How to understand stiffness infinity in structural mechanics?

In the force analysis, the stiffness infinity rod is regarded as a "passive rod", that is, the ordinary rod bears how much bending moment it bears, and it is regarded as an ordinary rod fixed at both ends If there is no bending moment at the end of the ordinary rod, then the stiffness infinity rod has no bending moment at that end.

The breakthrough of the solution generally lies in: when deformation occurs, the angle between the stiffness infinity rod and the ordinary rod will not change (the right angle is to maintain 90 degrees), which is equivalent to the angular displacement of the ordinary rod fixed at both ends at the end, and the size of the angular displacement should be calculated according to the geometric relationship, and then the bending moment of the stiffness infinity rod is determined according to the bending moment of the end of the ordinary rod.

There is a definition of a rigid body in theoretical mechanics, and this stiffness infinity should be understood with reference to the definition of a rigid body.

Any two points on a rigid body do not have a relative displacement under any external force, and for members with infinite stiffness, it can be assumed that it does not deform under any external force. On this basis, it can be understood that the generation of all bending moments is divided into two types, one is generated by the direct action of the force, and the other is generated by the deformation of the members in contact with each other to transfer the bending moments themselves.

In this way, to understand the problem of infinite stiffness, you only need to analyze the deformations of the contact cross-sections between adjacent members.

The bending moment diagram is a diagram of the internal forces, which are determined by the external forces, and as long as the external forces are known, the internal forces on any section must be found according to the cross-section method, including the bending moment. This allows you to draw a bending moment diagram. Therefore, the bending moment diagram has nothing to do with the stiffness of the member, regardless of whether the stiffness is infinity or not.

However, if the bending stiffness and tensile and compressive stiffness of the fixed beam at both ends are infinite, the members cannot be deformed, and the support reaction force cannot be found by using the deformation coordination condition.

So there's a logical relationship between who decides whom. <

Structural mechanics. Structural mechanics) is a branch of solid mechanics, which mainly studies the law of force and force transmission of engineering structures, and how to optimize the structure.

and mechanical engineering students are required to take the subject, which is applied to the construction industry and machinery manufacturing industry. The study of structural mechanics includes the composition rules of the structure, the response of the structure under various effects (external forces, temperature effects, construction errors, support deformation, etc.), including internal forces (axial force, shear force).

bending moment, torque), displacement (linear displacement, angular displacement), and dynamic response (natural period, mode shape) of the structure under dynamic loads, etc. There are usually three methods of analysis in structural mechanics: energy method, force method, displacement method, and the matrix displacement method derived from the displacement method later developed the finite element method, which became the theoretical basis for structural calculation using computers.

It won't be deformed, it's done in four words, it's simple and easy to understand!

What does the infinity of stiffness have to do with the internal force of the painting? The internal force diagram is only related to the structural form, i.e. the constraints, the span, and the stiffness, and how to deal with the load. The stiffness is used to find the displacement using the bending moment.

For statically determined structures, the internal forces are only related to the load.

4. Use the formula of moment of inertia.

Find angular acceleration.

The elapsed time t is found using the definite integral

The process is shown below: