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xaeyruudh
Master of Realmslore
USA
1853 Posts |
 Posted - 13 Apr 2014 : 23:30:16
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This is not directly related to FR, but I've been unsuccessful in googling it so hopefully Sage and Wooly will be patient with the off-topicness.
How do I calculate (or approximate well) how thick a piece of XYZ must be in order to remain intact and support its own weight? I'm willing to eliminate bendy/stretchy elements, because I'm sure they add too many variables.
A weird but no-more-complicated-than-necessary example: a slab of stone laid over a 10 foot square pit. Depends on the type/purity of stone, undoubtedly, but what traits/qualities of the stone would you be looking for in order to figure it out, and what equation would you plug those values into?
Maybe a simpler (?) example would be a pane of glass in a coffee table... assuming no special treatments or compositions to make it more durable, how does the size of the pane determine its minimum thickness?
Thank you for your education and brainpower. My own are insufficient to the task. 
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Edited by - xaeyruudh on 13 Apr 2014 23:31:21
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sleyvas
Skilled Spell Strategist
USA
11700 Posts |
Posted - 13 Apr 2014 : 23:48:56
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| when you look up the hardness in the DMG, what's its score? (sorry, couldn't resist) |
Alavairthae, may your skill prevail
Phillip aka Sleyvas |
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Kentinal
Great Reader
4685 Posts |
Posted - 14 Apr 2014 : 00:07:48
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Oh you want a simple formula I would guess. I am not sure one exists. Paper can be made thick enough to walk on if fastened and supported properly.
Glass also can be walked on. It becomes though not just a matter of thickness it is also proper spacing of supports. The longer the spam between support the thicker a platform needs to be.
A slab of stone likely 6 inches for 10 X 10 depending on quality of stone. Some stone is harder then others. It also matter how much the platform is expected to carry, the weight of a man or weight of 5 men. |
"Small beings can have small wisdom," the dragon said. "And small wise beings are better than small fools. Listen: Wisdom is caring for afterwards."
"Caring for afterwards ...? Ker repeated this without understanding.
"After action, afterwards," the dragon said. "Choose the afterwards first, then the action. Fools choose action first."
"Judgement" copyright 2003 by Elizabeth Moon |
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xaeyruudh
Master of Realmslore
USA
1853 Posts |
Posted - 14 Apr 2014 : 00:34:20
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Well, I can handle a complicated formula as long as I know how/where to find the values to plug in. 
I want to be able to do at least a little better than a one-size-fits-all estimate. To account for the difference between, say, limestone and basalt.
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Edited by - xaeyruudh on 14 Apr 2014 00:34:44 |
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Kentinal
Great Reader
4685 Posts |
Posted - 14 Apr 2014 : 01:52:13
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| I think I would rather invent a formula because of the many variables that are involved and D&D building materials are not the same as real world. Maybe somebody else can come up with something factors one needs to consider include, load, span, how supported (Pillars, two sides like a bridge or 4 sides like a floor tile) material hardness and even flexibility (something too rigid can crack due to vibration something too soft side off supports if too much load on surface). |
"Small beings can have small wisdom," the dragon said. "And small wise beings are better than small fools. Listen: Wisdom is caring for afterwards."
"Caring for afterwards ...? Ker repeated this without understanding.
"After action, afterwards," the dragon said. "Choose the afterwards first, then the action. Fools choose action first."
"Judgement" copyright 2003 by Elizabeth Moon |
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BEAST
Master of Realmslore
USA
1714 Posts |
Posted - 14 Apr 2014 : 03:30:12
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Like Kentinal said, flexibility or bendiness is actually something you shouldn't be too quick to set aside. It's just as important as the hardness of the material.
Think of a sword. If it's hard, you would think that you should be able to smash just about anything, right? But if isn't flexible enough, then when you smash something with it, the sword will absorb a lot of the shock or impact energy, and it'll crack. (My understanding is that that is actually why samurai used to carry so many extra swords into battle.)
Something can be too hard and brittle. You want a bit of flexibility, plasticity, and/or elasticity in it.
But I'm not necessarily saying that your stone block should be a trampoline or anything...
Bouncy, bouncy, basalt!  |
"'You don't know my history,' he said dryly."
--Drizzt Do'Urden (The Pirate King, Part 1: Chapter 2)
<"Comprehensive Chronology of R.A. Salvatore Forgotten Realms Works"> |
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Ayrik
Great Reader
Canada
7970 Posts |
Posted - 14 Apr 2014 : 03:33:19
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D&D is a game, not a simulation.
Pick any reasonable thickness you like, you can even claim it‘s a unique material (being used in a unique environment) which is similar but not-exactly-identical to those used in our real world. A dwarf will likely demand a floor slab be twice as thick, but be able to (reluctantly) make it half as thick. A mage might prefer material which fiddles with gravity or density or bouyancy, and might be very particular about intrinsic material qualities (and their precise dimensions, geometries, or features). A skilled thief can likely fashion flooring which will fail under desired loads or conditions, as needed.
