Fatigue analysis of large - scale statue structures

Because large sculptures often contain slender components such as arms and ribbons, they are susceptible to structural fatigue under repeated wind loads over long periods, which must be given sufficient attention during the design process.

This article by Boqian Sculpture Company will take the long cantilever arm of the Thousand-Hand Guanyin bronze statue in Changsha as an example to mainly introduce the average wind force component in wind load, and consider the fatigue effect of the sudden disappearance of wind load on the structure. The study will be carried out from the following aspects.

① Calculate the stress distribution of the structure under wind load and when the wind load disappears.

② Calculate the stress time history spectrum of the structure using wind load time history spectrum

③ Applying Miner's linear cumulative damage theory and nominal stress (SN) analysis method, fatigue problems under wind loads are analyzed using Goodman criterion 1.

Winds in nature can be divided into abnormal winds and benign winds. Winds that rarely occur, such as tornadoes, are called abnormal winds, while those that are not abnormal winds are called benign winds. The wind loads studied in general architectural design are the latter, which can be expressed as three types: downwind force, crosswind force, and torsional moment. The latter two often cause vortex resonance in the structure, resulting in a complex response to the structure. They are generally not considered separately in steel structure buildings.

Based on extensive wind measurement data, it can be seen that the wind's time history curve along the wind direction contains two components: a long-period component, whose value is often above 10 minutes, and a short-period component, which is only a few seconds. Based on these two components, wind is actually divided into mean wind (i.e., steady wind) and fluctuating wind (often called gusts and gusts) for analysis. Mean wind is considered as the velocity, direction, and other physical quantities of the wind's force on a building within a given time interval, all of which are considered to be quantities that do not change with time. Considering that the long period of wind is much larger than the natural period of a general structure, its effect is equivalent to static force. The closer to the ground, the lower the wind speed. Fluctuating wind is caused by the irregularity of wind and has a shorter period. Its effect is dynamic and will cause structural vibration. It decreases with increasing height. Fluctuating wind is much smaller than mean wind, and buildings within a certain height range cannot be subjected to very strong wind load dynamic stress. Therefore, the changes in internal forces caused by dynamics are small stress cycles and will not suddenly disappear. Compared with the presence of wind load, the changes in internal forces of the structure are very large, making it more meaningful to study the Bohr problem of structures under this stress state.

Basic Theory of Fatigue Analysis

Fatigue-related concepts

Fatigue is defined as the failure of a material or structure when it is subjected to repeated loads of varying strength, even if the stress value does not exceed the material's strength limit or is even lower than the elastic limit. This phenomenon of material or structural failure under repeated alternating loads is called fatigue failure.

Fatigue and fracture are the main causes of failure in engineering structures and components. The American Society for Testing and Materials (ASTM) defines fatigue in its "Standard Definition of Terms Related to Fatigue Testing and Data Statistics" (ASTM E20672) as: the development of localized structural changes in a material subjected to disturbance stress at one or more points and after a sufficient number of cycles of disturbance.

Classification of fatigue

Fatigue can be classified from different perspectives. Based on the research object, it can be divided into material fatigue and structural fatigue. Material fatigue studies the failure mechanism of materials, the influence of chemical composition and microstructure on fatigue strength, fatigue testing methods for standard specimens and data processing methods, the basic fatigue characteristics of materials, the influence of environment and operating conditions, and the macroscopic and microscopic morphology of fatigue fracture surfaces. Its characteristic is the use of standard specimens for experimental research. Structural fatigue, on the other hand, focuses on components, joints, and even complete machines, studying their fatigue performance, fatigue-resistant design methods, life estimation methods, fatigue testing methods, the influence of shape, size, and manufacturing processes, and methods to improve their fatigue strength.

Fatigue strength, fatigue limit and fatigue life

The magnitude of fatigue strength is measured by the fatigue limit, which refers to the maximum stress S that a material or component can withstand for an infinite number of stress cycles under a certain cyclic characteristic R without fatigue failure. It is generally denoted by S_f. Because the fatigue limit of a material varies with the loading method and stress ratio, the fatigue limit under symmetrical cyclic loading is usually taken as the basic fatigue limit of the material.

Fatigue life is the number of stress or strain cycles that a specimen can withstand before fatigue failure, typically denoted by N. The fatigue life of a specimen depends on the mechanical properties of the material and the applied stress level. Generally, the higher the ultimate tensile strength of the material and the lower the applied stress level, the longer the fatigue life of the specimen; conversely, the lower the ultimate tensile strength and the lower the applied stress level, the shorter the fatigue life. The curve representing this relationship between the applied stress level and the fatigue life of a standard specimen is called the material's S/N curve.