11 25cm 1375am l l 109m A 10cm A 10cm A 10cm A 109m A 109m A Geometry of the main truss Note that the dimensions of our structural model are all consistent with the dimensions shown for Truss 16 in the Gallery of Structural Analysis Results The Gallery shows that each of the six top chord members has a length L To achieve a total span length of 60cm as the design requirements specify we must use L10cm Now the remaining dimensions are calculated using this same value of L For example the Gallery shows the overall height of the truss as 1375L Since we have defined L as 10cm the height of our structural model is g b 3 E 2 m b h I S q lt 5 Height 1375L 137510cm 13 75cm Once we have determined the geometry of the truss we can calculate the loads According to the design requirements the bridge must be capable of safely carrying a 6kilogram mass placed on the structure at mid span The weight of a 6kilogram mass is m sec2 w mg 6kg981 J 5886N Again we will apply this load by placing a stack of books onto the top chord of the truss The weight of the stack will be supported on six jointsiC D and E on each of the two main trusses Assuming that the weight of the books will be distributed equally to these six joints the downward force applied to each joint is Total Load 5886N 981N Number of Jomts 6 Load per Joint Note that we could have gotten this same result directly from the Gallery of Structural Analysis Results The diagram for Truss 16 shows that a downward load of 01667W is applied to each of the three center topchord joints For a total load W5886N the load at each joint is Load per Joint 01667W 016675886N 981N A complete free body diagram of the truss looks like this 1981N 1981N 1981N A B c D E F G J K Lxl 4 4 4 4 4 4 10cm 10cm 10cm 10cm 10cm 10cm Free body diagram of the main truss The bridge will be supported only at its ends thus the reactions RA and R0 are shown at Joints A and G Check Static Determinacy and Stability Before we can use the equations of equilibrium to analyze a truss we must first verify that it is statically determinate and stable As we saw in Learning Activity 3 the mathematical condition for static determinacy and stability is 2 m3 wherej is the number ofjoints and m is the number of members Our structural model has 13 joints and 23 members Substituting these numbers into the equation above we find that 2j and m3 are both equal to 26 so the mathematical condition for static determinacy and stability is satisfied Calculate Reactions Now we can begin the structural analysis of our truss by calculating its unknown reactions Since all loads and reactions act in the vertical direction we can use the sum of forces in the ydirection XFy to find the unknown reactions RA and RG 25w RA RG 981 981 981 0 58 Since the structure the loads and the reactions are all symmetrical about the centerline of the truss the two reactions RA and RC must be equal Substituting RA RC into the equilibrium equation above we get RA RA 2943 0 2R 2943 RA 147N T And since RA Rt7 then RG 147N T Note once again that we could have gotten this same result directly from the Gallery of Structural Analysis Results The diagram for Truss 16 indicates that each reaction has a magnitude of 025W For a total load W5886N each reaction is 025w 0255886N 14 7N T Calculate Internal Member Forces At this point in the design process we must determine the internal force in each member of the truss As long as the truss is statically determinate we can always calculate internal member forces by applying the Method of Joints just as we did in Learning Activity3 However when we use a truss configuration from the Gallery of Structural Analysis Results we can determine these forces with considerably less effort Each truss in the Gallery is presented with a complete set of internal member forces calculated for the loading shown The internal forces are shown in terms on the total applied load W To determine the internal member forces for our specific loading we just substitute W5886N for each member For example the Gallery indicates that Member AB in our structural model has an internal force of 0 167W Therefore the force in Member AB FM is FAB 0167W 01675886N 983N 983N compression Similarly the Gallery shows that the internal force in Members CD and AH are 70394W and 0301W The refo re Fm 0394W 03945886N 232N 232N compression FM 03o1w 03015886N 17 7N 17 7N tension Recall that a minus sign indicates compression while a plus sign indicates tension b 3 E 2 m b h I S q lt 5 Can you calculate the remaining internal member forces Use the Gallery of Structural Analysis Results to calculate the internal member forces for all remaining members in our truss Use a total load W5886N Determine Member Sizes Now we will determine the size of each member in our structure Our objective is to ensure that each member is strong