8.17. A pavement sub-base is modeled as two layers of dif- ferent materials surrounded by rigid walls as shown in Fig. P

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8 17 A Pavement Sub Base Is Modeled As Two Layers Of Dif Ferent Materials Surrounded By Rigid Walls As Shown In Fig P 1 (96.89 KiB) Viewed 25 times

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8.17. A pavement sub-base is modeled as two layers of dif- ferent materials surrounded by rigid walls as shown in Fig. P.8.17. The top layer fits snugly between the rigid walls. The bottom layer has a 1/2-in. gap on each side. Find the change in height of the two layers when a uniform pressure is applied such that the gap just closes. Assume plane strain and ignore friction. Take E₁ = 10,000 psi, v₁ = 1/2, E₂ = 6,000 psi, and v₂ 1/4. [Hint: First show from Hooke's law for material Tix = T₂ = -p and that e = 0 (i.e., all deformation is in Eyy material ). Taking Typ, show that p = = -p, show that p = E₂/199v₂ (1 + = that zz yy v₂) from the constitutive law for Exx and & Now compute E from the remaining constitutive equations and get the desired result A.] yy -200" P 20" 1 Rigid 2 Rigid Figure P.8.17. 4 10"