Don't tip over the crane

There's a 10# load (the bucket) hanging from the boom, which is at a 30 degree angle


The 10# load is pulling down on the boom, and since the boom is attached to the crane mast ( the vertical column)

by the boom lines, that 10# force is really pulling on the crane and trying to tip it over.

What about the boom? The weight of the boom  (11#) acts like another load that's also trying to tip over the crane.

These 2 forces  are called the  OVERTURNING MOMENT

The formula for moment is:

Moment  = Force  x  Distance 

The Force is the 10# load - actually it's the force of gravity that's pulling the bucket down.

What about the Distance?

The boom is 4ft long, - the distance from the tip of the boom (where the force is pulling down)

to the pivot is 4ft. But that's NOT  the shortest distance from the line of force to the pivot.

You forgot what the line of force is- go back and watch the video.


We need the perpendicular distance (90 degree).

So we draw a right triangle- with a 30 degree base angle and a hypotenuse of  4ft.

To find DISTANCE/load we'll use the cosine function.

Cos 30 = Dload / Hyp.

cos 30 = .866

.866 = Dload / 4ft

     Dload= 3.464ft 

 Next we plug in the numbers

 M = F x D

M = 10# x 3.464 ft

M = 34.64ft pounds or 34.64 ft#

 Now for the boom. It weighs 11# so we have to find M/boom

M = F x D

We know the force is 11#, and  the distance is measured at right angles from the line of force to the pivot. So where's the line of force?

For the bucket, the line of force went through the center of mass, or the center of gravity (CG) of the bucket- that makes sense.

 Is the CG of the boom in the middle (halfway up the length)? It would be if the weight of the boom were evenly distributed along

the length of the boom- but the tip of the boom is heavier ( it has  all those pulleys and steel bolts, etc. plus the jib.)

We found the CG of the boom to be 32" ( 2.6ft) from the pivot.


Now we have a similar triangle with a 2.6ft.  hyp.

To find DIST/boom

Cos 30 = Dboom / 2.6ft

Cos 30 = .866

.866 = Dboom / 2.6 ft

D/boom = 2.25ft

M = F x D

 M = 11# x 2.25ft

M= 24.75ft#

TOTAL M      24.75ft# + 34.64ft# = 59.39ft# 

So the turning force(moment) that's trying to tip the crane over -the OTM- is almost 60ft#.

 What's preventing this? - the righting moment- RM.