White Paper: Mechanically Laminated Beams

Click on the figures to enlarge and view captions.


Figure 1

For many hundreds of years, builders have found needs and applications for timbers bigger than any that they could readily and within the trees from local forests. An obvious solution lies in bundling smaller timbers to make larger ones (Fig. 1). This can work well, and even ease installation, but it's not as structurally efficient as using solid sections of the same size. Builders, even early ones, recognized the value of generating some composite action between components of a bundle, with attendant gains in load capacity, reduced member sizes, or both. Modern glue technologies can yield composite action at least on a par with Mother Nature's. Before we had reliable glues, however, we relied on mechanical connections to induce composite action.

Builders have applied a lot of ingenuity and effort in developing composite action among grouped timbers. The literature contains many examples of mechanically laminated beams, some nearly breathtaking in their elegance, others in their costliness. Innately, none of them can offer the same degree of composite action as solid or glue-laminated timbers. Even given modern forests of smaller trees and modern gluing techniques, however, there are still some undeniable reasons to mechanically laminate smaller timbers into bigger ones. Most concern aesthetic impacts in our exposed and celebrated timber structures. Some building owners simply have trouble with the "stripiness" and the industrial appearance of modern Glulams, while very deep natural solid beams such as 8x16s can distort unattractively during seasoning.

Building realities can also make mechanical lamination a tempting option even for contemporary builders interested in replacing large timbers that are still available as solid sawn timbers. With the ability to assemble larger beams from an assortment of smaller ones, shops can maintain smaller inventories. Those inventories can also be used more fully, because keyed beams hide a couple of faces, providing a good place to put larger knots where they are subjected to minimal bending stresses and where they might conceivably contribute to local shear force resistance, to good effect.

Figure 2 Design, Analysis, Detailing. Keys in mechanically laminated beams resist interlayer slip between the individual laminate of the beam, thereby inducing composite action. While simply sprinkling a lot of keys along the beam can be effective, actually understanding the micro issues of the individual keys, and the macro issues of the assembled beam and its overall role in the structure, quickly becomes involved.

Specific design concerns with keys include their proportions, slope, grain orientation, shape and material. Most wooden shear keys are rectangular solids, about three to four times longer than they are deep, and their grain can be oriented to run with or across the grain of the beam (Fig. 2). The basic design option is whether to slope the keys with respect to the surface of the beam or to set them level. Sloped keys are loaded in pure compression and are not subject to shear forces. (They also resist interlayer slip in only one direction.) Unsloped or level keys resist slip by transferring bearing forces from one beam layer at one notch edge to the other beam layer at the distant notch edge. This eccentric load path crushes one half of each notch face and induces internal shear stress in the key as the force is shifted from one side of the key to the other.

A second option is whether to orient the grain of the key parallel or perpendicular to the grain of the beam. Keys whose grain runs with the beam's can fail in crushing at the bearing surfaces and in shear parallel to the grain. If such keys are sloped, they present a more complex shear transfer path and are far less likely to fail in shear. Keys whose grain runs across the grain of the beam can fail in compression perpendicular to the grain, and in what we might call "rolling shear" across the fibers, rather than shear parallel to the grain as in a level key oriented with the grain.

Keys oriented with their grain parallel to the beams must be cut from wider stock. They are more fragile than one might imagine; typically they are made of manufactured or glued-up stock. Nor is end-grain-to-end-grain bearing as stiff as designers might think (the National Design Standard even prohibits designing past 75 percent of allowable compressive capacity in some cases): the sawn ends of cellulose cells cut into one another.

A third option is the shape of the key. For many reasons, from allowing pre-loading to relaxed fabrication tolerances, wedge-shaped keys are handy for designers and builders alike. The keys can be single wedges, fitted to commensurately tapered notches, or matched pairs (folding wedges) used between parallel bearing faces.

Keys have been made from many materials, but a classic protocol is to use hardwood keys in softwood beams and cast-iron keys in hardwood beams. Hardwood keys are almost always installed such that they are compressed perpendicular to the grain. This side-grain bearing governs the crushing capacity over the end-grain bearing of softwood beams (for most combinations of wood species), but this can actually be a desirable feature if wedged shear keys are used. This discrepancy in bearing capacities at the contact faces makes it easier to induce fairly uniform compression in the keys during fabrication. We have used modern engineered wood products like Parallam as keys, for increased bearing and shear capacity and handier sizing. To avoid losing composite action as unseasoned keys shrink, large keyed beams require gluing up dry stock for their commensurately large keys.

