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14.12 The cantilevered beam shown in the accompanying figure is used to support a load acting on a balcony. The deflection of the centerline of the beam is given by the following equation: -wx? y = -(x²-4Lx+6L) 24 EI where y = deflection at a given x location (m) w = distributed load (N/m) (m) E = modulus of elasticity (N/m²) I = second moment of area (m*) X = distance from the support as shown (x) L = length of the beam (m) ELA maldor Problem 14.12 Using Excel, plot the deflection of a beam whose length is 5 m with the modulus of elasticity of E =200 GPa and I=99.1×106 mm4. The beam is designed to carry a load of 10,000 N/m. What is the maximum deflection of the beam? r sis-

14.12 The cantilevered beam shown in the accompanying figure is used to support a load acting on a balcony. The deflection of the centerline of the beam is given by the following equation: -wx? y = -(x²-4Lx+6L) 24 EI where y = deflection at a given x location (m) w = distributed load (N/m) (m) E = modulus of elasticity (N/m²) I = second moment of area (m*) X = distance from the support as shown (x) L = length of the beam (m) ELA maldor Problem 14.12 Using Excel, plot the deflection of a beam whose length is 5 m with the modulus of elasticity of E =200 GPa and I=99.1×106 mm4. The beam is designed to carry a load of 10,000 N/m. What is the maximum deflection of the beam? r sis-

Elements Of Electromagnetics
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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**Cantilevered Beam Deflection Analysis** The cantilevered beam shown in the accompanying figure is used to support a load acting on a balcony. The deflection of the centerline of the beam is given by the following equation: \[ y = \frac{-wx^2}{24EI} (x^2 - 4Lx + 6L^2) \] Where: - \( y \) = deflection at a given \( x \) location (meters) - \( w \) = distributed load (Newtons per meter) - \( E \) = modulus of elasticity (Newtons per square meter) - \( I \) = second moment of area (meters to the fourth power) - \( x \) = distance from the support (meters) - \( L \) = length of the beam (meters) **Illustration Description:** The illustration accompanying the problem displays a cantilevered beam with a length \( L \) and a uniform distributed load \( w \) acting across its length. The beam is fixed at one end and free on the other, with the applied load directed downward. The distance \( x \) represents the position along the beam from the fixed support. The diagram helps visualize the problem setup for calculating deflections. **Problem Statement (Problem 14.12):** Using Excel, plot the deflection of a beam whose length is 5 meters with the modulus of elasticity \( E = 200 \) GPa and \( I = 99.1 \times 10^6 \) mm\(^4\). The beam is designed to carry a load of 10,000 N/m. Calculate and determine the maximum deflection of the beam.
Transcribed Image Text:**Cantilevered Beam Deflection Analysis** The cantilevered beam shown in the accompanying figure is used to support a load acting on a balcony. The deflection of the centerline of the beam is given by the following equation: \[ y = \frac{-wx^2}{24EI} (x^2 - 4Lx + 6L^2) \] Where: - \( y \) = deflection at a given \( x \) location (meters) - \( w \) = distributed load (Newtons per meter) - \( E \) = modulus of elasticity (Newtons per square meter) - \( I \) = second moment of area (meters to the fourth power) - \( x \) = distance from the support (meters) - \( L \) = length of the beam (meters) **Illustration Description:** The illustration accompanying the problem displays a cantilevered beam with a length \( L \) and a uniform distributed load \( w \) acting across its length. The beam is fixed at one end and free on the other, with the applied load directed downward. The distance \( x \) represents the position along the beam from the fixed support. The diagram helps visualize the problem setup for calculating deflections. **Problem Statement (Problem 14.12):** Using Excel, plot the deflection of a beam whose length is 5 meters with the modulus of elasticity \( E = 200 \) GPa and \( I = 99.1 \times 10^6 \) mm\(^4\). The beam is designed to carry a load of 10,000 N/m. Calculate and determine the maximum deflection of the beam.
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