Demo #1: Single-Panel Truss - Sites at Lafayette

Demo #1: Single-Panel TrussThe Screen The Form Diagram shows the simplest possible truss, a trianglemade of three members. It is supported on a pin at one end and a roller at the other,and supports a single load at its apex. Its Force Polygon is to the right and numericalmember forces are tabulated below.The Toggle Switches include:Return to Starting Position: Clears away all that you have done and puts everything back where it was.Circle Load: Activates an animation in which the load on the apex of the truss rotates continually.Keep Load Vertical: Prevents the load from being applied at any angle other than vertical.Extend Lines of Action: Adds extensions of the lines of action of the three external forces on the truss.You may move any node that is marked with a yellow circle. All the other parts of the screen will change instantaneously toreflect the consequences of each move–the reactions are recalculated, the force polygon is modified, and the values of memberforces change.Play TimeUse the mouse to interact with the truss in any way that you like. Move some of the yellow circles to explore thepossibilities and discover how the various features work. Try the various toggles.Notice that there are three ways to see what’s happening to the forces in the members of the truss:1. The truss members grow thinner as the force decreases, and thicker as the force increases.(Note: There are limits on the thickness/thinness of the members at which no further change occurs)2. The lines of the Force Polygon grow longer as forces increase, and shorter as forces decrease.3. The numerical values for member forces in the table at the bottom change.Influence of Truss DepthToggles On: Return to Starting Position; Keep Load VerticalClick on the top node of the truss. Move it up slowly, increasing the depth of the truss, and watch what happens tomember forces. You can see the changes by looking at the changes to the length of the Force Polygon or by lookingat the changes in the force magnitudes in the table. What happens to the member forces as the depth increases?Move the top node down slowly, decreasing the depth of the truss. What happens to the member forces as the topnode approaches the lower chord? Why? What physical constraints may exist that limit the maximum depth of atruss?Inverting the TrussContinue moving the top node down until it crosses the lower chord. What happens to the magnitude and sense ofthe forces in the truss members as the top node crosses the lower chord?What happens to the member forces after the top node has crossed the lower chord, as the node continues to movedownward, away from the lower chord?Changing the LoadToggles On: Return to Starting Position; Keep Load Vertical.Click on the yellow circle at the top of the arrow that represents the load on the top of the truss.Move the yellow circle up and down, increasing and decreasing the load. What happens to the forces in themembers of the truss as you do so.

Changing the Form of the TrussToggles On: Return to Starting Position; Keep Load Vertical.Click on the top node of the truss again and move it from side to side. What happens to the reactions as you do this?What happens to the member forces?Move the top node slowly leftward until it is directly over the left support. What happens to member forces at thispoint? What happens when the top node moves still farther leftward, outside the left support?Click the Toggle on for “Return to Starting Position,” then move the left support up and down, watching whathappens to member forces as you do this.Changing the SpanToggles On: Return to Starting Position; Keep Load Vertical.Move the right support rightward, increasing the span of the truss, and note what happens to member forces. Moveit leftward until the span is very small. Generally speaking, what is the influence of span on member forces?Changing the Direction of the LoadToggles On: Return to Starting Position. Be sure all other toggles are off.Click on the yellow circle at the top of the load arrow and move it left and right. What happens to the memberforces as you do this? What happens to the reactions? Notice the difference in the directions of the reactions at thepin connection and at the roller.Align the load so that its line of action runs directly along the axis of one of the top chords of the truss. Whathappens to the forces in the other two truss members when you do this? What is the magnitude of the force in themember with which the load is aligned?Concurrence of External ForcesToggles On: Return to Starting Position; Extend Lines of Action.There are three external forces acting on the truss: the load, and the two reactions. Click on the top node of the trussand move it from side to side. The broken green lines extend the lines of action of these forces. Formulate a generalrule about these lines of action.Turn on the Circle Load toggle and watch what happens. Does this confirm the rule that you just formulated? Whatother things can you learn from watching the action?What kinds of loads can be transmitted through a pin connection? Through a roller?

