Find the stresses in the stepped beam shown in Fig. 12.23 when a moment of \(1000 \mathrm{~N}-\mathrm{m}\) is applied at node 2 using a two-element idealization. The beam has a square cross section \(50 \mathrm{~mm} \times 50 \mathrm{~mm}\) between nodes 1 and 2 and \(25 \mathrm{~mm} \times 25 \mathrm{~mm}\) between nodes 2 and 3 . Assume the Young's modulus as \(2.1 \times 10^{11} \mathrm{~Pa}\).

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1 -0.25 m 1000 N-m 2 FIGURE 12.23 Stepped beam. -0.40 m- 34