Re: How do Newtons laws apply to engineering a bridge?

How do Newton's laws apply to engineering a bridge?

Newton's 1st Law: An object's velocity does not change unless a net
force is applied to the object.

Newton's 2nd Law: The product of object's mass and acceleration is equal
to the vector sum of all the forces applied to that object.

Newton's 3rd Law: For every action there is an equal, opposite reaction.

Newton's laws were created to describe how objects move. Since the
typical bridge doesn't move with respect to the earth, according to
Newton's laws, the net forces on the bridge must be zero. Since this
question is addressed to the engineering section, and engineers take
shortcuts wherever they can reasonably get away with it, we will ignore
the fact that the earth itself is moving around in space.

Consider a rock sitting on the Earth. Since the rock isn't moving, the
net forces on it must sum to zero. There are two forces here. The
gravitational attraction between the rock and the earth pulls the two
together. The materials that compose the rock and the earth deform until
they push outward just enough to exactly counter the gravitational
attraction between the two objects.

Now consider a bridge between the rock and the earth. The bridge is just
an extension of the earth's crust here. It is deformed just enough to
push outward with a force that exactly counters the weight of the rock.
The earth is deformed just enough to push outward with a force that
exactly counters the weight of the rock and the bridge.

Newton's laws apply to a bridge just like anything else. But because a
bridge doesn't move beyond a bit of deflection, Newton's laws aren't
very directly applicable to engineering a bridge. They mostly just hide
in the background as a supporting framework, supporting the more
sophisticated math and analysis that goes into engineering the bridge.

An example of a bridge design topic that rests on the foundation of
Newton's laws is mechanical resonance. Mechanical resonance considers
how the bridge will vibrate when you apply different forces to it. (For
example, a loaded truck driving over the bridge.) On this scale each
part of the bridge does indeed move - but the relationships describing
how each part of the bridge moves are pretty complicated. The mass and
strength and shape of each part of the bridge all affect the final
behavior of the bridge.