enough to safely carry its internal force If the internal force is compression we ll use atube for the member If the internal force is tension we ll use adoubled bar just as we did on the original Grant Road Bridge in Learning Activity 1 Tubes Member AB carries load in compression so we will use a tube for this member To determine the required size of the tube we will use the compressive strength vs length graph we created in Learning Activity 2 That graph is shown below 10mmx lOmth ibe i i i i i 50 7 7 6mm 10mm tpbe l 45 m t 40 7 Actual Strength 45M 30 l l 7 Required Strength 197N 197E39 Compressive Strength newtons 0 2 4 b 8 106 12 14 lb 18 Length cm Selecting the required tube size for Member AB Selecting the required tube size is a fou r step process 1 Determine the member length MemberAB is 10cm long 2 Calculate the required strength using the equation Required Strength Factor of Safety Internal Member Force The design requirements specify that the factor of safety will be 20 and above we determined that the internal member force Ii is 983N compression So the required strength is Required Strength 20FAB 20983 19 7N compression This calculation tells us that MemberAB must be a tube with a compressive strength ofatlea5t197 newtons 3 Now plot the point corresponding to Length10cm and the Strength197N as shown above 4 Finally determine the smallest available tube size that has astrength larger than 797 for the same length To do this start at the point you plotted in Step 3 and draw a line straight upward to the closest strength curve In this case a 6mm x 10mm tube with a length of 10cm has a compressive strength of about 45 newtonsi considerably greater than the required strength of197N Therefore we can safely use a 6mm x 10mm tube for Member AB Note that we also could use a10mm x 10mm tube for Member AB With a compressive strength of about 50 newtons this member is even stronger than the 6mm x 10mm tubeibut quite a bit stronger and more expen sive than it really needs to be Note also that we could probably use a tube that is considerably smaller than 6mm x 10mm except that we have no test data available for any smaller member sizes Any tube with a com pressive strength greater than 197N for a10cm length would be perfectly acceptable for Member AB Whatever member size we decide to use for Member AB we should use the same one for its twin Member FG on the opposite side of the truss Members AB and FG have the same internal force and the same length so they should use the same member size By taking advantage of symmetry in this manner we can save a lot of work because we only really need to determine member sizes for half of the members in the truss Now let s use the same procedure for Member CD Like Member AB the length of Member CD is 10cm Its required strength is Required Strength 20Fw 20232 464N compression When we plot Length10cm and Strength464N on the graph the point falls between the two strength curves as shown below Therefore the 6mm x 10mm tube with its compressive strength of 45N is not strong enough for Member CD Only the 10mm x10mm tube will work because its actual strength of SON exceeds to required strength We will use a IOmm X10mm tube for Member CD and for its twin Member DE b 3 E 2 m b h I S q lt 5 Actual Strength 50M mx 4 gt39 10mmx10mm tube Required Strength 464N 6mm x10mm tube a 65m 390 4 o Compressive Strength newtons w o o N o Length cm Selecting the required tube size for Member CD The sizes of the remaining compression members can be determined in exactly the same manner The only aspect of this process that presents a new challenge is finding the lengths of the diagonal members Consider Member BH as an example lfwe visualize this member as Sam the hypotenuse of a right triangle as shown here then we can use the Pythagorean theo rem to find its length BH 75cm BH 75 5 9o1cm This is Step l of the fou rstep process Once you have determined the length BH you can complete the remaining three steps exactly as we did above Can you determine the sizes of the remaining compression members Using our graph of compression strength vs length determine appropriate member sizes for Members BC BH Cl and CJ Then use symmetry to determine the member sizes for all remaining compression members Tension Members We will use bars for all members that carry load in tension To determine the sizes of the bars we will use the tensile strength vs member width graph we created in Learning Activity2 600 8 o Required Strength 354 N w 9quot 4 Tensile Strength newtons B 3 o o 0 1 2 3 4 5 55 7 3 9 MemberWidth mm Selecting the required width of Member AH Let s use MemberAH as an example The procedure for determining the size of this member is as follows 1 Calculate the required strength just as we did for compression members Required Strength 20FAH 20177 354N tension This