Dynamic vertical wheel load
As a result of a sudden drop of a full load, a slip of the sling or a sudden braking action during the travel of a fully loaded crane (where the load includes the self-weight of the
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crane), a dynamic effect on the wheels is generated, thereby increasing the static wheel load. This effect is defi ned by an impact factor that is multiplied by the static wheel load to give the dynamic wheel load. Thus
maximum dynamic vertical wheel load = static wheel load × dynamic factor (ϕ).
The dynamic factor varies depending on the class of duty (loading class) of the crane.
Table 2.1 gives various loading classes. Groups of loads and dynamic factors to be considered as one characteristic crane action are listed in Table 2.2. The equations listed in Table 2.3 should be used to calculate the values of the dynamic factors ϕi.
The vertical dynamic factors can be evaluated as follows.
For hoisting classes HC1and HC2, for example, referring to Table 2.3, we have the dynamic factor ϕ1 for vertical loads: 0.9 < ϕ1 < 1.1. Assume ϕ1 = 0.9, the lower value for vibrational pulses. We also have
ϕ2 = ϕ2, min + β2vh
where ϕ2, min = 1.05 and β2 = 0.17 for hoisting class HC1, and ϕ2, min = 1.1 and β2 = 0.34 for hoisting class HC2 (see Table 2.4). In addition,
Vb = steady hoisting speed = 1.3 m/s (assumed).
Therefore
for class HC1: dynamic factor = ϕ2 = 1.05 + 0.17 × 1.3 = 1.27;
for class HC2: dynamic factor = ϕ2 = 1.1 + 0.341.3 = 1.54.
Thus, referring to Table 2.2 and assuming the group of loads 1, we have the following:
for class HC1: ϕ = ϕ1ϕ2 = 0.9 × 1.27 = 1.14;
Table 2.1. Recommendations for loading classes (based on Table B.1 in Eurocode 1, Part 3)a
Item Type of crane Hoisting class S-class
1 Hand-operated cranes HC1 S0, S1
2 Assembly cranes HC1, HC2 S0, S1
3 Power house cranes HC1 S1, S2
4 Storage cranes with intermittent operation HC2 S4
5 Storage cranes and spreader bar cranes, with continuous operation
HC3, HC4 S6, S7
6 Workshop cranes H2, H3 S3, S4
7 Overhead travelling cranes and ram cranes,
|with grab and magnet operation
HC3, HC4 S6, S7
8 Casting cranes HC2, HC3 S6, S7
9 Soaking-pit cranes HC3, HC4 S7, S8
10 Stripper cranes, charging cranes HC4 S8, S9
11 Forging cranes HC4 S6, S7
a The bottom part of the table has been omitted as the types of crane in the bottom part are not relevant in this context.
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Table 2.3. Dynamic factors ϕι for vertical loads (based on Table 2.4 of Eurocode 1, Part 3) Dynamic
factor ϕi Value of dynamic factor
ϕ1 0.9 < ϕ1 < 1.1
The two values 1.1 and 0.9 refl ect the upper and lower values of vibrational pulses ϕ2 ϕ2 = ϕ2, min + β2vh, where vh = steady hoisting speed in m/s
For ϕ2, min and β2, see Table 2.4
ϕ3 ϕ3 = 1 −Δm (1 + β3)/m, where Δm = released or dropped part of the hoisting mass, m = total hoisting mass, β3 = 0.5 for cranes equipped with grabs or similar slow-release devices, and β3 = 1.0 for cranes equipped with magnets or similar rapid-release devices.
ϕ4 ϕ4 = 1.0 provided that the tolerances for rail tracks as specifi ed in EN 1993-6 are observed
Table 2.4. Values of β2 and ϕ2, min (based on Table 2.5 of Eurocode 1, Part 3)
Hoisting class of appliance β2 ϕ2, min
HC1 0.17 1.05
HC2 0.34 1.10
HC3 0.51 1.15
HC4 0.68 1.2
Table 2.2. Groups of loads and dynamic factors to be considered as one characteristic crane action (based on Table 2.2 of Eurocode 1, Part 3)a
Groups of loads
Ultimate limit state
Test load
Accidental load
Item Description Symbol
Section of Eurocode 1,
Part 3 1 2 3 4 5 6 7 8 9 10
1 Self-weight of crane Qc 2.6 ϕ1 ϕ1 1 ϕ4 ϕ4 ϕ4 1 ϕ1 1 1
2 Hoist load Qh 2.6 ϕ2 ϕ3 ϕ4 ϕ4 ϕ4 η 1 1
3 Acceleration of crane bridge
HL, HT 2.7 ϕ5 ϕ5 ϕ5 ϕ5 – – – ϕ5 – – 4 Skewing of crane
bridge
Hs 2.7 – – – – 1 – – – – –
5 Acceleration or braking of crab or hoist block
HT3 2.7 – – – – – 1 – – – –
6 In-service wind Fw Annex A 1 1 1 1 1 – – 1 – –
7 Test load QT 2.10 – – – – – – – ϕ6 – –
8 Buffer force HB 2.11 – – – – – – – – ϕ7 –
9 Tilting force HTA 2.11 – – – – – – – – – 1
aη is the proportion of the hoist load that remains when the payload is removed; it is not included in the self-weight of the crane.
