Given: A beam is supported at its ends by supports which are 12 m apart. There is a deflection of 3 cm at the center, and the deflected beam is in the shape of a parabola.
Need to find: How far from the center is the deflection 1 cm
Here EF are the ends of the beam and they are 12 m apart.
IJ is the deflection of 3 cm at the center. We know,
that the distance IF= 12/2 = 6 m = 600 cm and the deflection IJ = FH = 3 cm.
So, the coordinate of the point F is (600, 3)
Let, the equation of the parabola is: x2 = 4ay
F point is on the parabola. So, putting the coordinates of F in the equation we get,
x2 = 4ay
⇒ 3600 = 4a x 3
⇒ a = 300
Here KL denotes the deflection of 1 cm.
So, at the point L the value of y-coordinate is (3 – 1) = 2
So, by the equation,
⇒ x2 = 4ay = 4 x 300 x 2 = 2400
⇒ x = 49 cm.
So, the distance of the point of 1 cm deflection from the center is 49 cm.