A propped cantilever beam is loaded by a bending moment of the magnitude M_B 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. 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) 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 M_B ;
A propped cantilever beam is loaded by a bending moment of the magnitude M_B 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.
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) 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 M_B ;
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:
b)
Using the provided data:
- cross-section width w = 14 mm,
- cross-section hight h = 82 mm,
- length of the beam L =2 m ,
- beam material’s Young’s modulus Q =233 GPa,
- applied bending moment M_B = 9 kN.m
The value of the deflection at Point B caused by M_B ( Part I) can be calculated as: __mm
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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