Technical
26
28 NSC
January 19
For the purpose of this example, consider load group 1 from
Table 2.2 of BS EN 1991-3:
φ1 Qc + φ2 Qh + φ5 (HL + HT)
where HL and HT are caused by acceleration or deceleration of the
crane bridge and for simplicity will not be considered further. From
Table 2.4 of BS EN 1991-3, the upper-bound value of φ1 = 1.1 and
the value of φ2 is given by:
φ2 = φ(2,min) + β2 vh
where vh is the steady hoisting speed and β2 is a coefficient.
According to Table 2.5 of BS EN 1991-3, for hoisting class HC3,
φ2,min = 1.15 and β2 = 0.51. Taking the steady hoisting speed as
vh = 1.0 ms-1, the value of φ2 is 1.66. Applying the dynamic factors
gives the following loads:
The crane end carriage will be assumed to have wheels 2.0 m
apart and the loads are distributed between them as indicated in
the table below (the weight of the crane bridge is assumed not
to be distributed evenly). The ultimate loads on each wheel are as
indicated:
The maximum moment in the beam occurs when the centre of
the span bisects the distance between the resultant of the loads
and a wheel load as shown in figure 1.
Figure 1: Ultimate bending moments
The maximum bending moment is 1190 kNm. Assuming a
uniform bending moment between compression flange restraints,
using the Blue Book, a 610 × 229 UB 125 with restraints at 2.0 m
centres has a buckling resistance moment (with C1 = 1.0) of
1230 kNm which is satisfactory for ultimate loads. The elastic
modulus of the beam We is 3220 cm3.
As indicated above, BS EN 1991-3 gives a simplified approach to
calculating the fatigue damage equivalent load Qe which may be
expressed as follows:
Q e = fat Qmax,i = fat,1(Qmax,i )1 + fat,2(Qmax,i )2
where φfat,j = (1 + φj ) ⁄ 2 and the index j refers to the dynamic factor.
Substituting values for φ1 and φ2 gives φfat,1= 1.05 and φfat,2 = 1.33.
and calculating the characteristic and fatigue damage equivalent
loads gives the following results:
Item Load (kN) Proportion of
load
Load on end
carriage (kN)
End carriage and bridge (Qc) 164 50% 82
Crab (Qc) 36 90% 33
Payload (Qh) 300 90% 270
Item Dynamic factor Factored Load on end carriage (kN)
End carriage and bridge (Qc ) 1.1 90
Crab (Qc ) 1.1 36
Payload (Qh ) 1.66 448
Item Load Wheel 1 (kN) Load Wheel 2 (kN) Total (kN)
End carriage and bridge (Qc ) 50 40 90
Crab (Qc ) 18 18 36
Payload (Qh ) 224 224 448
Ultimate load (factor = 1.35) 393 381 774
/The_Blue_Book
/Fatigue_design_of_bridges#The_mechanism_of_fatigue