calculation tells us that Member AH must have atensile strength of at least 354 newtons 2 Now start at Strength354N on the vertical axis and draw a horizontal line to the strength vs width line as shown above 3 Then draw a vertical line down to the horizontal axis This value 55mm is the smallest width that will safely carry a tension force of 354N 4 Finally decide on the actual bar size you will use MemberAH must have a total width of at least 55mm But since we are using doubled bars for all tension members the width of each individual bar must be half of 55 or 275mm In practice it would be very difficult to measure and cut cardboard bars precisely 275mm wide so let s round up to the next whole millimeter We will use doubled 3mmwide bars for Member AH Can you determine the sizes of the remai ng tension members Using our graph of tensile strength vs member width determine appropriate member sizes for Members Bl HI I and JK Then use symmetry to determine the member sizes for all remaining tension members Check Member Sizes for Constructability At this point in the design process we have determined member sizes for the entire truss For each member we selected the smallest size tube or bar that can safely carry the corresponding internal force In doing so we have effec tively minimized the material cost of the truss However as we saw in Learning Activity 4 minimizing the material cost does not necessarily minimize the total cost of the structure Using many different member sizes might increase the costs of fabrication and construction because it can sometimes be difficult to connect different sized members together We can see this situation in our own truss design For the top chord we have selected a 6mm x10mm tube for members AB BC EF and FG and a10mm x 10mm tube for members CD and DE Thus at Connections C and Ewe will have to join two different member sizes together as shown at right This will create some serious challenges for the Constructor That s you 1 When two compression members are spliced together it is best for both tubes to be in contact with each other on all four sides so the internal compression force can be effec tively transmitted from one member to the other Here only two of four sides are in contact The only way we could ensure that all four sides are in contact would be to taper the 10mmx10mm tube 6mm x 10mm tube At Connections C and E two different tube sizes need at be joined Tapered 10mmx10mm tube The larger tube should be tapered so that both tubes are connected along all toursides b 3 E 2 m b h I S q lt 5 end of10mm x10mm tube as shown Building this joint will take a lot of time and building it well will be quite difficult Furthermore recall that in Learning Activity 1 we attached the two main trusses together by placing them upside down on the lateral bracing subassembly which was pinned to the building board That procedure won t work if the top surface of the top chord is not entirely at the same elevation For these reasons we can greatly simplify the construction of our bridge by using lOmm x 10mm tubes for all top chord members As a result Members AB BC EF and FG will be considerably strongeriand somewhat more expensiveithan they really need to be But the benefits gained from using a single tube size for the entire top chord will greatly outweigh the small additional cost of using four slightly oversized members Draw Plans Having decided what the size of each truss member should be we re now ready to draw the plans Specifi cally we will create the fullscale layout drawing on which we will actually build the main trusses and lateral bracing subassembly for the Grant Road Bridge n Learning Activity l this drawing was provided to you Now you re smart enough to do it yourself Before you can create the drawing get the necessary tools and supplies First you ll need a big sheet of paperiat least 30 centimeters wide and 65 centimeters long Craft paper shelf paper or even wrapping paper will work fine You ll also need a metric ruler a sharp pencil and an eraser to do the drawing A L If available a drawing board aTsquare and some draftsman s triangles will also be very helpful These tools will help you to draw parallel and perpendicular lines accurately If these tools are not available it would be a good idea to do your drawings on graph paper Try to find graph paper that is large enough to do the entire drawing on one sheet Your local office supply store might have largesize graph paper If not tape several standardsize sheets together being very careful to ensure that all of the grid lines on adjacent sheets are aligned As an alternative if you have access to appropriate computeraided drawing software and know how to use it you can use a computer to do the layout drawing The layout drawing we used in Learning Activity 1 was done entirely by computer