Why are there no problems in most cases, even though hardly anyone does the math?
This can be proven on the basis of calculations. Provided that, as described in Part 1, no technical errors are made.
As a basic principle, the securing force exerted by the pad must be at least as great as the force exerted by the load, and the load must not move.
Case studies
What would these barrel pallets do at a rolling angle of 37ยบ?
They would naturally slip or tip over. A rolling period of up to 2-3 times per minute is not unusual. The roll angle of 38ยบ would correspond to the maximum acceleration of 0.8 g transverse to the direction of travel.
Let’s take the classic block of five Euro pallets as an example, as described in Part 1.
The load units weigh 900 kg each and are 1.60 m high. The side length of the two blocks is 2.40 m each.
The question now is, how large must the stowage cushion be so that the force from the load is compensated by 80% of the cushion area?
Calculate the upholstery area:
Side length:
2.40 m x 0.8 = 1.92 m
Height:
1.60 m x 0.8 = 1.28 m
Gap width:
0,34 m
The width of the gap between the loading units results from the internal width of the container of 2.34 m, minus the pallet dimensions of 1.20 m + 0.80 m, i.e. 0.34 m.
Formula for the effective area of a baffle plate
The formula from the CTU code for the effective area of the cushion is as follows:
A = (bDB – ฯ * d/2) * (hDB – ฯ * d/2)
- bDB = width of the stowage cushion [m]
- hDB = height of the baffle [m]
- A = Contact area between dunnage bag and load [m2]
- d = gap between packages [m]
- ฯ = 3,14
Step 1
The formula contains the width (bDB) as well as the height (hDB) and the gap width (d).
In order to determine the respective initial dimension, the elements of the formula must be rearranged:
(bDB – ฯ * d/2) becomes (bDB + ฯ * d/2) and (hDB – ฯ * d/2) becomes (hDB + ฯ * d/2)
To stay with the example described, the production dimensions for the upholstery result from the following calculation:
Length/width = (bDB + ฯ * d/2) = 1.92m + 3.14 * 0.34/2) = 1.92m + 0.53m = 2.45m
Upholstery height = (hDB + ฯ * d/2) = 1.28m + 3.14 * 0.34/2) = 1.28m + 0.53m = 1.81m.
Step 2
The next step is to compare the permissible load on the pad with the force from the load. There must be at least a balance.
The CTU code specifies the following formula for the pad load:
FDB = A * 10 * g *PB * SF [kN]
- FDB = Force that the dunnage bag can absorb without exceeding the maximum permissible pressure (kN)
- PB = Burst pressure of the baffle plate [bar]
The value for the burst pressure must be requested from the supplier. The value ofPB = 0.55 bar applies to a standard cushion with level 1 and is used representatively in my calculation. - A = Contact area between dunnage bag and load [m2]
- SF = Safety factor
0.75 for dunnage bags for single use
0.5 for reusable dunnage bags
Using the values from the example above, the following results: FDB = 1.92 * 1.28 * 10 * 9.81m/s2 * 0.55 * 0.75 [kN] = 67.77 kN.
The force that this cushion can exert against a load is therefore 6,777 daN.
Step 3
The next step is to calculate the force resulting from the load.
Here are the formulas from the CTU code for a sliding/tilting load. However, it is important to note that the weight is given in tons and not in kilograms as usual.
Glide:
FLAG = m * g * (cx,y – ฮผstatic * 0.75 * cz ) [kN]
Tipping:
CHARGE = m * g * (cx,y – bp /hp * cz ) [kN]
Inserting the values from the example into the calculation results in the following:
FLoad = 2.7 to * 9.81 m/s2 * (0.8 – 0.3 * 0.75 * 0.2) [kN]
FLoad = 26.45 * (0.8 – 0.045) [kN]
FLoad = 26.45 * 0.755 = 19.97 kN = 1,997 daN
The securing force (6,777 daN) resulting from the stowage cushion is therefore 3.3 times greater than the force (1,997 daN) resulting from the load.
Conversely, this means that if the size of the cushion is selected so that the load is held flat, i.e. cannot tip, slide or turn, the securing force of the cushion is generally always sufficient.
Yours, Sigurd Ehringer
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Episode 20: Dunnage bags load securing – Part 1
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Episode 22: Floor loads on trucks
Tobias Kreft