Safety and reliability are key factors in the design of equipment for modern plants. Plant designers and operators must balance the need for cost-effective, compact, lightweight equipment against the demand for rugged machinery that can withstand harsh process conditions.

The following discussion offers rules and guidelines for assessing ultimate strength and for guarding against failure, fracture and collapse in mechanical equipment, piping, machinery assemblies and facilities. These rules and guidelines apply to a wide range of equipment, including fixed equipment, vessels, drums, storage tanks, heat exchangers, filters, towers, reactors and piping systems.

Plastic Behaviors, Nonlinearities and Ultimate Loads

Basic studies, such as elastic simulations and linear modeling, can’t provide accurate predictions on ultimate load capacity of equipment. These simplified analyses lack the ability to predict post-yield reserves and realistic ultimate (full) equipment capacity. They may not even be a good indicator of the linear range capacity.

Parts or components fabricated from typical ductile steels operating under normal conditions and static loads won’t collapse as soon as local yield occurs. Therefore, yielding of one or two points or small areas may not cause major concern. Collapse usually requires one of three things: plastic hinges forming a collapse mechanism, massive cracks developing or brittle fracture occurring.

Plastic hinges are where the full section has reached the yield stress (yield strength). Once the plastic moment has been reached, it can be assumed that the section offers only a small additional resistance to rotation, behaving like a hinge. In fact, there will be an increase in moment or force due to strain hardening.

The ultimate loads of an equipment, assembly or structure are related to the elastic-plastic behavior of its materials and members. To calculate ultimate loads, you need to consider load redistribution occurring after the first major yielding, geometrical and material nonlinearities and some other complicated factors. Nonlinearities arise from several sources, including geometry (large deflections and rotations), material behavior (elastic-plastic response) and contact between components.

Typically, an abrupt change in stiffness may occur when bodies come into or out of contact. Also consider residual stresses, such as those from welding and manufacturing processes, and all imperfections and defects in the calculation.

When the first major yielding occurs, if loads continue to increase, the plasticity spreads. To determine the ultimate strength of the equipment/structure, loads are applied proportionally and incrementally until collapse. However, as there could be many different modes of failure, buckling or collapse, and there might be complicated interactions between these different modes or mechanisms, it’s very challenging to predict how equipment or a structure would fail.

In other words, when dealing with post-yielding behaviors of equipment, structures, bodies, and frames, there could be various buckling and collapse mechanisms, such as shear buckling modes, overall plastic collapse modes, compression buckling modes, nonsymmetric plastic buckling modes or axisymmetric progressive collapse/folding modes. These have usually been highly nonlinear, complex elastic-plastic buckling and failure mechanisms. There could also be interactions and relationships between these buckling mechanisms and failure modes. This makes the study of ultimate behaviors extremely complicated.

For instance, there are typically interactions between yielding and buckling at relatively high loads. Transitions between the elastic behavior and ultimate behavior often occur in a series of nonlinear, complex steps as individual elements, members, and parts fully yield or buckle. This means ultimate strength is usually governed by interactions among yielding, buckling modes and collapse or failure mechanisms.

It’s necessary to consider all possible modes, interactions and relationships, as an equipment or structure would collapse in the mode associated with the lowest possible collapse load(s). Therefore, if you miss one or a few possible modes or potential interactions in the analysis, the predictions on the failure mode (and associated ultimate behavior) and maximum load-carrying capacity would become invalid. 

The rules explained above apply in many common practical cases, but not always. There might be other complex issues, such as fatigue under cyclic loads or brittle fracture. Fatigue and brittle fracture can cause failure at stresses below yield stress.

From Yielding to Collapse

In a typical, properly designed equipment, structure, frame or body that wouldn’t collapse by simple buckling or similar low-load mechanisms, there would be considerable post-yield reserve. After the first yield, but prior to the full formation of the first plastic hinge or collapse mechanism, the load-deflection curve is ideally quasi-linear. In this stage, it’s desirable that the load-deflection curve follows the slope of the original elastic trend. The first yielding occurs ideally well before the formation of a collapse or failure mechanism and initially produces a tiny volume of yielded material. This is followed by the expansion of the yield zone(s), during which stress redistribution takes place. Typically, there is a large plastic capacity reserve.

But even with loads that are two times more than the first yield, the deflections of the equipment (structure or frame) would remain less than 1% of the span. However, there are other effects that require great care. For instance, for parts and components with irregularities, openings, joints or similar, large plastic strains are soon evident around these locations. Sharp edges, stress concentration points, sharp notches, and similar features are of particular concern because cracks can initiate and propagate from them. The plastic zones around these irregularities and openings typically grow faster than in the surrounding material. Cracks can rapidly progress to failure.

Once the plastic zone or other critical cross sections fill, the plastic hinge/mechanism that forms eventually allows large, permanent deformations to occur. After the first plastic hinge, while the equipment/assembly/structure is theoretically collapsing (in bending, for instance), internal forces may increase, thereby supporting the growing external load(s). However, after the formation of the first plastic hinge, additional damage mechanisms can occur, including buckling and fracture. Therefore, it’s often difficult to predict what will happen, how the equipment or structure will behave and how it will collapse. The eventual behavior of each piece of equipment or structure would be different, and no standard way exists to predict it because of several factors, such as the highly nonlinear effects involved and the complexities and multiplicity of modes or mechanisms and their interactions.

