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your nonstop source of everything science of architecture, including information for the ARE, LEED, and PE exams.

Saturday, March 19, 2011

MIES - Pankow Foundation Project

Currently, I am working with Dr.'s Pessiki and Sause at Lehigh University on a project that may significantly improve America's chances at withstanding prevalent seismic activity on the west coast. After the tsunami in Japan (and even before that the tsunami off the coast of Indonesia in 2004), a group of geologists convened in the northwest at the University of Washington and discovered that it was highly likely that Cascadia (the environmental heart of the Pacific Northwest) would be rattled by a quake of similar magnitude. The only unknown was when it would hit.

But after careful research upon the soils near the Columbia River, a range was determined: anywhere within the next 50 years. When I heard that, I knew I had to act fast.

Any architect will tell you his foremost passion is his home. In many regards, vernacular architecture is the peak artform for a building because it is architecture in it's natural state. And there is no nature I like more than that of the Pacific Northwest - from the lush green and purple flower valleys to the overcast and yet ever-changing skies. It's somber but beautiful, just like a Raymond Carver short story or a Ken Kesey novel.

So when this information was put before me while I was watching a video at Portland State University, since I knew I was going to apply elsewhere (I was paying for classes while not enrolled at PSU) I looked for projects with a NEES affiliation that could bolster my engineering credentials while improving my architectural acumen for this kind of disaster. Over the course of a year, I looked at Rensselaer Polytech, SUNY at Buffalo, Virginia Polytech and Lehigh. I ended up at Lehigh before I could view either SUNY or Rensselaer.

So I am here, in Bethlehem, PA, blogging for the school and working on a shear wall which will not deform even when confronted by the sudden impact of a tsunami. We call it "elastic architecture" - it bounces back - but it is only in a primitive state of design. What I can say is that rather than simple longitudinal reinforcing at the base, it uses more lateral reinforcing throughout a concrete member with a singular steel rod (thicker than rebar) post-tensioned through the wall on a certain interval. Because of the singular rod, the unloading phase along the stress-strain curve acts in the exact opposite direction of the loading curve, allowing the concrete to move without permanent strain/deformation.

When the design comes further toward completion, I shall blog again. But until now, it is just a dream. And fortunately, it looks like I've finally got the tools for the job.


Monday, July 5, 2010

MIES - The Divisions in Our Backyards

The Divisions in Our Backyards (Boroughs and Suburbs)


Dorothy Parker once described Los Angeles as "72 suburbs in search of a city." She could have been describing the mix of cultures as well. From the wealthier Hancock Park to the dirt-poor Mid-City area, from the east coast influx to the Pacific Rim influx, Los Angeles, as Parker put it, has “always been and will remain very much the sum of all parts and never parts of a whole.” The divisions for these suburbs, it seems, were predominantly created by two sets of cultures that drove the interstate and fell sideways under the San Fernando Valley shadows near the beginning of the twentieth century. And inequality in equality has never been as pronounced over a century as it eventually became in L.A. Less than one percent of the makeup in the City of Angels is all the difference that separates Hispanics from Caucasians today, and with the ever-increasing influence of Latinos willingly taking more minimum wage jobs, it’s very foreseeable that within the next five years Caucasians could effectively become a minority in this dichotomy of cultures.

But this isn’t an argument about groups of people or what food is served where. This is about the greater divisions of our backyards, or how our backyards build an urban landscape that extends far beyond our daily lives. And two of the great American cities – Los Angeles and New York – present two striking contrasts to what those divisions can be.

In my own travels, I’ve found that Los Angeles and New York both speak for one land but utilize vastly different languages. Walking through downtown Los Angeles, under the haze of a summer day, one sees perhaps two or three people on the street at a time. The openness of a Martian, otherworldly realm of sun radiates all around, only to be cut off visually by the San Gabriel Mountains. Outside of the initial development built atop what was once a Spanish pueblo, Los Angeles remains very flat and wide, which can, at times, be simply overwhelming in it’s horizontality.

