On how were span-depth ratios derived.
On how were span-depth ratios derived.
(OP)
My friends
I need a reference text on this subject: How were the popular span-to-depth ratios for steel and reinforced concrete beams derived. I prefer the derivations, not general discussion.
Thanks in advance.
and for making this forum a great place.
ijr
I need a reference text on this subject: How were the popular span-to-depth ratios for steel and reinforced concrete beams derived. I prefer the derivations, not general discussion.
Thanks in advance.
and for making this forum a great place.
ijr






RE: On how were span-depth ratios derived.
RE: On how were span-depth ratios derived.
For concrete - no rules come to mind.
gjc
RE: On how were span-depth ratios derived.
thanks
ijr
RE: On how were span-depth ratios derived.
Good luck!
RE: On how were span-depth ratios derived.
The maximum fiber stress f at d/2 will be f = M.d/2I
so M/I = 2f/d where d is the depth of the beam.
Thus Δ = f.L2/4dE
Setting Δ as L/360 and re-arranging, gives L/d = E/90f
Setting Δ as L/240 gives L/d = E/60f
For a uniformly distributed load, Δ = 5wL4/384EI or 5ML2/48EI and the L/d ratio can be determined for any specified deflection and permissible fiber stress.
BA
RE: On how were span-depth ratios derived.
as a starting point to limit vibrations in floors and Fy/1000 x span for roof members
to limit ponding issues. I think it was in the "blue" steel manual.
RE: On how were span-depth ratios derived.
RE: On how were span-depth ratios derived.
I don't remember that suggestion and I don't agree with it. I do remember "Half the span in feet is the depth in inches." cited by mtu1972 which made sense for the low yield steels of the day. When using higher strength steel efficiently, d should increase and L/d should decrease because E is virtually identical for all steels.
Edit:
Now I agree with it.
Fy is expressed in ksi, so for an A36 beam spanning 28', 36/800 * 28*12 = 15.1".
For Fy = 50 ksi, 50/800 * 28*12 = 21".
AISC was correct.
BA
RE: On how were span-depth ratios derived.
RE: On how were span-depth ratios derived.
Edit: Fy = 36 ksi. Beam depth d = 36/1000 *L = 0.036L or L/27.8
If Fy = 50 ksi, d = 50/1000 * L = 0.05L or L/20
BA
RE: On how were span-depth ratios derived.
From: AISC 7th Edition Manual:
1st to 7th Edition Manual are a free download at AISC for members.
RE: On how were span-depth ratios derived.
Edit: It does make sense. See previous edits.
BA
RE: On how were span-depth ratios derived.
Rules of Thumb for Steel Design
rules based on observation, collected from peers, and derived
RE: On how were span-depth ratios derived.
I skipped quickly through the video but did not find any reference to the problem we are discussing. At 18:50, an approximate weight of beam is calculated by a rule of thumb with a span of 32' and an assumed depth of 18". At 20:00 a similar calculation is made for a 32' span and a 16" depth. No mention is made of how the depth was chosen, but 1/2" per foot of span seems to be the rule used, also a rule which I have used for many years as a preliminary choice of beam depth. If I missed the part of the video you are referencing, please indicate the time on the video where it starts.
I cannot see how any rule of thumb to limit deflection could suggest that L/d should be based on Fy/k where k is a constant. As I showed in an earlier post, the L/d ratio should vary inversely as the stress in the outer fiber. This means it should vary inversely as Fy. Moreover, Fy/k has units of stress whereas L/d is dimensionless, so the whole concept seems invalid.
If anyone thinks otherwise, please show me why you think so.
Edit: Please ignore the text in red and see earlier edits.
BA
RE: On how were span-depth ratios derived.
Bottom line, I think we're over complicating a simple concept with no benefit. For example, BA's derivation above showing L/d = E/90f - using that derivation, I'm starting with a 36" beam for a 20' span. I mean no disrespect to BA - I've been reading his responses to questions for years now and have learned a lot, I have a ton of anonymous internet respect for BA. But I think he missed the mark with this derivation, when as he stated above "1/2" per foot of span seems to be the rule used, also a rule which I have used for many years as a preliminary choice of beam depth". Why make things more complicated than they need to be?
RE: On how were span-depth ratios derived.
E/90f applies to constant moment over the entire span and deflection of L/360. Using f = 20,000 psi, it results in an L/d of 16.1; for a 20' span, d would be 14.9", not 36".
I would think that L/d ratios were derived on the basis of a uniform load with a fiber stress of 20,000 psi which was fairly prevalent at the time the rule of thumb was proposed and a deflection between L/360 (live) and L/240 (dead), say L/300 (combined).
so Δ = 5wL4/384EI or 5ML2/48EI
which is equivalent to 5L2/48E * 2f/d
Equating this to L/300 with E = 29,000,000 psi and f = 20,000 psi gives L/d = 23.2 (close enough to 24)
I don't know, but I am guessing this is where the 1/2" per foot of span came from.
I think I will leave the reinforced concrete beam deflections to others.
BA
RE: On how were span-depth ratios derived.
RE: On how were span-depth ratios derived.
BA
RE: On how were span-depth ratios derived.
Do 4000 beam designs, and keep track of the L/d ratio and types of three or four or five different loading conditions and you will be twice as smart/knowledgeable about that rule of thumb, as you were after you had done 2000 beam designs. Someone didn’t wake up one morning and say, ‘I’m gona formulate a simple rule of thumb, and bang, it happened.
RE: On how were span-depth ratios derived.
Like you observe, I don't think the presentation has anything specific about deflection. I think that it's only a suggestion that the relationship [d=1/2" X L (in feet)] has serviceability baked in. These rules of thumb were also put in a MSC article in 2000: Rules of Thumb
RE: On how were span-depth ratios derived.
BA
RE: On how were span-depth ratios derived.
This excerpt is from Steel Buildings: Analysis and Design By Stanley W. Crawley, Robert M. Dillon:
RE: On how were span-depth ratios derived.
BA
RE: On how were span-depth ratios derived.
The upshot is that rules of thumb can be more complicated than you think. They actually require you to know a little bit about what you are doing in the structural engineering business, or you may not apply them correctly. If we could only come up with one rule of thumb for everything, then we could do away with the guys who make the big bucks and staff all engineering depts. with a bunch of computer monkeys who applied that rule of index finger to everything..
RE: On how were span-depth ratios derived.
You are right and thanks.
But here is the dilemma. It is the experienced engineers, architects, plant planners, planners of bridge layouts etc, who use ROTs regularly. Not the junior guys who are keyboard happy. Those are usually happy showing off the graphics capability of the FE software of their choice or of the great 3D architect software like Revit that has a macro for almost every need. When I go to meetings, I usually joke the senior guys "did you do this yourself?". He/she does not have to reply, because it is the junior one who does all the presentation. A good design is consistent. And consistency has nothing to do with software.
thanks once more and again.