Ethan Clarke
Plastic hinges are a crucial concept in structural engineering, particularly in beam theory and earthquake engineering. They are defined as deformations in beams where plastic bending occurs, leading to large rotations at constant plastic moments. To determine the number of plastic hinges, it is essential to understand the degree of static indeterminacy of the structure. Each additional degree of indeterminacy necessitates the inclusion of another plastic hinge to establish a collapse mechanism. By utilizing performance criteria, such as observing steel yielding and analyzing hysteretic plots, engineers can identify the formation and location of plastic hinges within a structure.
| Characteristics | Values |
|---|---|
| How to find the number of plastic hinges | The number of plastic hinges required for collapse = degree of static indeterminacy + 1 |
| How to find the location of plastic hinges | By understanding the frame, using performance criteria, and observing hysteretic plots of moment versus rotation |
| Where plastic hinges are distributed | In beams, bent columns, and the protruding parts of structures |
| Plastic hinges and plastic design | Plastic design can lead to higher ultimate loads and deformations compared to traditional elastic design methods |
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What You'll Learn
Plastic hinges and structural engineering beam theory
Plastic hinges are a crucial concept in structural engineering beam theory, referring to the deformation of a beam section where plastic bending occurs. This phenomenon is particularly significant in earthquake engineering, where plastic hinges act as energy damping devices, enabling plastic rotation within a rigid column connection.
In structural engineering, the plastic hinge formation process involves a transition from elastic to ideally plastic behaviour at a specific moment value, known as the plastic moment (Mp). When a section of a beam undergoes fully plastic stress, it is considered to have formed a plastic hinge, resulting in a redistribution of internal forces within the structure. This redistribution leads to the development of additional plastic hinges until a collapse mechanism is achieved.
The number of plastic hinges in a structure depends on the loading mode and the specific characteristics of the beams. For instance, under acceleration loading, plastic hinges tend to be distributed on the beam, with fewer hinges present compared to modal loading. The distribution of plastic hinges is also influenced by the layer and direction of the beams. In some cases, there may be a large number of plastic hinges in the beams of the fifth and sixth layers due to differences in stiffness.
To determine the number of plastic hinges, engineers can utilise performance criteria, such as observing steel yielding and understanding the model's maximum demand regions. Additionally, hysteretic plots of moment versus rotation provide a visual means to identify hinge formation at specific locations. By applying these methods and considering the structure's loading conditions and beam properties, engineers can analyse the distribution and quantity of plastic hinges in a given system.
Furthermore, the use of FRP (Fibre-Reinforced Polymer) can influence the formation of plastic hinges. FRP plating prevents moment redistribution, requiring the moment capacity of the hogging region to be twice that of the sagging region. This restriction limits the formation of plastic hinges in the hogging regions, confining them primarily to the sagging regions.
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Plastic hinges in earthquake engineering
Plastic hinges are a crucial concept in earthquake engineering, where they serve as energy damping devices that enable plastic rotation within rigid structures. Their presence helps to limit forces and prevent the infinite loop of increasing forces that can occur when attempting to maintain elasticity during an earthquake.
In the context of earthquake engineering, plastic hinges are used strategically to control the deformation of structures. By intentionally introducing weaker members, engineers can designate specific locations for plastic hinges to form during an earthquake. This is often done in columns, as they are easier to repair than other structural elements.
The number and location of plastic hinges in a structure are influenced by various factors, including the level of axial load, transverse reinforcement, and shear span-to-depth ratio. It is important to understand the frame and the regions of maximum demand that can lead to severe damage, as these areas are more prone to plastic hinge formation.
To determine the number of plastic hinges, engineers can utilize performance criteria and hysteretic plots of moment versus rotation. These tools provide visual representations of hinge formation and allow for the estimation of yield curvature. Additionally, the section curvature performance criterion can be employed, considering the curvature variation along the member length, with regions of maximum curvature likely to form plastic hinges.
The distribution of plastic hinges within a structure is critical to its seismic performance. For example, increasing the number of plastic hinges in the Y-direction can enhance seismic performance. Moreover, the formation of plastic hinges depends on the loading mode, with fewer hinges observed under acceleration loading compared to other modes.
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Plastic hinges and the plastic collapse mechanism
Plastic hinges are a deformation of a section of a beam where plastic bending occurs. In earthquake engineering, they are also a type of energy-damping device that allows plastic rotation. When a structure is subjected to bending, it is assumed that an abrupt transition from elastic to ideally plastic behaviour occurs at a certain value of moment, known as the plastic moment (Mp). At this point, a plastic hinge is formed in the member.
Plastic hinges first appear at the bottom of a bent structure and then gradually increase from bottom to top in a frame structure. They are distributed on the beam under acceleration loading mode and are also distributed on bent columns. The number of plastic hinges required to form a collapse mechanism depends on the degrees of static indeterminacy of the beam. For each degree of static indeterminacy, an additional plastic hinge must be added.
