**1. Introduction**

Steel stiffened panels are used in naval, offshore, mechanical and civil engineering structures as their primary strength sub-structures. Occasionally, they are exposed to cryogenic conditions, e.g., due to the unwanted release of liquefied gas such as LNG (liquefied natural gas) or liquefied hydrogen as discussed in Paik et al. [1].

The ultimate strength is a primary criterion for the design of steel stiffened-plate structures [2–6], and it is essential to characterise the effects of cryogenic condition on the ultimate strength of such structures. The authors of this chapter have previously conducted collapse tests on full-scale steel stiffened-plate structures under axial-compressive loading at room temperature [1], at cryogenic condition [7] and at -80°C [8]. This chapter is part of a sequel to investigate the brittle fracture of steel stiffened-plate structures under cryogenic conditions. The tested structures were designed from a reference plate panel in an as-built containership carrying 1,900 TEU (twenty-foot equivalent units). They were fabricated at a shipyard using exactly the same welding technology as used in today's shipbuilding industry [9].

**Figure 1.** *Transition of the ductile-to-brittle behaviour for structural steel [5].*

Structural fracture modes are classified into three groups [3, 4]: rupture, ductile fracture and brittle fracture. Material rupture occurs when failure occurs by cracking associated with necking localisation during large plastic flow. If the strain at which a material fractures is small, with very little ductility, it is a brittle fracture. An intermediate fracture mode between rupture and brittle fracture is called ductile fracture with partial ductility. Fracture behaviour of ductile materials such as carbon steels is quite different from that of inherently brittle materials. Ductile materials generally exhibit slow stable crack growth during crack extension, but they can show a similar behaviour to brittle materials at specific environments such as very low temperatures or lower than the ductile-to-brittle fracture transition temperatures (DBTT) and/or impact loading. It is also recognised that the Bauschinger effect of materials cannot be neglected at sub-zero temperatures and cryogenic condition as the material behaviour in compression is distinct from that in tension [3, 10, 11]. **Figure 1** illustrates the transition of the ductile-to-brittle behaviour for structural steel.

To compute the failure behaviour of structures at cold (sub-zero) temperatures (or higher than the ductile-to-brittle fracture transition temperatures), constitutive equations of materials have been proposed in the literature [12–15]. It is recognised that most of previous studies are associated with predominantly ductile behaviour or at least with partial ductility, but studies applicable to entirely brittle fracture at cryogenic condition are lacking. It is also recognised that the approaches using the constitutive equations are not always practical for the ultimate strength analysis of supersized structures because they are too complex to apply for the problem.

This chapter presents a method for computing the ultimate compressive strength of steel stiffened-plate structures by nonlinear finite element method (NLFEM) using the multi-physics software package LS-DYNA implicit code. Mechanical properties of high-strength steel with grade AH32 used for fabricating the tested structure were obtained from tension and compression tests at low temperatures and cryogenic condition [7, 8], and a phenomenological relation of engineering stress versus engineering strain of the material was formulated. The material model is implemented into the LS-DYNA implicit code. To demonstrate the validity of the computational model, the NLFEM is compared to experimental results from a full-scale physical test.