But if you decide to use a computer you must ensure that you have the right software and the right hardware to do the job First the software must be a true technical drawing or computer aided drafting package like AutoCAD IntelliCAD or Tu rboCAD Presentation graphics programs like Pow erPoint are not appropriate for this job because they don t provide the necessary degree of precision Second you must have access to a printer or plotter capable of producing a fullscale hard copy of your drawing Once all of the necessary supplies and tools are on hand tape the paper to your drawing board or to a smooth flat tabletop Now sharpen your pencil and let s get to work Lay Out Centerlines We ll begin by drawing one main truss as shown below The drawing must be exactly full size760cm long and 1375cm high Use the dimensions provided in the sketch on page 57 to ensure that all joints and members are at their correct positions Label the joints with letters as shown Use only a single line for each member These lines are the centerlines of the members A 3 C 11gt Start the drawing by carefully laying out the centerlines of all members in one main truss It is critically important that all member centerlines intersect precisely at the joints as shown at right Oth erwise one of our basic assumptions about trusses will be violated When we analyze a truss we assume that its members carry load primarily in tension or compression but if the centerlines do not all intersect at a common point the members will bend when the truss is loaded Bending may cause some members to fail at a lower load than we designed them for So the performance of our structure will depend heavily of the accuracy of the member centerlines Draw them with care 5 39F 4 Right Member centerlines should intersect at the joints 515 b 3 E 2 m b h I S q lt 5 Draw Members Now we will draw the truss members using the member sizes we determined earlier in the design process Let s use Member C as an example Begin by placing your ruler perpendicular to the member centerline as shown in A Make two pencil marks to indicate the actual width of the member Since Member C is a 6mm x 10mm tube the two marks should be 6mm apart Each mark should be 3mm from the centerline Then make an identical pair of marks at the opposite end of the same member Finally use your ruler to draw two parallel lines connecting the marks as shown in B These two lines represent the outer edges of Member C If you measure accu rately and draw you r lines carefully the centerline will be exactly midway between the two edges Now let s follow this same procedure to draw Member CD a top chord Since this member is a10mm x 10mm tube the pairs of pencil marks shown in C are 10mm apart with each mark located 5mm from the centerline Again we draw the edges of the member by quotconnect the dots with two parallel lines as shown in D Since the entire top chord is made of identical 10mm x 10mm tubes we can actu ally draw the edges of the chord as two continu ous lines running all the way from Joint A to joint C With all members drawn the truss layout should look like this To draw a member lirst mark its width A then draw two parallel lines B uIlIuunnnualv Use the same procedure to draw the top chord Layout drawing of the main truss with all members completed Draw Gusset Plates A gusset plate is a structural element that connects two or more members together at ajoint Fora truss to carry load safely the connections between members and gusset plates should be stronger than the members themselves In our cardboard model we can achieve sufficient strength by connecting each member and gusset plate with a glue joint at least 2 centimeters long as shown at right These glue joints m Glueiointhetween memher are very similar to welds in an actual steel connection By 39quot39 mm using 2 centimeters as our standard quotweld length we will ensure not only that the connections are sufficiently strong but also that the gusset plates look reasonably realistic Gusset Plate The glue ioint connecting a member to a gusset plate should he at leastZ centimeters long On an Actual Bridge Project On modern structures members are connected to gusset plates with bolts or welds The strength of a bolted connection depends on the number of bolts used The strength of a welded connection depends on the length of the weld To design a connection the engineer first determines how much force the connection must be able to carry safely Based on this force the engineer determines the required number of bolts or the required length of the weld Finally the gusset plate is sized so that it is large enough to accommodate the S AllIllal BNINHVEI39I required number of bolts or the required length of weld As an example let s lay out the gusset plate forJointJ This connection joins Members I JK CJ and DJ together To