Properties for Design of Composite Structures. Neil McCartney

overTilde Subscript normal upper T Baseline upper Delta upper T comma"/>(2.221)

      where

(2.222)

      It is noted that the in-plane stresses are only linear functions of x₃. It then follows, on using (2.210), that all the equilibrium equations (2.120)–(2.122) are satisfied.

      It now only remains to determine the value of the displacement component u₃ describing the deflection of the beam. From (2.216) and (2.220)

(2.223)

      On using (2.215) and (2.222) it can be shown that

      (2.224)

      so that (2.223) may now be written as

(2.225)

      Integration with respect to x₃ then leads to

(2.226)

      As the shear stresses σ13 and σ23 are everywhere zero, it follows from (2.143), (2.209) and (2.211) that

      (2.227)

      Integration then yields

      (2.228)

      These relations must be consistent with (2.226) so that

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