The Form Diagram shows a six-panel truss with its Force Polygon to 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 truss can 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 truss can be moved; the black nodes will move as mirror images of the yellow ones.

You may move any node that is marked with a yellow circle. All the other parts of the screen will change instantaneously to reflect the consequences of each move–the reactions are recalculated, the force polygon is modified, and the numerical values of member forces change. The thicknesses of the truss members will also change.

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.

Use the mouse to play with the truss in any way that you like. Explore the possibilities and become accustomed to how the various features work. Try the various toggles, especially the mirrors.

Notice that there are three ways to see what’s happening to the forces in the members of the truss:

1. The members grow thicker as forces increase, and thinner as forces decrease. (Note: There are limits on the thickness and thinness of the members. Member thicknesses will not change after they reach these limits.)

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.

Toggles On: Keep Verticals Vertical, Keep Top Chord Level, Keep Uniform Panel Spacings

A. In what region(s) of the truss are the top and bottom chords most highly loaded? In what region(s) are the diagonals most highly loaded?

B. 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. Pay particular attention to the Force Polygon as you do this.

What is the general relationship between truss depth and member forces? What proportion of depth to span seems most reasonable to you?

Toggle Off: Keep Top Chord Level

C. Click on the middle node of the top chord. Move it down toward the bottom chord. Watch the Force Polygon to see what happens as this node approaches the bottom chord.

Toggles On: Return to Starting Position, Left-Right Mirror, Keep Uniform Panel Spacing, Keep Loads Vertical, Keep Verticals Vertical, Keep Bottom Chord Level.

A. Move the yellow nodes of the left half of the top chord up and down until you find a form for the top chord such that the forces in all the interior members of the truss are zero or nearly zero. It’s particularly helpful to watch the Force Polygon as you do this, trying to make all the lines that represent the forces in the interior members as short as possible.

What form does the truss take? Does the Force Polygon for this truss resemble the force polygon of any other structure that you can think of?

Look at the numerical values of member forces. Allowing for some variation because of the difficulty of achieving a 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?

Describe in the simplest possible words how this truss works.

B. Keep the truss form that you have found. Then Toggle On: Top-Bottom Mirror. What happens to the truss? What are the unique properties of this truss?

C. Toggles On: Return to Starting Position, Keep Loads Vertical, Keep Uniform Panel Spacing, Keep Verticals Vertical, Keep Bottom Chord Level.

Change the second load from the right to about three times the value of the other loads. (The Force Polygon may overlap the diagram of the form of the truss when you do this. You can move the Force Polygon to a more convenient location by clicking and holding on its top yellow circle). By trial and error, find a form for the top chord 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 you can think of?

Look at the numerical values for member forces again. What generalizations can you make?

D. 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 is the same in every segment of the curving top chord. Hint: First find a form that has constant force throughout the level bottom chord. Then experiment with the “verticals” in the truss, changing their inclinations, while you keep an eye on the force polygon to see that the lines that represent the forces in the top chord segments are of about the same length.

What is the role of the sloping “verticals” in helping to create constant force in the curving chord?

If you wish, you may also search for a form of truss with a level top chord and equal force throughout the curving bottom chord.

E. 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 truss at an angle of roughly 60 degrees from the vertical. (Notice what happens to the green Load Line in the Force Polygon when you do this). Experiment with this truss until you find a form for it such that it has more or less equal force throughout the level, bottom chord.

Toggles On: All toggles on except Keep Top Chord Level and Top-Bottom Mirror.

A. At this point, you should be seeing a gable truss on the screen, one that has a triangular form. Trusses of this shape are used to support gable roofs.

B. Take careful note of whether diagonals 2-3 and 4-5 are in tension or compression.

C. Without changing anything else, click on and off repeatedly the Keep Top Chord Level toggle. What happens to the forces in the interior diagonal members of the truss as its form changed from gable to parallel-chord? Can you guess why? Hint: Imagine the inverted form of a cable that is supporting the same loads as the truss. Have the cable pass through the two points of support and the top center node of each truss. Which form contains the other form in each case? Does the cable contain the outline of the truss, or does the truss outline contain the cable?

D. Wind loads on gable roofs are considered to act perpendicular to the roof surfaces. Furthermore, the forces on one surface are often considered to be suction forces. Such loadings can be analyzed easily by graphical means:

On the gable truss, make the loads on one side perpendicular to the slope of the roof and exerting pressure toward the interior of the building. On the other slope, make the loads perpendicular but pulling outward, away from the interior of the building.

Now look at the force polygon: What is the form of the load line? Can you find the forces in all of the truss members?