How to Comprehend Strength in Mechanics 1

1、 Strength

Definition: the ability of components or parts to resist damage (fracture) or significant deformation under external force. Key words are extracted, fracture is broken and deformation is significant.

For example, Sun Yue took the iPad as a weight scale, stood up, and the iPad screen cracked, which is not strong enough. For example, many big branches are broken by the wind when watching the sea every summer in Wuhan, which is not strong enough.

Strength is a parameter reflecting the failure of materials such as fracture. Generally, the strength includes tensile strength and compressive strength, which is the amount of material failure when the stress reaches. The unit of strength is generally MPa.

How to Comprehend Strength in Mechanics 2

Damage type

Brittle fracture: a sudden fracture that occurs without significant plastic deformation. For example, the fracture of the cast iron specimen along the cross section in the process of drawing and the fracture of the cast iron specimen along the inclined section in the process of torsion.

Plastic yield: the material produces significant plastic deformation, which makes the component lose working capacity. For example, the low-carbon steel specimen will have significant plastic deformation when it is stretched or twisted.

strength theory

1. Theory of maximum tensile stress:

As long as the maximum tensile stress  at a point in the member reaches the ultimate stress σb under the condition of unidirectional stress, brittle fracture will occur in the material. Therefore, the conditions for brittle fracture of components in complex stress state are as follows:σ1=σb

So the strength condition established by the first strength theory is:σ1≤[σ] 。

2. Maximum tensile strain theory:

As long as the maximum tensile strain ε 1 reaches the limit value ε u under unidirectional stress state, brittle fracture will occur: ε1=σu.

From the generalized Hooke’s Law:ε1=[σ1-u(σ2+σ3)]/E,therefore,σ1-u(σ2+σ3)=σb.

The strength conditions established according to the second strength theory are as follows: σ1-u(σ2+σ3)≤[σ].

3. Maximum shear stress theory:

As long as the maximum shear stress τ Max reaches the ultimate shear stress τ 0 under the state of unidirectional stress, the material will yield failure. τmax=τ0。

According to the stress formula on the inclined section of axial tension.τ0=σs/2(σs——Normal stress on cross section)From the formula: τmax=(σ1-σ3)/2。So the destruction condition is rewritten as σ1-σ3=σs。

According to the third strength theory, the strength condition is:σ1-σ3≤[σ]。

4. Specific energy theory of shape change:

As long as the shape change ratio at a point in the member can reach the limit value under the unidirectional stress state, the material will yield failure.

Therefore, according to the fourth strength theory, the strength conditions are:


2、 Stiffness

Definition: refers to the ability of members or parts to resist elastic deformation or displacement under the action of external force, that is, elastic deformation or uniqueness shall not exceed the allowable scope of the project.

Stiffness is a parameter that reflects the relationship between structural deformation and force, that is, the amount of deformation produced by how much force the structure is subjected to. In short, it is a spring, and the stiffness of spring is the tension divided by the elongation. The unit of stiffness is generally N/m。

Stiffness type:

When the applied load is a constant load, it is called static stiffness; when it is an alternating load, 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.

1. Bending rigidity: calculated according to the following formula:

How to Comprehend Strength in Mechanics 3

3、 Connection between the two

Based on the above theoretical understanding of strength and rigidity, compared with rigidity, the definition of strength is aimed at the failure under the action of external force, and the failure type is classified as plastic yield and brittle fracture, which is associated with the stress-strain curve in tension. As shown in the figure.

The curve in the figure can be divided into four stages:

1. Elastic deformation stage;

2. Yield stage;

3. Strengthening stage;

4. Local necking stage.

The definition of stiffness is to resist elastic deformation, which is carried out in the first stage. Under elastic action, it meets Hooke’s law. Observe the calculation formula of bending stiffness and torsional stiffness under static load, which is similar to Hooke’s law. It can be inferred that the measurement of stiffness is only carried out in the elastic deformation stage.

How to Comprehend Strength in Mechanics 4

After entering the next stage, the residual strain of the plastic strain fire will not disappear during the tensile process. Under the stress-strain curve, the stress is almost the same, while the strain increases significantly. At this time, the stress is the yield limit. And for the material, it enters into plastic yield

In the failure stage, after the strengthening stage, the strain increases with the increase of stress, and finally reaches the strength limit. It can be seen that the measurement of the strength is after the elastic deformation of the material and before the strength limit.

In conclusion, it can be concluded that both the stiffness and strength are measured at the failure stage of the part, while the stiffness can be measured by stress, and the strength can be measured by deformation. In the process of strain, the stiffness is in the former stage and the strength is in the latter stage. Therefore, in the condition measurement of part failure, as long as the stiffness requirements are met, sufficient stress can be resisted at the stage of elastic deformation, and The strength also meets the requirements of parts under such premise. According to this relationship, there will be all kinds of design in the actual production, such as the shaft in mechanical equipment. Usually, the size of the shaft is determined according to the strength condition first, and then the rigidity is checked according to the rigidity condition. Because of this, the rigidity requirement of precision machinery is very high, and the design of its section size is often controlled by the rigidity condition.

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