Conversely, New York is a checkerboard collection of arterials, some conforming to the more modern pattern, some willingly angling against the grain. Robert Moses, one of the more famous urban developers in New York, played God with the city’s fabric, and because of his efforts, New York seems more the creation of one man than a group of men. The boroughs, as a result, seem designed like the Indian caste system; Manhattan is the exalted land, Brooklyn and the Bronx are next in line, and Queens and Staten Island, fairly or unfairly, act as refuges considered undesirable (although progress appears imminent in both boroughs). Even from afar, one sees Manhattan “rise,” which gives the perception of a more linear vertical development. Quite literally, where the World Trade Center buildings once stood, is the top of a mountain. Just connect the topmost edges of the buildings, and you know exactly where the summit is. Not so surprisingly, it’s near the Empire State Building (which stood as the world’s tallest building for the majority of the twentieth century).

Still, the difference between a borough and a suburb is more than sheer geometric form. Typology, the study of urban types, also plays a very particular role in this distinction for both cities. Urban and rural development, road infrastructures, and growth boundaries are three of the more basic forms of communal organization, but there are other, more historical, forms of organization. In New York, for instance, toward the start of the seventeenth century, a system of barricades (which is how “Wall” Street gets its name, coincidentally) running perpendicularly began a pattern of 250-yard long blocks. “Blocks” were literally just the squares formed by the figure-ground diagram of the resultant city.

It should be noted that the word “borough” is very close to the words “bury” (English), “burgh” (Scottish), and “burg” (German). The word, at its roots, indicates the fortified settlements in their primal form, which is what New York was at the turn of the 1700s. Although in New York the word became synonymous with “subdivision,” the first modelers of New York (well before Robert Moses’ influence) saw this as a potential attacking point for the British in the Revolutionary War. So there was a unified effort to turn this form of defense into the form of the city.

Because of this strict adherence to this initial urban plan, buildings were compromised for any potential future growth, and therefore, New York became a sky-obsessed construction culture. Without any zoning codes intact (which came into existence toward the start of the twentieth century) the mantra of contractors and architects alike was to “build toward the heavens” and unfortunately, many construction workers sacrificed their respective lives for this dream to be true.

Although it too saw the gunfire of many fights in the Mexican-American War, Los Angeles is now considered more the result of a collective effort of pueblo settlers to build a new home. After Mexico had gained its independence from Spain in 1821, Governor Pio Pico made Los Angeles Alta California’s regional capital. Through a series of battles, the Americans eventually overcame the Mexicans and forced them into signing the Treaty of Cahuenga in 1847, which annexed the city and upper portion of the Baja region for the United States. But, in contrast to what is now the Mexican-American border, Los Angeles didn’t exactly cast Mexicans out after the conquest. Instead, there were too many jobs to be had – from railroad building to oil – which required tireless slave labor in life-threatening conditions. A fair number of Mexicans stayed behind to work, and this is one reason as to why the city’s graphical divisions began with a division in people.

Los Angeles boomed. By 1900, the population grew to more than 100,000, which caused subsequent problems with the city’s water supply. William Mulholland, another influential urban planner, planned the construction of the Los Angeles Aqueduct, which again, caused many Mexican citizens to come forth and offer their services. In the more affluent sectors, the motion picture and aviation industries literally flew to new heights, ensuring that the city would survive the Great Depression intact (no other city could ensure a surplus in the United States at the time). Millions of farmers in the Midwest, struggling to produce a dime with their harvests, headed west in search of riches. Few found it.

Stepping back for a bit, away from the history, one should keep in mind that cities (and particularly great cities) rise and fall. Rome definitely did, so did Paris and New York certainly did during the Revolutionary War. Wall Street’s famous bear and bull markets also remain very cyclical, ensuring that the timeless clichéd saying of “history repeats itself” never truly dies.

