Question

1800 mm long shaft abcd of diameter 60 mm over half its length ab and(10 marks)40 mm diameter for the remaining half-length bd, is subjected to a torque of900 nm at a section c midway between b and reacting torque at the supports?

Answer 1

The reacting torque at the supports of the given shaft is 45 Nm.

Step-by-step explanation:

To find the reacting torque at the supports for the given shaft, we can use the concept of torque. Torque is the product of force and lever arm distance. In this case, the torque at section C is given as 900 Nm. To calculate the reacting torque at the supports, we need to consider the different parts of the shaft.

1. For the half length AB of the shaft with a diameter of 60 mm, we can calculate the torque using the formula:

Torque = Force x Lever Arm Distance

Force = 900 Nm (given)

Lever Arm Distance = radius = (60 mm / 2)

= 30 mm

= 0.03 m

Substituting the values, we get:

Torque_AB = 900 Nm x 0.03 m

= 27 Nm

2. For the remaining half length BD of the shaft with a diameter of 40 mm, we can use a similar calculation:

Force = 900 Nm (given)

Lever Arm Distance = radius = (40 mm / 2)

= 20 mm

= 0.02 m

Torque_BD = 900 Nm x 0.02 m

= 18 Nm

The total torque at the supports is the sum of the torques at sections AB and BD:

Reacting Torque = Torque_AB + Torque_BD

= 27 Nm + 18 Nm

= 45 Nm