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Figure 1. Engineers are constantly being challenged to solve the world's new and complicated problems. Many of these problems initially seem impossible to solve, but engineers find a way to make things happen! In the 20th century, engineers developed previously unimaginable things such as electricity, mass transportation, thousands of different automobiles, and even space travel.

Engineers often look back in history to learn from past engineering successes and failures as they design and build amazing new things. Every day, engineers are thinking of ways to improve on what already exists as well as developing brand new ideas that have never been created before. In , the tallest building in the world, the Taipei , was completed see Figure 1. Located in Taiwan, the Taipei —named for its floors—stands at 1, feet, more than a quarter mile tall!

For engineers to come up with a plan for this building and other similarly challenging structures , they must be creative and think "outside the box. Let's talk about buildings. What makes a building strong? If students give answers regarding the materials used [concrete, steel, wood, etc. Let's brainstorm some ideas. Consider the pyramids in Egypt. Those buildings are very strong and have lasted hundreds of years.

They have a very distinctive shape that aids in their strength. Structures must be able to remain standing despite large amounts of force put on them by weight and other factors such as earthquakes or wind. Using different geometric shapes, structures are supported in different ways.

Figure 2. The Greek Parthenon, circa BC. An example of a building using two different shapes, triangles and columns, is the Parthenon, a very successful engineering feat. The Parthenon began construction over two thousand years ago in BC—at the height of the Athenian empire—and is still standing today see Figure 2. The Parthenon was a temple built to represent the power and strength of the residents of Athens, Greece. This is an excellent example of a well-built structure that engineers can study, enabling them to learn better designs from the past for the future.

Now that we've brainstormed for a little while, let's begin our activity.

ISBN 13: 9780750668491

Today you all are going to be engineers with a specific problem: you must build a structure to hold up as many books as possible using only the materials provided. To solve this problem, think like an engineer. As you work with your team, follow the engineering design process—be creative and think "outside of the box. And, do not be deceived by using paper and straws to build a structure; paper is very strong when used to its best advantage!

Hint: think shapes; see Figure 3. Figure 3. The strength of columns—even when made of paper. Figure 4. What is the best geometric shape? Design Process: Before the re-design, ask the students to write out the design process for their designs. What is the need? How is the problem defined? If the students are having trouble, do the first few steps with the whole class. Re-Design Practice: Have the students list any design or fabrication changes they would make to the structures. Have them consider buildings and structures they see in their everyday life.

Are there any similar characteristics shared by the different buildings? Presentation: Have the students give a short minute presentation about their design to the class. In the presentation, ask them to explain some of the cool features of their projects and show which shapes they used to make their structure strong. Have them tell the class how many books their structures were able to hold and describe the failure mode of their designs.

Figure 5 shows the three types of failure modes.


Most structures fail by buckling and a few by compression. Have them give a few ideas of how they could make their structure even stronger i. Figure 5. Modes of failure: Buckling, compression and shear. Pijaudier-Cabot, Random particle model for fracture of aggregate or fiber composites. International Journal of Fracture 69 — Hillerborg, M.

Petersson, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research 6 — Li, Modulus of rupture: size effect due to fracture initiation in boundary layer.

Li, Zero-brittleness size-effect method for one-size fracture test of concrete. Li, Scaling of cohesive fracture with ramification to fractal cracks. Wittmann, Aedificatio Publishers, Freiburg, Germany — Lemaitre and J. Chaboche, Mechanics of Solid Materials. Cambridge University Press, Cambridge, U.

Broek, Elementary Engineering Fracture Mechanics , 4th ed.

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  3. Eisenstein series and the Selberg trace formula I by Don Zagier from Automorphic Forms, Representation Theory and Arithmetic: Papers, Presented at the Bombay Colloquium 1979 (Tata Institute Studies in Mathematics);
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  6. Louis Hadjian, — Preprints, U. Shah and S. Swartz, published by SEM Soc. Pfeiffer, Determination of fracture energy from size effect and brittleness number, ACI Materials Journal 84 — Size Effect on Fatigue Crack Growth 2 7. Wave Propagation and Effect of Viscosity 1 7.

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    Microplane Model 2 8. Simple, Practical Approaches 1 8. Nonlocal Concept and Its Physical Justification 1 8. Prevention of Spurious Localization of Damage 2 8. Limitations of Cohesive Crack Model 3 9. Asymptotic Scaling Analysis 15 9. Case 1. Case 2. Case 3. Zdenik P.