The Rankine theory of failure is one of the most widely used theories to evaluate the strength of engineering structures and materials. It is named after William John Macquorn Rankine, a Scottish civil engineer and physicist who first proposed the theory in the 19th century.
The theory states that a material or structure fails when the maximum shear stress in the material or structure surpasses the shear strength of the material. The maximum shear stress occurs when the principal stresses are equal and opposite in direction, and the shear stress acting on the material is at its highest.
The Rankine theory of failure assumes that the material is perfectly elastic until it reaches its ultimate strength, after which it fails suddenly, making it a brittle failure theory. The theory also assumes that the failure will occur along a plane of maximum shear stress or in other words, failure will occur where the shear stress is maximum, which is at a 45-degree angle to the principal axis.
The Rankine theory of failure is also used to calculate the maximum stresses and loads that a structure can sustain without failing. The theory is applied to a variety of applications such as determining the maximum force that can be applied to a beam without it breaking, the maximum load a bridge can support, or the maximum pressure a pipeline system can handle.
Despite its limitations, the Rankine theory of failure remains a popular tool among engineers as it provides a simple and quick way to evaluate the performance of structures and materials. However, it must be used in conjunction with other theories and analyses to get a comprehensive understanding of the behavior of the structure or material being evaluated.
Is Rankine theory used for brittle material?
The Rankine theory is a well-known theoretical approach widely used for the determination of the strength of soil and other materials. In geotechnical engineering, the Rankine approach is used to determine the shear strength parameters (cohesion and internal friction angle) of cohesive soils and rocks.
However, it is not typically used for brittle materials such as ceramics or brittle metals, as these materials do not exhibit significant plastic deformation (i.e., permanent deformation) before fracture. The Rankine theory is primarily applicable to soils and rocks, which are considered ductile materials that undergo significant plastic deformation before failure.
The theory is based on the assumption that the failure of a material occurs when the max shear stress, which is generated in the material, exceeds the shear strength of the soil or rock. The shear strength parameters of a material are defined as the maximum shear stress that it can sustain before failure, and the stress required to overcome the resistance offered by the interparticle friction and particle cohesion.
In contrast, brittle materials exhibit a linear elastic behavior that cannot undergo significant plastic deformation before the failure. Therefore, the failure criteria for brittle materials is different from that of ductile materials, and the Rankine approach is not suitable for the analysis of these materials.
The failure of brittle materials can be described by different theories such as Griffith’s theory, which explains the failure of brittle materials based on the stresses caused by the presence of cracks and other defects in the material.
The Rankine theory is not typically used for brittle materials since these materials do not exhibit significant plastic deformation before fracture. The theory finds its primary application in the determination of shear strength parameters for cohesive soils and rocks, which are considered ductile materials.
The analysis and design of brittle materials require the use of other theories that consider their specific characteristics and behaviors.
What does Rankine earth pressure theory state?
Rankine earth pressure theory is a concept that is widely used in the field of civil engineering and geotechnical engineering. It deals with the various forces exerted on retaining structures that are constructed to hold soil, rocks or any other materials, and prevent them from collapsing. This theory provides valuable insights into the complex and dynamic behavior of soils and the forces that act on them.
According to the Rankine earth pressure theory, the pressure exerted by soil mass can be divided into two components – active and passive. These two components are dependent on the relative motion between soil mass and retaining structure. The active pressure is the force that is exerted by soil on the retaining wall when the soil is moving away from the structure.
It can be explained as the lateral pressure of the soil mass that tries to push the wall outward.
On the other hand, the passive pressure is the force that is exerted by soil on the retaining structure when the soil is moving towards the structure. It can be explained as the lateral resistance provided by the soil mass which tries to hold the wall in place. The passive pressure is always greater than the active pressure as the soil offers more resistance to movement towards the wall than away from it.
