To Build a Bridge Part VII: Standing Tall

Any bridge with more than one span has a pier [Note: laymen will use the term 'span' to refer to an entire bridge.  Presumably because the term "Spans the entire width of the river" just means crosses the river.  But technically it means the place between supports.  So if there's a big pier in the middle of the river then there's actually two spans to get over the river].  Essentially just whatever is holding up the bridge between either end.  Some bridges have lots of piers, some have none, Greenfield has exactly one.  A pier can be many different things and built many different ways.  Unless it's an entirely timber structure, it's almost always made out of concrete (steel is inefficient for this application) but it can be shaped and formed and designed in all sorts of different ways.

The Lake Pontchartrain Causeways have a lot of spans and piers.

Typically the easiest and the cheapest pier for standard bridge uses a series of columns.  Taller bridges, ones crossing over multi-layered roadways or deep rivers and trenches, may use a single, very large column per pier.  Because Greenfield is wide and just crosses the one road: the multi-column approach was used (there are more approaches you can use, and a lot more subcategories, but this is good enough for a start).

Designing these piers requires looking at a large number of different loading patterns.  What if there's one truck pushed all the way over to the side of the road here, and no others?  What if there's one at the edge, but then one spaced 15' closer to center?  What about the wind loading?  What direction?  For Greenfield, I calculated (using some programming code I wrote, not by hand) around 50,000 different loading cases.  It doesn't scratch the surface of the number of possible combinations you could check under the code.  In fact, I calculated that if I checked every load placed to the nearest foot only, that it would be approximately 10^21 different combinations.

You can see the columns in various stages of completion.  The ones on the far end are poured and the forms stripped.  In the middle the rebar has been placed and forms placed around it that will give the column its shape.  On the close end only the rebar cage has been placed.

I'm actually responsible to make sure the bridge won't fail under any of those combinations, and there's nothing that says I only have to check to the nearest foot, if something spaced at 3 inches is more critical then that's my responsibility too!  This is where being an engineer actually means doing engineering rather than just calculating.  A sense of what controls, where, and what level of precision is required makes you a good engineer.  Being good at calculations just makes everything after the actual engineering easier.  In truth, 50,000 is way too many checks, but since it's the computer's time (and I ran my code in about 20 seconds) it wasn't worth taking hours of my time to pare down the possibilities to something more sensible.

The strength of the column is only counted for the section that is the same top to bottom.  In other words, that fancy looking, extra wide bit on top actually isn't designed to do anything.  When you see a column with a little cut running around the outside (if you look for them, you'll see these everywhere, from bridges to parking structures, to exposed building columns) know that this means that nowhere in the column is the outer bit considered for strength.  By cutting one inch out anywhere to make it look pretty, you're essentially wasting that concrete all the way up and down the column.

Of course if I'm wrong, and I excluded some critical case somewhere: that's on me.  Knowing that there are one hundred thousand quadrillion permutations isn't going to get me off the hook if something happens.  It's a sobering thought.

The columns are built to connect into the footings below (see To Build a Bridge Part IV: A Firm Foundation).  The rebar sticking out of the footing that now forms the column had to be placed before the footing was poured, so it's critical the shape and height are right, which can be hard to measure for thin pieces of steel sticking 20' in the air and moving around.

But here's the more interesting aspect of designing piers: the weight on the pier rarely controls the design.  For really tall piers that start to suffer from "slenderness effects" (the same thing that keep a sheet of paper from being able to hold much weight: it's plenty strong, but it deforms when load is placed on it) weight can control.  But for most pier columns, adding load to the column actually helps it stay up.

These are considered "slender columns", and for them, the total amount of vertical load will actually be critical.

Any one of the columns on the Greenfield bridge (there are seven in total) are rated to hold about six million pounds.  And that's what it's rated at, in truth it could support a lot more than that.  What controls the design of these columns are loads applied horizontally.  Temperature changes in the bridge superstructure that will push on the columns.  Vehicles braking on the bridge.  Believe it or not, wind controls the design more times than not.  Crash loads, where a truck simply breaks through the barriers around them and hits a column at full speed.  So if you want to see a bridge column break: don't keep loading up the bridge: just drive really fast on top of it and then hit the brakes.  Only we designed for that too so you're just out of luck.

