Worked example for single point grommet lift#
Purpose of this example is to illustrate the definitions and use of MBL, global and local factors, bending and friction.
This is done using a very simple model:
Input#
The diameter of the circles is 2.0m
The mass of the body is 300t
The MBL of the grommet is 900t
The nominal length of the grommet is 20m
Definition of MBL and MBL of wire#
The MBL of the grommet is set to 900t. This is the MBL of the grommet when used in a typical way, like in this example. The MBL of the cable-laid rope is half of that: 450t. This definition is in line with DNV / IMCA / EN codes where the WLL is defines at twice the minimum breaking force of the unit rope.
The diameter, weight and EA of the rope are estimated from the provided MBL.
Estimation of Grommet properties#
The values for MBL, diameter, weight and EA can either be provided by the user or can be estimated by DAVE. In case of estimation at least one of the values needs to be supplied. In this example that value is the MBL. The section below demonstrates how the automatically derived values are calculated. A table for all situations is given in sling and grommet properties.
Diameter#
The diameter is estimated to be 108.1mm. This is done as follows:
The diameter is derived from annex G of BS EN 13414-3:2003+A1 :2008 / EN 13414-3:2003+A1 :2008 (E). This table gives the relation between the WLL (working load limit) and diameter. To convert from MBL to WLL the diameter based safety-factor (SF = 6.33 - 0.022d = 6.33 - 0.022 * 108 = 3.95) is used. WLL = MBL / SF = 900 / 3.95 = 228t. A working-load limit of 228t corresponds to a wire-diameter of 108mm
Estimation of weight#
The weight is derived from the cross sectional diameter and the density of steel. The steel area of a wire rope is \( {0.68 \cdot \pi \over 4} ({d_s \over 1000})^2\). A cable-laid grommet contains 7 sub-ropes. The combined diameter of the 7 sub-ropes is 3 times that of the individual ropes. The area is \(3^2\) = 9. This means that an area 9 times as large as that of a single sub-rope contains 7 times the amount of material.
\( As = {7 \over 9} {0.68 \cdot \pi \over 4} ({d_s \over 1000})^2 = 0.00486 m^2\)
The density of steel is 7850 kg / m3 resulting in a mass per length of 38.1kg/m
Estimation of EA#
The stiffness of the grommet wire is derived from the area the numerical results presented in a paper (“simple determination of the axial stiffness for large-diameter independent wire rope core or fibre core wire ropes” M Raoof and T J Davies). This paper derives a relation between the modulus of elasticity (E) of steel rod and that of a rope with the same diameter. The estimation by DAVE uses a factor of 0.6 for this relation.
This factor of 0.6 is for going from steel rods to a a rope meaning that the stiffness of a rope is effectively 0.6x that of a steel rod with the same steel area.
Reasoning that the step from IWRC to a cable laid construction is similar to going from steel rods to a IWRC, the factor of 0.6 is applied twice.
Property |
Value |
Unit |
---|---|---|
As |
0.00486 |
m2 |
E_steel |
210e6 |
kN/m2 |
Factor from steel rod to IWRC |
0.6 |
[-] |
Factor from IWRC to cable-laid |
0.6 |
[-] |
EA |
\(3.7 \cdot 10^5\) |
kN |
It is noted that DNVGL also provides guidance for estimation of the EA in section 16.2.6.13:
Situation |
Formulas for E and A |
Value [kN] |
---|---|---|
in combination with a 1.25 SKL for 4-sling lifts using matched pairs of wire single laid slings |
E = 25kN/mm2 |
\(2.3 \cdot 10^5\) |
for indeterminate 4-sling lifts using four single laid slings of un-equal length |
E = 80kN/mm2 |
\(7.3 \cdot 10^5\) |
These values from the DNV guidance are around the estimation given by DAVE.
Total properties#
The total properties of the grommet are derived from the properties of the wire and the length.
In this example the length of the grommet is defined to be a nominal length of 20m.
Section |
Length of wire |
Length of wire |
---|---|---|
Straight sections |
The distance between the centers of the pins is 20m - 300mm = 19.7m |
39.4m |
Bended sections |
The diameter of the wire itself is 108mm. This makes the radius of the bent equal to \((300+108) /2 = 204mm\). |
1.28m |
Total |
Sum of above |
40.68m |
Weight#
The total weight is the length of wire time the weight per length: \(40.68m \cdot 38.1 kg/m \) = 1551 kg
Stiffness (EA/L)#
The total stiffness (EA/L) is derived from the length between the centers of the pins and the stiffness of the configuration shown above.
For this situation this is approximately equal to 2x EA of the wire divided by the nominal length: \(2 \times 3.7 \cdot10^5 / 20 \) = 3.68e4 kN/m.
The exact stiffness is slightly lower as is corrects for the amount of wire in the bends as well resulting in a slightly lower stiffness:
2 * EA * (length-in-straight-sections / total_wire_length) / distance_between_pins = 3.67e4 kN/m
Analysis#
The rigging analysis checks if the expected loads are less than the allowable loads. The relation between those two is expressed in a Unit-Check (UC).
In this example the global load factors for weight, cog position and dynamics are all set to 1.0 for ease of the example.
Yaw factor / Rigging length variation#
For the example the yaw factor is replaced by a variation of rigging lengths. For this purpose a single loadcase is created in which the length of the grommet is increased by 2.0x its diameter.
Note that the length variation is applied on the ultimate length, meaning that the wire length is in fact increased by 4d.
One may expect the load to be equal in both loadcases. This is however not the case. The load in the loadcase with an increase grommet length is slightly higher. This is because the weight of the grommet itself is considered as well. The weight is calculated from the diameter and the length, so a longer grommet is heavier. Therefore the load-case with the increased length is governing.
Partial safety factors#
The majority of the partial safety factors are directly specified by the user. Only exception is bending which is calculated automatically.
Bending#
Bending is calculated automatically using the standard formulation:
\(1 \over {{1-{0.5 \over {sqrt(D/d)}}}}\)
For D = 2.0m and d = 0.108 this yields 1.13 [-].
Friction#
Friction is implemented as an additional force distribution AFTER calculating statics. This is determined automatically based on the number of circles that the grommet runs over. The reasoning is that every bend can add 10% of friction. For the current configuration with two bends this results in a 55%/45% load distribution.
Final check#
The maximum expected load (including friction) follows directly from the load-cases. In this example the loadcase “tension #1” is governing with a tension of 1625.88N in the grommet with increased length.
As all global factors are set to 1.0 this directly yields the factored load. Note that this is the load in the wire of the grommet, not the grommet as a whole. As such is equals half the lifted mass plus the weight of the grommet and divided using 45%/55% load distribution; 0.55 * (300t + 1.5t ) .
The allowed load is the MBL of the cable-laid rope (half of the MBL of the whole grommet, see MBL section above) in combination with the partial safety factors.
Finally the unity check is the factored load compared to the allowed load. In this case the UC <= 1.00 which means the result of the check is OK.