Q. 53.6( 5 Votes )

A beam is supported at its ends by supports which are 12 m apart. Since the load is concentrated at its center, there is a deflection of 3 cm at the center, and the deflected beam is in the shape of a parabola. How far from the center is the deflection 1 cm?

Answer :

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 = 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.


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