The bank in the figure is considered to be a person sitting and the force exerted on the board is given as 300 N. The elasticity module of the boards that make up the bench E = 7 GPa, Calculate the collapse at the point where a person sits, since the width of a board is 150 mm and the height is 30 mm. (Hint: Consider the AB board as if it is built into points A and B.)

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter2: Axially Loaded Members
Section: Chapter Questions
Problem 2.4.4P: A horizontal rigid bar ABC is pinned at end A and supported by two cables at points B and C. A...
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The bank in the figure is considered to be a person sitting and the force exerted on the board is given as 300 N. The elasticity module of the boards that make up the bench E = 7 GPa, Calculate the collapse at the point where a person sits, since the width of a board is 150 mm and the height is 30 mm. (Hint: Consider the AB board as if it is built into points A and B.)

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Step 1

Consider an inbuilt beam as shown below.

Mechanical Engineering homework question answer, step 1, image 1

Step 2

For an inbuilt beam deflection at the point of action of load can be calculated as,

Mechanical Engineering homework question answer, step 2, image 1

The moment of inertia of the cross-section can be calculated as,

Mechanical Engineering homework question answer, step 2, image 2

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