Tuesday, October 13, 2009

Bracing Situation III: Tension Design Shortcomings

When I left off the the previous post in this series, it was with the note that, while wood is strongest in tension parallel to grain, what holds for wood as a material quality does not always translate into something useful when it comes to building structures with wood. The reason I say that is because it is generally not possible to connect wood pieces together so as to take any real advantage of the strength wood has in tension parallel to grain. How so?

When joining pieces of wood together, especially when it comes to outdoor structures exposed to regular trashings from the sun and rain, freezing and thawing, etc., the choices come down to all-wood connections, such as mortise and tenon, bridle joints, scarf joints, etc, and simpler, usually cheaper connections which are reinforced with metal fasteners, be they nails, screws, threaded rods, metal straps or brackets.

In the simplest form, the pieces of wood to be connected are left intact at the joined locations, and are bolted, screwed and/or nailed together side by side. This was the case with the down brace depicted in the previous post. With a fastener passing crosswise through the sticks of wood, though tension or compression is indeed resisted by the piece generally as loads are applied, at the connection zones the mode of loading changes - from tension parallel to grain, it becomes shear parallel to grain. This is clearly illustrated in Hoadley's fine book "Understanding Wood" (pg. 119):


The load that precipitates shear on the piece may be a pushing or pulling one along the longitudinal axis of the stick - shear parallel to grain is shear, regardless of push or pull. Here's an example of a covered bridge post that has failed in shear parallel to grain:


Notice how the brace has pushed up and sheared off a section of the post.

So, how do shear parallel to grain strength values compare to tension parallel to grain values? I'll post the chart from yesterday again - click on it to enlarge if you find yourself squinting:


It is readily apparent that shear parallel to grain values are significantly lower than the values for tension - or compression - parallel to grain. Though tension parallel to grain values are double (or more) those for compression parallel to grain, the compression parallel to grain strength is still some 5 times greater (on average, dependent upon species and moisture content) than shear parallel to grain. Clearly, the limiting factor for tension connections is the shear parallel to grain strength of the material.

Here's another telling drawing from Understanding Wood, showing the ASTM testing procedure for tension parallel to grain:


The notable thing is the despite only testing the midsection of the piece of wood, a mere 3/8" x 3/16" in cross section, the ends of the piece have to be enlarged considerably - to a 1" x 1" section- so as to preclude shear parallel to grain problems from affecting the test. The ramification of the above fact is that when a structural member is designed to be large enough so that its attachment fastenings can safely transmit the required loads, the cross section of the piece turns out to be far greater than needed along its entire length to carry tensile loads. Put another way, if the piece of wood to be placed in tension is not sized up to compensate for the weakness of the material in shear parallel to grain, the connection will invariably be prone to failure. if the piece of wood is up-sized to compensate, you are adding unnecessary weight to the structure, further exacerbating the loading problem at the joints.

Wood structures do not often fail from tension loads, but it does happen, as in this example from a warehouse truss lower chord failure:


Here's another example, again from a bottom chord, this time in a covered bridge:


Both above-pictured failures of timber in tension seem to associate to the presence of bolts passing through the member, thus decreasing the amount of fiber in that area. It's hard to comment from those pictures as to the mechanism of failure.

Compounding the problem in outdoor structures employing metal fasteners is that temperature variations between night and day are considerable at most times of the year, and thus dew forms. The dew point for metal, fine conductor that it is, is much lower than that of wood, so moisture condenses around metal fasteners more readily than it does on wood. Moisture around metal then is in direct contact with the surrounding wood, which gets moist, and thus rot tends to precipitate at such locations. Look at any old nailed fence and you will see the points of failure and greatest degrade are invariably at the fastener locations. The same goes for a down-braced gate - the lower end of the brace in particular also suffers from being closer to the ground, thus tending to pick up soil bacteria from rain splash which further accelerates the rot out. Topping that all off is the fact that moisture cycling and transfer in a piece of wood is most manifest at the ends (end grain) of the stick, and thus the degrade in a stick exposed to moisture cycling tends to also be most pronounced at the ends, where the rot-inducing metal fasteners are often located.

Further compounding the problem is that when wood is at a higher moisture content, as it would be at the humid times of the year, it will be weaker in strength. And finally, wood might resist a certain shear load if it is but intermittent or temporary, but with a braced gate, the loads on the parts from gravity are continuous. As Hoadley puts it, in a description of static bending strength (this also applies to other forms of wood strength like shear parallel to grain, etc.),

"...wood loaded to failure [within] one second (rather than the standard 5- to 10-minute duration)...would show about 25% higher strength. If held under sustained load for 10 years, it would show only 60% of the static bending strength. To put it another way, if a beam must support a load for 10 years, it can carry only 60% as much load as it carries in the static bending test. This reveals that in addition to the immediate elastic response which is apparent upon loading, there is an additional time-dependent deformation called creep."

