Solve Prob. 8–24 using Castigliano’s theorem.

Data from Prob. 8–24

Determine the slope and displacement at the end A of the beam. Take E = 29(10³) ksi, I = 170 in⁴. Use the method of virtual work.

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Castigliano's Theorem. Setting P = 20 kN, its actual value, and applying Eq. 8-28, 3 kN Ac 3 kN ↓ = = = |x₁|1₁ - 2 m 0 M₁ M ¹(34x₁4x1)(0.5x₁1) dx₁ *(18x2)(0.5x₂) dx2 ΕΙ ΕΙ JM dx aP/EI 234.7 kNm³ 192 kN.m³ ΕΙ ΕΙ M' (c) Fig. 8-28 + M₂ 5² 426.7 kN m³ ΕΙ