Are the concepts of strength and stiffness always confused? Just read this and you'll understand
Many people are always confused about the concept of strength and stiffness in mechanics, and today we will talk about our own understanding. The book says that in order to ensure the normal operation of the mechanical system or the entire structure, each part or component must be able to work properly. The task of safety design of engineering components is to ensure that the components have sufficient strength, stiffness and stability.
Stability is well understood, the ability to maintain or restore the original form of equilibrium under force. For example, the sudden bending of the thin rod under pressure, the folding of the load-bearing of the thin-wall member, or the instability of the column of the building leading to the collapse, is well understood. Today I'm going to talk about the understanding of stiffness and strength.
intensity
one
Definition: The ability of a member or component to resist damage (fracture) or significant deformation under the action of external forces.
For example, Sun Yue used the ipad as a weight scale, stood on the ipad screen cracked, which is not strong enough. For example, when Wuhan looks at the sea every summer, many large branches are blown off by the wind, which is also not strong enough.
Strength is to reflect the material fracture and other damage parameters, strength is generally tensile strength, compressive strength, etc., that is, when the stress reaches the amount of material damage, strength unit is generally mpa.
1.1
Failure type
Brittle fracture: A sudden fracture that occurs in the absence of significant plastic deformation. For example, the fracture of cast iron specimens along the cross section during stretching and the fracture of round cast iron specimens along the oblique section during torsion.
Plastic yield: The material produces significant plastic deformation and makes the member lose the ability to work, such as low carbon steel samples will have significant plastic deformation when stretched or twisted.
1.2
Strength theory
Maximum tensile stress theory: As long as the maximum tensile stress σ1 at a point in the member reaches the ultimate stress σb in the unidirectional stress state, the material will be brittle fracture. Therefore, the condition for brittle fracture failure of a member whose danger point is in a complex stress state is: σ1=σb. Therefore, the strength condition established according to the first strength theory is: σ1≤[σ].
Maximum tensile strain theory: As long as the maximum tensile strain ε1 reaches the limit value εu in the unidirectional stress state, the material will be brittle fracture failure, ε1=εu. Generalized Hooke's law: ε1=[σ1-u(σ2+σ3)]/E, so σ1-u(σ2+σ3)=σb. The strength condition established according to the second strength theory is: σ1-U (σ2+σ3)≤[σ].
Maximum shear stress theory: As long as the maximum shear stress τmax reaches the ultimate shear stress τ0 in the unidirectional stress state, the material will yield failure. τmax=τ0. According to the stress formula on the axial tensile oblique section, we can see that τ0=σs/2(σs is the normal stress on the cross section) can be obtained from the formula: τmax=(σ1-σ3)/2. So the failure condition is rewritten as σ1-σ3=σs. According to the third strength theory, the strength conditions are: σ1-σ3≤[σ].
Specific energy theory of shape change: As long as the specific energy of shape change at a point in the member reaches the limit value under unidirectional stress state, the material will yield failure. So according to the fourth strength theory of strength condition is: SQRT (22 + 12 + sigma sigma sigma 32-1 sigma sigma 2 sigma 3-2 - sigma sigma 3 sigma 1) < (sigma)
stiffness
2
Definition: refers to the ability of a component or part to resist elastic deformation or displacement under the action of external forces, that is, the elastic deformation or the only one that should not exceed the scope allowed by the project.
Stiffness is a parameter that reflects the relationship between the deformation of the structure and the force, that is, the amount of deformation generated by the structure by how much power, simply put, is a spring, the tension divided by the elongation is the stiffness of the spring. The unit of stiffness is usually N/m.
2.1
Stiffness type
When the applied load is a constant load, it is called static stiffness; When the load is alternating, it is called dynamic stiffness. Static stiffness mainly includes structural stiffness and contact stiffness, structural stiffness refers to the stiffness of the member itself, mainly including bending stiffness and torsional stiffness.
Bending stiffness is calculated as follows:
Where P is the static load (N) and δ is the elastic deformation in the load direction (μm). The torsional stiffness is calculated as follows:
Where M is the acting torque (N·m), L is the distance from the torque acting point to the fixed end (m), and θ is the torsion Angle (°).
The connection between the two
3
Based on the above theoretical understanding of strength and stiffness, the definition of strength is aimed at the failure under the action of external forces. The types of failure are classified as plastic yield and brittle fracture, which are associated with the stress-strain curve during tension. As shown in the figure.
The curve in the figure can be divided into four stages: I, elastic deformation stage;
II. Yield stage;
III. Strengthening stage;
IV. Local necking stage.
The definition of stiffness is to resist elastic deformation, which is carried out in the first stage, and Hooke's law is satisfied under elastic action. The calculation formula of bending stiffness and torsional stiffness under static load is observed, similar to Hooke's law, and it can be inferred that the measurement of stiffness is only carried out in the elastic deformation stage.
After entering the next stage, the plastic strain or residual strain does not disappear during the tensile process, under the stress-strain curve, the stress is almost constant, and the strain increases significantly, at this time the stress is the yield limit, and for the material, it enters the failure stage of plastic yield. After entering the strengthening stage, the strain increases with the increase of stress and finally reaches the strength limit. It can be seen that the strength is measured after the elastic deformation of the material and before the strength limit.
In summary, it can be concluded that both stiffness and strength are measured at the failure stage of parts, and stiffness can be measured by stress, and strength can be measured by deformation. In the strain process, the stiffness is in the previous stage and the strength is in the later stage. Therefore, in the condition measurement of parts failure, as long as the stiffness requirements are met, sufficient stress can be resisted in the elastic deformation stage, and the strength can meet the requirements of the parts under such a premise. In accordance with this relationship, there will be various designs in actual production, such as the shaft in mechanical equipment, usually the size of the shaft is first determined according to the strength conditions, and then the stiffness is checked according to the stiffness conditions. The rigidity requirements of precision machinery for the shaft are therefore set very high, and the design of its cross-section size is often controlled by the stiffness conditions.