What is the size threshold for something tunneling underground to cause an earthquake, and what relationship might there be between tunneler size and the magnitude of the earthquake that follows?

The tunnel size does not impact an earthquake, or at least not as a first order effect.

The collapse of a tunnel could create a sinkhole, but for most cases your tunnel very close to the surface and/or have a very large tunnel. Unless this was a large event you probably wouldn’t notice it if you didn’t see or hear it occur.

Now what does create earthquake in relationship to tunnels is pressure release. This usually occurs during the tunneling process, but outside forces can do the job just as well.

Typically this occurs where gas (typically natural gas) or liquids (typically water unless the tunnel was prospecting for something like oil) under pressure burst into the tunnel. the change in pressure can affect a sizable area like a large hydraulic ram relaxing beneath a whole area. Granted that is unlikely to affect a very large area, but it has occurred.

Another version would be frakking or similar technologies. Drill a hole and apply hydraulic pressure until something underground blows out. Here you adding pressure to a system with a sudden release. Again wide area effects are uncommon, but if you’re doing this all the time, across a large area, you will get periodic wide effects.

When did modern architecture begin?

Most architects and historians peg the beginnings of modern architecture (now being called mid-century modern) at the founding of the Bauhaus school in Germany. So 1919.

Of course, Walter Gropius and Le Corbusier (two of the greatest modern architecture architects) were practicing before this time so you will find a few different answers.

How does the thermal expansion of rebars not compromise the structure of encasing concrete?

Steel has a coefficient of about 10.8 and concrete about 12. As mentioned before these are pretty close. But, they are different.

In this case it is most likely that the concrete will be applying force to the steel rather than the other way around (with thermal stresses). When a material is constrained we can take the thermal change convert into amount of linear expansion and plug that into the modulus of elasticity to find out the equalizing force is to the expansion.

Basically, change in temperature creates stress within the system. If it becomes too much you see fracturing.

If wood is stronger than metal for building homes, businesses, and skyscrapers, why can people chop it in half but not metal?

This is a common example that engineers and material chemists love, but this is only part of the story.

Individual wood fibers are roughly as strong as mild steel. The problem is that while steel exists as roughly a whole uniform crystallin composite, wood is an aligned fiber bundle held together by a cellulose matrix called cambra. This cambra is only as strong as, well wood.

Let’s look at this another way. First off, I feel that most people understand that steel is a very strong material as long as you heat it to a point of property change (around 400F for those that care). On the other hand let’s take something very strong like carbon fiber strands. But, they are only a few inches long. And to bind them all together, Jello. You could correctly point to this object stating that it has strength characteristics that among the greatest in material science. But, in practice the fiber lengths are so short that it really comes down to the strength of the Jello, not the carbon fiber.

Wood has a similar comparison. It also explains why it is so easy to chop into pieces. While steel, you still need to chop through those crystal bonds. Good luck with that.

What house materials are the least flammable?

Reinforced concrete and solid grouted reinforced CMU are the most fire-resistant.

Heavy steel with fireproofing is considered equivalent.

Brick masonry.

Light gauge metal framing with fireproofing.

Heavy timber (6×6 and bigger).

Light gauge metal framing without fireproofing.

Wood-framed would be the least fire-resistant.

As a side note, you need to be careful with stone, clay, and other solid materials as they vary a great deal in their fire resistances.

Also, some might note that some of these materials are incombustible, but this list is dealing roughly with fire resistance.

How are speed limits for roads determined?

The simple and unsatisfying answer is traffic engineers doing traffic analyses.

A bit more in-depth answer is that roads are broadly divided into highways, arterials, collectors, and streets. Highways connect cities. Arterials are the major routes within cities. Collectors are branch or minor streets but not residential. Streets are your typical residential street. Roads can change categories as they go along.

Most of the road sizes are determined when the city is/was planned with smaller roads branching from larger ones down to residential streets. Engineers determine the traffic loading either by measuring existing traffic amounts or by estimating loading from city use maps (this is large part of what your city planning department does).

Once they have a model of traffic loads on each road they assign a speed limit or adjust the size/loading of the road. This gets reviewed by a number of city departments who ask questions, clarifications and/or for adjustments. Once all departments have been satisfied the city instructs the Public Works department to install the speed limit signs accordingly.