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Answer
𝐹rod = 44.58 kN
Solution
The problem describes a statically indeterminate beam system. The beam is fixed at the
left end (cantilever), supported by an elastic rod at 𝑥 = 5 m, and pinned at the right end (𝑥 =
9 m). We must determine the force in the rod and the internal force diagrams.
1. System Parameters and Geometric Properties
• Beam length: 𝐿 = 5 + 2 + 2 = 9 m.
• Uniformly distributed load: 𝑤 = 10 kN/m for 0 ≤ 𝑥 ≤ 5 m.
• Point load: 𝑃 = 20 kN at 𝑥 = 7 m.
• Beam properties: 𝐼 = 23.25 × 10−6 m4 , 𝐸 = 210 × 106 kN/m2 .
• Rod properties: Diameter 𝑑 = 20 mm = 0.02 m, Length 𝐿rod = 2 m.
• Rod cross-sectional area:
𝜋𝑑2 𝜋(0.02)2
𝐴rod = = ≈ 3.14159 × 10−4 m2
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Answer
𝐹rod = 44.58 kN
Solution
The problem describes a statically indeterminate beam system. The beam is fixed at the
left end (cantilever), supported by an elastic rod at 𝑥 = 5 m, and pinned at the right end (𝑥 =
9 m). We must determine the force in the rod and the internal force diagrams.
1. System Parameters and Geometric Properties
• Beam length: 𝐿 = 5 + 2 + 2 = 9 m.
• Uniformly distributed load: 𝑤 = 10 kN/m for 0 ≤ 𝑥 ≤ 5 m.
• Point load: 𝑃 = 20 kN at 𝑥 = 7 m.
• Beam properties: 𝐼 = 23.25 × 10−6 m4 , 𝐸 = 210 × 106 kN/m2 .
• Rod properties: Diameter 𝑑 = 20 mm = 0.02 m, Length 𝐿rod = 2 m.
• Rod cross-sectional area:
𝜋𝑑2 𝜋(0.02)2
𝐴rod = = ≈ 3.14159 × 10−4 m2
4 4