start the layout measure 2 centimeters from the center of the joint the point where the centerlines intersect outward along the centerline of Member HI and make a pencil mark perpendicular to the cen terline Do the same for the otherthree members as shown Now connect the four marks with a series of straight lines The gusset plate for Joint is now complete Repeat this process for the remaining joints The completed main truss layout drawing should look like the illustration on the following page Laying out a gusset plate 517 Layout drawing 01 the main truss with all members completed Note that the gusset plates at Joints A and C have been squared off on the bottom and outside edges The bottom edges ofthesetwo gusset plates will serve as the supports forthe bridge These edges should be perfectly horizontal and about 15 centimeters long as shown below left These gusset plates alone won t be strong enough to support the bridge Recall that we calculated the reactions at Joints A and G as 14 newtons eacht Sincethese reactions are directed upward theywill cause compression in the gusset plates at A and Cl These gussets are just flat sheets of cardboard thus they will buckle with only a slight application of compressive force To keep them from buckling we ll need to reinforce them with a short section of10mm x 10mm tube oriented vertically as shown below right F 4 Gusset 7 Plate a 10mm x 10mm tuba Varmm v 1 z l m Mem39m r r 39 D 3 d Member GM M 39 i39 A 39quotl r 39 39 IlIIIIIIA 10mm also serve as support tuhe oriented vertically You may recallthatthe layout J 39 g 4 inl 39 a A eluded I I I truss layoutt With two copies available we were able to build both halves of each truss simultaneously resulting in a considerable timesaving during construction Of course 39 39 39 g use in 39 a Ano39 39c m J 39oL acomputer sothe second copy olthetruss quot 39 39 J L d quot 39tothefirstt lfyou are doingyour layout drawing by hand it is best to use just one truss layoutt lfyou try to draw a second copy by hand it probably won39t be identiml to the first and the two halves ofthe truss won39t line up correctly Just remem ber that if you draw only one truss layout you39ll need to use it fourtimesionce for each half ofthe two main trussest Lay Out Top Lateral Bracing The layout drawing for our design must also include the top lateral bracing subassembly shown below Begin by drawing the member centerlines as we did for the main trusses The centerlines of the two top chords should be 10 centimeters apart This will ensure that the total width of the bridge from one outside edge to the other will be 11 centimetersithe roadway width specified in the design requirements Because this bridge is a deck truss the struts Members AA BB CC and so forth must also serve as floor beams Thus we will use 6mm x 10mm tubes for these members rather than the 6mm x 6mm tubes used for the struts in the original Grant Road Bridge We ll use single 3mm bars for the diagonal bracing Top Lateral Bracing Layout Transfer Gusset Plates Now that the layout drawing is complete we ll need to transfer the gusset plate outlines to filefolder cardboard without cutting up the drawing The easiest way to do this is with tracing paper Place a sheet of tracing paper on top of the layout drawing and trace the outline of each gusset plate onto the tracing paper Then photocopy the tracing paper to transfer the gusset plate outlines onto cardboard as described in Learning Activity 1 Page 124 As an alternative you can also use carbon paper to do the transfer Place a file folder beneath the layout drawing with a sheet of carbon paper face down between the drawing and the file folder Then carefully trace over the outline of each gusset plate to transfer it directly to the cardboard Actually you don t really need to transfer every gusset plate On the main truss layout note thatJoint A is identical to Joint G B is identical to F H is identical to M and so forth You can transfer only the gusset plates at Joints A B C D H J and I then make a set of identical copies for the corresponding joints on the opposite side of the truss Similarly on the lateral bracing subassembly you only need to transfer the gusset plates atJoints A and B All remaining gusset plates in the subassembly are identical to one or the other of these two Create a Schedule of Truss Members and a Schedule of Gusset Plates The Schedule of Truss Members is an important part of the plans and specifications for our bridge design It summarizes the type size and length of every structural member in the bridge and thus serves as an important reference for the Constructor In formulating the schedule we note that the 10mm x 10mm top chord is per fectly straight from one end of the bridge to the other Thus we could actually make each top chord from a single tubeiifwe could find a file