CAL contributor Stuart Edwards takes readers on a fun exercise, to look at how to best rig the original trophy distributed at the first Crane Industry Council of Australia National Conference in 1998.
THE TRADITION OF annual awards being presented at the CICA national conference began in 1998. The idea was drawn from similar awards in the crane and rigging industries in other countries, with some cross-fertilisation from awards in other industries.
Awards recognising excellence in lifting projects, and industry service through state and national industry bodies, and two icons of the past are remembered with trophies struck in their memory.
In a short time the awards have become an integral part of the CICA national crane conference. The trophies for the ﬁrst few years were of polished timber with engraved brass plates, which forms the basis of our technical article. Apparently these early trophies were heavy and needed a firm grip to hold onto them so we are going to look at the forces involved to hold one.
First off how heavy is one of these guys? This is as simple as volume (length x width x height) x density. Refer image on the right, and the calculation below.
Volume = 85 mm x 175 mm x 25 mm = 371,875 mm3
Mass = 371,875 mm3 x 8.4 x 10-3 g/mm3 = 3123.75 grams
Volume = 35 mm x 150 mm x 100 mm – (15 mm x 35 mm / 2 x 100 mm) = 498,750 mm3
Mass = 498,750 mm3 x 0.6 x 10-3 g/mm3 = 299.25 grams
Total mass = 3123.75 grams + 299.25 grams = 3,423 grams
Seems this trophy is heavy enough to be a replacement counterweight for a well know articulated crane…
You might notice this is broken down in the table below further into subsections, more about this when we discuss calculating the centre of gravity.
Centre of gravity
The mass is only one part of the story. This trophy also has an offset centre of gravity. Working this out basically comes down to adding up mass x distance for each subsection from a base point to determine a moment for each (refer diagram for numbering of each subsection / element). Add up the total of the moments (for example 294,669.38 g.mm for the x direction), then divide by overall mass (294,669.38 g.mm / 3,423 g) and voila you have the centre of gravity (= 86.09 mm from the end). Repeat and rinse for the z direction. It’s easiest to add this up in a table like the one below (a excel version can be obtained for free from firstname.lastname@example.org).
Tip: For determining the centroid of segments as shown below, the centroid of a rectangle is always in the middle. The centroid of a triangle is always 1/3 the length of the triangle from the base.
Now comes the part where the above two items come together. Let’s say we hold it as pictured on the right. To determine the force acting on the fingers we need to take moments about the thumb position. For simplicity let’s say the thumb provides force to the end of the trophy so the centre of gravity is 86.09 mm away and the finger force acts 46 mm away from the end as pictured below. The moment the fingers need to counteract is 3,423 g x 86.09 mm = 294,668.38 g.mm. Divide by their lever arm (294,668.38 g.mm / 46 mm = 6.4 kg. And thus the mystery of why these trophies need to be held so tightly is solved.
These forces will be increased by acceleration. Let’s say you are lifting it up at 1.2 G. The overall force on your fingers would be (3,423 g x 86.09 mm x 1.2) / 46 mm = 7.7 kg.
Naturally these formulas can be used for a lot crane or rigging related tasks: the sky is the limit. (Ed. Note: subject to boom length).