Question

at what distance a should the journal bearing supports at a and b be placed so that the magnitude (absolute value) of the deflection at the center of the shaft is equal to the deflection at its ends?

Answer 1

For the magnitude of the deflection at the center of the shaft to be equal to the deflection at its ends, the journal bearing supports at points A and B should be placed at a distance equal to one-third of the length of the shaft.

Step-by-step explanation:

For the magnitude of the deflection at the center of the shaft to be equal to the deflection at its ends, the journal bearing supports at points A and B should be placed at a distance equal to one-third of the length of the shaft.

Let's assume that the distance from point A to the center of the shaft is 'x'. Then, the distance from point B to the center of the shaft will be '2x'.

To find the value of 'x', we can use the equation:

x = (length of the shaft) / 3

For example, if the length of the shaft is 9 units, then the journal bearing supports should be placed at distances of 3 units (point A) and 6 units (point B) from the center of the shaft.