There are many methods of determining bending stiffness and properties, such as bending force and bending moment, which are related to bending stiffness. Examples of methods for measuring bending stiffness are the resonance bending stiffness method for paper and the 4-point bending stiffness method for corrugated fibreboard. Methods like those of Taber and Clark and the 2-point bending resistance method according to L&W are all examples of "bending-stiffness related" methods, i.e. methods which do not really measure bending stiffness but which measure something which correlates with bending stiffness.
The measurement results are usually reported in the form of a bending resistance or bending moment. These bending-stiffness-related methods are characterized by the fact that the measurement results are strongly dependent on the test format and on other measurement conditions.
The measurement of tensile stiffness involved some theoretical problems which we have learned to handle with the help of theories of materials mechanics, measurement methods and correct equipment. The measurement of bending stiffness makes even greater demands on method and measurement equipment, if we are really to measure what we intend to measure. In this chapter, we shall now consider bending stiffness by studying the theories of mechanics of materials in order to obtain a better understanding of this important property. The ambition is to understand the stresses which interact when a material is exposed to a bending moment. I therefore exclude basic mathematical derivations, such as the general calculation of moment of inertia.
Two principles for bending stiffness measurement
Two different principles are utilized for the determination of bending stiffness. The first is the beam bending principle, which is in turn subdivided into the 2-point, 3-point and 4-point methods, depending on the number of load application points on the sample. The second is the resonance stiffness principle where the natural frequency of free vibration is utilized.
Theory for bending stiffness in beam bending
Since paper is an extremely complicated material from a bending stiffness point of view, we choose to describe the bending stiffness theories starting from a rectangular beam of metal. The beam is assumed to be weightless so that its own weight need not be introduced into the discussion.
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