To Build a Bridge Part VI: The Law of Bridges

You may or may not be familiar with building codes.  Across the world, just about every country has some kind of "code" that determines how and what you're allowed to build.  Want a shed in your backyard?  There will be laws about how high it can go, what it can be made out of, and how strong it has to be.  In the United States these codes are written on the state and local level (counties and cities get into the game too).  Well, building bridges has the same kind of rules and laws associated with it as building a shed in your backyard.  A little more complex but the idea is the same: the government has some minimum requirements for structures put up under its jurisdiction.  If you want to build your house out of straw you're probably going to get a visit from an unhappy inspector to inform you that it won't stand-up to the wind loads it's likely to see and maybe you should consider brick.

The Three Little Pigs is actually a story about the importance of government regulations and shoddy contractors

How do you determine what kind of traffic loading the bridge will see?  How do you decide what stresses your concrete or steel will experience?  How do you handle cracking in the concrete?  How do you know the section your designing is strong enough?  These may seem like questions that should be answered by just having an education in structural engineering, but they're actually variable depending on all sorts of assumptions.

You asked for concrete that can handle a compressive load of 4,000 pounds per square inch (that's called "4ksi concrete" and is pretty standard stuff, if a bit low-end) but what will actually show up?  You need to protect the reinforcing steel in the concrete from the elements so it doesn't corrode.  You decide to embed it far enough to be protected, but how far is that?  How long does it need to last and how fast do invasive chemicals penetrate the concrete?

When the concrete around the rebar falls off (typically this process is called "spalling") the rebar is exposed to the humidity and any other chemicals around, which for bridges, means the highly corrosive agents put down to prevent icing.  The rebar can deteriorate rapidly and loose the strength it needs to support the concrete.

That's what the code is for.  Every single state in the union has their own bridge design code because, apparently, physics changes depending on what state borders you're currently in.  It's really annoying.  But it's also not as bad as it sounds.  A group called AASHTO (The American Association of State Highway and Transportation Officials) has put together, and updates, a national code that determines all these things.  It is 1,600 pages long, and generally looks like this:

Knowing and following 1,600 pages of this is my job.  Now you know why engineering has such a high attrition rate.

This code is not the law, it's a document put out by an organization who has no legal authority.  At least not in that way.  But what most states do is adopt the AASHTO code as a body, and then have their own manual that goes on top of it to either clarify, add, remove, or otherwise change the provisions in AASHTO.  You can see Wisconsin's bridge manual here.  Once the state adopts any document as their code: it becomes law.  So most states say something like: "Except when our manual we've written differs from it, the AASHTO code is law". 

When we design a bridge, we have to "stamp the plans", which means literally stamping plan-sets and calculations with a "PE" stamp.  That's a professional engineering stamp that you get when you're licensed   Because each state has a different code, you have to be licensed in every state you want to work in separately   Most states, if you are licensed in another one, just require some paperwork.  Some states, in particular those with a lot of earthquakes (like California or Washington) will require a lot more than that.  By stamping the plans, you're taking personal responsibility for the design of that bridge.

Because the code is law: should something happen to the bridge, you don't necessarily have to prove that your design would work in the world, but rather that it conforms to the local code.  It's pretty rare that something designed to code falls down, but it happens.  In extreme events (mostly earthquakes)  and in some other, rare, instances like the Tacoma Narrows bridge.

The code is created after a lot of research and discussion.  A full discussion of code creation is a massive topic, which I will not be covering.  Instead I'll say that there are right ways and wrong ways to put together a code.  Bridge code isn't necessarily done the wrong way, but it's not the right way either.  Code for building design is, to me, a lot more elegant and efficient and produces a more consistent and usable code.  This of course changes from country to country: I'm only knowledgeable about US code.

There are various considerations when designing a code about how to lay it out, what to include, what to leave to the designer, etc...  One of the important descriptions of a building code is if it's "prescriptive" or "performance based".  A totally prescriptive code will tell you exactly what to do in all cases.  "For spans between 45 and 50 feet, use a prestressed, concrete girder of exactly these dimensions with exactly this reinforcing pattern and exactly this..."  A performance based code will tell you what is expected of the structure: "After a magnitude 7.5 earthquake, the girder can have cracks no larger than 1 inch".

The problem with prescriptive codes is that they can't actually cover everything, and so are both really expensive to build to (since they have to design for worst case uses which are probably rare) and leave little guidance or direction for uncovered cases.  Or just result in the under-design of situations the code-creators didn't consider.  Their advantages are that they're hard to screw-up a design with and are easy to use.  If boring.

