Question 1 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 B 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
a)
Let RR represent the reaction force at Support B. By releasing the beam at Support B and imposing a force RR at Point B, the deflection of the beam consists of two parts,i.e.
Part I- the deflection caused by MBMB ;
Part II- the deflection caused by RR
Please treat R, w, h , L , E as variables in this step , the mathematical equation for the deflection at Point B caused by RR ( Part II) can be written as
b)
Using the provided data:
- cross-section width w = 19 mm,
- cross-section hight h = 100 mm,
- length of the beam L =3 m ,
- beam material’s Young’s modulus Q =206 GPa,
- applied bending moment MBMB = 12 kN.m
The value of the deflection at Point B caused by MBMB ( Part I) can be calculated as
(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
kN;
the value of the horizontal reaction force at Support A can be calculated as
KN
the absolute value of the reaction moment at Support A can be calculated as
kN.m
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