Ethan Clarke
In structural engineering beam theory, a plastic hinge is a deformation of a section of a beam where plastic bending occurs. When a beam is subjected to yield stresses throughout its depth, it cannot take further loads, and if an additional load is applied, the beam rotates at that section. This is called a plastic moment, and a plastic hinge is formed at that section. The plastic hinge allows large rotations to occur at a constant plastic moment. The formation of plastic hinges can be observed in the development of a structure, with a gradual increase from bottom to top in the frame structure.
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What You'll Learn
Plastic hinges and plastic moment capacity
In structural engineering beam theory, a plastic hinge is a deformation of a beam section where plastic bending occurs. When a certain value of moment, known as the plastic moment, is reached, a plastic hinge is formed in the member. The plastic moment capacity of a section is reached when it is subjected to yield stresses throughout its depth, and it cannot take further loads. If an additional load is applied, the beam rotates at that section, and this is called the plastic moment capacity.
Plastic moment capacity is greater than the yield moment because, in the plastic stage, all the fibres are yielded, whereas in other stages, only the outer fibre yields. The plastic moment capacity of a section is also known as the maximum moment capacity of that section. It is the moment at which the section can no longer resist further increase in the bending moment and will start to rotate.
The formation of plastic hinges can be observed in frame structures, where they first appear at the bottom of the structure and then gradually increase from bottom to top. The number of plastic hinges required for the collapse of structures varies with the degree of indeterminacy.
In plastic design, moment redistribution is considered, allowing for the load to be redistributed from the hogging region to the sagging region. This can be achieved by reducing the capacity of the sagging region and increasing the capacity of the hogging region. However, the use of FRP precludes moment redistribution, requiring an elastic distribution of moments.
It is important to note that reaching the plastic moment capacity does not mean the beam has failed, only that it cannot take additional loads. The beam will still have some resistance and will redistribute the load like a simply supported beam.
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Plastic hinge formation and structural collapse
In structural engineering beam theory, a plastic hinge forms when the moment capacity of a beam section is reached, and it can no longer support additional loads. This is known as the plastic moment (Mp), and it marks the transition from elastic to plastic behaviour. The plastic hinge allows large rotations at a constant plastic moment Mp, and its length depends on cross-sections and load distributions.
Plastic hinge formation is significant because it indicates the limit of a structure's load-bearing capacity. When a plastic hinge forms, the beam can no longer support additional loads, and further loading will lead to structural collapse. This is because, at the plastic hinge, the beam rotates due to the moment, redistributing the load like a simply supported beam.
To prevent structural collapse, engineers must ensure that the specified limits of stress and deflection are not exceeded. Plastic hinges can be utilised in design to allow for controlled deformation and energy dissipation, particularly in earthquake engineering. By inserting a plastic hinge at a plastic limit load, a kinematic mechanism is formed, permitting displacement while potentially avoiding catastrophic failure.
The minimum number of plastic hinges required for collapse depends on the degree of static indeterminacy of the beam. For each degree of indeterminacy, an additional plastic hinge is necessary to form a collapse mechanism. By placing hinges at the locations of maximum bending moment, engineers can control the collapse mechanism and ensure structural stability until the plastic moment Mp is reached.
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Plastic design and moment redistribution
When designing structural elements, the initial approach typically involves elastic design, assuming that materials remain within their elastic range. However, this conservative approach may not fully utilize the capacity of the structure. By considering plastic design, engineers can take advantage of the structure's ability to undergo plastic deformation beyond the elastic limit, allowing for additional load-bearing capacity.
Plastic hinges play a crucial role in moment redistribution. A plastic hinge forms when a cross-section reaches its plastic limit, and the beam rotates at that section. This rotation allows for internal bending moment redistribution within the structure. The rotational capacity of plastic hinges determines the amount of moment that can be redistributed to other parts of the structure.
To ensure structural safety, it is essential to understand the plastic moment capacity of a cross-section, which is the maximum moment it can withstand before plastic hinge formation occurs. By calculating the plastic moment capacity, engineers can design structures that can redistribute moments effectively without collapsing.
