Table 3 provides a summary of the post section sizes used in the analysis, the plastic moment capacities MP and lateral collapse loads Fc obtained from FEA and from Equation (1)。 The FE analyses in general predicted slightly higher collapse loads and corresponding plastic moment capacities than those that were determined using Equation (1) which refers to a simple analysis method。

The vertical loading sequence which occurs directly after removal of the lateral load, is used to ensure that the ROPS can support the mass of the vehicle if it comes to rest in an upturned positioned。 This is a strength load case which means that the structural members that resist this load must possess adequate capacity to avoid premature failure。 For the K275 ROPS, the vertical loading is applied to the beam linking the two posts of the ROPS。 As the ROPS has already developed plastic hinges at the post beam junctions during the lateral loading phase, it is necessary for only one further hinge to form at the midspan of the beam before a beam

collapse mechanism will be formed。 The vertical collapse load for the ROPS (FCV may be estimated by using Equation (2)。

FCV = 4MP2/L (2)

where L is the length of the beam between supporting posts and MP2 the plastic moment capacity of the beam about its strong axis。

Similar to the vertical loading stage, the longitudinal loading sequence is also a strength load case that ensures that the ROPS has sufficient strength in the direction of its longitudinal axis to withstand a rollover in this direction。 An estimate of the maximum collapse load (FCL) of the structure may be established using Equation (3), which assumes that the section can develop the full plastic moment capacity of each post about an axis that is normal to the longitudinal direction of the ROPS posts。

FCL = 2MPx /Le (3)

where MPx represents the plastic moment capacity of the ROPS posts about their local X-X axis in Figure 14。 Details of the plastic moment capacities and collapse loads that were calculated using Equations (2) and (3) and from FE analyses have been summarised in Tables 4 and 5。 Through studying the response behaviour of each ROPS configuration with the stiffness distributions as shown, it was envisaged that the adequacy of the code provisions particularly with reference to the minimum lateral load and energy absorption requirement could be established。

Lateral Load Analysis – Energy Absorption Prior to DLV Infringement

Full scale ROPS models with the post section geometries outlined in Table 3 were subjected to finite element analysis using the displacement controlled solution method and involved loading of the ROPS up to the point of DLV encroachment, set at 500mm。 The lateral load deflection  response  up  to  this  deflection  limitation  was  recorded  for  each  analysis and

presented in Figure 14。 The load deflection responses in Figure 14 indicate an initial stiff elastic response。 After the peak load was reached, the stiffness of each model reduced substantially and the load carrying capacity began to fall。 This behaviour was characterised by significant yielding and the formation of plastic hinges at the ends of each post which gave rise to a significant increase in the lateral deflection experienced by each model。 The analyses were continued until the zone of the DLV was impeded。 As expected, it is evident from this Figure that the load carrying capacity of a ROPS was proportional to the plastic moment capacity of its posts。

Figure 15 shows the variation in energy absorbed by each model with increasing lateral deflection。 These results were as expected and clearly indicate that the energy absorbed by each model increases with increasing lateral deflection and ROPS post stiffness。 Further to this, the direct relationship between plastic moment capacity of the ROPS posts and the amount of energy absorbed, has been shown in Figure 16。 It is clear that the energy absorbed by each model is proportional to the plastic moment capacity of the ROPS posts。