Question

A 3-meter long cantilever weighing 80 N·m−1 carries an end load of 0.9 kN. What is the total clockwise moment applied to the beam? (You must provide an answer before moving to the next part.) The total clockwise moment applied to the beam is ______ N·m.

Answer 1

3060 N-m

Step-by-step explanation:

length of the cantilever = 3 m

weight of the cantilever = 80 kN/m

End load carried P = 0.9 kN = 900 N

The total weight of the cantilever = (weight per meter) x (length)

total weight W = 80 x 3 = 240 N

This total weight is assumed to act at the center of the cantilever at point 1.5 m from the end of the cantilever

The cantilever is fixed at one end.

Moment about a point = Weight x ⊥d

where

⊥d is the perpendicular distance from the hinged point to the point where the weight acts

In this case, the hinged point is from the fixed end of the beam.

Perpendicular distance between the load P to the hinged point = 3 m

The total clockwise moment on the beam will be due to the weight of the beam acting at the center, and the weight at the end of the beam.

M = (W x 1.5) + (P x 3)

M = (240 x 1.5) + (900 x 3)

M = 360 + 2700

M = 3060 N-m