A propped cantilever beam is loaded by a bending moment of the magnitude Mã 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 A MB X Figure Q1 Assuming the positive deflections and positive vertical reaction forces are upward, calculate o the value of the reaction forces at points A and B o the absolute value of the reaction bending moment at point A

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter9: Deflections Of Beams
Section: Chapter Questions
Problem 9.3.17P: -17 A cantilever beam AB is acted upon by a uniformly distributed moment (bending moment, not...
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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 II) can be written as 

(Hint : to input equation R2LQ2wh , you can type  (R^2*L)/(Q^2*w*h) )

 

b) Using the provided data:

  • cross-section width w = 20  mm,
  • cross-section hight h = 93   mm,
  • length of the beam L =3   m ,
  • beam material’s Young’s modulus Q =226 GPa,
  • applied bending moment MB = 11 kN.m 

The value of the deflection at Point B caused by MB ( Part I) can be calculated as ......(in mm)

A propped cantilever beam is loaded by a bending moment of the magnitude Mã 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
A
MB
X
Figure Q1
Assuming the positive deflections and positive vertical reaction forces are upward, calculate
o the value of the reaction forces at points A and B
o the absolute value of the reaction bending moment at point A
Transcribed Image Text:A propped cantilever beam is loaded by a bending moment of the magnitude Mã 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 A MB X Figure Q1 Assuming the positive deflections and positive vertical reaction forces are upward, calculate o the value of the reaction forces at points A and B o the absolute value of the reaction bending moment at point A
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