Ironically, that truth sort of died in Los Angeles, which arguably amounted to a new paradigm in urban design. There was no bust, only boom. After the Second World War, the city began to sprawl, for better or worse, into the reaches of the San Fernando Valley. New plots for development, neither urban nor rural in their entireties, blossomed from under the highways, and cultures tugged at what land wasn’t utilized for commercial development. In many ways, iron mills, steel mills, and other industrial businesses made their money from company profits and by acting as landlords. In doing so, the outer realms of Los Angeles became poorly zoned half-urbanism, half-rental housing districts. Thus the term, “suburb.”

“Suburb” remains a tricky description for what Los Angeles’ development was. What Dorothy Parker had in mind might differ from what William Levitt had in mind when he built Levittown as a prototypical suburb in the 1950s. What Levitt did was propose “new towns” in the green belts that encompassed major cities like Philadelphia and New York. Accompanied by the garden city movement toward the middle of the twentieth century, Levitt set the standard for small-scale, reproducible construction that veterans from the war could purchase at an affordable price. These “suburbs” would still utilize city services, such as electricity and water, but remained independent from the city, which the inhabitants saw as an asset.

In Los Angeles, that independence never existed. And instead of the city coming out to meet the communities, it was always the other way around, as Dorothy Parker so eloquently put it. Suburbs, in Los Angeles, were almost the equivalent of social discrimination in context. It almost meant “less than urban,” which could easily be construed to mean “less than affluent.” Over a larger period of time, this would lead to cultural conflicts and racially oriented gangs, a problem in such places as Compton, which has never been truly solved.

In New York, the issue was a lack of real estate. In Los Angeles, the issue was a glut of real estate, and a significant drop-off in home value depending on where you lived. Although Rodeo Drive and Park Place remain some of the highest-end streets one can drive on, the roads themselves, in context with the cities they helped build, remain the one constant in both boroughs and suburbs. A division is present, and depending on who plans the city, whether it is a group of designers or a clash of cultures, a direction will be given.

In New York, that direction was up. In Los Angeles, it was outward. Whether it is to the heavens we build or to the horizons, our fences remain at the wiles of our initial ambitions. The 7-11 on a corner street with an abundance of unnecessary parking space is one result; a tight shotgun rundown tenement building is the other. In cities like Portland, Oregon and Minneapolis, Minnesota, this growth curve can be checked, and zoning and growth boundaries can be better defined. Indeed, the answers to modern city life will emerge from the smallest urban sectors and not the largest. But our greatest problems lead to our greatest answers, and for this, one can only thank New York and L.A.

Thursday, July 1, 2010

SS - Finite Element Analysis


Finite element analysis is useful, even essential, for achieving optimum results with new composite materials (carbon, Kevlar). Of course, the method can also be used for work with metals (steel, aluminum, titanium). But how does it work? Well, the essence of FEA is to break a large stress analysis problem into many smaller ones, which are then collectively solved by computer. This calculus-like appeal of finite element analysis method is one reason it has become a proven tool of structural engineering.

A very basic example of where finite element analysis might be used is the fabrication of a bike frame, which needs to be stiff enough, strong enough and also light enough to withstand the live load of a person while being aerodynamic and slender in form for optimum velocity.

The Trek 2000, a bike manufactured at the beginning of the last decade, was one of the first to utilize this kind of structural engineering. The following is the design stages they implemented to fabricate the bike form (from sheldonbrown.com, a respected biking site):

"1) Construct a complete finite-elements model for the new frame design, as well as for two popular high performance frames: a Trek 770 (Reynolds 531C steel) and a Vitus 979 aluminum frame (manufactured by Bador of France), all of equal size (60 cm). The Trek 770 and the Bador frames are the "base cases" against which the new design was compared.

2) Apply a variety of loading conditions to all frames to calculate their response characteristics.

