## 1 Introduction  
Truss towers are multi-element, self-supporting structures, rigidly fixed to the base. Due to many factors such as large height, relatively low material consumption, and simple ejection process, steel truss towers are the most obvious choice for a tower structure. With respect to their use, a number of types can be identified [1], namely, antenna towers, architectural towers, transmission towers, chimney towers, light towers, viewing towers, or water towers.  
The experience shows steel truss tower failures may be attributed to different reasons. Such issues were explored in many studies [2; 3; 4; 5]. The truss performance in a potentially dangerous condition may result in the structural collapse of the whole tower. Examples of failures of truss towers were discussed in study [6]. Failures and collapses of steel truss towers may be caused by various factors, which often occur simultaneously. The most common causes are related to errors in design, such as inappropriate determination of external loads or wrong loading diagram of the structure. Flaws in erection include, among others, faulty workmanship of connections, the weakening of individual bars, attachment of additional gear (unaccounted for in the design). A common cause of failures of towers with main legs made from closed sections is water freezing in them, which leads to the bursting of sections. In such cases, the indirect cause lies in careless workmanship of welded connections, which allows water penetration into the section. Another cause of failure may be the action of abnormal wind or snow loads,or both loads combined. Because of a large range of load variation, the design assumptions sometimes do not account for abnormal natural phenomena like vehement storms, whirlwinds, or hurricanes. Another important failure-contributing factor is the corrosion of steel sections and connections, which leads to their reduced capacity. The action of corrosion depends, to a large extent, on the provision of adequate anticorrosion protection and the severity of the corrosion environment. Other factors that can lead to the failure of truss towers include non-uniform settlement of the ground underneath main leg foundations, mining-induced damages, failures of connections, and vehicles crashing into the structure.  
Taking into account the threats mentioned above, it is clear that computer simulations of truss towers deformations and failures represent a relevant research focus [7; 8; 9; 10]. Full-scale investigations provide equally important findings [8; 9]. An important issue is also proper condition evaluation of existing truss structures [5; 11], which aims at the identification of a potentially dangerous state. In case a failure of the structure element that might result in the collapse is found, it is necessary to design proper strengthening of the structure to ensure its safe performance [2; 4]. The subject of failure scenarios includes work on progressive failure, in which local failure of a structural component can cause failure of the whole structure [12; 13].  
The reliability analysis of truss structures has been investigated in many studies, e.g., in [14; 15; 16; 17], where various methods of estimating the reliability index have been proposed. The evaluation of truss tower reliability when individual single elements fail also constitutes an important research area. In study [18], the author emphasises the need for investigations into the failure of statically indeterminate structures. It may happen that a failure of a single element of the structure leads to a redistribution of internal forces that results in the exceedance of the capacity of subsequent bars, bringing about the occurrence of a mechanism, i.e., the structure failure. In this paper, the impact of the failure of individual elements on the overall reliability of the tower is analyzed.