If one moves away from metal fastenings at the connection points, and opts for all wood joinery, some problems remain. While the durability is likely improved, the connection of one piece of wood to another with joinery, be it a mortise and tenon, bridle joint or half lap, involves a reduction in the size of the piece at the connection. The piece is only as strong as its smallest section.

In a full depth half lap joint for example the maximum amount of wood that could remain after cut out is 50% for each half of the joint. Then, say, if that half-lap were pegged, the actual mechanical strength if the joint is going to be reduced to the pegs and their mortises for the most part, and the remaining wood will be under 50% of total cross section per side:


Now, given the mechanism of loading in this connection is again shear parallel to grain, a peg could be more or less substituted for the bolt in the first drawing in terms of its mechanical performance in the receiving stick (albeit, a peg is not nearly as stiff as a bolt). A mortise and tenon joint, of typical proportions would leave a tenon at 1/3 the thickness of the receiving piece, and then there is the peg, which again brings us to a shear parallel to grain issue. The above picture depicts a longitudinal connection or splice; in a down-braced gate, the brace might suffer from the same shear, while the receiving pieces for the lap, the stile and/or lower rail, would be loaded more or less somewhere between tension perpendicular to grain, and shear parallel to grain - and the strength values for tension perpendicular to grain are even poorer than for shear parallel to grain in most (if not all) species.

In fact, when it comes to designing pegged wood connections, the timber framing practice is now to follow the established engineering standards for bolted timber connections: compression joints require a minimum 3x peg diameter measured in length of material which remains in the tenon beyond the peg - the relais, or 'relish' as it is termed. For tension joints however, 7x peg diameter is the minimum. All things being equal, a tenoned tension connection is more more than twice as weak a connection than one in in compression, and must be compensated for by more than doubling the relish in the tenon if the tension joint is to perform adequately.

Let's look at a simple diagram depicting the loading issues with a down-braced gate:


This illustration is from Newlands "The Carpenters Assistant", p. 176. In the drawing above, 'a' is the stile from which the gate hangs, 'b' is the lower rail, and 'c' the down brace. The circle marked 'W' indicates the loading the gate experiences. With this loading, it is obvious that component 'c', the down brace is in the role of a tie, while 'b' is in the role of a strut. Further, the connections where the brace joins the hanging stile, 'a' and where it joints the lower rail 'b' will both be tension connections. Only the joint between the hanging stile and the rail will be a compression connection.

As Newlands succinctly puts it,

"...if timber be used for the brace 'c', it is evident that the strength of the brace has very little to do with the stability of the framing; that, in point of fact, the stability is due entirely to the strength of the nails, or to the slight resistance to tearing that the fibers of the timber between where the nails are driven and the end of the brace offer; or it must be insured by adding and iron strap to each end of the brace. But this extra iron is expensive...".

Not only were blacksmith-produced iron straps more expensive, the same premature rot issues detailed above in this post would associate to such construction, and more so on the lower end of the gate nearer the soil. The 'slight resistance to tearing' that Newlands mentions is of course shear parallel to grain.

In the final post in this thread, I'll take a look at why an up-braced solution to supporting a hinged gate or door is best, more so even than 'X-braced', and show what good construction detailing for such a gate or door might comprise.

Thanks for swinging by today. Please close the gate behind you when you leave :^)

Go to part IV (<-- a link)

4 comments:

  1. You picked a perfect time for this series as I've got to build a gate to go with the arbour I'm finishing off.

    The gate was designed with a up brace before I read this so I'm glad to see it appears to be the best way.

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  2. Hi Chris,
    Very enlightening. My vote on the brace poll (based solely on my thinking how things work) was the down brace. Because I figured if you were going to load up a right angled joint, best to do it where off angled loads are relieved and not add unnecessary weigh. So the down brace , if properly constructed should suffice. But, I've been wrong before...
    Steve

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  3. Hi Chris. You have an excellent blog, pictures, and topics. I found Bracing Situation after viewing Disney's Snow white And The Seven Dwarfs (1937), noticed that the door of their mine has a "down" brace. I think the reason we see so many of these errors is that we all experience episodes or periods of inattention when we don't notice the difference until it is too late. There is a minor typo 60% down the page "...component 'b', the down brace is in the role of a tie, while 'b' is in the role of a strut." The first 'b' should be 'c'. The superiority of the "up" brace also applies to construction in materials other than wood. Any fastener, whether screw, bolt, rivet, nail, or adhesive, will weaken with time and load, and the "up" brace has the best chance of distributing some load to an adjacent joint(s) before permitting the gate or door to sag.

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  4. Hi Darrylh,

    thanks so much for pointing out that typo! I have duly made a correction.

    ~Chris

    ReplyDelete

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