There are three types of offset shrinkage multipliers.
1. The first is given in UGLY's Electrical Reference. On page 140 the shrink for offsets is given as hypotenuse - side adjacacent.
The hypotenuse in triangle ABC is AC. The side adjacent is AB. The shrink is defined in Ugley's as distance AC - distance AB. For convenience this is called the geometric shrinkage. Distance BC is the height and angle 2 is the offset bend angle.
The shrinkage multiplier for this shrinkage can be determine by solving:
Multiplier x height = shrinkage
Shrinkage Multiplier = shrinkage / height
Distance AC can be found by:
Sine of 2
= BC/AC
AC = BC / sin 2
Distance
AB can be found by:
Tangent of 2 = BC/AB
AB = CB/Tan 2
Then shrinkage = AC - AB
shrinkage = BC / sin2 - BC/Tan 2
Shrinkage Multiplier = (BC / sin2 - BC/Tan 2) / BC
This reduces to:
Shrinkage Multiplier = (1 / sin2 - 1/Tan 2)
Using trigonometric identities this reduces to:
Shrinkage Multiplier = tan(2/2)
Since the tan of 0 degrees is equal 0, the value of this expression is 0 at zero degrees.
Since the tan (90/2) is 1, the value of the multiplier at 90 degrees is 1.
The values for this shrinkage multiplier are constant for given angles and does not vary for different radii or heights.
This method does not use the length of the bend or arc in the calculation.
2. The second shrinkage multiplier is determined by:
Calculator Shrinkage Multiplier = Shrinkage / Offset Height
The Calculator is located at bottom of this page and uses the equations previously described.
3. The third shrinkage multiplier are those given in Zip tables found
in handbooks and manuals and largely the result of Benfield's Tables as
published in the Benfield Conduit Bending Manual. These values are shown
in Table 1. These values are constant and do not vary with a
change in radii or height. These values assume that there are no bends or
arcs in the offset, and that the conduit follows a broken straight line path
(which it doesn't.) These shrinkage multiplier values can be calculated
using the calculator below by setting the radius to 0 and adjusting the angle. A
change in height does not effect the calculated shrink multiplier while the
radius is set to zero.
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Multiplier in inches |
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Table 1
Below are four charts made using an Excel Spreadsheet showing some typical differences in the three Shrinkage Multiplier Values. The spreadsheet is available by clicking here: If you are using IE and have Excel 2003 in your system you should be able to download and use this spreadsheet. Simply enter the height and radius and charts for other values will be calculated for you.
When new radii and height values are entered in the Excel spreadsheet the yellow plot representing the calculator values is the only one that changes. The values for Geometric and Table Shrinkage Multipliers remain the same because these values are not effected by different radii or heights.
Chart 1
Chart 2
Chart 3
Chart 4
Figure 1 illustrates proof that the calculator is calculating shrinkage correctly. Notice that the calculator shrinkage multiplier in Chart 4 is 0.57 for 90 degrees, but the geometric multiplier is 1.0. How can this be?
Assume that we have a piece of 4 inch conduit 62.8 inches long. Now bend two 90's using a radius of 20 inches with a total height of 40 inches. The developed lengths are (2)1.57(20 in.) or 62.8 inches. The new linear length is 40 inches (see below.) The total shrinkage is 62.8 in. - 40 in. or 22.8 inches. To get this shrinkage of 22.8 inches we have to multiply the height of 40 inches by the Shrinkage Multiplier. With algebra then the shrinkage multiplier is equal to 22.8 in. /40 in. or 0.57. This is an impractical bend, but it illustrates the calculator's accuracy and the effect of the gain around the bends.
Figure 1