Answered: Пи (a) М — — Рх х V = -P (b)

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Пи (a) М — — Рх х V = -P (b)

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

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter1: Introduction To Statics

Section: Chapter Questions

Problem 1.8P: In some applications dealing with very high speeds, the velocity is measured in mm/s. Convert 8mm/s...

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Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

The cantilevered beam in Fig. a has a rectangular cross section and is subjected to a load P at its end. Determine the displacement of the
load. EI is constant.

Expert Solution

Step 1

The moment of the beam about the section is,

By the method of Macaulay’s double integration method.

Here, EI is the flexural rigidity, y is the deflection at x distance, and M_x-xis the moment at section.

From the above expression,

Step 2

Integrate the above expression with respect to x.

Integrate the above expression with respect to x again.

Here, C₁ and C₂ are the integrati1ng constant.

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