folder 62 centimeters long We can t of course so we ll have to build each top chord in three segments each about 21 centimeters long If you use alegal size file folder you can make the top chord in only two segments b 3 E 2 m b h I S q lt 5 The lengths provided in the Schedule of Truss Members are only approximate The Constructor will cut them to their exact lengths as the trusses are built The Schedule of Gusset Plates shows the number of each type of gusset plate that will be used for the truss connections Build the Bridge The plans and specifications for the new Grant Road Bridge are complete If this were a traditional design bid build project your work as the Design Professional would be mostly done You would present your com pleted design to the Owner who would then procure a Constructor through competitive bidding But because we are using designbuild project delivery you have full responsibility for both design and construction There s no time to waste The residents of Hauptville are anxious to have Grant Road reopened to traffic It s up to you to make it happen To build the new Grant Road Bridge follow the same procedure we used in Learning Activity 1 The result should look like the photo below The completed hridge model Once you have completed your quality control inspection place the bridge on two desks positioned 58 centimeters apart Place six coins on the top chord at Connections C C D D E and E Then place books one at a time on top until the total mass of the stack is 6 kilograms The new Grant Road Bridge is now open for traffic Congratulations of the successful completion of the project R I a E 2 m I n l S q lt 55 The completed Grant Road Bridge with Bkilogram loading in place How are math science and computer technology used in the engineering design process How did mathematical tools scientific principles and computer technology contribute to the creation of our design for the Grant Road Bridge Give at least two examples in each area Conclusion In this learning activity we quotput it all together We applied scientific principles mathematic tools engineer ing concepts experimental data and practical considerations to design a truss bridge Our design was carefully tailored to meet the needs of the Town of Hauptville to be safe to be constructable and to be aesthetically pleasing We validated the design by building and testing itiand itworked We conclude this projectiand this bookiwith a strong sense of accomplishment not only for the bridge we designed and built but also for the skills we acquired along the way Learning engineering isn t easy but learning engineering is worth every ounce of effortyou put into it To learn engineering is to open a new doorione that leads to a world of limitless possibilities for creative accomplishment and service to society The door is now open But how do you enter Every bridge begins in the mind of an engineer There s probably one in your mind right now Build it Answers to the Questions 1 Can you calculate the remaining internal member forces The table below provides all internal member forces for the truss 2 Can you determine the sizes of the remaining compression members The table below shows the tube sizes you should get if you follow the fourstep process outlined on page 510 for compression members The two intermediate computationsirequired strength and member lengthiare included as well b 3 E 2 m b h I S q lt 5 3 Can you determine the sizes of the remaining tension members The table below shows the member widths you should get if you follow the fou r step process outlined on page 513 for tension members The two intermediate computationsirequired strength and required widthiare included as well 4 How are math science and computer technology used in the engineering design process We used the following mathematical tools to develop our design The Pythagorean Theorem 7 to find the lengths of diagonal truss members Trigonometry 7 to write equations of equilibrium in our structural analysis Algebra7 to solve equilibrium equations for unknown internal member forces Vectors 7 to represent forces in our structural model We applied the following scientific principles and concepts to develop our design Force 7 to represent loads reactions and internal member forces Compression and tension 7to represent the direction of internal member forces Equilibrium 7 to calculate reactions and internal member forces Relationship between force and mass 7 to convert the load from kilograms to newtons We used computer technology to develop our design as follows Spreadsheet 7 to analyze and graph the experimental data from strength testing The West Point Bridge Designer 7 to find an efficient truss configuration Computeraided drafting software 7 to draw the plans an alternative to drawing by hand Some Ideas for Enhancing This Learning