Figure 3 Shear keys resist slipping between the two laminae into which the keys are fitted. Whether sloped or level, keys transfer forces on an innately eccentric load path--one that tends to pry the two laminae apart. All keys, including level keys, "want to roll," and this tendency must be prevented (Fig. 3).

The two common ways to prevent laminate from separating because of key prying are by internal fasteners or external clamping straps. Both methods involve fabrication, performance and aesthetic considerations.

In addition to the micro design issues involved with the keys themselves, we also need to look at their macro positioning within the beam. In practice, these micro-macro distinctions are handled not separately but holistically. For any combination of key dimensions and beam and key material, there is a minimum key spacing that ought to be held. If the keys are too close to one another, the interkey chunks of the beam will simply shear off. Once this minimum spacing is met, however, the designer is left with several considerations. Shear keys are eponymous, in that they ought to be located where the laminated beam is resisting shear forces. In practice, this means the keys are generally more effective when located near the beam supports. In uniformly loaded applications (with the resulting linearly variable shear force along the beam), the key spacing can gradually increase toward midspan, which is a nice way to visibly reflect the variable shear action in the finished beam (Fig. 4).

Figure 4 Point loading, on the other hand, makes for zones with uniform shear forces to resist, and evenly spaced keys can reflect this.

We have already mentioned the iterative nature of key detailing; a first stab at a key dimension can well prove to require an unworkably large minimum spacing. More, and smaller, keys can often generate more composite action than a few heavy ones.

A holistic and even more esoteric process is also required when analyzing a structure with any composite members. The range of shear key effectiveness in generating composite action is none through total, and neither limit is actually achievable. For example, keying two 8x8s together will result in a beam that is somewhere between a 16x8 (no composite action) and an 8x16 (full composite action). When combining two square timbers, generating full composite action makes the resultant beam twice as strong and four times as stiff when compared with two timbers that can slide freely by one another. In a simple application, this means that a fully composite beam can carry twice as much load before breaking and will detect a quarter as much. Some historic papers on the topic claim simple keyed beam efficiencies in the 50 percent to 80 percent range. In more complex, "redundant" structures--ones with multiple load paths--the load share carried by any path is a function of its relative stiffness. This means that the thorough analyst needs to establish the degree of composite action, model that in the structure, and then assess whether that amount of keying makes the beam strong enough to resist the attracted load. It might even happen that an overloaded keyed beam could be rendered acceptable by reducing the keying specifications. It is also possible that a temporarily overloaded keyed beam might be resuscitated by simply jacking it and replacing the crushed or sheared keys.

Fabrication Realities. The issues confronted in fabricating a key-laminated beam are rich in aesthetic, economic and structural questions. Many timber framers have a straightforward definition of craftsmanship: minimal gaps, at least initially. This protocol, though, can make for problems when fitting shear keys. Getting a single level key to fit "snugly" against four separate potential bearing faces cut in two large timbers can be a frustrating exercise. Getting all the keys along a beam to fit at the same time can be downright maddening, expensive and unlikely.

Figure 5 The two most direct ways to simplify the fitting process are to use wedged keys and to introduce deliberate initial gaps. Wedged keys can be singular, fitting between non-parallel bearing faces, or paired (folded), bearing on parallel faces. Wedges allow for "tuning" the keys, or equalizing the initial compression they feel, through balanced tapping installation. The composite action we are trying to induce can be very sensitive to the key stiffness, both initially and as loading is applied. A very small amount of initial "gap take up" when the assembled beam is loaded can translate into significant losses in both stiffness and strength. The four potential bearing faces yield four combinations of two faces that bear initially, and only one of those combinations is the one sought. When the fabricator tries to make all four potential bearing faces snug, it is nearly inevitable that one of the pairs of opposing bearing faces will tighten first, and that many of them will be in the wrong direction, resisting interlayer slip in the direction opposite the one that will occur with loading. It's much more effective to use (and far easier to produce) wedged shear keys that fit into dados over cut so that the intended bearing faces always bear first during fit-up (Fig. 5).

Figure 6 An advantage of sloped keys is that they need not have deliberately gapped housings, since they bear on only two faces (see Fig. 2). The disadvantage, though, is that sloped keys resist slip in only one direction. Though improbable, if by chance unsloped keys can be installed to work in both directions, they may yield a beam that can generate at least some composite action even under reversed loading. For most beams, this reversibility is not any special advantage--gravity loads generally act in only one direction and sloped keys can point up, toward midspan. Lateral loads, on the other hand, can and do reverse direction, and with equal magnitude.

