The cantilever beam shown below has a length \( L \), moment of inertia \( I \), and is made from a material with modulus of elasticity \( E \). The load \( P \) is applied at the end of the beam.a. Derive the maximum deflection of the beam and show that \( \delta_{\text{max}} = \frac{PL^3}{3EI} \). Hint: \( M(y) = EI y''(x) \).b. Consider \( E = 29 \times 10^3 \) ksi, \( P = 6 \) kip, \( I = 204 \) in\(^4\), and \( L = 15 \) ft with the length and moment of inertia measured with \(\pm5\%\) and \(\pm10\%\) accuracy, respectively. In 3 significant figures, calculate the deflection and express the variation of its worst-case error.**Diagram Explanation:**The diagram illustrates a cantilever beam fixed on one end with a load \( P \) applied at the free end. The beam has a length \( L \) and demonstrates a deflection downward, marked as \( \delta_{\text{max}} \), which is the maximum deflection at the free end due to the load.

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The cantilever beam shown below has a length L, moment of inertia I, and is made from a material with modulus of elasticity E. The load P is applied at the end of the beam. Hint: M(y) = a. Derive the maximum deflection of the beam and show that max = Ely" (x) PL³ 3EI = b. Consider E = 29 × 10³ ksi, P = 6 kip, I 204 inª, and L = 15 ft with the length and moment of inertia measured with ±5% and ±10% accuracy, respectively. In 3 significant figures, calculate the deflection and express the variation of its worst-case error. P Smax

The cantilever beam shown below has a length L, moment of inertia I, and is made from a material with modulus of elasticity E. The load P is applied at the end of the beam. Hint: M(y) = a. Derive the maximum deflection of the beam and show that max = Ely" (x) PL³ 3EI = b. Consider E = 29 × 10³ ksi, P = 6 kip, I 204 inª, and L = 15 ft with the length and moment of inertia measured with ±5% and ±10% accuracy, respectively. In 3 significant figures, calculate the deflection and express the variation of its worst-case error. P Smax

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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