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Anonymous users2024-02-07The moment of inertia of the cross-section is an inherent property of the cross-section, and its magnitude has nothing to do with the amount of force, nor is it that the greater the moment of inertia, the greater the force, but the bending tensile stress may have a certain relationship with it, and I am not very clear, I forgot.
You can take a look at the books on the mechanics of materials.
But what is certain is that it has nothing to do with the force.
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Anonymous users2024-02-06(max)=|m|(max)×y(max)÷i(z)
is the normal stress of the cross-section, m is the bending moment of the cross-section, y is the distance to the neutral axis of the cross-section, and i is the moment of inertia of the cross-section to the neutral axis.
This formula applies to isometric beams subjected to transverse forces, and it indicates that the maximum normal stress of the beam occurs at the lower edge of the cross-section with the largest bending moment value.
After calculating the maximum normal stress of the beam, it is compared with the ultimate stress of the beam (the ultimate stress is determined by experiments), and if it is greater than the ultimate stress, the beam will fail.
That is, it must be satisfied: |m|(max) y(max) i(z) u), u) is the ultimate stress of the beam.
According to the above formula, under the condition of ultimate stress (u), the greater the moment of inertia of the cross-section, the greater the maximum bending moment that the beam can bear, that is, the greater the bearing capacity of the beam.
However, it is important to pay attention to the applicable conditions of the formula, which is only applicable to the bending isometric beam (the meaning of the straight beam of equal cross-section), and this formula is not applicable to the member subjected to tensile compression, and the bearing capacity of the member has nothing to do with the moment of inertia of the cross-section, but only to the ultimate tensile and compressive stress of the member itself.
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Anonymous users2024-02-05ExtremeMoment of inertiaThe difference between the moment of inertia and the moment of inertia is:
1. The moment of inertia and the polar moment of inertia are used in 2 different forms of force. The moment of inertia is the moment of inertia of the cross-section for a neutral axis, and the polar moment of inertia of the cross-section is the moment of inertia of the point of the cross-section.
2. The moment of inertia is used for bending stress.
Because the material mainly undergoes bending deformation, which is the moment of inertia of the material to the shaft, and the polar moment of inertia is used for torsional stress, because the material mainly undergoes torsional deformation, which is the moment of inertia of the material to the point.
3. Some symmetrical cross-sections also have such a characteristic, that is, the moment of inertia twice the polar moment of inertia, such as circles and rectangles.
4. The definition of the polar moment of inertia is ip = 2 da, that is, the area is centroid of the cross-section.
Reintegration of the square of the moment. For a circular section, the polar moment of inertia and the torsional moment of inertia are the same thing and can be equivalent.
Physical Meaning of Polar Moment of Inertia:
The physical meaning of moment of inertia is the property of a cross-section that resists bending. Structural design chain trouble.
In the process of calculation, the moment of inertia ix of the component is the square of the distance between the area of each microelement of the cross-section and the distance of each microelement to the neutral axis parallel or coincident with the x-axis.
The integral of the product. It is mainly used to calculate bending moments.
The bending stiffness of the cross-section about the x-axis under action.
In the process of structural design and calculation, the moment of inertia iy of the component is the integral of the area of each microelement of the cross-section and the square product of the distance of each microelement to the neutral axis parallel or coincident with the y-axis. It is mainly used to calculate the bending stiffness of the cross-section around the y-axis under the action of bending moment.
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Anonymous users2024-02-04The formula for calculating the moment of inertia is: iz=.
The 4 after d indicates the 4th power.
Polar moment of inertia: Since 2 = x 2 + y 2, the polar moment of inertia and the cross-section special quadratic axis allow the mathematical relationship in the excavation distance as shown in the above left figure, that is, the polar moment of inertia of the cross-section for any point is equal to the sum of the quadratic axes of the cross-section of any set of orthogonal coordinate systems with this point as the origin capacity of the intercept sliding face.
