Resistant, stable and rigid structures

A bookcase can fail in three ways: the shelf breaks, the entire bookcase topples forward, or the structure twists into a rhombus shape. Match each failure with the condition that is broken — strength, stability, or rigidity — and explain in your own words what each of the three conditions means.

The figure shows a bridge structure made of joined triangles, with a load in the centre.

Explain why this structure is made of triangles and not rectangles: what happens to the bars of an articulated rectangle when pushed from the side, and why a triangle, on the other hand, cannot deform without breaking a bar.

Build a hinged square using four toothpicks and sticker dots (gomets), and a triangle using three toothpicks. Push each one from the side and answer:

1. a) Describe what happens: which one deforms without breaking and which one does not?
2. b) What piece would you add to the square to make it rigid?

A cube shelving unit without a back panel shifts to one side, taking on a rhomboidal shape when pushed sideways. However, if a back panel is screwed on (or two cross braces are placed behind it), the structure does not deform.

Based on this situation, answer the following questions:

1. a) Of the three basic conditions a structure must satisfy (strength, stability, and rigidity), which one failed in the initial shelving unit? Justify your answer.
2. b) Why does the back panel solve this problem, despite being a very thin material?
3. c) How is this solution related to the triangulation technique used in structures?

The centre of gravity is the point where the weight of an object is "concentrated": if you hold it right at that point, it stays balanced. Explain the idea with a simple example (balancing a ruler on a finger) and reason why that point is higher in a full glass than in the same empty glass.

An object is more stable the wider its base is and the lower its centre of gravity is. Apply this rule by ordering from least to most stable: a pencil standing upright on the table, a full water bottle, and an Egyptian pyramid, and explain in each case the role played by the base and the height of the weight.

The figure shows two objects with their centre of gravity marked and the vertical line dropping from it: one with a wide base and the other narrow and tilted.

Explain, looking at where the vertical line from the centre of gravity falls relative to the base of support in each object, why the first stays upright and the second topples over, and state the general rule of stability in your own words.

The Leaning Tower of Pisa does not fall because, even though it is tilted, the vertical line from its centre of gravity still falls within its base. Explain this rule in your own words and apply it: reason how far a tower could tilt before toppling over and why counterweights or widened foundations help.

There are four basic types of structure: frame (beams and columns), triangulated (truss/triangular), suspension (tensioned cables), and shell/laminar (a curved sheet that supports itself). Classify these examples: the skeleton of a building under construction, a harbour crane, a suspension bridge, and a car bonnet.

Classify these structures into frame, triangulated, suspension, or shell/laminar, justifying your answer: a bookcase made of stacked cubes, the structure of a Ferris wheel, a washing line with taut ropes between two walls, and a plastic bottle supporting the weight of a book on top.

An empty plastic bottle can support a person's weight without being crushed, even though the plastic sheet is extremely thin.

1. a) Explain what type of structure it belongs to based on its morphology.
2. b) Justify why its curved and closed shape gives it a resistance that the same flat sheet would not have.
3. c) Give another example of this type of structure that you can find at home.

Choose the most suitable type of structure (frame, triangulated, suspension, or shell/laminar) for each case and justify it: (a) a bus stop shelter, (b) a $60\ \text{m}$ footbridge over a river with no supports in the middle, (c) a tent with tensioned poles, and (d) the village water tank.

Match each situation with the idea of stability that explains it: (a) a bicycle supported on two wheels falls over with a light gust, but does not with a kickstand, (b) floor lamps have a heavy, wide base, and (c) a lorry loaded very high is more dangerous around bends than one loaded low. Explain what changes in each case: the base of support or the height of the centre of gravity.

The figure shows four schematic structural typologies (from a to d):

1. A bridge is planned to span a 300 m wide gorge without intermediate supports, as well as the roof for a large, open-plan sports arena. Justify which of the four structures you would choose for each case and why you would rule out scheme a) in both situations.

2. In scheme b), a worker removes the interior diagonal bars to open up space for a window. Predict what will happen when the structure supports a horizontal load and justify which basic requirement (strength, stability, or rigidity) will be compromised.

3. In scheme d), justify why that curved shape withstands loads better than a flat plate made of the same material and thickness.

A tower crane is erected on a construction site to lift loads of up to 2,5 tonnes:

1. Analyze the mechanical stresses that develop in its main components when it holds a suspended load at the end of the jib: determine which one works in bending, which in compression, and which in tension, justifying each case based on how the element tends to deform.

2. A novice worker suggests removing the concrete counterweight at the end of the workday, arguing that «with no load to lift, removing that weight will prevent fatiguing the tower at night». Rebut his proposal technically by explaining the function of the counterweight and what would happen to the crane if it were removed.

3. Justify why the base is anchored to a large underground concrete footing and which basic structural requirements (strength, rigidity, or stability) this anchorage ensures against side winds.