Architectural Question

[Ogrork the Mighty]

This question is for all the engineers/architects out there.

Approximately (and I do mean approx) how far can an arch/roof span before a pillar is needed? Does height make a difference?

I'm curious b/c many architectural D&D designs have huge spans with no pillars. Of course, we can default to magic but I'm curious as to what an approx guide for the use of pillars would be.

Maybe something like one pillar per 25-ft high x 25-ft long span?

 

[handforged]

Although I am neither an architect or an engineer, I will attempt an answer.

A true arch could theoretically span any distance as long as the material it was made of and the ground under the bases of the arch could support the weight.

Look at the St. Louis Arch. It spans 630 feet and is 630 feet tall, but is not a true arch. It is a catenary arch (picture holding a string and copying the curve obtained).

In European cathedrals where great spans are crossed with arches, the piers that hold them up are massive at the base. So a more interesting formula would be how much area should the footprint of all the supports for a roof be depending on the size of the roof and the height of the walls.

~hf

 

[jgbrowning]

This question is for all the engineers/architects out there.

Approximately (and I do mean approx) how far can an arch/roof span before a pillar is needed? Does height make a difference?

I'm not an architect, but I know this question really depends on what material you're using to create the arch.

So, what material are you using and maybe someone who can help you more will chime in?

joe b.

 

[Agemegos]

Approximately (and I do mean approx) how far can an arch/roof span before a pillar is needed? Does height make a difference?

Height makes a difference. An arch can't be lower than half its width until the invention of elliptical and sectional arches (mid-Mediaeval). And higher arches and domes are heavier, placing more stress on foundations.

The dome of the Pantheon in Rome has a diameter of 38 metres (125 feet). (2nd Century AD concrete, still standing.)

The dome of the church of Hagia Sophia (now a mosque) in Istanbul (Constantinople) has a diameter of 30 metres (100 feet). (6th Century masonry, still standing.)

The Roman bridge at Alcantara (early 1st century masonry, still standing) has a span of 30 metres (98 feet).

The widest Gothic arch in Europe is in the nave of the cathedral in Girona, which is 23 metres (75 feet) wide (mediaeval masonry).

The nave of St Peters in Rome (Renaissance masonry) is 25 metres (82 feet) wide.

The widest timber roof of any mediaeval building I know of is that of Westminster Hall, which is 21 metres (68 feet) wide. (14th-century hammer-beam trusses, still standing.)

The widest tunnels before the invention of blasting were about 8 metres (25 feet) wide, such as the Roman road tunnel between Naples and Puzzuoli (dug in 36 BC, still in use). 2 metres wide and 2 metres high (six feet by six feet) was a much more common width (eg for drainage tunnels), since it is a large enough to work without inconvenience and not so wide as to be unnecessarily expensive. The width of ancient and mediaeval tunnels is not, however, dictated by the mechanical limits of the structure so much as by the colossal expense of tunnelling. An eight-metre-wide railway tunnel is nowhere near the structural limit of a self-supporting roof in strong stone such as Hawkesbury Formation sandstone (but it is beyond the limit of some weak shales).

 

[silentspace]

Agemegos' examples are exceptional structures, often of great symbolic importance to an empire.

Some other notes...

- The Pantheon was made with concrete, a special formula that the Romans discovered. The formula for concrete was lost in the Middle Ages.

- In the Rennaissance they started to use steel to reinforce structures.

- The St. Louis arch, of course, uses modern construction materials and techniques, is very tall in relation to its height, cost a lot of money, and is anything but typical.

As far as typical spans...

- In normal wood buildings, spans over 20' were rare (flat floors, not arches). This holds true today, spans over 20' are still rare, and are usually only achieved with engineered lumber.

- In modern concrete construction (two-way composite slabs), spans of 30' are common (varies greatly depending on loads). (20th century - Roman concrete was not steel-reinforced)

- In modern steel construction, spans of 40' are typical. (20th century)

Of course, buildings of great importance might have spans greater than these.

 

[Stormrunner]

Well, a quick websearch got me to the PBS Building Big website,
http://www.pbs.org/wgbh/buildingbig/index.html
where we learn that the domes of the Pantheon and Hagia Sophia, 142' and 102' in diameter respectively, were the largest domes in the world until the 1400s, and were considered architectural marvels. So figure anything over 100' diameter requires magic, exceptional architectural skill, and/or special materials.
Since a dome is essentially an arch which has been rotated, I'm guessing what holds true for domes generally holds true for arches as well.

Height has two indirect effects. One is weight - the taller the building, the more tonnage is pressing down on the support columns and the walls. The dome of St Peter's Cathedral in the Vatican had to be reinforced with huge iron hoops, like a barrel, to prevent the sheer weight from pushing the sides of the dome outwards and causing a collapse. The flying buttresses of a Gothic cathedral take much of the load off the walls, allowing the cathedral to soar to great heights without requiring the walls to be 50 feet thick at the base (and allowing the walls to be pierced with large windows, making the interior MUCH better illuminated than most large buildings had been until then). The other effect is wind shear - the taller the big flat wall, the stronger the force of the wind pushing against it.

 

[Ogrork the Mighty]

I'm thinking stone, but wood is also appropriate.

So I'm thinking, as a rule of thumb, that a span of 50 feet requires an arch at least 25 feet high (2:1 ratio). With more advanced architectural skills, maybe a 75-foot span that's 25 feet high (3:1).

That's good for arches/spans, but how do pillars fit in? Maybe every 25-foot span needs a pillar? If you include arches, then perhaps you can simply daisy-chain multiple spans together?

 

[silentspace]

Instead of giving you a number, I'll tell you how arches are/were constructed.

The most common arch in Europe is the Roman Arch, which is based on a circle, or half a circle. So the height of the arch is half the span. In Roman times, and in the Middle Ages, vaults were built by stacking stones, one on top of the other. The stones were supported by temporary wooden structures, which were removed after the vault was finished.

So to build a 50 ft span, if we assume the vertical walls of the room are 10 feet high before the arch starts (seems kind of low in proportion to the height, but let's just take that as an example), then the high point in the room will be 10+25=35 feet high. In those days, that's the equivalent of a 3-4 story building. So in order to build one 50 ft vault, you would build a 3-4 story building out of wood. You would then stack stone blocks up on top of it. When you put the keystones in, you can then take the 3-4 story building apart.

Adjust to your world's construction methods and economics. Or just ignore it all, like everyone else does!

 

[Kid Charlemagne]

Most D&D maps bear little resemblance to real-life architecture. Rooms in the interior of buildings with no light sources, 200 ft by 200 ft rooms with 10' ceilings and no support columns, and so on. It's so frequently ridiculous that the few maps I see that actually seem realistic stand out as a result.

Agemegos gives great examples of the upper limits of building capabilities. I'd allow dwarves to somewhat exceed the Pantheon's dome, due to superior building techniques, but otherwise I'd think very long and hard before going beyond that.

 

[Gregor]

The dome of the church of Hagia Sophia (now a mosque) in Istanbul (Constantinople) has a diameter of 30 metres (100 feet). (6th Century masonry, still standing.)

Yes, but the dome of the Hagia Sophia also fully collapsed and the structure required the addition of 4 large buttresses in the 9th century. Moreover, evidence has also suggested that the replaced dome has cracked and partially caved in twice since the 9th century renovation. However, for a 6th century structure, a 102 foot dome constructed out of masonry is absolutely stunning.

Cheers,

edit - not to mention that the structure was completed in only 5 years!