A long beam whose nonhomogeneous cross-section is made up of an aluminum channel section, E =...

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A long beam whose nonhomogeneous cross-section is made up of an aluminum channel section, E = Eo, and a titanium cover plate, E = 2.2E, is shown in Fig. 9.13(a). An idealization of this cross-section is shown in Fig. 9.13(b). There is no appreciable mechanical loading on the beam (N = My = M = 0), but a temperature gradient through the cross-section of the beam can be approximated so that the thermal strain in the cover plate is 2.5a,To, while that throughout the channel is laoTo. Calculate the thermally induced stress at: (i) the top of the cover plate; and (ii) at the bottom of the channel. Let the dimension a = 12t. E Nr MyT Eo lyy A* -2- - Egu AT) A - [32] =()+(2) Ali Nr(x) = +E(E/E)[ATA] MyT(x)= =-E0 * () 3 i[ ATA); = Eq A" -y Ea AT E=2.2 10' (b) E=E = 70 GPa t, typ. A long beam whose nonhomogeneous cross-section is made up of an aluminum channel section, E = Eo, and a titanium cover plate, E = 2.2E, is shown in Fig. 9.13(a). An idealization of this cross-section is shown in Fig. 9.13(b). There is no appreciable mechanical loading on the beam (N = My = M = 0), but a temperature gradient through the cross-section of the beam can be approximated so that the thermal strain in the cover plate is 2.5a,To, while that throughout the channel is laoTo. Calculate the thermally induced stress at: (i) the top of the cover plate; and (ii) at the bottom of the channel. Let the dimension a = 12t. E Nr MyT Eo lyy A* -2- - Egu AT) A - [32] =()+(2) Ali Nr(x) = +E(E/E)[ATA] MyT(x)= =-E0 * () 3 i[ ATA); = Eq A" -y Ea AT E=2.2 10' (b) E=E = 70 GPa t, typ.