Architecture Structure Problem
The Architecture Structure Problem is essentially how to make the largest indoor space, build the largest tower and span the greatest distance, with the most efficient use of available resources (including labor). The correlated goal is to make the inside space usable, by allowing light in to illuminate the inside, regulate temperature without choking smoke, and safe from the elements , fire , water and wind.
What we know of history, and therefore what has shaped Human culture and destiny, has been dependent upon the materials used in their buildings and records. Ecology as much as technology has chosen the winners and losers of History. Water, fertile land, defensible borders and eventually minerals resources (Iron cuts copper, Steel cuts iron) are as much the cause of Empires as the Leaders and Philosophers we revere.
We know virtually nothing of the great cultures of Africa, except from the records of Middle Eastern and Oriental cultures that interacted with them at their height. They built out of the abundant wood that surrounded them, perhaps the easiest of materials with which to carve and build, and among the least resistant to the ravages of age and humidity. The Egyptians (and Judeans/ Hebrews/ Jews) had no useful wood resources, thus were forced to use the most harder to carve and heavier stone and clay for building and recording their records. We know much about their history, mythology and culture, and archaeology in the Holy Land AKA The Levant AKA The Middle East continues to illuminate the Past daily.
The oldest standing structures, the Egyptian pyramids, use a tremendous amount of heavy stone material and large land foot print to reach what was for it's time a majestic height worthy of a King's resting place. However, most of the material is used in holding the structure up against gravity and it's internal weight, with very little "living" (ha ha ha) space inside for the corpses and treasure. Where there is space, the small tunnel like and larger chambers are free space engineered using beams and columns only. To be clear, RIGHT ANGLES, HORIZONTALS, AND PERPENDICULARS are the very beginnings of architecture and Freemasonry. There are few inches of inside space not used to hold up the stone itself. The larger stones were moved across the desert from the quarries on wooden sledges, wetting the sand in front and pushed - pulled by many hands and feet.
If the Bible spends a lot of time describing the actual dimensions and furnishings of King Solomon's Temple in both the pre-exile Northern Kingdom copy which became Kings (written during Jeremiah, before 586 B.C.E.), and the post Babylon Exile Southern copy which became Chronicles (written during Ezra,516 B.C.E.), (remember, in BCE, larger numbers are EARLIER than smaller numbers, as time goes towards ZERO and restarts counting up in the Christian Calendar) it is both to awe the reader with the splendor of the structure, preserve mystical and practical principles, many of them elaborated inFreemasonry. (see The Sources of all Bibles). It is bragging about the amount of inner space and height (3 levels) coaxed from stone and timber from Lebanon. THERE IS NO GOOD BUILDING WOOD in Judea, so most other structures are small, made of stone and clay/ mud. This has huge implications for the crucifixion confusion in both Maccabees and the New Testament.
With the discovery of iron, first in Turkey/ Assyria, new building materials became available with first cast iron, then wrought iron, copper, steel, steel reinforced concrete, steel I-Beam configuration girders,etc. Over time structures could be designed and built to greater heights (think Empire State Building), with less materials (think the Eiffel Tower) and more interior space (think Christopher Wren and Robert Hooke's St. Paul's Cathedral), bridges could be designed to span longer waterways (Lake Pontchartrain in LA). And function could be supplemented with beauty, either the elaborate beauty of a Gothic Cathedral or the striking simplicity of Frank Lloyd Wright design.
Material Science, a subset of Engineering, is concerned with mapping out the properties of materials, so the best material can be utilized in the desired structure. It is related to Alchemy, and painting, as early painters made their own pigments, and the end results were considerably enhanced or destroyed by this chemistry. Leonardo da Vinci's experiments with pigments allowed his figures life like flesh tones and shadows (without poisoning himself, a concern when experimenting with lead and mercury).
But Leonardo, of course, was the Original Renaissance Man, and an engineer as well as painter. His experiments theorized that wire's strength was related to it's length, using different wire of various materials, length and thickness. It was crude, but inspiring.
It inspired Galileo, who disproved of Leonardo's theory that wire's strength was related to it's length; Robert Hooke who captured it in Hooke's Law,"ut tensio sic vis" or "as the extension, so the force" AKA F= -Kx.; Then Augustine Couchy AKA Augustin-Louis Cauchy made it mathematically clearer; Leonhard Euler clarified it for different structural materials so the load-carrying and deflection characteristics of beams could be mathematically, rather than empirically, tested (don't have to have it fall down to know it is not strong enough). This was one of the ancient secrets of the Operative Freemasons, along with the capstone, how to make a Square and the Arch;
The Triangle as a truss, counter-weighing cables, distribution of weight through tension and compression, all allow modern structures to be designed not to fall down on the drawing table and in the computer, which saves a lot of bother.
Highly recommend the video lecture series by Stephen Ressler Ph.D from The Great Course, entitled Understanding the World's Greatest Structures: Science and Innovation from Antiquity to Modernity ...struggle through the math as best you can.... the concepts are more important for those of us not actually building buildings, as they provide an insight into Nature, and Nature's God, by philosophical analogy.
A big thank you to WB Justin, Dr. Phil and Dr. Nomad, and Dr. Stephen Ressler and Prof. William R. Cook, whom I don't know personally.
Resources; THE CATHEDRAL lectures, Prof. William R. Cook (especially lecture 4 on Vaulting), and Understanding the World's Greatest Structures: Science and Innovation from Antiquity to Modernity, Stephen Ressler Ph.D. both from The Great Courses, all highly recommended - http://www.thegreatcourses.com ; http://www.washingtonpost.com/news/morning-mix/wp/2014/05/02/the-surprisingly-simple-way-egyptians-moved-massive-pyramid-stones-without-modern-technology/?tid=hp_mm&hpid=z3