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DESIGN OF STRUCTURAL ELEMENTS

Section – 1: Properties of Timber Materials

Introduction

Wood, steel and concrete are actually extraordinarily complex materials. Of the three, wood was used first as a structural material, and some of the otherwise inscrutable vocabulary of structural analysis derives from this fact: the notion of an "outer fiber" of a cross-section; or even the concept of "horizontal shear" are rooted in the particular material structure of wood.

Only certain material properties are of interest to us here -- specifically, those that has some bearing on the structural behavior of the elements under consideration. The most obvious, and important, structural properties are those relating force to deformation (extension), or stress to strain. Knowing how a material sample contracts or elongates as it is stressed up to failure provides a crucial model for its performance in an actual structure. Not only is its ultimate stress (or strength) indicated, but also a measure of its resistance to strain (modulus of elasticity), its linear (and presumably elastic) and/or non-linear (plastic) behavior, and its ability to absorb energy without fracturing (ductility).

Ductility is important in a structural member because it allows concentrations of high stress to be absorbed and redistributed without causing sudden, catastrophic failure. Ductile failures are preferred to brittle failures, since the large strains possible with ductile materials give warning of collapse in advance of the actual failure. Glass, a non-ductile (i.e., brittle) material, is generally unsuitable for use as a structural element, in spite of its high strength, because it is unable to absorb large amounts of energy, and could fail catastrophically as a result of local stress concentrations.

A linear relationship between stress and strain is an indicator of elastic behavior -- the return of a material to its original shape after being stressed and then un-stressed. Structures are expected to behave elastically under normal "service" loads; but plastic behavior, characterized by permanent deformations, needs to be considered when ultimate, or failure, loads are being computed. Typical stress-strain curves for wood, steel and concrete are shown below.

The most striking aspect of wood, steel, and concrete stress-strain curves is the incredibly high strength and modulus of elasticity (indicated by the slope of the curve) of steel relative to concrete and wood. Of equal importance is the information about the strength and ductility of the three materials in tension versus compression. For example, structural carbon steel, along with its high strength and modulus of elasticity, can be strained to a value 60 times greater than shown above in both tension and compression, indicating a high degree of ductility. Concrete, on the other hand, has very little strength in tension, and fails in a brittle (non-ductile) manner in both tension and compression. Wood has high tensile strength compared to concrete, but also fails in a brittle manner when stressed in tension; in compression, however, wood shows ductile behavior.

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Aside from this stress-strain data, material properties can also be effected by environmental conditions, manufacturing processes, or the way in which loads are applied. These material-dependent responses are discussed below for timber.

Wood is the stuff inside trees; timber is wood suitable for (or prepared for) use in structures; lumber is timber cut into standard-sized planks. Since we build with lumber (which is also timber, which is also wood), all three of these terms are used, depending on the context.

The basic structure of wood can be understood by examining its situation within the tree: the trunk consists of a bundle of cellulose tubes, or fibers, that serve the dual purpose of carrying water and nutrients from the ground to the leaves; while providing a cellular geometry ("structure") capable of supporting those leaves and the necessary infrastructure of branches. Various loads stress the tree trunk in axial compression (dead load and snow load); and in bending (wind load, eccentric dead and snow load). When we cut lumber from the tree, we do so in a way that allows it to be stressed within building structures in the same manner that it was stressed while in the tree. Thus, saw cuts are made parallel to the longitudinal fibers of the wood, since it is the continuity of these fibers that give the wood strength.

Cutting

Lumber cut from a tree immediately has three structural defects, compared to wood in the tree itself: First, it is virtually impossible to cut every piece of lumber so that the orientation of the fibers, or grain, is exactly parallel to the edges of the wood planks. This means that the full potential of the wood's strength is rarely achieved.

Second, the continuous path of those fibers leading from trunk to branch -- a functional and structural necessity within the tree -- becomes a liability when the tree is cut, as it results in knots and other imperfections which weaken the boards. Wood is graded to account for these and other imperfections.

Third, the shear strength of the wood -- that is, its ability to resist sliding of the cellular fibers relative to each other -- is much lower than its strength in tension or compression parallel to those fibers. While a low shear strength is perfectly adapted to a tree's circular cross-section, it is not necessarily appropriate for the rectangular cross-sections characteristic of lumber. Why this is so can be seen by comparing the two cross-sectional shapes: with a circle, a great deal of material is available at the neutral axis (where shear stresses are highest) so the "glue" or lignin holding the fibers together can be relatively weak; but when the tree is cut into rectangular cross-sections, relatively less material is present at the neutral axis, and shear stresses are therefore higher. For this reason, the structural efficiency of lumber with a rectangular cross-section, that is, all lumber, is compromised by a disproportionate weakness in shear.

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Seasoning.

