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5_28 - 5.28 The concrete[E = 29 GPa pier shown in Fig P5.28...

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5.28 The concrete [ E = 29 GPa] pier shown in Fig. P5.28 is reinforced using four steel [ E = 200 GPa] reinforcing rods, each having a diameter of 19 mm. If the pier is subjected to an axial load of 670 kN, determine: (a) the normal stress in the concrete and in the steel reinforcing rods. (b) the shortening of the pier. Fig. P5.28 Solution (a) Equilibrium: Consider a FBD of the pier, cut around the upper end. The concrete will be designated member (1) and the reinforcing steel bars will be designated member (2). Sum forces in the vertical direction to obtain: 1 2 670 kN 0 y F F F Σ = − = Geometry of Deformations: 1 2 δ δ = Force-Deformation Relationships: 1 1 2 2 1 2 1 1 2 2 F L F L A E A E δ δ = = Compatibility Equation: Substitute Eqs. (c) into Eq. (b) to derive the compatibility equation: 1 1 2 2 1 1 2 2 F L F L A E A E = (d) Solve the Equations: Solve Eq. (d) for F 2 : 1 2 2 1 2 2 2 1 1 1 1 2 2 1 1 L A E L A E F F F A E L L A E = = (e) and substitute this expression into Eq. (a) to determine F 1 : 1 2 2 1 2 2 1 2 1 1 1 2 1 1 2 1 1 1 670 kN y L A E L A E F F

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