Plastic hinges can be located by understanding the model and identifying the regions with maximum section curvature, which are likely to form plastic hinges. Hysteretic plots of moment versus rotation also provide a visual means of determining whether hinges have formed at a particular location.
The plastic collapse mechanism refers to the process by which a structure collapses due to plastic hinge effects. This occurs when the entire cross-section reaches its yield stress, which is the maximum bending moment that a cross-section can resist. When this point is reached, a plastic hinge is developed, and the structure becomes an unstable mechanism.
To predict structural instability due to the plastic hinge collapse mechanism, the deflections at the mid-span of the beam are monitored. When a plot of the deflections becomes unstable, with a large increase in deflections for a very small increase in loading magnitude, the collapsing pressure due to plastic hinge effects can be defined. This is indicated by a steep slope in the deflection versus load curve.
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Plastic hinges in statically indeterminate frames
Plastic hinges are a crucial concept in structural engineering beam theory. They refer to the deformation of a beam section where plastic bending occurs. In earthquake engineering, plastic hinges act as energy damping devices, allowing plastic rotation within a rigid column connection. This is particularly important in the context of statically indeterminate frames, where the formation of plastic hinges can significantly influence the behaviour of the structure.
In statically indeterminate frames, the plastic design approach can lead to higher ultimate loads compared to traditional elastic design methods. As a point in the frame reaches its plastic moment (Mp), a plastic zone is created, forming a hinge. This hinge rotates further while maintaining Mp and redistributing the load to other structural parts. The hinge formation process repeats, leading to the creation of additional hinges and, eventually, a plastic collapse mechanism for the entire structure or a portion of it.
The distribution of plastic hinges within a frame is influenced by various factors, including the loading mode, direction, and structural characteristics. For example, under acceleration loading, there tend to be fewer plastic hinges, and they are primarily distributed on the beam, especially in the middle area. In contrast, under static loading, plastic hinges can form in either the beam or the columns. Additionally, the protruding layers of a structure tend to have a higher concentration of plastic hinges due to differences in stiffness.
To locate the plastic hinges within a statically indeterminate frame, several methods can be employed. One approach is to utilize performance criteria, such as the "section curvature" criterion. By understanding the model and identifying the regions with maximum section curvature, one can predict the likely formation of plastic hinges. Hysteretic plots of moment versus rotation also provide a visual means of determining hinge formation at specific locations. Furthermore, the distribution of plastic hinges can be analysed through elastoplastic analysis, considering the attainment of plastic moments in different sections of the structure.
It is important to note that the formation of plastic hinges in statically indeterminate frames can have both positive and negative consequences. On the one hand, plastic hinges can act as a safety mechanism, limiting the forces on a structure during earthquakes or other extreme events. By intentionally introducing weaker members, engineers can control where plastic hinges will form, preventing damage to critical structural components. On the other hand, the formation of plastic hinges can lead to a redistribution of internal forces, potentially resulting in the collapse of the structure if the hinges do not rotate sufficiently or if the collapse mechanism forms too rapidly.
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Locating plastic hinges
To locate plastic hinges, it is essential to understand the behaviour of the structure under consideration. For instance, in the context of earthquake engineering, plastic hinges form when longitudinal rebars yield. Hysteretic plots of moment versus rotation provide a visual method to determine the presence of hinges at specific locations. Additionally, performance criteria can be set to alert engineers when yield curvature is reached for different structural elements.
Another approach to locating plastic hinges involves utilising the "section curvature" performance criteria. By understanding the model and identifying regions with maximum demand that can lead to severe damage (plastic hinges), engineers can analyse the variation of curvature along the member length. The regions with maximum section curvature are likely to form plastic hinges. However, it is important to recognise that plastic hinge formation depends on various parameters, including the level of axial load, transverse reinforcement, and shear span to depth ratio.
In the case of a pre-Northridge steel moment connection, the design may involve haunches to extend the plastic hinge away from the connection. This introduces the question of determining the distance of the plastic hinge from the connection, both before and after the incorporation of haunches.
Furthermore, the distribution of plastic hinges can vary depending on the loading mode and structural characteristics. For example, under acceleration loading, there tend to be fewer plastic hinges, and they are distributed on beams or bent columns, with a gradual increase from the bottom to the top of the frame structure. Protruding parts of certain layers may also exhibit a higher concentration of plastic hinges.
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Frequently asked questions
The number of plastic hinges required for a structure to collapse is equal to the degree of static indeterminacy of the beam plus one.
A plastic hinge is the deformation of a section of a beam where plastic bending occurs. It is also a type of energy damping device that allows plastic rotation.
Plastic hinges form when the longitudinal rebars yield. This can be observed through hysteretic plots of moment versus rotation.
While a frictionless hinge permits free rotation, a plastic hinge allows large rotations to occur at a constant plastic moment.
Plastic hinges play a crucial role in the design of statically indeterminate frames. By allowing for higher deformations, they enable structures to reach higher ultimate loads compared to traditional elastic design methods.