Demo #2: Six-Panel TrussThe Screen The Form Diagram shows a six-panel truss with its Force Polygonto the right and a numerical tabulation of member forces below.The Toggle Switches include:Return to Starting Position: Clears away all that you have done and puts everything back where it was.Gable Form: Converts the truss to a triangular configuration for a gable roof.Equalize Loads: Maintains all loads at the same value.Keep Uniform Panel Spacings: Maintains horizontal spacings of vertical members.Keep Verticals Vertical: Maintains vertical members in vertical orientations.Keep Loads Vertical: Prevents loads from being applied at angles other than vertical.Keep Top Chord Level: Maintains a level, horizontal, straight top chord.Keep Bottom Chord Level: Maintains a level, horizontal, straight bottom chord.Top-Bottom Mirror: Keeps the truss symmetrical about its horizontal center line. Only the yellow nodes in the top of the trusscan be moved; the black nodes will move as mirror images of the yellow ones.Left-Right Mirror: Keeps the truss symmetrical about its vertical center line. Only the yellow nodes in the left half of the trusscan be moved; the black nodes will move as mirror images of the yellow ones.Notice the color-coding: Loads are gray, reactions are green. Red is compression, blue is tension, and yellow is zero-force.Members and numbers change color as members change from compression to tension to zero force.Play TimeUse the mouse to play with the truss in any way that you like. Move some of the yellow circles to explore thepossibilities and discover how the various features work. Try the various toggles.Influence of Truss DepthToggles On: Keep Verticals Vertical, Keep Top Chord Level, Keep Uniform Panel SpacingsIn what region(s) of the truss are the top and bottom chords most highly loaded? In what region(s) are the diagonalsmost highly loaded?Click on the leftmost node of the top chord. You’ll find that you can move the entire top chord up and down with it.Move the top chord up slowly, and watch what happens to member forces.Move it down slowly, and watch what happens to member forces as the top chord approaches the bottom chord.What is the general relationship between truss depth and member forces? What proportion of depth to span seemsmost reasonable to you?

Influence of Truss FormToggles On: Return to Starting Position, Left-Right Mirror, Keep Uniform Panel Spacing,Keep Loads Vertical, Keep Verticals Vertical, Keep Bottom Chord Level.Move the yellow nodes of the left half of the top chord up and down until you find a form for the top chord suchthat the forces in all the interior members of the truss are zero or nearly zero. It’s particularly helpful to watch theForce Polygon as you do this. Try to make all the lines representing the interior member forces as short as possible.What form does the truss take? Does the Force Polygon for this truss resemble the force polygon of any otherstructure that you can think of?Look at the numerical values of member forces. Allowing for some variation because of the difficulty of achievinga perfect truss form with the mouse, verify that forces in the verticals and diagonals are either zero or very small.What generalization can you make about the forces in the six segments of the bottom chord?Keeping the truss form that you have found, Toggle On: Top-Bottom Mirror.What happens to the truss? What are the unique properties of this truss?Changing of LoadingChanging the Toggles On: Return to Starting Position, Keep Loads Vertical, Keep Uniform Panel Spacing, Keep VerticalsVertical, Keep Bottom Chord Level.Change the second load from the right to about three times the value of the other loads. (The Force Polygon mayoverlap the diagram of the form of the truss when you do this. You can move the Force Polygon to a moreconvenient location by clicking and holding on its top yellow circle). By trial and error, find a form for the topchord such that the forces in all the interior members of the truss are zero or nearly zero.What form does the truss take? Does the Force Polygon for this truss resemble that of any other structure that youcan think of? Look at the numerical values for member forces again. What generalizations can you make?Form of TrussChange the Toggles On: Return to Starting Position, Keep Uniform Panel Spacings, Keep Bottom Chord Level,Left-Right Mirror, Keep Loads Vertical.Toggles Off: Keep Verticals Vertical.Experiment with the form of the truss until you find a form of truss with a level bottom chord in which the force isthe same in every segment of the curving top chord. Hint: First find a form that has constant force throughout thelevel bottom chord. Then experiment with the “verticals” in the truss, changing their inclinations, while you keepan eye on the force polygon to see that the lines that represent the forces in the top chord segments are of about thesame length.What is the role of the sloping “verticals” in helping to create constant force in the curving chord?Changing Toggles On: Return to Starting Position, Keep Panel Spacings, Keep Bottom Chord Level.Double (more or less) the second load from the left. Then change its direction so that it strikes the node of the trussat an angle of roughly 60 degrees from the vertical. (Notice what happens to the green Load Line in the ForcePolygon when you do this). Experiment with this truss until you find a form for it such that it has more or less equalforce throughout the level, bottom chord.

