A propped cantilever beam is loaded by a bending moment of the magnitude MB at the point B as shown in Figure Q1. The cross-section of the beam is a rectangle of the width w and the hight h that are constant along the length of the beam L. The beam material's Young's modulus is Q. AY O A B M₂ X Figure Q1 Assuming the positive deflections and positive vertical reaction forces are upward, calculate the value of the reaction forces at points A and B the absolute value of the reaction bending moment at point A

A propped cantilever beam is loaded by a bending moment of the magnitude MB at the point B as shown in Figure Q1. The cross-section of the beam is a rectangle of the width w and the hight h that are constant along the length of the beam L. The beam material's Young's modulus is Q. AY O A B M₂ X Figure Q1 Assuming the positive deflections and positive vertical reaction forces are upward, calculate the value of the reaction forces at points A and B the absolute value of the reaction bending moment at point A

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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Concept explainers

Types of loading

In mechanical terminology, the term load indicates that external force/weight, either constant or variable, acts on a mechanical member/structure. The weight of an object of a specific material is also an external load, and the external force that works on a structure comes under the categories of loading. The external load generates its effects as stress and strain in the structure.

Question

A propped cantilever beam is loaded by a bending moment of the magnitude MB at the point
B as shown in Figure Q1. The cross-section of the beam is a rectangle of the width w and the
hight h that are constant along the length of the beam L. The beam material's Young's
modulus is Q.
AY
O
X
Figure Q1
Assuming the positive deflections and positive vertical reaction forces are upward, calculate
the value of the reaction forces at points A and B
O the absolute value of the reaction bending moment at point A

(a)
Let R represent the reaction force at Support B. By releasing the beam at Support B and
imposing a force R at Point B, the deflection of the beam consists of two parts,i.e.
Part I- the deflection caused by MB;
Part II- the deflection caused by R
Please treat R, w, h, L, E as variables in this step, the mathematical equation for the
deflection at Point B caused by R (Part can be written as
(Hint: to input equation
R²L
Q² wh
, you can type (R^2*L)/(Q^2*w*h) )

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