The Rankine theory is based on the assumption that the soil mass is homogeneous, isotropic and has a vertical slope. It also assumes that the soil is perfectly elastic and follows Coulomb’s friction law. The theory is valid when the soil mass is at rest and the wall has no lateral movement. The theory is applicable only when the two components of the lateral earth pressure are proportional to the vertical stress at any point.
The Rankine earth pressure theory has many practical applications in designing retaining structures for various purposes such as dams, tunnels, highways, and buildings. The theory helps to determine the stability of the retaining structure for the calculated load and provides an insight into the safe limit of the structure.
It also helps to calculate the maximum tension and compression that a structure can withstand without failure.
The Rankine earth pressure theory is an essential concept in the field of civil engineering and geotechnical engineering. It provides a valuable tool to predict the pressure exerted by soil mass on retaining structures and ensures the stability of such structures. Understanding this theory can help engineers design and construct safer and more reliable structures.
What is the difference between Rankine’s theory and Coulomb’s theory?
Rankine’s theory and Coulomb’s theory are two different theories used to predict failure in soil mechanics.
Rankine’s theory is a theory that focuses on the active and passive pressures on the soil retaining structures, specifically walls. It is used to calculate the total active and passive forces acting on the retaining wall. The active forces are caused by the soil pushing against the wall, and the passive forces are caused by soil resisting the movement of the wall.
The theory assumes that the soil failure surface is a plane surface that is oriented at an angle of 45 degrees with the horizontal plane, and the failure surface penetrates the soil below the wall. Rankine’s theory uses the concept of soil cohesion to calculate the allowable passive and active force on the soil retaining structure.
On the other hand, Coulomb’s theory, also known as Coulomb’s wedge theory, is used to predict the stability of a soil mass, assuming the soil mass failure occurs due to a wedge/ sliding block of soil. This theory assumes that soil behavior is similar to that of a rigid, homogeneous material, and the failure surface is a plane surface that bisects the angle of the natural slope, also known as the angle of repose.
Coulomb’s theory calculates the factor of safety for the soil mass by comparing the shear strength of the soil to the shear stresses acting on the soil mass.
The key difference between Rankine’s theory and Coulomb’s theory is that Rankine’s theory is used to analyze retaining structures, while Coulomb’s theory is used to analyze slopes and determine the stability of soil masses. Additionally, Coulomb’s theory relies on the wedge failure model and assumes rigidity of the soil mass, while Rankine’s theory assumes plasticity of the soil and predicts the active and passive forces on the retaining wall.
Is Rankine theory valid for column?
The Rankine theory, also known as the column theory, is a widely used method for analyzing the stability of columns under compression. This theory was first proposed by the Scottish civil engineer William J. M. Rankine in the mid-19th century, and it remains one of the most fundamental principles of structural engineering.
The theory is based on several assumptions, including the assumption that the column is perfectly straight and that the material is homogeneous and isotropic. Additionally, the Rankine theory assumes that the load is applied gradually and that the resulting deformation is small.
While the Rankine theory has been widely used and accepted for many years, some researchers have raised concerns about its validity for certain types of columns. For example, some experts argue that the Rankine theory may not be applicable to columns with unusual cross-sectional shapes, such as those with tapered or curved designs.
Furthermore, the theory does not take into account the effects of shear or bending, which can significantly affect column stability in some cases. As a result, more advanced theories, such as the Euler and Bernoulli theories, have been developed to address these issues and provide a more comprehensive approach to column analysis.
While the Rankine theory remains a valuable tool for many structural engineers, it is important to recognize its limitations and consider alternative methods when analyzing columns with unique characteristics or load conditions. the most appropriate method for analyzing columns will depend on a variety of factors, including the type of structure, the load conditions, and the desired level of accuracy.
What are the 4 failure theories?
The four failure theories are the Maximum Shear Stress Theory, the Maximum Principal Stress Theory, the Maximum Principal Strain Theory and the Maximum Distortion Energy Theory. All these theories are used in material science and engineering to predict the failure of a material or structure.
