## 2 Non-Linear Finite Element Analysis
### Finite Element Modeling
#### 2.1.5 Loadings  
All loadings associated with in-place actions that contribute to the dynamic masses must be included in the dynamic analysis [28]. The dead loads not contributing to the overall structural stiffness were incorporated as inertia masses input because these masses, including the weight of all pipes,  
Figure 7: Finer mesh size at used in the connection region. contribute to the inertia mass in the dynamic behaviour of the overall structure. The inertia mass of pipes was determined by assuming all pipe size as 400 mm diameter \(\times\) 12.7 mm thickness with a span length of 5 m. The weight of each pipe was 1.2 tonnes. At the same time, the miscellaneous dead loads such as smaller pipes, cable tray, electrical lines, grating, and handrails were included in the model. A total inertia mass of 10.2 tonne (100 kN) at each pipe location were assumed and included in the model. The total mass based on the assumed inertia masses gives a conservative scenario, besides maintaining the same total mass as in the original steel frame presented by [PERSON] and [PERSON] [15]. The weight of the pipes on the rack was modelled by applying mass inertia at four prescribed locations as shown in Figure 8.  
During the gas explosion process, the atmospheric pressure increases dramatically to a maximum pressure with the propagation of the blast wave, and then it slowly decreases to a negative value with respect to the standard atmospheric pressure. The negative phase pressure occurs because the shockwave forces the air to move as it spreads outward from the explosion centre and creates a lack of air behind, causing a partial vacuum or negative pressure phase. This negative phase can be ignored in structural design [29]. However, the negative phase of the blast pressure is important in order to accurately predict the responses of blast loading on structures [30], and it is unconservative if the negative phase is ignored [31]. The original pressure-time history output of blast simulation is not practicable to be used in structural dynamic analysis and needs to be idealized [32]. [PERSON] et al. reference [30] summarised typical nominal blast overpressures for offshore structure according to industrial standard guidelines. The durations of these loads were reported to be between 50 and 200 msec and considered to be close to typical offshore structure natural periods (between 300 to 1100 msec). [PERSON] et al. [33] also proposed an overpressure load of 0.9 bar and 2.25 bar as the lower and upper level events for hydrocarbon explosions, respectively. During an explosion event, the following three fundamental consequences can occur; namely, the blast overpressures, dynamic pressures (drag loads) and projectiles, missiles, and shrapnel. Among these consequences, the explosion overpressures are generally considered to be the most critical measurement. In the absence of project-specific data, it has been suggested in a Chevron Engineering Standard that a load equal to one-third of the positive phase load can be considered for the negative phase pressure. The negative pressures are usually within the range 10-30% of the maximum pressure [34]. The explosion loads on open frame structures, structural components, equipment items and pipework are usually caused by dynamic pressure loads [35] containing drag loads, inertia loads, and  
Figure 8: Pipe inertia masses and locations. a pressure difference load. The first two loadings are similar to the fluid force terms in the Morrison equations (refer Equation (5)) [36]. \[F_{D}=\frac{\pi}{4}C_{m}\rho D^{2}\frac{\partial U}{\partial t}+\frac{1}{2}\rho v _{gas}^{2}C_{D}A \tag{5}\]  
\(F_{D}\) is the drag force, \(C_{m}\) and \(C_{D}\) are the inertial and drag coefficients. For small objects and typical gas velocities, the contribution of the inertia load is less than 1% of the force hence it may be neglected [37]. Therefore, the [PERSON]'s equation can be reduced and the magnitude of the drag forces on the steelwork elements can be calculated using Equation (6).