3) Identify which loading conditions are critical in the design, in terms of undesirable responses (high stresses, high deflections, etc.). Establish which loads may be safely ignored.

4) Look for relationships between strength, stiffness, and weight by studying (graphing, plotting, etc.) the output data from the previous steps. Seek intuitive insights from the data about each frame's structural character.

5) Recommend future designs, and apply the various critical load cases to gauge their performance."

Elements of Finite Element Analysis (essentially, the mechanics of materials values):

1. Thickness
2. Coefficient of Thermal Expansion
3. Density
4. Young's Modulus of Elasticity
5. Shear Modulus
6. Poisson's Ratio (ratio of transverse to axial strain)

Element Properties

1. Straight/curved one-dimensional elements exhibiting axial, bending and torsional stiffnesses are suitable for cables, braces, trusses, beams, stiffeners, grids and frames. Straight elements have two nodes (for two ends) whereas curved elements have three. Elements are always placed at the centroidal axis of actual members.

2. Two-dimensional elements for membrane action (planes) and bending action (plates, shells). Curvature of basic shapes (triangles, quadrilaterals) included. Nodes typically placed at corners, sometimes at edges, seldom inside the element (but it can happen). The placement of additional nodes increases accuracy in the determining what an element may or may not do.

3. Torus-shaped elements are used for elements involving multiple symmetries. This can include plates, shells (one-dimensional) and solids (two-dimensional). Essentially, the torus-shaped elements involve the multiples of the first two elements in various assortments.

4. Three-dimensional elements for modeling 3-D solids such as machine components, dams, embankments or other masses. Common elements include tetrahedrals and hexahedrals in structural analysis. Nodes are placed at the vertices and possibly in the element faces or inside the element.

Element Interaction

Elements are only connected at exterior nodes and cover the interlocked domains very accurately (in an ideal structural analysis). Nodes have displacements or degrees of freedom which include translations, rotations, and higher order derivatives of displacements (if necessary). The displacement of nodes causes the dragging of structural members, which helps approximate the nature of a structural solution or remedy should the building fail.

Most of the math for element interaction involves linear algebra, and for that, this blog respectfully declines at moment to delve into that rabbit hole (although we will get there in time, we promise!). Another method of design for structural members, which has gained steam thanks to the evolution of computers, is the direct stiffness method. And that is our next topic of concern.







Wednesday, June 30, 2010

SS - Determinacy


In statics, when the static equilibrium equations are sufficient to determine the internal forces and reactions of the structure, that structure is said to be statically determinate.

In solving for determinacy, three summations of forces (which are obtained by Newton's laws of motion) are used to determine whether a structure is determinate. If for three equations, three variables can be solved, then that structure is called statically determinate.

The three equations for equilibrium state the following:

Σ N = 0: the sum of the horizontal components of the forces equals zero;
Σ V = 0: the sum of the vertical components of forces equals zero;
Σ M = 0: the sum of the horizontal components of the forces equals zero;

Where N is considered the normal force, V the shear force and M the moment force. The units for N and V are either pounds (lb), kips (thousands of pounds) (k) or Newtons (N) / kiloNewtons (kN).

The Free Body Diagram

In beams, columns or other composite structural members, it is best to break the key components of bar forces into separate reactions acting against or along those members. This is called a free body diagram, and it is the fundamental building block of all statics in determining force vectors.

The classical scenario typically used for physics is the block on a slope. The block has some weight, w, which acts downward toward the surface of the earth. Against the slope, however, a partial fraction of that weight, called the normal force (-N) acts perpendicularly against the slope. An equal, but opposite reaction (N) is the result of the sum of vertical forces equaling zero.

In structural beams, N is a horizontal force, acting linearly throughout the member. A change of connotation in how one determines force is all structural analysis suggests. Instead of negative forces acting downward and positive forces acting upward, structural analysis is more interested in what members are in tension, and which are in compression. If a member is in tension, that force is outward and its value is positive. Conversely, if it is in compression, the force is inward and its value is negative.