The Maximum Shear Stress Theory, also known as Tresca’s Theory, suggests that failure occurs when the maximum shear stress in a material exceeds the shear strength of that material. Shear stress is the stress caused by forces that act in opposite directions parallel to the surface of the material. This theory predicts the failure of ductile materials such as metals, which tend to fail under shear stress.
The Maximum Principal Stress Theory, also known as Rankine’s Theory, states that failure occurs when the maximum principal stress in a material exceeds the tensile or compressive strength of that material. Principal stress is the stress caused by forces acting on a body in different directions. This theory predicts the failure of brittle materials such as ceramics, which tend to fracture when subjected to tensile or compressive stress.
The Maximum Principal Strain Theory, also known as Saint-Venant’s Theory, suggests that failure occurs when the maximum principal strain in a material exceeds the strain at which the material undergoes plastic deformation. Principal strain is the strain caused by forces acting on a body in different directions.
This theory predicts the failure of ductile materials such as metals, which tend to deform plastically before rupturing.
The Maximum Distortion Energy Theory, also known as von Mises’ Theory or the Shear Strain Energy Theory, states that failure occurs when the distortion energy in a material exceeds the yield strength of that material. Distortion energy is the energy accumulated in a material due to the deformation caused by shear stress.
This theory predicts the failure of ductile materials such as metals, which tend to undergo plastic deformation before rupturing.
The selection of the appropriate failure theory depends on the material being analyzed and the type of stress or strain that will lead to failure. Each theory has its own assumptions and limitations, and it is crucial to understand these in order to ensure the safety and reliability of structures and materials under different loading conditions.
What are the types of theories of failure?
Theories of failure are an important concept in the field of engineering and materials science. They are designed to help engineers and researchers predict the behavior of materials under different types of stress and strain over time. There are several different types of theories of failure, each of which provides different insights and perspectives on how materials fail.
The first type of theory of failure is the static theory. This theory is used to predict the behavior of materials under steady-state or constant loads, and it assumes that the failure of a material occurs when the maximum normal or shear stress reaches a certain level. The static theory takes into account the strength and deformation characteristics of a material, as well as any defects or damage present in the material.
The second type of theory of failure is the fatigue theory. This theory is used to predict the behavior of materials under cyclic loads, such as those experienced by machinery or infrastructure subjected to repeated use. The fatigue theory assumes that the failure of a material occurs when a critical number of cycles has been reached, and it takes into account the stress range, frequency, and amplitude of the cyclic loads.
The third type of theory of failure is the fracture mechanics theory. This theory is used to predict the behavior of materials under conditions of crack growth or propagation, and it takes into account the length, depth, and orientation of the cracks in the material. The fracture mechanics theory assumes that the failure of a material occurs when the stress intensity factor reaches a certain level, and it is used to design and test materials and structures that are subjected to high-stress environments.
The fourth type of theory of failure is the phenomenological theory. This theory is used to describe the behavior of materials under complex loading conditions, such as those experienced by materials in extreme environments or during natural disasters. The phenomenological theory takes into account the microstructure and composition of the material, as well as the various physical and chemical processes that occur when the material is subjected to stress or strain.
The types of theories of failure include static theory, fatigue theory, fracture mechanics theory, and phenomenological theory. Each theory provides different insights and perspectives on how materials fail, and they are used by engineers and researchers to design and test materials and structures that are safe, reliable, and durable.
What is the most commonly used failure theory?
The most commonly used failure theory in engineering is the Maximum Stress Theory, also known as the Tresca’s theory or the Coulomb’s theory. This failure theory is based on the assumption that failure in materials occurs when the maximum stress in the material exceeds the yield strength of the material at a given point.
According to this theory, different materials have different yield strengths, and it is the maximum stress that needs to be studied to determine whether the material will fail or not. For ductile materials, the yield strength often represents the onset of plastic deformation, beyond which the material undergoes significant yielding before it ultimately fails.
On the other hand, for brittle materials, the yield strength is not well defined, and the stress at which the material will fail is typically much higher than that of the yield strength.