A dead tree begins losing its internal water until its moisture content reaches equilibrium with the surrounding air. Two things then happen: the wood shrinks, especially perpendicular to the grain, and the wood gets stronger. As atmospheric humidity changes, the wood responds by gaining or losing moisture, expanding or shrinking, and becoming weaker or stronger. For structural design, the issue of strength versus moisture content is handled by assuming one of two conditions: either the wood is indoors, where the humidity is controlled and the moisture content of the wood is expected not to exceed about 19% (for glued laminated timber, this condition is met when the moisture content is less than about 16%); or outdoors, where the potential exists for the wood to take on added moisture and lose some strength. Lumber is generally air-dried or kiln-dried after it is cut and surfaced, so that its moisture content doesn't change radically during or after construction.

Volume.

Lumber contains both hidden and visible pockets of low strength, due to imperfections within or between the cellular fibers of the material and larger cracks or knots often visible on the surface. It is impossible to know where all these defects might be in any particular piece of lumber, but one can safely surmise that there will be more of them as the volume of the piece increases. As the number of defects increases, the probability that larger, or more damaging, defects will exist within critical regions of the structural element also increases. Since these regions of low strength can trigger brittle failure (wood is brittle when stressed in tension), large pieces of lumber will statistically fail at lower levels of stress than small pieces. This does not mean that large beams hold lesser load than small beams; it simply means that the average stress causing failure will be lower in larger beams. Interestingly, the theory is validated by test results for all categories of beams and tension elements, with one exception: increases in cross-sectional width seem to make beams stronger (but not tension members), opposite to what the theory of brittle failure predicts. The reason for this anomaly remains unclear, but may have to due with the fact that local failures at regions of low strength are more likely to cascade across the entire width of relatively thin cross-sections, and more likely to be contained as cross-sectional width increases. A horizontal break corresponding to a complete discontinuity between the lower and upper parts of a cross-section drastically reduces the cross-section's ability to resist bending moments, but has no effect on the section's ability to resist axial tension. This would explain why beams, but not tension members, seem to get stronger with increased width. On the other hand, increasing the depth of a structural element has no such beneficial effect, since even a complete vertical break within a cross-section neither increases nor decreases a member's bending or tensile strength. Because wide beams seem to be relatively stronger than narrow ones, the allowable stress in beams used flat (stressed about their weak axes) is higher than when they are used in their normal orientation, even though their total volume hasn't changed.

Duration of load.

Wood fails at a lower stress the longer it is loaded. This phenomenon is similar to the "fatigue" of metals, except that where metal fatigue is brought on by repeated cycling or reversals of stress, loss of strength in wood is purely time-dependent and will occur even under a constant load. Thus, wood can sustain a higher stress caused by a short-duration impact load then by a longer-duration wind, snow or live load.

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Species and grade.

Many species of wood can be used as lumber. Within each species, different grades are identified, depending on such things as overall density, knots, checks and other imperfections. Grading can be done by visual inspection (for "visually graded lumber") or with the aid of machines (for "machine stress rated lumber"). Since each species of wood is subdivided into numerous grades, the result is a multitude of possible material types, each with different structural properties. Practically speaking, the choices in any given geographical region are limited to what is locally available. For that reason, the material properties assumed when designing in timber are not arbitrarily selected from the lists produced by wood industry organizations, but are selected from the much shorter list of regionally-available species and grades. Allowable (permissible) stresses are published for various grades and species of wood, along with "adjustment" factors to account for the effects of moisture, duration of load, volume, and so on.

Related products.

Several wood-based products have been developed with structural applications: Laminated veneer lumber (LVL) is similar to glulam except that the laminations are much thinner, being sliced off a log like paper pulled off a roll, rather than being sawn; and the glued joints between laminations are vertical, rather than horizontal. The grain in each lamination is oriented along the longitudinal axis of the member so that, like glulam, it mimics the anisotropic fibrous structure of an ordinary piece of lumber. LVL is used for beams and girders only, and is manufactured in standard sizes consistent with the sizes of sawn lumber; while glulam can be custom-fabricated in an unlimited variety of sizes and geometries.

Plywood is similar to LVL except that alternate laminations (plies) are oriented perpendicular to each other, creating a dimensionally-stable structural membrane, used typically as a substrate (sheathing) for roofs and exterior walls; and as a sub-floor over joists in wood-frame construction. Plywood typically contains an odd number of plies, except when the middle two plies are "doubled up" as in 4-ply plywood; in either case, the top and bottom fibers point in the same direction (parallel to the long dimension of the plywood sheet). For this reason, plywood is typically oriented so that it spans in the direction of its long dimension. Where this doesn't occur, for example, in certain panalized roof systems, the lower bending strength of the plywood spanning in its short direction needs to be considered.

I-joists are manufactured from various combinations of flange and web materials, and can be used in place of sawn lumber beams. Flange material can be ordinary sawn lumber or LVL; web material is typically plywood or particle board. Cold-formed metal can also be used as a "web" material, creating a composite "truss-joist" consisting of wooden chords and metal diagonals.

Pre-fabricated trusses consisting typically of sawn members joined by metal connector plates can be used for both pitched roofs and flat floors. These products can be custom-fabricated, and are often structurally designed (engineered) by the manufacturer.