Modern material engineering is a balance of cost vs weight vs strength, plus a few dozen technically specialized properties which common language confusingly generalizes as “strength“, “hardness“, “toughness“, “brittleness“, etc. We custom design exotic materials to meet desired specifications, or we use common materials to meet known specs at lower cost, or we use composite materials (that is, a combination of different materials) to implement design compromises with a blend of the best characteristics each material offers. And we engineer generous safety margins over critical applications. We have no simple formulae to accomodate so many parameters, so we model the performance of our constructs in virtual simulations affected by worst-case-imaginable (within budgetary limits) stresses and failures. And always we build redundancies into large or complex things, so that failures can be circumvented or their impact less catastrophic.
An important consideration you didn‘t mention is how well your material ages. Specifically, how long will it last and meet design specs while exposed to expected conditions before it decays or fails? Marble slabs might last a hundred centuries, or they might suck up moisture and form spongy cracks or chips within three seasons. |
[/Ayrik] |
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Wooly Rupert
Master of Mischief
USA
36779 Posts |
Posted - 14 Apr 2014 : 04:35:55
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| It's not really something addressed by D&D, because you could fill an entire rulebook with different thicknesses for different materials, and another with the necessary physics to work it all out. The factors that Kentinal mentioned are all quite relevant, as is the distribution of any weight on the material. |
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xaeyruudh
Master of Realmslore
USA
1853 Posts |
Posted - 14 Apr 2014 : 05:22:06
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Ayrik, based on that metamagic rod thread from way back, I thought I could rely on you to go along on my ride into mathland. What is this "D&D is a game, not a simulation" madness? 
On a more serious note, thank you all for the input and the additional things to consider. I will come up with something and be happy(ish) with it. |
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Kentinal
Great Reader
4685 Posts |
Posted - 14 Apr 2014 : 05:56:39
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Well I offer idea of hit points to be used to calculate span how think an item needs to be unsupported. A two inch thick plank of wood can safely span 10 feet and has 20 hit points undamaged [1]. You could try to use this as a base line for all materials. Basic concepts you would need if span increases 10 percent the thickness needs to increase 20 percent the longer the span the thicker the material needs to be to hold up its own weight. For lessor spans it gets a little harder maybe 10 percent less span 5 percent less thickness. I have not run it though computer number crunching so percentages might need to be adjusted, however I can assure you the longer unsupported the thicker it needs to be, fully support it requires some thickness though not much.
Many later I will play with the numbers and percentages to see how believable they are.
[1] According to SRD 3.5, clearly can use other hit point system. |
"Small beings can have small wisdom," the dragon said. "And small wise beings are better than small fools. Listen: Wisdom is caring for afterwards."
"Caring for afterwards ...? Ker repeated this without understanding.
"After action, afterwards," the dragon said. "Choose the afterwards first, then the action. Fools choose action first."
"Judgement" copyright 2003 by Elizabeth Moon |
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Kyrel
Learned Scribe
151 Posts |
Posted - 14 Apr 2014 : 10:21:52
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Xaeyruudh. Try and have a look at this: http://webpages.sdsmt.edu/~lstetler/merlot/rock_mechanics.htm
Personally I'd just wing it, or try and work out something with a foundation in the Hardness of the material in question, and possibly the HP as well (and then applying some common sense to round it off). |
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Mapolq
Senior Scribe
Brazil
466 Posts |
Posted - 14 Apr 2014 : 16:37:20
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I'm a physicist, but you've got sound advice from people who work in materials engineering, which is better than I can give you in this topic. But if you still do want an equation, what I suggest is something like Kentinal's last idea. Try to get some general data on the materials you're interested in regarding the properties you feel are important. Then put the data in a curve, say thickness versus strongstuffiness (it's pretty arbitrary, really) for a particular geometry and material, and fit a function to it. It isn't something that would be done in the real world, but probably the best approximation you can get for a game without doing a course in Materials Engineering yourself to figure it all out.
Not sure how you could actually find data on that, though.  |
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xaeyruudh
Master of Realmslore
USA
1853 Posts |
Posted - 14 Apr 2014 : 19:31:10
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Yea, I'm not finding any data. I'm not having any luck googling things like elasticity or plasticity or 'at what point does XYZ break/shatter' but this link that Kyrel posted has some reading material.
I realize that nobody else cares about putting this level of detail into the game in this particular area. Most folks either don't like math that much, or if you do math all day for school/work you probably want to leave it out of your recreation. I'm in a weird middle ground where I like math and don't really ever use it so figuring out the dimensions and weights of stuff in-game is fun.
But I can recognize that really doing it right is deeper than I'm going to be able to go. |
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Ashe Ravenheart
Great Reader
USA
3240 Posts |
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Kentinal
Great Reader
4685 Posts |
Posted - 14 Apr 2014 : 20:22:05
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quote:
Originally posted by Ashe Ravenheart
Might this help? Beams Support
Alas that is of little use, it only calculates the support beans, not the floor itself. |
"Small beings can have small wisdom," the dragon said. "And small wise beings are better than small fools. Listen: Wisdom is caring for afterwards."
"Caring for afterwards ...? Ker repeated this without understanding.
"After action, afterwards," the dragon said. "Choose the afterwards first, then the action. Fools choose action first."
"Judgement" copyright 2003 by Elizabeth Moon |
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Mapolq
Senior Scribe
Brazil
466 Posts |
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Calling math/physics afficionados