The Maximum Stress Theory has been widely used in the design and analysis of different mechanical components such as beams, shafts, and pressure vessels. It is particularly useful in applications where the loads are known and static, as it allows the maximum stress in the material to be calculated accurately.
The theory, however, has limitations as it only considers the maximum stress in the material and does not take into account other factors such as the applied load and the stress concentration at the point of failure.
For this reason, other failure theories such as the Maximum Strain Theory, the Modified Mohr Theory, and the Von Mises theory have also been developed to address some of the shortcomings of the Maximum Stress Theory. These theories incorporate factors such as the applied load, the stress concentration, and the material properties to provide a more comprehensive approach to predicting material failure.
While the Maximum Stress Theory is the most commonly used failure theory in engineering due to its simplicity, it has its limitations. Therefore, other more comprehensive failure theories have been developed to provide a more accurate and reliable approach to predicting material failure.
What is failure theory explanation?
Failure theory explanation, also known as failure analysis, is the process of examining the reasons behind a failure of an object, material or structure. It is a crucial aspect of engineering and manufacturing industries as it helps to identify the root cause of the failure and provides insights to prevent future occurrences.
Failure theory explanation can often involve a detailed analysis of the material properties, manufacturing or fabrication process, environmental conditions, and the history of the object in question. This can involve conducting experiments and testing to determine the limitations and weaknesses of the material or product.
The goal of a failure theory explanation is to identify the root cause of the failure, whether it is due to the design, manufacturing process or usage, and then provide recommendations for how to prevent future failures. This is vital in improving the quality and safety of products, structures and systems.
For example, failure theory explanation can be used to determine why a bridge collapsed or why a metal component in a machine failed, leading to a catastrophic event. Engineers and experts can look at the material properties, the design, the manufacturing process, and the environmental conditions to understand why the failure occurred and identify any potential weaknesses or shortcomings.
Failure theory explanation is a critical aspect of engineering and manufacturing industries. Its purpose is to provide insights into why failures occur and provide recommendations to prevent future occurrences. This process can involve a detailed analysis of the material properties, manufacturing process, and usage history.
By identifying the root cause of a failure, engineers and experts can make improvements to products, structures, and systems to improve their quality and safety.
What is the problem with Rankine earth pressure?
The Rankine earth pressure theory is a widely used method for predicting the lateral pressure acting on retaining structures. However, this theory has been criticized for several reasons.
Firstly, the Rankine theory assumes that the soil is cohesionless and has a smooth, vertical failure plane. This is not always the case as in reality soil can be cohesive and may have multiple planes of failure due to the presence of soil layers, fissures, or surface irregularities. Therefore, using this theory may not always provide accurate predictions of the actual lateral pressure acting on the retaining structure.
Secondly, the Rankine theory assumes that the vertical stress distribution in the soil is homogeneous, which is not always the case in reality. The presence of non-uniform soil properties, such as varying soil density or a non-horizontal ground surface, can greatly affect the predictions of lateral pressure using this theory.
Thirdly, the Rankine theory does not consider the effects of soil deformation on the lateral pressure acting on the retaining structure. The soil can deform due to changes in the groundwater table level or due to the movement of the retaining structure itself. These deformations can significantly alter the lateral pressure acting on the structure, which is not accounted for in the Rankine theory.
Fourthly, the Rankine theory only provides a static analysis of the retaining structure and does not consider the effects of dynamic loading such as earthquakes, vibrations or rapid drainage. These dynamic forces can cause significant lateral pressure changes and can lead to failure if not accounted for in the design.
Finally, the Rankine theory does not consider the effects of soil strength mobilization, which can occur when the retaining structure moves away from the soil, causing the soil to gain strength and increase the lateral pressure acting on the structure. This phenomenon, known as arching, can result in higher lateral pressures than what is predicted by the Rankine theory.