If this bridge was designed to a rigid, prescriptive code, it likely would've fallen down.

The problem with performance based code is that it can be complicated to design with such little guidance, some aspects of design may not be considered when not spelled out by the code, and they open the designer up for more legal issues.  The advantages are they're much more flexible and allow for more accurate and efficient designs.  As well as giving a lot more guidance when working with unusual cases.  (When prescriptive code tells you that there must be rebar every foot of concrete no matter what that's what you put.  Performance based code would tell you that cracks can't develop that are larger than "x".  Thus, when looking at an odd scenario you have guidance from the performance based code about what you're trying to accomplish, and just a bar spacing from the prescriptive code which may or may not work).

No code is entirely one or the other once you get past assembling Lego models of Star Wars vehicles: they're all on a spectrum.  AASHTO is more prescriptive than some of the more sophisticated codes (I understand the Japanese have a very advanced, performance based code) but it has performance based elements as well.  And it's the law every bridge in the US is built to, or a modified version of it anyway.

Building my Deck (Without Any Skills)

Despite my complete lack of experience and lack of handyman skills of any kind, I decided that I was going to build a deck for myself.  As a structural engineer I figured I could design a plenty sturdy deck, but how it actually turned out was... uncertain.  Judge for yourself!

A small selection of framing lumber I dragged home.

 I planned out a 20'x12' deck with a wrap around step.  My back door sits around 20" to 2' off the ground, and where the borders of the deck are: it would be closer to 14"-18".  That's enough that you need either a railing or a step and I had no desire to separate myself from my yard.  So a step all the way around would meet code and not make me take a circuitous route to get to my lawn.

Starting to dump the lumber where the deck would go

 There had been a deck there before.  A little smaller and it was structurally unsound when I bought the house so I had it torn out.  However, I didn't have to mess with the siding at all: which was nice.  I attached some 2x10s to the house with lag bolts and used that to support 2x10 stringers coming out from my house.  On the other end, I put down 4x4 posts into the ground and concreted them in for the foundation.  Then I laid a pair of 2x12s out on top of them as a kind of pseudo-ground beam.

The support at the house and the foundation at the end have been put in place and I'm beginning to run my stringers from one end to the other.

A side view of the ground beams and some stringers waiting to be attached.

A simple, shear connection at the house, these are 2x10s set every 16"

The stringers have all been laid.  They overrun the ground beam by about 2', this cantilever helps balance the forces between the house and the ground-beam and reduces the stress in the beam as compared with putting the foundation at the full 12' away.

The full frame (minus the steps on the end, you can see the ones at the side).  The board at the end of the stringers helps keep them from twisting under a load and locks the deck together.

For the steps I have no "in process" pictures of, but I created them by hanging 2x6s out from the edges.  Framing the steps took three times as long as framing the rest of the deck.  What a pain!  I used hurricane ties to attach them on the side where they'd hang from the exterior beam, and then rock upwards on the beam second from the end.  A couple of nails would keep it from wobbling, but there was no tension to worry about with that beam so no special connection was used.

On the end of the deck (opposite my house) I used three straps per beam.  Two on the outside to hold the beam up, and one on the back to keep it from moving (where again, it pressed into the beam, so no tension force to worry about).  The steps on the side I placed every 2' or so.  At the end of the deck, I simply attached one to each stringer.

Now it's time to screw in the deck boards.  Not much to it, but a lot of work.  It was about 1,300 screws in all.

Due to quantity and, most importantly, length, I  had this package delivered.  The deck boards are all composite which costs (three times) more, but there is no staining or upkeep and they essentially last forever.

Completed deck!  At the corners of the steps, I put solar lights in.

Seems like a decent amount of deck, right?

The composite board wasn't a bad match for the house.

Final costs are broken down here.  The deck screws I counted under "decking" but all other nails and screws went under "connections".  Masonry includes, in addition to the 400 pounds of concrete I poured, a bunch of bricks I was going to use but didn't.  Or haven't, I may put some down on the side of the steps.  Miscellaneous includes the lights, a little spray paint, some gutter stuff and the delivery cost for my deck boards.

Connections	$     257.60
Masonry	$        35.14
Lumber	$     487.90
Decking	$  1,894.80
Tools	$        89.50
Misc	$        87.40
Total	$  2,852.34

The deck was a 20'x12' deck with the steps for a total deck surface of just under 290 square feet.  So for a composite deck with me doing all the labor, the cost was almost exactly $10/square foot.