Can you clearly distinguish the concepts and differences between internal force, stress, and strain? Come see it all today.
1. The concept of internal force
1. Definition
Internal force refers to the interaction force (additional internal force) between adjacent parts in an object caused by external force. The force exerted on the rod by the outside world is called external force.
Any object is composed of infinitely many particles, there is an interaction force between any two adjacent particles in the component, and the magnitude of the force is related to the relative position of the particles. When an object is subjected to an external force, the object deforms, the relative position of its internal particles changes, and the interaction force between them changes accordingly. We call the change of the force produced by the external force the additional internal force, or internal force for short.
2. Calculation method of internal force—section method
Obviously, the internal force is inside the component. If you want to solve the internal force, you have to expose the internal force. In this way, we use the cross-section method to solve the cross-sectional position of the internal force according to the needs. Hypothetically cut the section, the original member is balanced, and any part after cutting is also balanced, that is, any part on both sides of the section is in a balanced state under the action of external force and internal force on the section. Therefore, you can take any side of the section, study its equilibrium conditions, establish a balance equation, and solve the internal force on the section. The specific steps to solve the section are as follows.
Hypothetical cut: At the cross-section where the internal force is sought (usually the cross-section), the rod is imaginary divided into two by the cross-section.
Substitution: Take a part arbitrarily, and the effect of the discarded part on the remaining part is replaced by the corresponding internal force (force or force couple) acting on the section.
Balance: Establish a balance equation for the remaining part, and calculate the unknown internal force of the rod on the cut-off surface based on the known external force on it (at this time, the internal force on the cut-off surface is an external force for the remaining part). According to the basic assumption of uniformity and continuity, an arbitrary force should be continuously distributed on the section after cutting, and there are internal forces at every point on the section, but there are only six equilibrium conditions for an arbitrary force system in space, and we cannot solve all of them. The internal force of each point. According to the simplification of the force system, we simplify any force system of this internal force to a point of the section, usually to the centroid of the section, and obtain a principal vector and a principal moment, as shown in the figure below.
Taking the centroid of the section as the origin, establish a Cartesian coordinate system as shown in the figure, the x-axis is perpendicular to the cross-section, that is, along the axis of the rod, and the y-axis and z-axis are in the section plane. Decomposing the principal vector to the three coordinate axes can obtain three components: the axial force along the x-axis, and the shear force along the y-axis and z-axis.
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Decomposing the principal moments along the three coordinate axes yields three components: torque along the x-axis, bending moments along the y-axis and z-axis.
We also call these six components internal forces, but it should be noted that these six components are the resultant force or moment of internal forces. Solving the internal force of the bar later is to find the axial force, shear force, torque and bending moment, because these internal forces correspond to the basic deformation of the bar: tension and compression deformation, shear deformation, torsional deformation, bending deformation .
2. The concept of stress
Stress is the distribution concentration of internal force (stress is for a certain "point", when we want to describe the stress of a point, we should point out the position of this point and the orientation of the plane passing through this point), in order to describe the stress of a point on the section , take a micro-area DA around this point, as shown in the figure. The resultant force of the internal force system on this micro-area is DF. Since this area is small enough, we assume that the internal force is uniformly distributed, then we can obtain the average stress, and then take the limit of the average stress to obtain the total stress or total stress of this point , the direction of the total stress changes with the position of the selected point. Obviously, the total stress is a vector, and the relationship between its direction and the section is arbitrary. We then decompose the total stress into two components, one is called normal stress perpendicular to the section, and the other is called shear stress tangent to the section.
mean stress
total stress (total stress)
The total stress is decomposed into: the stress perpendicular to the section is called "normal stress", and the stress inside the section is called "shear stress".
The unit of stress: Pa, usually used: MPa, GPa.
3. Displacement, deformation and strain
1. Displacement
The position change of a point in the object before and after deformation, the displacement in material mechanics has linear displacement and angular displacement. As shown in the figure below, a concentrated force is applied to the free end of the cantilever beam, and the beam bends and deforms. If we examine the displacement of a certain section, such as the displacement of the free end, it is obvious that the centroid of the section will have a downward displacement, resulting in a linear displacement, and at the same time, the normal direction of the section will also change, that is, the section will rotate, resulting in an angular displacement. displacement.
2. Deformation
Changes in size and shape of an object under the action of an external force.
3. Strain
To measure the degree of deformation at a point of a component, the strain is also for a certain "point".
(1) Linear strain (measures the degree of change in the size of a point in an object).
As shown in the figure, we examine any point A in the component, and take any point B near point A. The length of AB is Dx. The component deforms under the action of external force, and both points A and B are displaced to new positions. The distance between becomes Dx+Ds, assuming that the deformation is uniform within the range of Dx, the average linear strain can be obtained
We take the limit of the above formula to get the line strain at point A
For plane problems, a small rectangle is shown in the figure, and the external force action line becomes a rectangle shown by a dotted line (the size changes). If the deformation is uniform within the range of Dx and Dy, there is an average line along the x and y directions strain.
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Take the limit respectively to get the linear strain in the x and y directions
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(2) Angular strain (measures the degree of change in the shape of a point in an object) is also called shear strain or shear strain.
Defined as the change in right angle.