Demo #3: Cantilever TrussThe Screen The Form Diagram shows a truss that cantilevers from a wallwith its Force Polygon to the right.The Toggle Switches include ones from Demo #2, plus one new one:Switch Pin and Roller: Click on it and notice what happens to the reactions and member forces.Influence of Truss DepthToggle on: Keep Top Chord LevelWhich members of the truss carry the largest forces? Why?Why are F1 and D8 zero-force members? What happens to F1 when you switch the pin and the roller?Click on the upper left-hand node of the truss. Move it up and down, and the entire top chord moves with it.What is the general relationship between truss depth and member forces?Move the entire top chord down slowly, approaching and finally crossing the lower chord. What happens tomember forces as the top chord approaches the lower chord? As it crosses the lower chord?Truss FormToggles on: Return to starting position, Keep uniform panel spacing, Keep loads vertical, Keep verticals vertical, Keeptop chord horizontalMake loads AB, BC, & CD each zero. Move the top chord up until you have about doubled the truss depthFind a form for the truss such that all verticals and diagonals have little or no force in them. What is the logic of thisform?Toggles on: Keep uniform panel spacing, Keep loads vertical, Keep verticals vertical, Return to starting position,Equalize loadsFind a form for the truss such that all verticals and diagonals have little or no force in them. What is the logic of thisform?Toggles on: All the above, plus Top-bottom mirrorFind a form for the truss such that all verticals and diagonals have little or no force in them. What is the logic ofthis form?Equilibrium of External ForcesToggles on: Return to starting position, Extend lines of actionMake fairly large changes in individual loads, including sloping some of the loads, and observe the effect of thesechanges on the lines of action of the external forces.Move the supports up and down continuing to observe the lines of action of the external forces.Formulate a general rule about the lines of action of the reactions and the resultant of the loads.

Demo #7: Minimum Material TrussThe Screen The Form Diagram shows the same six-panel truss that you workedwith in Demo #2.There’s a new twist: A rising and falling bar graph keeps track of howmuch your truss design weighs. You can’t change the loads, the span, orthe spacing of the loads, but you can change the form of the truss. Yourtask is to find a truss form that requires the least possible material.The Toggle Switches include all the ones you’re familiar with. There’s also a very handy button below the truss, bythe bar graph, that tracks the lowest weight truss found to data and returns to the best form you’ve found.The program computes the theoretical amount of material in the truss by multiplying the amount of force in eachmember by the length of that member, and summing all these quantities. It is assumed in this demonstration thatcompression members will not buckle.Designing a Minimum-Material Truss1. The loading is fixed in a symmetrical pattern. Would there be any advantage for the loading pattern shown tomake the truss itself asymmetrical (not mirrored about a vertical center line)? What can you predict about the bestform that will be found for this truss?2. Note that although you cannot move any of the top nodes, the bottom nodes can be moved at will. Alsodetermine which of the toggle setting can be used to make your task easier.3. You already know that by making a truss height greater, the member forces diminish. Can you produce awinning minimum-material truss just by making it very, very tall? Why or why not?4. Be sure to try some designs in which the “vertical” members of the truss are no longer vertical.5. When you’re at the point of paring the last bits of material out of the truss, here’s a strategy that can help: Thecomputer is so fast that it is calculating and remembering the volume of material in the truss at all times, even asyou move nodes around. This means that to fine-tune a good design, you can use the mouse to move each node in ascribbling motion over a very small area. Then hit the “Return to Best Form” button, and the best node location thatyour curser crossed in its travels will be shown, along with the lowest material volume achieved. Repeat themaneuver for every node.When You’ve FinishedWhat is the logic of the form that you’ve developed? Why does it use less material than most other forms? Arethere any real bridges or roof trusses that have this shape? What are the advantages/disadvantages of using thisshape truss as a bridge truss? What are the advantages/disadvantages of using this shape truss as a roof truss?Most trusses are subjected to a variety of loading patterns when in-service. You have optimized this truss for justone loading pattern. Will it be able to support other patterns as well? How will it do this?