Review of selected answers
| Arch 324/624, Introduction to Structural Design, University
of Virginia Copyright © 1996-2005Kirk Martini. Last Modified Fri Mar 25 2005, 01:57 PM |
Table
of Contents |
Question 1
The images below show two trusses with very different profiles: one is deepest at center span, while the other is shallowest at center span. Write a paragraph formulating a hypothesis to explain this difference.
ISS | 
ISS |
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The two different bridge trusses follow two different diagrams. The bridge truss with the deep center span follows the moment diagram. This bridge models classical truss theory where the truss is joint loaded and pin connected creating a straightforward moment diagram where the center is the deepest. The bridge truss with the shallow center span on the right follows the shear diagram. Along the xy plane the cables are tension members and the beams are compression members. The z plane has cable cross bracing. This bridge attempts to straighten out the diagram by mirroring the shear pattern, and having less weight in the middle and therefore lower bending stress. | The second bridge does indeed follow the form of its shear diagram, but that is not what is motivating the form. |
| Both trusses can be called funicularly shaped structures. They differ in their inverse funicular lines; TRUSS ONE acts as an arch above the supports, whose top chords are in compression, and bottom chords are in tension. TRUSS ONE'S compression and tension lines converge at the supports where the moment is zero.
Conversely, TRUSS TWO's funicular line hangs from the two towering support structures, with the truss' deepest profile at the points of greatest moment, at the towers. TRUSS TWO acts as a compressive arch below the road line and inversely as a funicular tension cable above the road line. TRUSS TWO's compression and tension lines converge at the bridge's mid-span where the moment is zero. | A simple explanation. |
| bologna | It's best to avoid doing homework right before lunch... |
| The bridge with the deepest profile at center span is a simple span condition. The connections are located at the points abive the supports. The bridge with the shallowest profile at center span is the cantilivered support situation as shown to us in class as the roman span example. The cantiliver has connections on either end of the center piece. The cantilevered support minimizes the moment by reducing the absolute magnitude of the moment diagram. This support situation allows for a longer span. | The comparison with the roman lintels is quite good. The simple span bridge is much like the simple span Greek lintel, and the second bridge is like the continuous roman lintel. |
 KM |
 KM |
 ISS |
 ISS |
Question 2
The images below show a truss supporting a long escalator; the image on the left is an overall view and the image on the right is a close up looking from underneath. Note that the top chord of the truss is a double member, while the bottom chord is a single member. Write a paragraph formulating a hypothesis to explain this difference.
KM | 
KM |
| My hypothesis is that the escalator is hung by the top of the truss, which allows the truss structure to be more stable than if it were hung by the bottom chord of the truss. If it is indeed hung by the top chord, this would cause the top chord to be in compression, and if the chord has more material it will be stiffer. | The top chord is indeed in compression, but that would also be true if the escalator were hung off the bottom. Why does the compression chord need to be stiffer? |
| The truss is basically a beam that is on a diagonal supported at the ends. In such a situation, the bottom chord is in tension, the top in compression. To avoid buckling on the compression side, a double chord is used. | This answer addresses the basic issue well. A follow up question is: why are the members of the top chord arranged side-by-side? |
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The trusses supporting the escalator are planar freestanding trusses. This is case that is usually avoided because it offers no opportunity for horizontal bracing. The freestanding truss, therefore, is far more prone to lateral buckling. The weakest point of the planar truss is the top chord, which is in compression. The bottom chord, because it is in tension, resists lateral movememt fairly well. Common solutions to this problem include the addition of transverse beams (which, in this case, would inhibit the passage of people on the escalator) and adding lateral dimension to the top chord to strengthen it. The orientation of the double member on top--which, in the photo, is strongest in the lateral direction--reveals that it is horizontal and not vertical movement that is being resisted. |
The truss is naturally stiff in the vertical direction, and so needs its additional stiffness in the weak axis direction on the compression edge. |
| salami | Remember about lunch... |
| The truss appears to be made of steel. The truss was constructed according to the fact that steel is stronger in tesion and weaker in compression. The top of the truss is in compression as the load of the escalator pushes down. The bottom is in tension. Thus, the members at the top were double to account for the reactions of steel to compression. The bottom remains at one member as steel performs well in tension. | There is a common misconception that steel performs better in tension than in compression, which is not really true; steel material properties are very similar in tension and compression. But, steel members in compression are prone to buckling, that is a property of the member, not the material. . |
| Arch 324/624, Introduction to Structural Design, University
of Virginia Copyright © 1996-2005 Kirk Martini. Last Modified Fri Mar 25, 01:57 PM |
Table
of Contents |