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 |- A 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 (b) (a) Let R represent the reaction force at Support B. By releasing the beam at Support B and imposing a force Rat 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 ● R²L Q² wh mm M Using the provided data: cross-section width w = 11 mm, cross-section hight h = 66 mm, • length of the beam L = 3 m, • beam material's Young's modulus Q =240 GPa, applied bending moment MB = 6 kN.m The value of the deflection at Point B caused by MB (Part I) can be calculated as , you can type (R^2*L)/(Q^2*w*h)) (c) Based on the given values of dimensions and material parameters, the value of R can be calculated as KN; the value of the vertical reaction force at Support A can be calculated as the value of the horizontal reaction force at Support A can be calculated as the absolute value of the reaction moment at Support A can be calculated as kN; KN kN.m
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 |- A 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 (b) (a) Let R represent the reaction force at Support B. By releasing the beam at Support B and imposing a force Rat 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 ● R²L Q² wh mm M Using the provided data: cross-section width w = 11 mm, cross-section hight h = 66 mm, • length of the beam L = 3 m, • beam material's Young's modulus Q =240 GPa, applied bending moment MB = 6 kN.m The value of the deflection at Point B caused by MB (Part I) can be calculated as , you can type (R^2*L)/(Q^2*w*h)) (c) Based on the given values of dimensions and material parameters, the value of R can be calculated as KN; the value of the vertical reaction force at Support A can be calculated as the value of the horizontal reaction force at Support A can be calculated as the absolute value of the reaction moment at Support A can be calculated as kN; KN kN.m
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 9.11.5P: Beam AB has an elastic support kR at A, pin support at B, length L, height h (see figure), and is...
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Transcribed Image Text: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
H
(c)
A
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
(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
(b)
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
R²L
Q² wh
Using the provided data:
X
mm
, you can type (R^2*L)/(Q^2*w*h))
• cross-section width w = 11 mm,
• cross-section hight h = 66 mm,
length of the beam L =3 m,
• beam material's Young's modulus Q =240 GPa,
applied bending moment MB = 6 kN.m
The value of the deflection at Point B caused by MB (Part I) can be calculated as
Based on the given values of dimensions and material parameters,
the value of R can be calculated as
kN;
the value of the vertical reaction force at Support A can be calculated as
the value of the horizontal reaction force at Support A can be calculated as
the absolute value of the reaction moment at Support A can be calculated as
kN;
KN
kN.m
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