Mechanical Properties of a Meter Rule

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Mechanical Properties of a Meter Rule.

AIM:

To investigate the mechanical properties of a meter rule via practical experimentation.

INTRODUCTION

The mechanical properties of materials are its fitness and ability to resist applied or external forces. By external force is meant any force outside of a given piece of material which tends to deform it in any manner.

Knowledge of these properties is obtained through experimentation either in the employment of the wood in practice or by means of special testing apparatus in the laboratory. Owing to the wide range of variation in meter rulers it is necessary that a great number of tests are made and that so far as possible all disturbing factors be eliminated. For comparison of different kinds or materials a standard method of testing is necessary and the values must be expressed in some defined units. For these reasons laboratory experiments if properly conducted have many advantages over any other method.

One object of such investigation is to find unit values for strength and stiffness, etc. These, because of the complex structure of the materials, cannot have a constant value which will be exactly repeated in each test, even though no error be made. The most that can be accomplished is to find average values. On account of the great variability in strength of different specimens even from the same material and appearing to be alike, it is important to eliminate as far as possible all extraneous factors liable to influence the results of the tests.

The mechanical properties that I will consider are:

  • Stiffness and elasticity
  • Tensile strength
  • Compressive or crushing strength
  • Transverse or bending strength
  • Toughness
  • Hardness

BACKGROUND KNOWLEDGE:

Study of the mechanical properties of a material is concerned mostly with its behaviour in relation to stresses and strains, and the factors affecting this behaviour. Stress is a distributed force and may be defined as the mutual action:

  • Of one body upon another or
  • Of one part of a body upon another part

As the stress increases there is a corresponding increase in the strain. This ratio may be graphically shown by means of a diagram with the stress on the y-axis and the strain on the x-axis. This is known as the stress-strain diagram. Within the limit mentioned above the diagram is a straight line. The greater the resistance a material offers to deformation the steeper the vertical axis will be the line. If the results of similar experiments on different materials of a meter rule are plotted to the same scales, comparison is easy.

The two kinds of internal stresses that I am interested in are:

  • Tensile
  • Compressive

When external forces act upon a beam in a direction away from its ends or a direct pull, the stress is a tensile stress. The strain is an increasing.

When a forces act toward the ends or a direct push, the stress is a compressive stress. The strain is a decreasing.

These stresses may act together, producing compound stresses, as in flexure. When a bow is bent there is a compression of the fibres on the inner or concave side and an elongation of the fibres on the outer or convex side.

Stress = Load (or Force)                   Strain = Change in length (or extension)

Area                                                Original length

Bending stress = 3PL                                       Bending modulus = PL³

                           2wt²                                                                4wt³y

Where P = normal force, L = beam length, w = beam width, t = beam thickness,                                   y = deflection at load point.

To work out the maximum surface stress I shall use the formula:

3dEt

2l²

Where d = deflection of the beam at the load, E = modulus of elasticity,             t = beam thickness, l = beam length

Stiffness is the property by means of which a body acted upon by external forces tends to retain its natural size and shape, or resists deformation. Thus a material that is difficult to bend or otherwise deform is stiff.

One that is easily bent or otherwise deformed is flexible. Flexibility is not the exact counterpart of stiffness, as it also involves toughness and pliability.

If successively larger loads are applied to a body and then removed it will be found that at first the body completely regains its original form upon release from the stress--in other words, the body is ~elastic~. Eventually a point will be reached where the recovery of the specimen is incomplete. This point is known as the ~elastic limit~, which may be defined as the limit beyond which it is impossible to carry the distortion of a body without producing a permanent alteration in shape. After this limit has been exceeded, the size and shape of the specimen after removal of the load will not be the same as before, and the difference or amount of change is known as the ~permanent set~.

Elastic limit as measured in tests and used in design may be defined as that unit stress at which the deformation begins to increase in a faster ratio than the applied load. In practice the elastic limit of a material under test is determined from the stress-strain diagram. It is that point in the line where the diagram begins perceptibly to curve.

Permanent set is due to the ~plasticity~ of the material. A perfectly plastic substance would have no elasticity and the smallest forces would cause a set. Lead and moist clay are nearly plastic and wood possesses this property to a greater or less extent. The plasticity of wood is increased by wetting, heating, and especially by steaming and boiling. Were it not for this property it would be impossible to dry wood without destroying completely its cohesion, due to the irregularity of shrinkage.

A substance that can undergo little change in shape without breaking or rupturing is ~brittle~. Chalk and glass are common examples of brittle materials. Sometimes the word _brash_ is used to describe this condition in wood. A brittle wood breaks suddenly with a clean instead of a splintery fracture and without warning. Such materials are unfitted to resist shock or sudden application of load.

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The measure of the stiffness of a material is termed the modulus of elasticity. It is the ratio of stress per unit of area to the deformation per unit of length.

   

E = Stress          = Force x Length

                                           Strain            Area x Extension

It is a number indicative of stiffness, not of strength, and only applies to conditions within the elastic limit. It is nearly ...

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