Deflection concepts and related info

Started by Reninco, March 05, 2021, 04:36:26 PM

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In building a structure, we want it to be strong enough and stiff enough to resist all expected forces.
Since most building material has the capacity to flex before it breaks one must consider how to control that flexibility or deflection...the primary examination for most buildings is for deflection.

A quote from forum contributor Don_P on two key items of structural concern.
QuoteStrength is a life safety issue, it is a "must".
Deflection is a serviceability issue, it is a "may". Things like cracked drywall, opening trim, planes out of plumb, excess vibration (may occur). These are qualitative things rather than safety issues... (but are still important and need to be considered)
Deflection Concepts
Deflection: is the bending from the original position of an element when a load is applied.

Typical Elements of residential construction: Beams, joists, rafters and studs.
Loads can be: from its own weight but usually it is referenced as the added load.
Typical added loads: Snow, wind, people, or stuff like cows and waterbeds.
Deflection is determined by many items, key items are how load is distributed or applied to the beam or element.
Point Load

Uniform Loading

Progressive Load

Deflection will also be influenced on how the beam is supported.
This shows the beam is able to pivot across the end supports
Beam simple cow

This shows the beam is fixed by a bolted plate and not able to pivot across the end supports – it has slightly less deflection
Beam fixed ends cow

A cantilevered beam with a point load

A cantilevered beam with a progressive load, in this case the designer puts the lighter cows the furthest from the end connection...perhaps anticipating a higher stress at the connection; the designer also increased the connection plate size.

There can be many combinations of end supports, each affecting deflection; this shows a fixed and a pivot.

Deflection will also be influenced by:
     The material of the beam such as wood or steel
     The shape of the beam such as square, rectangle or I shapes
     The size of the beam - most consideration is given towards the depth (tallness) of the beam
Loads can act in any direction, for instance wind can push horizontally on a wall or upward on a roof truss or even by suction.
The deflection concept is quite old with documented concepts and pictures from DaVinci with improved concepts by Galileo as shown in his classic picture.

The more correct mathematical formula was created in the 1750s and is still used today.
Engineers by their focus of education are associated with mathematically solving beam deflection. Some builders by their focus of experience are also associated with solving beam deflection. Most oversight jurisdictions allow a "non-engineer" to calculate beams or other load bearing assemblies if the structure is under a certain size.
Before you decide about one person or another... it has been my experience that both have also made some tremendous blunders.
The picture below is not from a third world country and it was designed by "engineers".

This one was produced by builders...perhaps for their own use.

Experience would be the deciding factor in selection of either trade.
How much is too much for beam deflection – wind on a bridge will create deflection...this seems quite large.

Rather than referencing a certain distance of deflection... a ratio of calculated deflection and span length is commonly used as a reference. Written a number of ways: D/L, D over L, D:L, Dead Load/Span Length (DL/L), Live Load (LL/L), Total Load (TL/L), or Delta D
For residential houses one of the key points (see opening paragraph) is to avoid cracking by reducing deflection. Items of concern are brittle finishes such as drywall joint compound, plaster, grout and masonry. Glass is another obvious item I'll mention later. Many tests have been done in an attempt establish a standard ratio but since most structures are from many "assemblies" we assign different ratios to different assemblies. Restating: this ratio is the deflection from load in relation to the span distance. The chart below (from typical building codes) gives minimum ratios per type of assembly. I'll discuss missing reference notes in a later post. 

As an example a hypothetical floor with:
a span of 360 inches max deflection is 1 inch
or 180 inch span max deflection is ½ inch
or a 90 inch span max deflection is ¼ inch
or a 45 inch span max deflection is 1/8 inch
More information in my next post...


The idea of a best "reference" deflection ratio goes back to the early 1800's with the ratio suggested around 1/400 with references of higher ratios that should be used for brittle finishes.
For residential style of framing the ratio's mentioned in the 1930's are around 1/360 with no assembly singled out as weaker or stronger. As more houses were built and assemblies became somewhat standardized the lower deflection values were adopted...and I got a hunch cost considerations also played a big part.
Bridge designers have ratios between 1/600 to 1/1200 depending on material used, span length, wind and road loads - easily over 1 mil lbs in some form of unique loads.
Residential and commercial codes have taken the variables mentioned (the ingredients) above and produced cookbooks (a prescriptive path or recipe with predicted results) for span tables for floor girders, joists, rafters and studs. The table below (a recent code book value) for floor joists gives all the pertinent information. 1/360 deflection ratio is for all the spans of all the grades and species at common spacings. Actually by using these you get a slightly longer span due to "load sharing" from adjacent spans than from individually calculating a single joist deflection (see adjustments para below). Notice with different dead loads equate to different span capabilities. It also worth a reminder these are maximum spans or deflection limits.

Rafters have a greater allowed deflection, much of this based on a better chance of seeing or getting a even applied load from snowfall or from someone adjusting a TV antenna. - Shown is the 1:240 chart for rafters with attached ceilings. Again a reminder, those are maximum spans.