Or put it more simply, when your muscles are in tension, you build bigger biceps, and that typically is a positive outcome. Structurally, you're better with bigger, stronger muscles. Alternatively, when your muscles are compressed, there is a force acting against you, a negative force (which may include a bench press, dumbbells or some other voluntary load). You must prove elastic against that force in order to withstand it (which is the definition of compression).

A standard free body diagram may look something like this:
Where there may be a point load (or concentrated load), distributed load (in kN/m), reaction forces (at A in this diagram), distances for the loading forces and reaction forces, and subsequent shear vectors (V) and moment vectors (M) at cut cross-sections in the member. As a result of where the cut is taken, V and M with vary either linearly or parabolically. Or not at all. It all depends on the degree of loading (whether it is one point, continuously linear or curvilinear). The way it affects V and M, however, is another blog, however, and will not be included here.

All in all, though, there are two main considerations when analyzing a structure. One is stability, which is also another post. And the other one (which tells you something about stability) is determinacy. Without determinacy, it is very hard to predict what happens for a structure. Therefore, it is the preeminent consideration for all of structural analysis.

Now take a look at the top diagram. Why are the members and trusses either determinate or indeterminate (not solvable by equilibrium equations)? Recall that roller reactions have only one force they exhibit (vertical to loading), pins have two (vertical and horizontal) and fixed connections have three (vertical, horizontal and rotational to loading). Consider this a bit of a quiz. But feel free to take your time and look closely.




Saturday, June 26, 2010

SS - Cables



SS - Shear, Moment, Deflection Diagrams Review




SS - Fatigue




Structural design takes into consideration two different modes for failure - fatigue and fracture. Whereas it is commonplace (and correct) to believe fracture is the more dangerous form for failure, the fatigue of a member is more critical to design for. If a material is about to fail due to cyclic loading, this means the maximum stress values are less than the ultimate tensile stress limit, and thus the material will eventually fail to a smaller subjected load.

Continual loads will form gradual cracks that accumulate at a microscopic level in a material. These cracks eventually find their ways to the face of a structural member, and the compilation of the cracks will eventually result in fracture. If a structural member is formed into a certain shape, such as rectangular holes or sharp edges, like the reentrant corners in a building undergoing seismic surface waves, the material will be subjected to elevated local stresses, which will result in the increased rate of fatigue in the member.

Fatigue Life

The fatigue life, N(f), is the number of cyclic loadings a material sustains before it fails. It is NOT measured in seconds or time. Only in number of loadings.



Fatigue Observations from Cracks

The process of fatigue is a gradual one, taking an extend period of time, so the slow build-up of stresses typically results in a darker, more layered cross section when a structural member finally breaks. The brighter more silvery portion of the cross is where a sudden fracture occurs in a member.

Also, fatigue is a stochastic process, meaning that it is random. The path for fatigue cannot be determined, although it might look similar from a quick observation.

Some obvious factors influencing fatigue would be temperature, surface finish, grain size, material type, texture, direction of loading, geometry, atomic structure, internal stresses and oxidation (if present). Fatigue strength can be measured to a maximum of 10^3 to 10^8 cycles (this is typically for steel members, which provide the greatest overall fatigue strength for an extended period of cycles).

Designing for Fatigue

1. Design to keep a structural member below it's fatigue limit
2. Design for a fixed life after which a user should replace the member with a new one (called a "lifed part" and this process is called "safe-life" design practice)
3. Inspect the member periodically for cracks. Replace when cracks exceed a critical length. Employ nondestructive techniques to determine crack length.

Where Fatigue Occurs:


In the graph above, fatigue occurs between the ultimate tensile strength and fracture stress. Although cracks form before the ultimate tensile strength, it is more important to design for this later region at an early stage. That way, one will prevent a critical build-up of stresses at any portion in the cross-section of structural member.