To the extent that posts and beams (and knee braces) are involved in resisting these lateral loads, keyed versions would be much more effective (Fig. 6). Knee braces can introduce interesting interactions among posts and beams, even as they resist simpler gravity loading. A very stiff and long knee brace, for instance, could reverse the shear in the beam between the brace mortise and the post. Again, load paths are redundant and carry load in proportion to their relative stiffness; a very limber post makes for an anemic knee brace and a braced beam that can act as though it were just simply supported.

Before leaving the nitty-gritty of fabrication, we note certain possibilities of detailing. Wedged keys, for example, allow a fabricator to camber the beams. Simply driving the wedges in harder can do it, with limber enough timbers and low enough taper angles. Alternatively, timbers can be bent before or as wedges are installed. While this technique can be a potent way to fight off sag under live loading, it usually makes initial key installation much trickier.

Figure 7 Especially deep beams can be assembled from more than two members, from non-square members and even from differently sized members. Each of these introduces complexities and opportunities. Tall stacks of timbers, for instance, get involved because of the varying bending and shear stresses, up and down, within any given cross section. The closer they are to the neutral axis of the assembled beam, where the shear stresses in the assembled cross section are larger, the bigger the shear keys need to be. Meanwhile, the designer would prefer smaller keys and notches the closer they are to the top and bottom of the assembled beam, where the bending stresses are greatest.

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Finally, it can be tempting to use heavy springs under the heads of through bolts used as clamps, in an effort to maintain prying resistance even as the timbers shrink (Fig. 7).

Historic Examples. Keyed beams have a long and varied history. Cases of keyed beam usage have been documented over the last 300 years in Europe, many in bridges (Fig. 8).

Jacob Leupold (1674-1727), the versatile German mechanic and instrument maker, in 1726 depicted early instances of keyed beams used for their composite behavior (Fig. 9).

Nearly a hundred years later, Thomas Tredgold (1788-1829), a British railway engineer and one of the founders of modern civil engineering, described built-up and key-laminated beams in some detail in his Elementary Principles of Carpentry (1820). Tredgold advocated for a tapered top on the upper layer of the keyed beams, such that metal bands could be used for clamping and, while he did acknowledge keys could be used to generate composite action, he also recommended a joggled beam that used a cast-iron wedge to forcefully mate the bearing faces before putting the beam in service and iron straps to keep the laminate together (Fig. 10).

The idea of a joggled beam was nothing new, but Tredgold's recommendation was unequivocally bad by any standard. The strength of a beam is a function of its depth squared; joggling a beam to produce interaction reduces the effective depth and thus the beam's efficiency. Belief in one's ability to match all the bearing faces of a joggled beam seems quite optimistic, and any benetfit a cast-iron key would provide in forcefully mating all the bearing faces would prestress (and probably overload) the bottom layer in tension before any actual load were applied--and that's assuming we ignore the bolt-hole drilled right through the point of maximum bending stress.

Nearly 70 years after Tredgold's work, Edgar Kidwell, an American engineer familiar with copper mining in Michigan and a professor at the newly formed Michigan College of Mines, performed full-scale tests on a large variety of built-up beam configurations, publishing the results as "The Efficiency of Built-up Wooden Beams" in an 1897 publication of the American Institute of Mining Engineers  (Fig. 11).

Kidwell's testing was extremely thorough, and his main findings about key clamping, orientation and the like were essentially the same as those we arrived at independently. (Kidwell also unabashedly and succinctly debunked Tredgold's earlier recommendations.)

At the same time Kidwell was using keyed beams for mining timbers, railroad engineers were using keyed beams for bridge girders and roof structures. As railroaders were already keen to use metal, cast-iron keys were commonly employed, to the point that certain cast-iron keys were commercially available to anyone for use in built-up beams. Such keys can still be clearly seen in a railroad service building in West Lebanon, New Hampshire (Fig. 12).

Shortly after the turn of the 20th century, mechanically laminated timber beams diminished rapidly in use because of a shortage of materials as well as the advent of structural steel and reinforced concrete. Their use has been revived when warranted by their aesthetic appeal.

Contemporary Examples. For examples of large keyed beams such as appear in Fig. 1, it's hard to imagine anything grander than a structure in central California framed by Cascade Joinery (Bellingham, Washington) for this "all-large project." The clamping hardware was a celebrated opportunity, a preferred alternative to concealed lag screws, and appropriate to this amazing collection of long-span beams and clustered posts (Fig. 13).

Figure 13 Figure 14
Figure 15 Figure 16

Clustered posts appear again in the work of Randall Walter AIA of Benson Woodworking in Walpole, N.H., who used a copse of heavy keyed posts to support keyed beams in a house in Wawona, California. As large and spectacular as the recycled timbers may be, the keys are in a class unto themselves. The client, who builds high-end auto components, used his own facilities to cast and plate the keys, which are housed and bolted to the timbers (Figs. 14-16).

