A propped cantilever beam is loaded by a bending moment of the magnitude MB at the...
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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 RL Q 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 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 RL Q 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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For part a we are looking to find the mathematical equation for the deflection at point B caused by the reaction force R Part II This is a problem from structural engineering mechanics specifically de... View the full answer
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