Activity The best way to enhance this learning activity is to provide students with many and varied opportunities to design and build bridges If the students do not have the algebra or trigonometry background necessary to do a truss analysis using the Method of Joints then their choices for truss configurations must necessarily be limited to those provided in the Gallery of Structural Analysis Results Appendix B If students do have the mathematical skills to apply the Method of Joints then they can design bridges of practically any span or con figuration It can be particularly effective to combine Learning Activities 4 and 5 into a single project Students begin by designing a24meter bridge with the West Point Bridge Designer Once they have found an efficient or interesting truss configuration they design and build a 140 h scale model of the same structure using the procedures described in Learning Activity 5 This twophase project uses the computer in the role for which it is best suited7exporing many different design alternatives relatively efficiently But it also ensures that stu dents do not merely use the computer as a quotblack box By working though the design of the 140 h scale model manually they gain an appreciation for the challenging mathematical calculations the computer performs so effortlessly ENGR 1202 7 Introduction to Civil Engineering Final Fall 2002 December 11 2002 In Class Final Instructions 3 problems on two pages 100 points total open book and notes show all calculations for partial credit start at 800 AM end at 1100 AM Wednesday December 11 2002 Problem 1 50 points Truss Strength The truss t0 the left is made from three 15 balsa wood members The bottom two F nodes are supported by a pin and roller support Each member has a crosssection that is l in by l in Calculate the magnitude of the downward force F that you predict would cause the truss to break Use 5000 and 500000 psi as the tensile strength and Young s modulus of elasticity Hint assume a load and calculate safety factors Problem 2 25 points Unit Conversions a A 600N load is applied to a bridge during testing What is the mass of the load on earth in slugs and kg What are the units for the coef cients in these two equations b Velocity ms Coefficient R m23 S mm 12 jdb7665doc l ENGR 1202 7 Introduction to Civil Engineering Final Fall 2002 December 11 2002 0 Flow m3s Coefficient g ms212 D m32 Problem 3 25 points Matlab a Write a Matlab script that does the following It creates two vectors X1 and X2 X1 has the integers from 1001 to 2000 in it The vector X2 is formed by taking the square roots of the corresponding values in X1 A scalar variable county is then set equal to the number of values in X2 that are gt 40 and lt 42 The variable county is displayed to the screen with some eXplanatory teXt EXample display to screen There are this many values gt 40 and lt 42 89 jdb7665doc 2 ENGR l 202 7 Introduction to Civil Engineering Test No1 Spring 2002 February 27 2002 Test Format and Instructions 3 problems on 2 pages 2040 points 100 points total closed book and notes up to 6 pages handwritten notes show all calculations for partial credit start at 400 or 500 PM end at 450 or 550 PM Wednesday February 27 2002 1 Dimensional Consistency and Unit Conversions 40 points a For the following dimensional equations nd the base dimensions of the parameter k Each letter enclosed in square brackets is the abbreviation for one of the seven base dimensions M L 3 k N T Ml 1Ll 392 b On earth an object with a mass of one slug weighs how much in pounds and newtons c It takes 5 days to fill a 300acre pond to a depth of 5 feet What ow does this correspond to in m3s and gpm gallons per minute 2 Buckling Strength 20 points Ifa balsa wood member Young s Modulus of Elasticity 144 XlO8 lbftz has a crosssectional size of 025 X 025 and a buckling strength of 20lb what is its length moment of inertia for square crosssection h412 h length of side irlh lt41 rlnr P2091 nF i ENGR 1202 7 Introduction to Civil Engineering Spring 2002 3 Truss Analysis 40 points The following questions refer to a truss with these node locations node 1 00 node 2 59 node 3 100 The three applied loads are either vertical or horizontal and have these magnitudes F1401b F2401b F3401b Answer the following questions regarding this truss a Give the magnitude of the force F F1 F2 Test No1 February 27 2002 mem 3 pm roller b Draw a free body diagram for node 3 You don t need to calculate the member or reaction forces 0 If F3 0 lb and member 2 is under tension with a load of 20 1b what is the load on member 3 Unit Conversions and Constants 11b448N g322fts2981ms2 1m3281ft 60 sec1min 1 day 86400 sec irlh lt41 rlnr Dana 6 AF ENGR l 202 7 Introduction to Civil Engineering Test No1 Spring 2002 February 27 2002 1 acre 43560 ftz 1 ft3 748 gallons irlh lt41 rlnr Dana 4 AF