Small yielding typically appears to strengthen the surrounding components or structure if adverse effects, such as cracks or brittle fracture, are not involved. This theoretical strengthening is due to several factors, such as stress redistribution, strain hardening and the nature of plastic-elastic deformations. The level of this strengthening might differ from one piece of equipment to another and from one structure to another. On the other hand, there have been cases in which the yielding or damage leads to instability and weakens the equipment or structure, including the formation of cracks. But in most practical cases, under normal conditions and static loads, structures, equipment or assemblies can carry more loads from the first yielding to the threshold of potential failure or collapse. 

Brittle Fracture

Ultimate ductile failure is routinely assumed for many parts and components fabricated from mild or low-alloy steels commonly used in facilities. However, brittle fracture can occur depending on many factors and parameters such as operating/service temperature, loading rate, geometry, residual stresses, manufacturing details, imperfections and defects. A brittle fracture is characterized by the sudden failure of the material at a stress usually below its yield strength.

Brittle fracture has the potential to be a serious problem that is usually called “crack propagation” at a relatively high speed. In simple terms, the cracks can potentially spread fast, and then there is a sudden failure, collapse or disintegration. In most cases, some of the internal elastic strain energy stored in the equipment/body/structure is released and used to fracture the cracked part or component.

There are guidelines to follow to reduce the risk of brittle fracture. An appropriate choice of steel with sufficient toughness is the first step. Even though a grade of steel may be ductile at room temperature, it becomes brittle at temperatures below a certain “transition temperature,” which depends on material composition, strain rate, thickness, residual stresses, fabrication or welding flaws and stress triaxiality. The material should be selected so that the lowest operating or service temperature of the equipment or structure exceeds the transition temperature (depending on thickness and other details). The welds and welded parts are known to be vulnerable to brittle fracture through various mechanisms, including lamellar tearing of welded elements.

As a rough indication, for many commonly used steels at thicknesses of 6 mm or less, the permissible service temperature ranges from -15°C to -21°C. As another rough indication, doubling the thickness increases the permissible service temperature by 10°C. For example, for many ordinary/conventional steels, the service temperature is -20°C for a thickness of 6 mm. This is typically -10°C and 0°C for thicknesses of 12 mm and 24 mm, respectively. There have been other factors that could affect the service temperature and brittle fracture threshold. Parts and components under considerable strain during fabrication may experience brittle fracture at higher temperatures. As a rough indication, where a part or component is subjected to more than 1% outer bend fiber strain during fabrication, the permissible service temperatures for each steel type might be increased by 20°C.

The chemical composition of steel has a marked influence on its ductility. Typically, brittleness is increased by the presence of excessive amounts of most non-metallic elements, while ductility is increased by the presence of some metallic elements. Steel with a large grain size tends to be more brittle, and this is significantly influenced by heat treatment and thickness.   

Key Factors and Parameters

The key to assessing equipment, assemblies, structures or frames under extreme loads lies in their ultimate behavior. Also, real safety factors are determined based on the ultimate load-carrying capacity, not on oversimplified elastic or linear theories. Elastic properties may have little relation to ultimate behaviors. It’s important to consider the actual capacity of equipment or structures rather than relying on oversimplified measures such as the elastic modulus. Therefore, plastic and post-yielding behaviors and associated parameters are more important than elastic properties for equipment, packages, structures and frames.

The key parameters and important properties are related to the predicted (dominant) plastic mechanism or collapse or failure mode of the specific equipment, part or structure under study. For instance, plastic section modulus may be a poor indicator of ultimate capacity, especially if plastic bending is not the dominant plastic mechanism.

As a rule of thumb, there are three key factors that are often neglected: geometrical details, load application and boundary conditions. The geometrical details of equipment, structures or bodies — such as thicknesses, variations in thickness, geometrical imperfections and distortions — are critical to the ultimate load-carrying capacity and buckling or failure modes. The load application and associated details, such as the eccentricity of the load, play a vital role in the buckling and collapse modes. Boundary conditions have always been critical in buckling and potential collapse modes. 

Transverse Loads, Bending and Compression

Transverse loads and bending on parts and members usually cause more deflection and higher stresses than similar-sized axial loads. The bending stresses and deflections of parts, members and beams are frequently a main consideration for serviceability.

There have been more cases of local buckling, damage, or collapse in parts and members under compression than under tension. In other words, there have been many modes of local elastic and plastic buckling under compressive loads. This is particularly applicable to thin-walled equipment, thin-walled piping or hollow or shell structures under compression, bending or a combination thereof.

Intense Local Lateral Loads

Great care should be taken when equipment, assemblies, structures, bodies and frames are subject to intense local lateral loads. Particularly, local stresses would be very high when a large, thin-wall structure is subjected to intense local lateral load(s). An example of such an intense local lateral load could occur when a piping branch is connected directly to a large-diameter pipe. Another example is nozzles with relatively high nozzle loads on equipment such as large vessels or tanks. 

In the case of intense local loads, the surrounding reinforcements and structure to the point of the load application play a significant role in the overall behavior, local stresses, possible yielding of the area and post-yielding behavior. 

Conclusion and Final Notes

This article offers rules and guidelines for assessing ultimate strength of equipment and facilities of chemical processing plants. After the elastic limit (yield stress), the behavior is complex and nonlinear. Collapse usually requires one of three things: plastic hinges forming a collapse mechanism, massive cracks developing or brittle fracture occurring. Fatigue and brittle fracture can cause failure at stresses below yield stress.