Notice DF #2 2x10 can go to 25'-8". I can assure you a #2 26' 2x10 will droop even without an applied load even if it's crowned the correct way. Perhaps it might work if it was stickered and allowed to dry for a number of months. Probably doesn't really matter as I haven't seen a 26 foot dimensional at the lumber yard in a long long time...the last I remember was split for most of its length.
Rafters with no attached ceiling at 1:180 allowable deflection

The charts shown above are abbreviated for forum style topics, they actually consist of many many pages of specifications, links for code book charts have been given in many topics here.
When using code prescribed tables or cookbooks it's important to consider the footnote section of tables. They use the term "adjustments" and "other loads" quite often.
Here is a short list...humorous sarcasm intended.   
Attic, living, office, storage, slope, wall ht, tie or no tie, seismic A or B or C, rain on snow load, crush load, impact load, 7-day load, snowload, vehicle load, vehicle point load, townhouse, residential, commercial, commercial warehouse, agricultural, secondary supported, wind, uniform, point, cantilever, sunroom, patio, window glass frame steel, window glass frame aluminum, window glass frame titanium...and references to code sections that seem to not exist.
Many masonry products recommend 1:700 ratio, my tile guy response is you can never get it stiff enough...and I don't think this is a euphemism for anything other than floor or wall deflection.
Truss Plate Institute (TPI) has a maximum horizontal deflection of 1 1/4" for scissor trusses but in dead load they are allowed to flex more than that...I am assuming they are assuming the dead load will be "built-in" into the structure. But there are a couple of ass's in that last sentence so one should be careful with all the assuming.
I personally have seen two fifty year snow events deflect long span common trusses bottom cords more than 6" which was good considering they could have failed as other nearby trusses did. Repeating the first line of this (most) wood frame houses deflection controls sizes but consideration is still given to strength.
Manufactured Joist Deflection
Weyerhaeuser's solid wood truss (TJI) deflection chart for 360 – 480 spans. Also plenty of footnotes for their product. TJI uses the same deflection formulas mentioned from the 1750s.

TJI Rafter deflection with deflection values circled; one footnote not shown: ...for stiffer deflection criteria use higher live load values or use load condition software for more direct sizing.

One more post of information and some preferences...


Consideration and Preferences
1. What the assembly does and how it will perform over time with different loading conditions that may be applied.
2. Avoid assemblies near others with huge deflection ratio differences
3. If using a drywall finish, I span over large unavoidable deflection differences with an explanation for the reasoning given to the drywall hanger guy.
4. Address problem areas: solid brick chimney or interior column, large hidden post to header loads, ceiling spans where a supporting wall shortens the span, double loads from snow.

5. Is vibration control is needed?
6. Is cost a consideration?
7. Compare to past assemblies that performed as expected
Calculate all common ratio reference values.
Check the calculation for strength issues.
I use to do this by hand then the burden of all math busy work was solved with the wonder of excel – many of these apps have been posted in the forums and most are quite good.
Here is a portion of my beam calc sheet with reference notes for each deflection ratio. All the numbers get spit out then I also have my sheet calculate a 1" deflection then gives the ratio just as a comparison... in this example you can see the span is 160" (1" deflection in 160" span is 1/160).
Notice there is very little difference in deflection between 1/520 and 1/720 ratios...If I were doing tile I would not go above 1/520 in this case as very little is gained if anything.
The beam strength factor or service factor or safety factor or shear limit or ignorance factor is +19%. I already have "fudge" built into my loads so I am comfortable with anything above 110%.

I hope these posts help clarify the term deflection that is often mentioned in these forums, please feel free to ask a question or comment.

For the more studious types I have purposely omitted actual loading and terms like section modulus, Load and Resistance Factor Design (LRFD) and Allowable Strength Design (ASD) in an attempt to make the topic more digestible to the bulk of the forum readers.


This chart is from old school span tables but is still relevant today. I added color changes at key points to make it easier to read in this style of forum discussion.
I have picked a dimensional shape used in typical framing that can be found in any lumber yard. I am omitting the size and strength value as this is just an example so readers can easily see the changes in deflection and service factors with span change.
I started with a seven foot span (84") with a uniform load of 700 lbs.
Each row is 6 inches longer and 50 lbs heavier... which is realistic loading for floor and some roof framing members.
SF is the service factor or safety factor.
Ratio is the length compared to actual deflection.
As a reminder the formula takes many variables into consideration to establish deflection and shear limits – deflection and service factors are not simple additive results etc.


Kinda interesting stuff.  I was worried that the roof on our cabins woodshed might not take the snowload.  2x4spanning 8' that's basically flat.  3-1/2" slope in 8'. 2x4 on edge. 24" on center as I was short on lumber.  It's remote so no lumber yards.  I want to add more 2xs to make it 1' on center for roof. 
    The snow gets kinda deep.  There was 6' deep snow on the ground.  There's no real foundation. I cut some 6" thick wafers from some old utility poles that set on the mostly spagna moss n tree roots. Been there a few years now . Here's a summer picture for reference.  I'll get some snow pics.


I like to use the AWC span calculator, found here
That is the Maximum Span version. There is also a Span Options version that can help a lot too for comparing.
There should be a link on that page to D/L an android or apple app. As long as you have internet it works anywhere. Handy.
Just because something has been done and has not failed, doesn't mean it is good design.


Quote from: Blessed on April 11, 2021, 01:42:09 PM
Kinda interesting stuff.  I was worried that the roof on our cabins woodshed might not take the snowload.  2x4spanning 8' that's basically flat.  3-1/2" slope in 8'. 2x4 on edge. 24" on center as I was short on lumber.  It's remote so no lumber yards.  I want to add more 2xs to make it 1' on center for roof. 
    The snow gets kinda deep.  There was 6' deep snow on the ground.  There's no real foundation. I cut some 6" thick wafers from some old utility poles that set on the mostly spagna moss n tree roots. Been there a few years now . Here's a summer picture for reference.  I'll get some snow pics.

Using the calculator MtnDon posted and a snow load of 60 lbs, #2 HemFir 2x4 rafters can span 7' 6" with a 12" spacing.  On a 24" spacing the resulting allowable span is just 5' 5".  Granted, it's just a woodshed, but I would put in those additional rafters.
My cabin build thread: Alaskan remote 16x28 1.5 story