Neil McCartney

Properties for Design of Composite Structures

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f Baseline Over k Subscript upper T Superscript m Baseline EndFraction plus StartFraction 1 Over mu Subscript t Superscript f Baseline EndFraction EndEndFraction comma"/>(4.196)

      which are valid only if μtf≤μm, and the bounds are reversed if μtf≥μm.

      4.10.5 Transverse Shear Modulus

      The bounds for transverse shear modulus are given by

      StartLayout 1st Row upper V Subscript f Baseline mu Subscript t Superscript f Baseline plus upper V Subscript m Baseline mu Subscript m Baseline minus StartStartFraction left-parenthesis mu Subscript t Superscript f Baseline minus mu Subscript m Baseline right-parenthesis squared upper V Subscript f Baseline upper V Subscript m Baseline OverOver upper V Subscript m Baseline mu Subscript t Superscript f Baseline plus upper V Subscript f Baseline mu Subscript m Baseline plus StartFraction k Subscript upper T Superscript m Baseline mu Subscript m Baseline Over k Subscript upper T Superscript m Baseline plus 2 mu Subscript m Baseline EndFraction EndEndFraction less-than-or-equal-to mu Subscript t Superscript eff Baseline 2nd Row less-than-or-equal-to upper V Subscript f Baseline mu Subscript t Superscript f Baseline plus upper V Subscript m Baseline mu Subscript m Baseline minus StartStartFraction left-parenthesis mu Subscript t Superscript f Baseline minus mu Subscript m Baseline right-parenthesis squared upper V Subscript f Baseline upper V Subscript m Baseline OverOver upper V Subscript m Baseline mu Subscript t Superscript f Baseline plus upper V Subscript f Baseline mu Subscript m Baseline plus StartFraction k Subscript upper T Superscript f Baseline mu Subscript t Superscript f Baseline Over k Subscript upper T Superscript f Baseline plus 2 mu Subscript t Superscript f Baseline EndFraction EndEndFraction comma EndLayout(4.197)

      which are valid only if

StartFraction 1 Over mu Subscript t Superscript f Baseline EndFraction plus StartFraction 2 Over k Subscript upper T Superscript f Baseline EndFraction less-than-or-equal-to StartFraction 1 Over mu Subscript m Baseline EndFraction plus StartFraction 2 Over k Subscript upper T Superscript m Baseline EndFraction period

      The bounds are reversed if

StartFraction 1 Over mu Subscript t Superscript f Baseline EndFraction plus StartFraction 2 Over k Subscript upper T Superscript f Baseline EndFraction greater-than-or-equal-to StartFraction 1 Over mu Subscript m Baseline EndFraction plus StartFraction 2 Over k Subscript upper T Superscript m Baseline EndFraction period

      4.10.6 Axial Shear Modulus

      The bounds for the axial shear modulus are given by

      upper V Subscript f Baseline mu Subscript upper A Superscript f Baseline plus upper V Subscript m Baseline mu Subscript m Baseline minus StartFraction left-parenthesis mu Subscript upper A Superscript f Baseline minus mu Subscript m Baseline right-parenthesis squared upper V Subscript f Baseline upper V Subscript m Baseline Over upper V Subscript m Baseline mu Subscript upper A Superscript f Baseline plus upper V Subscript f Baseline mu Subscript m Baseline plus zero width space zero width space mu Subscript m Baseline EndFraction less-than-or-equal-to mu Subscript upper A Superscript eff Baseline less-than-or-equal-to upper V Subscript f Baseline mu Subscript upper A Superscript f Baseline plus upper V Subscript m Baseline mu Subscript m Baseline minus StartFraction left-parenthesis mu Subscript upper A Superscript f Baseline minus mu Subscript m Baseline right-parenthesis squared upper V Subscript f Baseline upper V Subscript m Baseline Over upper V Subscript m Baseline mu Subscript upper A Superscript f Baseline plus upper V Subscript f Baseline mu Subscript m Baseline plus zero width space zero width space mu Subscript upper A Superscript f Baseline EndFraction comma(4.198)