The evolution of moment redistribution can be categorized into two stages: elastic redistribution and plastic redistribution. Elastic redistribution occurs during the elastic stage of reinforcement due to concrete cracks and arrangement variations. Plastic redistribution, on the other hand, takes place after the yielding of tensile reinforcement due to the plastic rotation of critical regions. By considering both stages, engineers can optimize their designs for moment redistribution.
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Plastic hinges in earthquake engineering
In earthquake engineering, plastic hinges are used as energy damping devices, allowing plastic rotation or deformation of an otherwise rigid column connection. They are designed to limit the forces imposed on structures by large displacements during earthquakes. By intentionally creating weak points in certain members, plastic hinges can be strategically placed to control and contain the deformation.
Plastic hinges are formed when a beam or member reaches its plastic moment capacity, which is the maximum moment that can be transmitted to connecting structural members. At this point, the beam or member can no longer support additional loads, and plastic bending occurs, resulting in the formation of a plastic hinge. This hinge allows for large rotations at a constant plastic moment, and its length depends on cross-sections and load distributions.
In the context of earthquake engineering, the location of plastic hinges is carefully considered. For example, in earthquake-prone bridges, plastic hinges are typically located in the columns rather than the superstructure or foundation. This is because columns are easier to repair or reinforce compared to other structural elements. Additionally, the plastic moment capacity of columns can be calculated and used to design girders that can withstand these moments.
The use of plastic hinges in earthquake engineering is a form of "plastic design," which allows for the redistribution of moments. By incorporating plastic hinges, structures can avoid the infinite loop of increasing forces that occurs when trying to maintain elasticity during an earthquake. Instead, plastic hinges act as fuses, limiting the forces and providing a controlled point of deformation.
It is important to note that the formation of plastic hinges does not necessarily indicate the failure of a beam or member. Even after reaching the plastic moment, the beam can still exhibit resistance and redistribute the load like a simply supported beam. This understanding of plastic hinges and their behaviour is crucial for designing resilient structures in earthquake-prone regions.
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Plastic hinges and load distribution
Plastic hinges are a deformation of a section of a beam where plastic bending occurs. In earthquake engineering, a plastic hinge is a type of energy damping device that allows plastic rotation or deformation of an otherwise rigid column connection. When a structure is damaged under an earthquake, the distribution of plastic hinges can be obtained, with the hinge points shown as red dots.
The formation of plastic hinges is important to understand in structural engineering. Most engineering analysis assumes linearly elastic behaviour, but this can leave a lot of structural capacity untapped. Structures often have more load-carrying capacity than a linearly elastic analysis suggests. Plastic hinges form when the elastoplastic capacity of the material is exhausted and the section becomes fully plastic. At this point, any further loading will cause free rotation at the location of the plastic hinge.
The number of plastic hinges required for the collapse of a structure depends on its degree of indeterminacy. For example, a propped cantilever with four potential reactions could withstand the formation of one plastic hinge without collapsing. However, if enough plastic hinges form to exhaust all redundancy in a structure, it will collapse.
In terms of load distribution, the load can be increased past the point at which a member first yields, and up to the point where the system forms a mechanism. This can be done as long as the beam is not buckling under flexure and hinge curvature or rotation requirements are met. Once plastic hinges form, the negative moment will redistribute to the positive region until a hinge forms at the centre of the beam, causing collapse.
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Frequently asked questions
In structural engineering beam theory, a plastic hinge is the deformation of a section of a beam where plastic bending occurs. A plastic hinge enables a structure to be analysed continuously by inserting a plastic hinge at any section reaching its plastic moment.
A plastic moment is a certain value of moment at which an abrupt transition from elastic to ideally plastic behaviour occurs. When a plastic moment is reached, a plastic hinge is formed.
The maximum moment at a plastic hinge is the plastic moment capacity of the section. This is the moment at which the plastic hinge is formed.