Figure 17

On a smaller scale are the keyed beams in a simple bent building in New Hampshire's Lake Country, built by Hunter Timber Frame Structures in Alton for an owner who wanted a post-free great room. Rather than using yet another hackneyed transverse hammerbeam, builder and designer went to two decoratively striking longitudinal keyed beams, big enough for an interesting effect, set high enough not to feel oppressive. Two interior posts supporting the roof are simply cut off and land on the keyed beams. Note that the single point load, arriving from above at midspan, makes for simple uniform key spacing (Fig. 17).

When building a new clubhouse for the Tewksbury Country Club in Massachusetts, north of Boston, we at Benson Woodworking had only recently started keying beams, and we recognized an opportunity to lose unprecedented amounts of money by tooling up for the many very large keyed elements designed into the frame. The 72-ft.-square open main room has only four interior posts. A three-piece keyed hip rafter crosses the top of each post on its way from corner to crown.

Figure 18

Each post also supports two heavy, widely spaced keyed girts, on which the jack rafters break. Rather than key together three solid timbers to get the required depth, we used deep, heavy shear blocks. This shape exacerbated the load flow eccentricity and accompanying prying action. We used very heavy coil springs on the upper ends of the through-bolt clamps in an effort to maintain clamping even after shrinkage. This solution was appealing if not entirely successful (Fig. 18).

 

Figure 19Keyed Beam Testing. To design keyed beams to comply with modern building codes, a method of accurately predicting not only a keyed beam's strength, but also its stiffness, is critical. Many theorists have developed mathematical models to analyze a beam with interlayer slipping, a great starting point for one author's (Miller) recent research at Michigan Technological University. The theory was expanded, first to account for beams with more than two laminate and, as well, the effect of very widely spaced keys, which are prone to compression and rotation. We developed an analytical model requiring not only the modulus of elasticity of the key and timbers, but also the grain orientation, key inclination, and the number and stiffness of clamping connectors. All of these parameters come into play when determining the amount of interlayer slip in a keyed beam.

Small-scale testing on individual key configurations determined their actual stiffness, which we compared to predicted stiffness. As anticipated, the keys compressed and tried to rotate; longer keys oriented along the grain of the beam compressed more, but were much less prone to rotating, showing that a delicate balance determines optimal individual key configuration (Fig. 19).

Figure 20The analytical model's predicted results closely matched the actual key stiffness from physical testing. With a bit of confidence in predicting the stiffness of individual shear keys, the next step was to jump headlong into predicting the capacity and stiffness of full-scale keyed beams. Several keyed beams, stacked 8x8 yellow poplar timbers, were loaded with one-third-point loads until failure. We recorded the amount of vertical displacement and the applied load as well as the amount of slip between the laminate until the keyed beams failed. White oak keys (compressed perpendicular to the grain) as well as Parallam PSL keys (compressed parallel to the grain) were tested. Fig. 20 shows a keyed beam with Parallam PSL shear keys.

Once adjusted for timber and key moisture content and specific gravity (both of these affect the element's stiffness), the analytical model quite accurately predicted actual beam behavior. As expected, the keyed beam behaved somewhere between how simple stacked beams would behave and how a full-depth solid beam would behave.

Early in this article, we mentioned that hardwood keys when loaded perpendicular to the grain will crush before the end grain in the corresponding timber notch, and that, when keys are installed with end-grain to end-grain bearing, the fibers will interpenetrate. Both of these phenomena were regularly observed during our keyed-beam testing (Figs. 21-22).

Figure 21

Figure 22

 

 

 

 

 

 

 

 

Testing a few keyed beams, however, was not sufficient to fully vet the analytical models. We required additional data. Rather than conduct more tests, which take time, money and a lot of material, we judged Kidwell's test data sufficiently complete to be compared with our analytical model. (And, by happy coincidence, we conducted our tests at the same university where Kidwell had conducted his, 110 years earlier.) Kidwell had tested several different species of keyed beams made from two and three laminate, using both hardwood and cast iron keys. In all cases, within a reasonable coefficient of variation for wood species, Kidwell's test results were consistent with the predicted results from the analytical model.

The downside of our analytical model, however, is the amount of computational effort required: it is mathematically intense. The pragmatic engineer in us wants this process to be simplified and easily implemented. To this end, the European Union's Eurocode 5 models the interlayer slip using an effective (adjusted) modulus of elasticity and section modulus. While convenient, this method still requires calculating the individual shear key stiffness and is only applicable for uniformly spaced shear keys on a beam subjected to a sinusoidally distributed transverse load. In other words, the simplification is quite restrictive.

