Properties for Design of Composite Structures. Neil McCartney
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Название: Properties for Design of Composite Structures

Автор: Neil McCartney

Издательство: John Wiley & Sons Limited

Жанр: Техническая литература

Серия:

isbn: 9781118789780

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СКАЧАТЬ equals 2 h upper W sigma Subscript normal upper A Baseline equals 2 upper W integral Subscript 0 Superscript h Baseline sigma 11 left-parenthesis x 3 right-parenthesis d x 3 comma upper F Subscript normal upper T Baseline equals 2 h upper L sigma Subscript normal upper T Baseline equals 2 upper L integral Subscript 0 Superscript h Baseline sigma 22 left-parenthesis x 3 right-parenthesis d x 3 comma"/>(2.233)

      where σA and σT are the effective axial and transverse applied stresses. On substituting (2.220) and (2.221) into (2.233), the following effective axial and transverse stresses are obtained

      The relations (2.234) are now expressed in the form

      On substituting (2.220) and (2.221) into (2.237) the following relations, enabling the determination of the effective axial and transverse bending moments per unit area of cross section, are obtained

      upper M Subscript upper A Baseline plus one-half h zero width space sigma Subscript upper A Baseline equals h left-bracket upper E overTilde Subscript upper A Baseline left-parenthesis one-half epsilon overbar Subscript upper A Baseline plus one-third h ModifyingAbove epsilon With caret Subscript upper A Baseline right-parenthesis plus nu Subscript upper A Baseline upper E overTilde Subscript upper T Baseline left-parenthesis one-half epsilon overbar Subscript upper T Baseline plus one-third h ModifyingAbove epsilon With caret Subscript upper T Baseline right-parenthesis plus one-half nu overTilde Subscript a Baseline sigma Subscript t Baseline minus one-half upper E overTilde Subscript upper A Baseline alpha overTilde Subscript upper A Baseline upper Delta upper T right-bracket comma(2.238)

      upper M Subscript normal upper T Baseline plus one-half h sigma Subscript normal upper T Baseline equals h left-bracket nu Subscript normal upper A Baseline upper E overTilde Subscript normal upper T Baseline left-parenthesis one-half epsilon overbar Subscript normal upper A Baseline plus one-third h ModifyingAbove epsilon With caret Subscript normal upper A Baseline right-parenthesis plus upper E overTilde Subscript normal upper T Baseline left-parenthesis one-half epsilon overbar Subscript normal upper T Baseline plus one-third h ModifyingAbove epsilon With caret Subscript normal upper T Baseline right-parenthesis plus one-half nu overTilde Subscript normal t Baseline sigma Subscript normal t Baseline minus one-half upper E overTilde Subscript normal upper T Baseline alpha overTilde Subscript normal upper T Baseline upper Delta upper T right-bracket period(2.239)

      On using (2.235) and (2.236) it follows that

      2.18.3 Some Special Cases

      It is useful now to consider some important special cases that arise very often when considering the bending deformation of materials.

      2.18.3.1 Four-point Bending Tests

      The previous analysis can be used to determine the stress and strain state in beams subject to four-point bending. The analysis will apply near the mid-plane between the planes normal to the beam axis that contain the contact points of the inner rollers used in the experiments. For this case σA=σT=σt=MT=ΔT=0 and the relations (2.235), (2.236), (2.240) and (2.241) reduce to the form