Static moment:
The static moment (area x plane inner axis once) is the integral of the product of the area of the microelements and the distance of each microelement to the specified axis on the cross-section, which is called the static moment of the cross-section to the specified axis sx= yda.
The static moment is the area moment, which is an important cross-sectional characteristic of the component, which is obtained by multiplying the area of the cross-section or a certain part of the cross-section by the distance between the centroid of this area and the mandrel of the whole cross-section, and is used to calculate the stress.
Note: The moment of inertia is multiplied by the distance to the second power, the static moment is multiplied by the distance by the first square, and there is a difference between the moment of inertia and the area moment (static moment).
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Anonymous users2024-02-03Moment of inertiaThe physical meaning refers to the property of a cross-section that resists bending.
In the process of structural design and calculation, the moment of inertia of the component is the square of the area of each microelement in the cross-section and the distance between each microelement and the neutral axis parallel or coincident with the x-axis.
The integral of the product. It is mainly used to calculate bending moments.
The bending stiffness of the cross-section about the x-axis under action.
In the process of structural design and calculation, the moment of inertia iy of the component is the integral of the area of each microelement of the cross-section and the squared product of the distance from each microelement to the neutral axis parallel or coincident with the y-axis. It is mainly used to calculate the bending stiffness of the cross-section of the rock hunger around the y-axis under the action of bending moment.
Introduce. The static moment (area x plane inner axis once) is the integral of the product of the area of the microelements and the distance of each microelement to the specified axis on the cross-section, which is called the static moment of the cross-section to the specified axis sx= yda.
The static moment is the area moment, which is an important cross-sectional property of the component, which is the centroid of the area of the section or a part of the section multiplied by this area.
The distance between the mandrel to the entire cross-section is used to calculate the stresses.
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Anonymous users2024-02-02Moment of inertiai = mass x vertical axis quadratic).
The moment of inertia is the distance l from the center of mass m* centroid of the object relative to a point (around the rotation of the Hovolt concession point).
Angular moment of in-moment. Moment of inertia * angular velocity.
life examples; The skater rotates slower with his arms outstretched, and faster when he retracts his arms.
Because when m is constant, the arm shrinks l, and the moment of inertia decreases.
If the angular moment of inertia is conserved, the angular velocity will increase.
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Anonymous users2024-02-01Moment of inertiaThe physical meaning of the section is the property of the section to resist bending. The physical meaning of moment of inertia refers to the property of a section that resists bending. In the process of structural design and calculation, the moment of inertia ix of the component is the square of the area of each microelement in the cross-section and the distance between each microelement and the axis of the neutralized blocking tong parallel or coincident with the x-axis.
The integral of the product. It is mainly used to calculate bending moments.
The bending stiffness of the cross-section about the x-axis under action.
Explanation of the difference between polar moment of inertia and distance of inertiaThe moment of inertia is a quantity that reflects the torsional characteristics of a cross-section. The polar moment of inertia of a section at a point is equal to the integral of each microarea on the section multiplied by the distance from the microarea to the point of the macrosquare over the entire section. The polar moment of inertia is commonly used to calculate the stress and deformation of the shaft under torque.
The product of inertia is the cross-section for two orthogonal axes.
The product of inertia is equal to the integral of the distance of each micro-area on the cross-section multiplied by the area of the micro-equilibrium mu to the two coordinate axes over the entire cross-section.
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Anonymous users2024-01-31Moment of inertiaThe physical meaning refers to the resistance of the mountain ruler section to bending.
A pair of orthogonal coordinate axes with an inertia product equal to zero is called the principal axis of inertia. The moment of inertia of the graph for the principal axis of inertia is the principal moment of inertia.
When the intersection of a pair of principal inertial axes and the centroid of the section.
When coincident, the pair of axes are centroid principal axis of inertia. The moment of inertia of the graph for the centroid principal axis of inertia is the centroid principal moment of inertia.
Physics is the foundation of philosophy, and philosophy is the sublimation of physics!!
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