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for class HC2: ϕ = 0.9 × 1.54 = 1.38.
The following vertical dynamic factors may be used as guidance for various hoisting classes:
For hoisting class HC1, light-duty hand-operated cranes, assembly cranes, power house cranes and intermittently used storage cranes: dynamic factor ϕ = 1.1 (mini- mum) to 1.25.
For hoisting class HC2, medium-duty cranes (normally in factories, workshops and warehouses, and for casting and in scrapyards with continuous operation): dynamic factor ϕ = 1.25 to 1.4.
For hoisting class HC3, heavy-duty cranes (in foundries and for intermittent grab and magnet work, forging, charging etc.): dynamic factor ϕ = 1.4 (minimum).
Generally, the crane manufacturer will provide the dynamic factor along with the crane wheel loads when details of the duty (class), the span of the crane and the lifting capacity are given to the manufacturer. In our case, the vertical dynamic factor (ϕ) provided by the crane manufacturer is 1.4.
Transverse horizontal force (surge) on a crane girder during travelling of crane
This transverse horizontal surge is generated owing to the following factors:
Thrust from sudden application of the brakes of the crab motor, causing abrupt stoppage of the crab and load when traversing the crab girders. This thrust is resisted by the frictional force developed between the crab wheels and crab girders, is then transferred to the crosshead girders of the crane, and is fi nally transferred as point loads through the main wheels of the crane into the top fl ange of the crane girders.
A crane often drags weights across the shop fl oor. If the weight is very heavy, this pulling action induces a transverse horizontal component of force (a point load) on the crane girders through the crane wheels.
The transverse horizontal force generated by either of the above causes or by a combination of both of them is transferred to the crane girders through the double-fl anged crane wheels on the end carriages, and cranes are designed to avoid the possibility of derailment.
It is quite diffi cult to determine the value of this force quantitatively, as there are unknown factors besides the above facts. American specifi cations stipulate that the horizon- tal transverse force on each gantry girder is equal to 10% of the load lifted. The Brit- ish code of practice BS 2573-1: 1983 (British Standards Institution, 1983) specifi es the following:
value of total transverse horizontal force = 1/10 × weight of (lift load + crab).
Eurocode 1, Part 3 stipulates the same value. Therefore
value of total transverse horizontal force = 1/10 × weight of (lift load + crab).
This force should be shared equally between the two gantry girders.
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Longitudinal horizontal force
During the travelling of the crane, the sudden application of brakes induces frictional resistance to the sliding of the locked wheels upon a rail fi xed to the gantry girder. This frictional resistance, in turn, generates a horizontal force along the length of the gantry girder, and fi nally transfers to the columns that support the gantry girder. Assume that the coeffi cient of friction μ for steel sliding on steel is 0.2. Consider the maximum vertical wheel load on the gantry girder, which occurs when the load lifted is at the nearest allow- able position to the gantry girder. So,
maximum wheel load on the nearest gantry girder = maximum reaction from crane (load lifted + half the dead weight of crane) = W = R.
For example, if the load lifted is W1, the self-weight of the crane is W2, the distance of the load lifted from the nearest gantry girder is l and the crane span (centre to centre of cross- head) is L, then
maximum on-wheel load = W1(L − l )/L + W2/2 = W = R.
Therefore
longitudinal horizontal force developed = Rμ = 0.2R.
The American code of practice specifi es that the longitudinal force is equal to 10% of the maximum wheel load. The British code of practice BS 2573 specifi es that the longitu- dinal force is equal to 5% of the maximum wheel load, assumed to be acting on one gantry girder nearest to the load lifted. Eurocode 1 stipulates that the longitudinal force applied to the gantry girder should be calculated as follows (the equation numbers given in this chapter refer to Eurocode 1, Part 3):
HL,i = ϕ5Ki/nr (2.2)
where
nr = number of gantry girders = 2,
K = driving force (the value should be provided by the crane supplier), ϕ5 = dynamic factor (see Table 2.5),
i = integer to identify the gantry girder (i = 1, 2).
We shall follow the crane manufacturer’s instructions here, which specify the longitudinal force applied to the gantry girder. Therefore we adopt HLi = 5% of the maximum wheel load, assumed to be acting on one gantry girder nearest to the load lifted.
Table 2.5. Dynamic factor ϕ5 (based on Table 2.6 of Eurocode 1, Part 3) Value of the dynamic factor ϕ5 Specifi c use
ϕ5 = 1 For centrifugal forces
1.0 ≤ ϕ5 ≤ 1.5 For systems where forces change smoothly 1.5 ≤ ϕ5 ≤ 2.0 For cases where sudden changes can occur
ϕ5 = 3.0 For drives with considerable backlash
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