I attached a free body diagram for a better understanding of this problem.
We start making summation of Moments in A,
[tex]\sum M_A = 0[/tex]
[tex]P(6cos\theta)-981(4cos\theta)=0[/tex]
[tex]P=654N[/tex]
Then we make a summation of Forces in Y,
[tex]\sum F_y = 0[/tex]
[tex]654+R-981 = 0[/tex]
[tex]R=327N[/tex]
At the end we calculate the angle with the sin.
[tex]sin\theta = \frac{3m}{4m+2m+2m} = \frac{3m}{8m}[/tex]
[tex]\theta = 22.02\°[/tex]
To calculate the tension in the string and the reaction at point A, We must know about the concept of Bending moment.
A bending moment is the measure of the bending effect that may occur when an external force is been applied. It is calculated by multiplying the magnitude of the force with the perpendicular distance between that point and the force.
The tension in the string will be equal to 654 N, while the reaction at point A will be equal to 327 N.
Given to us
The uniform 100-kg I-beam is supported initially by its end rollers on the horizontal surface at A and B.
By means of the cable at C, it is desired to elevate end B to a position 3 m above end A.
To calculate the angles angle q made by the beam with the horizontal in the elevated position.
We will use the trigonometric function,
[tex]Sin\ \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]Sin\ \theta=\dfrac{\text{Elevated height of the beam}}{\text{Length of the beam}}[/tex]
[tex]Sin\ \theta=\dfrac{3}{8}\\\\\theta = 22.024^o[/tex]
Further, we will calculate the Bending moment about point A,
The bending moment is calculated by multiplying the force and the perpendicular distance between that force and the point, therefore,
[tex]\sum M_A = 0[/tex]
[tex](100\times 9.81)(4Cos\ \theta) = T(6Cos\ \theta)[/tex]
where T is the tension in the string,
Substitute the values,
T = 654 N
Similarly, we will calculate the Bending Moment about Point C,
[tex]\sum M_C = 0[/tex]
[tex]R\cdot(4\ cos\ \theta) = T(2\ cos\ \theta)\\\\[/tex]
where T is the tension in the string and R is the reaction at point A,
Substitute the values,
R = 327 N
Hence, the tension in the string will be equal to 654 N, while the reaction at point A will be equal to 327 N.
Learn more about Bending Moment:
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