AY E | Figure Q1 X

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