A

Shear

I ■

Figure 2.19 Modes of load application. Compression (a) occurs where applied forces are aligned and tend to crush a material. Tension (b) occurs where applied forces are aligned and tend to pull a material apart. Shear (c) occurs where applied forces are not aligned and tend to slide one part of a material in one direction and the other part of the material in the opposite direction

Figure 2.20 Diagrammatic representation of a beam supported at each end with a load concentrated at its mid span. The large arrows indicate the direction of the applied load on the beam, whilst the small arrows indicate the resulting stresses within the beam as it bends. Compression and tension are concentrated on the surface of the beam at mid span, whilst shear stress is concentrated along the neutral axis at the ends of the beam

Figure 2.20 Diagrammatic representation of a beam supported at each end with a load concentrated at its mid span. The large arrows indicate the direction of the applied load on the beam, whilst the small arrows indicate the resulting stresses within the beam as it bends. Compression and tension are concentrated on the surface of the beam at mid span, whilst shear stress is concentrated along the neutral axis at the ends of the beam

  • the neutral axis). Given the span, cross-sectional dimensions and the magnitude and position of loads on a beam (regardless of the material used), the magnitude of the bending stresses can be computed using an engineering concept known as the Flexure Formula
  • Hoadley, 1980). In wood, the level of bending stress which results in failure of a wooden beam, i.e. the breaking strength, is called the modulus of rupture.

It is tempting to consider strength to mean simply the maximum resistance of wood. However, another important aspect of strength is the reality that mechanical loading of a material is always accompanied by deformation. Deformation in an object under load is expressed as strain. Strain is defined as the change in dimension per unit of original dimension:

change in dimension (in) original dimension (in)

Though strain is expressed in units per unit (e.g. inches per inch), it is nevertheless simply a fraction or ratio.

Consider the simultaneous stress and strain behaviour during the progressive loading of a

M X

Figure 2.21 Stress strain diagram. A block of wood under a load in compression perpendicular to the grain is shown in (a). The relationship between stress and strain (defined in section 2.5.1) is shown in (b), where moderate loading is applied and stress (e.g. x) does not exceed the proportional limit (ct'). Behaviour in this range is elastic, i.e. when the load (stress) is removed, the wood returns to its original dimension (strain is recovered). In (c), as additional load (stress) is applied (X) and the proportional limit (ct') is exceeded, dimensional change (strain) is no longer proportional to the applied load (stress). In the graph, this is the point at which the line that shows the effect of loading begins to curve. With most wood properties, the proportional limit is also the elastic limit, and dimensional change (strain) beyond the elastic limit is not reversible when the load (stress) is removed. Once the proportional limit has been exceeded in (d), even though the applied load (stress) is removed, the wood does not return to its original dimension (residual strain). Residual strain in wood is called set

Strain E

Strain E

Strain E

Figure 2.21 Stress strain diagram. A block of wood under a load in compression perpendicular to the grain is shown in (a). The relationship between stress and strain (defined in section 2.5.1) is shown in (b), where moderate loading is applied and stress (e.g. x) does not exceed the proportional limit (ct'). Behaviour in this range is elastic, i.e. when the load (stress) is removed, the wood returns to its original dimension (strain is recovered). In (c), as additional load (stress) is applied (X) and the proportional limit (ct') is exceeded, dimensional change (strain) is no longer proportional to the applied load (stress). In the graph, this is the point at which the line that shows the effect of loading begins to curve. With most wood properties, the proportional limit is also the elastic limit, and dimensional change (strain) beyond the elastic limit is not reversible when the load (stress) is removed. Once the proportional limit has been exceeded in (d), even though the applied load (stress) is removed, the wood does not return to its original dimension (residual strain). Residual strain in wood is called set

wood member, for example, a block of wood under a load in compression perpendicular to grain, as shown in Figure 2.21a.

Under moderate loading, the relationship between stress and strain is indicated by Figure 2.21b. Note that strain is proportional to stress, and behaviour in this range is elastic, that is, when stress is removed, strain is recovered. However, as shown in Figure 2.21c, as additional stress is applied, a proportional limit, o, is reached, beyond which strain is no longer proportional. With most wood properties, the proportional limit is also the elastic limit, and strain beyond the elastic limit is not reversible; when stress is removed, strain is not reversible. As shown in Figure 2.21d, removal of stress beyond the proportional limit results in residual strain, called set. Dents in the surfaces of furniture or the loosening of mortise and tenon joints are examples commonly associated with compressing wood perpendicular to grain beyond its proportional limit. In most cases, there is no meaningful maximum load, since continued compression would result in increasing resistance, even after the wood had been crushed beyond usefulness.

With many strength properties, such as compression parallel to grain (i.e. along the grain) or bending, a maximum load is reached at levels of 1.5-2 times the proportional limit load. Maximum load may be accompanied by fracture or other consequential failure.

Within the proportional limit, the ratio of stress to strain is called the modulus of elasticity, or Young's Modulus (E):

E = stress/strain

Since the units of strain cancel out to give a ratio or number without dimensions, the result of this calculation is still a stress. It is that stress which would in theory double the length of a specimen if it did not break first. It can also be regarded as the stress to produce 100% strain (Gordon, 1976). Whereas strength is a measure of the force or stress needed to break an object, Young's modulus or E is concerned with how stiff, flexible, springy or floppy a material is. To quote from J.E. Gordon's excellent The New Science of Strong Materials: 'A biscuit is stiff but weak, steel is stiff and strong, nylon is flexible (low E) and strong, raspberry jelly is flexible (low E) and weak. The two properties (modulus and strength) together describe a solid about as well as you can reasonably expect two figures to do' (Gordon, 1976).

The modulus of elasticity is especially important in bending as it serves as a convenient rating of relative stiffness among different woods. In many applications, the rigidity of the wood may be as critical as its breaking strength.

Certain strength characteristics of wood cannot be described in terms of pure stress values, as they involve complex loading or resistance which cannot be readily analysed. An example is the hardness value of wood, which measures the indentation resistance of wood. This property is determined by an empirical test which simply measures the amount of force required to embed a standard tool (a hemisphere of 0.44 in diameter) into a wood surface.

Wood Working for Amateur Craftsman

Wood Working for Amateur Craftsman

THIS book is one of the series of Handbooks on industrial subjects being published by the Popular Mechanics Company. Like Popular Mechanics Magazine, and like the other books in this series, it is written so you can understand it. The purpose of Popular Mechanics Handbooks is to supply a growing demand for high-class, up-to-date and accurate text-books, suitable for home study as well as for class use, on all mechanical subjects. The textand illustrations, in each instance, have been prepared expressly for this series by well known experts, and revised by the editor of Popular Mechanics.

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