      4.10.7 Axial Thermal Expansion

      The bounds for the axial thermal expansion are given by

      StartLayout 1st Row upper V Subscript f Baseline upper E Subscript upper A Superscript f Baseline alpha Subscript upper A Superscript f Baseline plus upper V Subscript m Baseline upper E Subscript m Baseline alpha Subscript m Baseline plus StartStartFraction 4 left-parenthesis nu Subscript upper A Superscript f Baseline minus nu Subscript m Baseline right-parenthesis left-parenthesis ModifyingAbove alpha With caret Subscript upper T Superscript f Baseline minus ModifyingAbove alpha With caret Subscript upper T Superscript m Baseline right-parenthesis upper V Subscript f Baseline upper V Subscript m Baseline OverOver StartFraction upper V Subscript m Baseline Over k Subscript upper T Superscript f Baseline EndFraction plus StartFraction upper V Subscript f Baseline Over k Subscript upper T Superscript m Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction less-than-or-equal-to upper E Subscript upper A Superscript eff Baseline alpha Subscript upper A Superscript eff Baseline 2nd Row less-than-or-equal-to upper V Subscript f Baseline upper E Subscript upper A Superscript f Baseline alpha Subscript upper A Superscript f Baseline plus upper V Subscript m Baseline upper E Subscript m Baseline alpha Subscript m Baseline plus StartStartFraction 4 left-parenthesis nu Subscript upper A Superscript f Baseline minus nu Subscript m Baseline right-parenthesis left-parenthesis ModifyingAbove alpha With caret Subscript upper T Superscript f Baseline minus ModifyingAbove alpha With caret Subscript upper T Superscript m Baseline right-parenthesis upper V Subscript f Baseline upper V Subscript m Baseline OverOver StartFraction upper V Subscript m Baseline Over k Subscript upper T Superscript f Baseline EndFraction plus StartFraction upper V Subscript f Baseline Over k Subscript upper T Superscript m Baseline EndFraction plus StartFraction 1 Over mu Subscript t Superscript f Baseline EndFraction EndEndFraction comma EndLayout(4.199)

      where

      ModifyingAbove alpha With caret Subscript upper T Baseline equals alpha Subscript upper T Baseline plus nu Subscript upper A Baseline alpha Subscript upper A Baseline period(4.200)

      These bounds are valid only if (νAf−νm)(α^Tf−α^Tm)(μtf−μm)≥0, and the bounds are reversed if (νAf−νm)(α^Tf−α^Tm)(μtf−μm)≤​​0.

      4.10.8 Transverse Thermal Expansion

      The bounds for the transverse thermal expansion are given by

      StartLayout 1st Row upper V Subscript f Baseline ModifyingAbove alpha With caret Subscript upper T Superscript f Baseline plus upper V Subscript m Baseline ModifyingAbove alpha With caret Subscript upper T Superscript m Baseline minus StartStartFraction left-parenthesis StartFraction 1 Over k Subscript upper T Superscript f Baseline EndFraction minus StartFraction 1 Over k Subscript upper T Superscript m Baseline EndFraction right-parenthesis left-parenthesis ModifyingAbove alpha With caret Subscript upper T Superscript f Baseline minus ModifyingAbove alpha With caret Subscript upper T Superscript m Baseline right-parenthesis upper V Subscript f Baseline upper V Subscript m Baseline OverOver StartFraction upper V Subscript m Baseline Over k Subscript upper T Superscript f Baseline EndFraction plus StartFraction upper V Subscript f Baseline Over k Subscript upper T Superscript m Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction less-than-or-equal-to ModifyingAbove alpha With caret Subscript upper T Superscript eff Baseline 2nd Row less-than-or-equal-to upper V Subscript f Baseline ModifyingAbove alpha With caret Subscript upper T Superscript f Baseline plus upper V Subscript m Baseline ModifyingAbove alpha With caret Subscript upper T Superscript m Baseline minus StartStartFraction left-parenthesis StartFraction 1 Over k Subscript upper T Superscript f Baseline EndFraction minus StartFraction 1 Over k Subscript upper T Superscript m Baseline EndFraction right-parenthesis left-parenthesis ModifyingAbove alpha With caret Subscript upper T Superscript f Baseline </p> </div><hr> <div class= Скачать книгу