3. A board whose width changes as w(x) = 2(√I-√) (0≤x≤ L), as shown is fixed on the left edge. Here L is the length of the board. The material has an area mass density (per unit area) of pkg/m² dA w(x) = 2(√L-√) L F(x,y) a) What is the weight of the board? Derive it by integrating weight of a differential element, dA located at z and that has a width w(a) as shown. b) What is the moment of the weight of the board about the y-axis. Derive it by integrating the moment applied by the differential element, dA, located at distance z away from the fixed edge. c) An additional distributed load, that is constant along the width but changes with distance as F(x, y) = kæ² N/m², is applied on the board (the gray surface in the figure is the force function). What is the moment applied by this external load on the fixed edge. Solve this using a similar approach as step (b).

3. A board whose width changes as w(x) = 2(√I-√) (0≤x≤ L), as shown is fixed on the left edge. Here L is the length of the board. The material has an area mass density (per unit area) of pkg/m² dA w(x) = 2(√L-√) L F(x,y) a) What is the weight of the board? Derive it by integrating weight of a differential element, dA located at z and that has a width w(a) as shown. b) What is the moment of the weight of the board about the y-axis. Derive it by integrating the moment applied by the differential element, dA, located at distance z away from the fixed edge. c) An additional distributed load, that is constant along the width but changes with distance as F(x, y) = kæ² N/m², is applied on the board (the gray surface in the figure is the force function). What is the moment applied by this external load on the fixed edge. Solve this using a similar approach as step (b).

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.13P: Figure (a) shows the cross section of a column that uses a structural shape known as W867...

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