Theoretical Formula of the Super Nuclear Bomb

　　Since I proposed the theory of the Super Nuclear Bomb, I have known that many reads want to know the theoretical formula. In fact, the theoretical formula is the same as what I said then, and everyone can derive the formula from my articles. However, I think I have to propose this formula to answer everyone's question, so that I must derive this formula from my SNB theory. This is a mathematical problem, and it must be solve by several sphere and geometric equations.

　　I take three circles which adopt the same radius, and link three lines of its centers to form a triangle. And then, I want to solve the ratio of the triangle's inner circular areas, and it means the surface area of U235 atomics divided by the regular surface area of a U235 particle. Besides, I take three spheres which adopt the same radius, and link six lines of its centers to for a tetrahedron. And then, I want to solve the ratio of the tetrahedron's inner sphere volumes, and it means the ratio of outer U235 atomics divided by inner U235 atomics. Please see the following equations:


　　
　　


　　

　　

　　

　　


　　How do you use this formula? As every researcher knows, the atomic radius of U235 is 156nm, and the critical mass of U235 is 48.8kg. Hence, if you want to build a 1.0 Tera-Joule super nuclear bomb, you shall choose 0.25mm as the particle radius of U235. Of course, you have to take the equipments to make it become small particles, and please don't let it achieve the critical mass before you use it really. If you want to check your design, you can take the Richter magnitude scale to measure your design energy.





References

1. Wikipedia, Uranium, http://en.wikipedia.org/wiki/Uranium
2. Wikipedia, Solid angle, http://en.wikipedia.org/wiki/Solid_angle
3. Wikipedia, Tetrahedron, http://en.wikipedia.org/wiki/Tetrahedron
4. Wikipedia, Sphere, http://en.wikipedia.org/wiki/Sphere
5. Wikipedia, Critical mass, http://en.wikipedia.org/wiki/Critical_mass
6. Wikipedia, Richter magnitude scale, http://en.wikipedia.org/wiki/Richter_magnitude_scale

Theoretical Problem in LRFD III

　　The final version of Working Stress Design was the ACI 318 1963 Code（Taiwanese Civil 401-56）, but the Ultimate Strength Design had been discussed for several years. In 1955, the united convention of ASCE and ACI proposed the USD method, and they defined the primitive factor of safety for this design method. In 1971, the ACI 318 1971 Code adopted USD to replace WSD completely, and the primitive factor of safety was shown as following formula.


　　In this definition, ACI seems to make an obvious fault, and it's the dead load must be considered not only the numerator but also the denominator. Why? When an engineer designs a building, he doesn't just calculate the live load. However, nobody cares about this fault, so that everybody has forgotten it. Actually, the factors of dead load 1.2 and live load 1.6 are the wrong combination, so that the factor of safety produced a unreasonable result to lead the buildings lighter too much.

　　The best definition of factor is not the possibility, but the ratio of dead load and live load. However, the primary problem is the engineer cannot know the final results before he starts to calculate the building. Besides, in order to avoid somebody misunderstanding the building weight, I design a simple building example of the 12 floors and 36m building (non-stairs) by the USD method. Actually, the building is the prototype of the Building of Ching-Min Huang Office, and I intend to raise the height of the 1st floor and consider the roof as a coffee house. Both of width and length are 15m, and the thicknesses of floor and wall are 15cm and 12cm, respectively. There are 12 columns which section is 80cm x 80cm, and the beam section are 30cm x 50cm and 40cm x 65cm. In addition, the windows and holes are approximately 30% of the walls which are not including 3 shear walls. About decorating the building, the beams and columns are approximately 2% of its weight, and the plates and walls are approximately 5% of its weight.




　　　　　　




　　Can these factors be defined by and mathematical method? No, this problem cannot be solved, and the primary reason is that the unknown coefficients are more than the controlled equations. Even if the buildings are always the similar forms, the dead loads of structures shall be interdependent with the factor of dead loads. Hence, whatever the factor of dead load is, the buildings shall generate different results. It means any value of factor is possible, so that the load combination is not the only one solution.

References

1. N. J. Everard & J. L. Tanner；譯：李寬材 & 羅慕麟（1974）鋼筋混凝土四百題，五南出版社。
2. 國立編譯館（1974）鋼筋混凝土，復興書局。