The Rankine earth pressure theory has limitations in accurately predicting the lateral pressure acting on retaining structures due to its assumptions, lack of consideration of deformation and dynamic loading effects, and not accounting for soil strength mobilization. These limitations require an accurate and effective analysis method that considers these aspects to ensure a safe and reliable design.
What is the soil mass based on the assumption of Rankine theory?
The Rankine theory, also known as the Rankine Earth Pressure Theory, is a classical theory in soil mechanics that is used to analyze the lateral pressure exerted by soil on a retaining structure such as a wall or a foundation. The theory, which is based on the concept of soil mass, assumes that the soil is a cohesive material that can be divided into horizontal slices or layers, each of which has different properties and exerts a different amount of pressure on the retaining structure.
The soil mass, according to the Rankine theory, is treated as a sliding wedge that is composed of a number of horizontal slices or layers. Each layer is considered to be homogeneous and to have a constant angle of friction and cohesion. The angle of friction is the angle of the failure plane with the horizontal, while cohesion is the inherent strength of the soil due to the bonding forces between the soil particles.
The soil mass is assumed to be in a state of equilibrium, meaning that the forces acting on each slice of soil are balanced. This equilibrium state is maintained as long as the forces acting on the soil mass do not exceed the strength of the soil.
The Rankine theory considers two types of lateral earth pressure: active earth pressure and passive earth pressure. Active earth pressure is the lateral pressure exerted by the soil on a retaining wall or a foundation when the wall or foundation is moving away from the soil. Passive earth pressure, on the other hand, is the lateral pressure exerted by the soil on a retaining wall or a foundation when the wall or foundation is moving towards the soil.
The soil mass based on the assumption of Rankine theory is a cohesive material that can be divided into horizontal slices or layers, each of which exerts a different amount of pressure on a retaining structure. The theory assumes that the soil is in a state of equilibrium and considers two types of lateral earth pressure: active and passive earth pressure.
What is the advantage of Coulomb’s theory over Rankine theory?
Coulomb’s theory and Rankine theory are two different approaches to analyze the behavior of soil under different loading conditions. The key difference between the two theories is that Coulomb’s theory considers the shear strength of soil, whereas Rankine theory focuses on stress distribution and failure of soil.
In this context, Coulomb’s theory has its unique advantages over Rankine theory.
Firstly, Coulomb’s theory is widely used in practical applications because it is relatively more straightforward and more accurate than Rankine theory. Coulomb’s theory is based on a simple and intuitive concept, which is the Coulomb’s law of friction. According to the law, shear strength is proportional to the normal stress on the soil surface, and the angle of friction represents the maximum angle at which the soil will remain stable.
These parameters can be easily measured in the laboratory, and the results can be compared with the field data to validate the theory. In contrast, Rankine theory involves a complex analysis of stress fields, which is not easily applicable to real-world problems.
Secondly, Coulomb’s theory provides a better understanding of soil behavior under different loading conditions. Coulomb’s theory considers the effects of pore pressure and soil saturation on shear strength, which are critical factors in the stability of slopes and retaining walls. Coulomb’s theory also considers the effects of an infinite number of possible failure planes, while Rankine theory is limited to analyzing only horizontal failure planes.
Therefore, Coulomb’s theory provides a more comprehensive analysis of soil behavior, which can lead to more accurate predictions of soil stability and failure.
Lastly, Coulomb’s theory is well suited for the design of foundations and retaining walls. Coulomb’s theory provides a simple and intuitive method for designing foundations and retaining walls that can withstand the maximum shear stresses that may occur. The theory can be easily applied to different soil types and loading conditions, which makes it highly useful in engineering practice.
Furthermore, Coulomb’s theory allows for the determination of the factor of safety, which is critical in ensuring the long-term stability of structures.
Coulomb’S theory has several advantages over Rankine theory in the analysis of soil behavior. Coulomb’s theory is more accurate, provides a better understanding of soil behavior, and is well-suited for the design of foundations and retaining walls. Therefore, it is the preferred method of analysis in practical applications.