Answered: Describe the procedure that provides…

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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Question

Describe the procedure that provides a method for determining the
slope and deflection of a beam?

Expert Solution

Step 1

To provide:

A method for determining the slope and deflection of a beam

Slope:

The angle made by a tangent drawn to the elastic curve with the axis of the beam is known as slope

Deflection:

The vertical displacement of any point on the beam up-to elastic curve is deflection of that point

Note: For design of the beam based on stiffness criteria maximum deflection of the beam must be less than the allowable deflection.

There are 5 methods to find slope and deflection of a beam

Double Integration/ Macaulay's Method : This method is suitable for prismatic beam only and where equation of bending moment remains constant through out the section.
Modified Macaulay's Method: It is an improvement over double integration method and it is suitable for prismatic beam with discontinuous loading.
Area moment method: This method is suitable for both prismatic and non prismatic beam, it is used where it is easy to draw M/EI diagram and easy to find area and centroid of the M/EI diagram, easy to find zero slope and zero deflection point.
Strain energy method : This method can be use for both prismatic and non prismatic but mostly used for cantilever beam
Conjugate beam method : This method can be used for both prismatic and non prismatic beam

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