So where does all this leave us? With an analytical model able to accurately predict the stiffness and strength of a keyed beam, regardless of key configurations, location and number of laminate, but needing significant computational effort. At this point, no shortcuts or simplifications appear possible to be made to the process. Keyed beams, deceptively simple in concept, are hard to analyze and fabricate.

The Future of Keyed Beams. As long as we continue to build timber structures, from time to time we are going to want solid timbers larger than are practically available. Keyed beams will fill part of this demand but, given material and architectural restrictions, we are always going to want a little bit more. The next logical step in delivering more out of the same amount of material is to prestress keyed beams, such that their internal stresses will counteract part of their external load stress. This technique falls under the same theory as that of slightly offsetting key notches and using a pair of opposing wedges to forcefully realign them, inducing some positive camber. But inducing large amounts of camber by using opposed wedges will most likely result in localized crushing of individual keys and notches, which effectively limits this method to countering at most the structure dead weight.

Figure 23-24The cambering theory is taken a bit further in Derevyagin's beams, named after the Russian engineer who developed them, and consisting of timbers bent across a loading frame in opposite fashion to their in-service deflected shape. While the timbers are bent, notches are made by chain mortiser at the proper spots, and wood plates inserted into the notches. Once released from the loading frame, the natural tendency for the beams to spring back is resisted by the wood plates, resulting in a positively cambered beam. The internal stresses in what will be the top layer of the beam in service are still substantially in tension, whereas the bottom layer is mostly in compression. Figs. 23-24 show the fabrication of Derevyagin's beams, kerfed on the unseen faces against checking on the seen faces.

Figure 25The bending of the timbers against the loading frame results in much larger prestressing and cambering than is possible just by driving wedges. An additional purported benet of Derevyagin's method is that the conguration pinches the wood plates such that eccentric prying forces are reduced, while simultaneously providing some clamping force to keep the laminate together. We are at work on a version of Derevyagin beams that, instead of wood plates fitted to kerfs, relies on pegs in drilled holes in the shear plane, where the bearing faces remain parallel and vertical. Fastening the beam with SIP screws will restrain the keys from rolling.

Conclusions. We continue to design, fabricate and install key-laminated beams and posts (Fig. 25). We are convinced that they offer aesthetic, structural and inventory benefits. We have learned much in our work to date about the realities of fabricating these surprisingly sophisticated structural elements. The fabrication tolerances can be daunting, even without considering the dimensional changes wrought by new timbers shrinking in place, while "dry" recycled timbers can be quite waterlogged and unexpectedly deteriorated, causing problems if assembled into keyed beams. We expect and hope to continue developing our expertise in their use. There are compelling aesthetic, structural, economic and green justications for using mechanical lamination. We wish the very best to others in their beam-keying efforts.


--Ben Brungraber and Joe Miller


Bibliography

Eurocode 5: Design of Timber Structures. EN 1995-1-1:2004(E). Brussels: CEN, 2004.

Forchheimer, P. "†ber Zusammengesetzte Balken." Zeitschrift des Vereines deutscher Ingenieure, 36:100-103, 1892.

Goodman, J.R. Layered Wood Systems with Interlayer Slip. Dissertation, University of California, Berkeley, 1967.

Hoor, D., J. Natterer, K. Mohler, and K.-H. Goetz. Timber Design and Construction Sourcebook. New York: McGraw-Hill, 1989. 

Karlsen, G. G., D.Sc., ed. Wooden Structures. A. B.Kuznetsov, trans. Moscow: Mir Publishers, 1967. 

Kidwell, Edward. "The Efciency of Built-up Wooden Beams." Transactions of the American Institute of Mining Engineers, 2/1897-7/1897:732-818, 977-993. See also http://books.google.com/books?id=WEwLAAAAYAAA&prints ec=titlepage&source=gbs_summary_r&cad=0#PPA732,M1 

Leupold, J. Theatrum Ponticiale: oder Schauplatz der BrŸcken und BrŸcken-Baues. Leipzig, 1726.

Snow, J. P. "Wooden Bridge Construction on the Boston and Maine Railroad." Journal of the Association of Engineering Societies, 14:500-512, 1895.

Strukel, M. Der BrŸckenbau. O.W. Backman, Kuopio, Finland, 1900.

Thelandersson, Sven and Hans J. Larsen, eds. Timber Engineering. John Wiley & Sons, Hoboken, N.J., 2003.