Most of the time a variable load is a variable distributed load, VDL as opposed to a uniform distributed load, UDL. The variable changes from one rate to another which is either greater or less than the first. This represented as a wedge.

Cases were this comes in is where loads are applied at an angle such as roof wedges.

Fixed end – can’t move in any direction, can’t rotate.

Hinge end – can’t move in any direction, can rotate around the hinge.

There are differences in the math, but it depends greatly on your load case (or you can go straight for the Euler-Bernoulli equations if you’re a purist.)

Yes, but you need to be near the extremes before you start noticing a difference from the outside world.

Your statement of 50 times bigger is too imprecise for this question.

At 50 times the mass. you would scientific equipment to tell the difference, but you likely would never know.

At 50 times the diameter, we are in small star territory. We are still talking about insignificant changes.

At 50 times the mass, but the same diameter. Things are starting to get interesting but still wouldn’t get to a 1% difference with everything else remaining the same.

At 50 times the mass and a diameter of a grain of sand. Now we’re talking, but you’d still need to get within a foot of thing (I’m approximating, as I’m too lazy at the moment to work out the actual distance.) Should you decide to get within a foot of that thing you should notice a decent level of change, but you’d probably be too busy dying horribly to take note as it ripped chunks off of you.

Chairs usually aren’t used for reinforcement. They are placed to provide your placement distance in horizontal concrete, like slabs.

There isn’t a specific distance, but usually a separation sufficient to prevent large sags. In the US since 18″ on center is so common, a spacing of 3′ (every other crossing) is common. Any spacing can be used as long as the resulting rebar sag is acceptable.

Bricks are made either with clay or concrete (depending on the type). They are either molded in forms or cut with wires like a cheese cutter. Lastly, they are either air dried or fired like clay pots.

It would be probably the best-known example of Byzantine architecture.

Basically, Eastern Romans after they split from the Empire, then later adopted by middle eastern culture like the Ottomans and Muslims.

Okay, there’s a lot of parts to this.

Either a commercial or home could have either a sloped roof or flat roof if that was important to either.

Commercial buildings that are larger that chose a sloped roof would end up with a very large structure as the roof. If this didn’t serve additional functions it would just be a large waste of space and materials.

A lot of commercial buildings use the roof to mount loud or hot equipment. While this does occur in houses it happens much less. Flat roofs make this easier.

There is a general assumption that commercial buildings will have a greater amount, or at least a more knowledgable amount, of maintenance. This plays a part in the roofing design decisions. A sloped roof will shed water in all cases. A flat roof requires that the drains be checked periodically and cleaned. Also, with equipment people are more likely to check. It may be only once a year on commercial buildings, but have you been on your house roof even in the last few years?

Aesthetics play a large part. Houses tend to have attractively styled roofs. Commercial buildings may have partial roofs for this purpose, but large sections are never seen and therefore efficient only.

Lastly, there a laws that dictate a lot of different aspects. Heights, what can be seen from the street, the roof may be required to have specific properties due to location or use.

I could keep going, but I’m sure you get the idea. It is both a matter of form and function and most building designers, architects, engineers.. have come to similar decisions when it came to construction.

Actually, we already do.

Outside of air conditioning and heating, which I don’t believe to be part of your question, we have a variety of materials and technologies just for this purpose.

The most straight forward scenario is wall insulation. Basically, this isolates the air conditions inside the structure from the outside. So, any changes you make to one don’t greatly affect the other.

But, you’re looking for something better, right?

We are starting to use “cool” materials in warm/hot climates and “warm” materials in cold climates. Basically, most of your heat gain from sunlight occurs outside the visual spectrum of humans, so we have materials that are either more reflective or more absorbant to those wavelengths. Mostly this occurs on the roofs which receive the majority of the sunlight, but walls can be used as well.

You may have heard of “energy-efficient windows”, but these things are far cooler than you might imagine. Yes, they are insulated, but voids are filled with inert gases that transfer less heat across the medium (yes, I understand that that isn’t technically correct, but it close enough for this level of discussion). They also have a metal film between the layers of glass that works like an anode collecting sunlight energy and transferring into the wall mass where it increases the wall temperature slightly as opposed to the interior air mass moderately.

We use thermal mass walls in cold climates. Ever leaned up against a brick or concrete wall that’s been in the sun for a while. It’s warm if not hot. We do this in targeted areas within cold climate buildings. This has to be done in a very calculated way. Doing this without thought will likely create more temperature discomfort than easing it.

The last wall technology is about 60 years old. Phase change materials. You don’t see these a lot for two reasons. They are expensive compared to other solutions, and when they fail, they really fail. Basically, you have containers within your walls filled with specifically design salt solutions. Different components will change between gas-liquid and liquid-solid within our comfortable temperature range. What this means is that not only do they provide insolation they also provide endothermic and exothermic reactions to increase or decrease air temperature as they attempt to maintain equilibrium.

There is one other good old technology we like to use that pre-dates the greeks but it isn’t really a wall technology. The good old deciduous tree. Plant these near your wall on the sunny side, but far enough that none of the branches will touch the building. During the summer they are full of leaves and block the sun. During the winter no leaves and the sun warms up the wall.

There are others, but things start getting really obscure from here. Hope that helps.

Yes, but it’s going to get pretty thick if you don’t want cracks.

On most soil, you can get away with about 8″ thick. It will need to be nearly a perfect rectangle no length longer than about 100′and the short span must never get less than half the long length.

If you get outside of these proportions you need to increase the thickness rapidly. A longer slab will break up due to ground friction as it cures, so it needs to be thick enough to counter that. If any portion is narrower than others it needs to be thick enough to deal with that concentration of stresses.

You can end up with a three-foot thick slab on a seemingly normal-sized house fairly quickly.

Or, you use a 4″ slab with reinforcement that handles almost all typical situations with 6″ slabs handling virtually all reasonable heavy use situations.

Short answer: yes, but not a very good one.

Obsidian is very similar to common glass. This means that it has very high compressive values with very low tensal values. Hitting a “sword” against another object puts it in a state of bending (compressive and tensal forces at the same time) which means it will break with relatively little force. Hit it hard it is likely to fracture explosively (relatively speaking).

It would be heavy and difficult to construct.

Generally, I would recommend against it.