How to calculate the bending deflection of the steel plate, the calculation of the bending force of

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The formula for calculating the deflection is: ymax=5ql 4 (384EI) (EI is the bending stiffness of the beam under the action of uniform load Q of the simply supported beam of length L).

The deflection is related to the magnitude of the load, the cross-sectional dimensions of the component, and the material physical properties of the component.

Deflection – The linear displacement of the centroid of the cross-section along the perpendicular direction to the axis during bending deformation is called deflection and is denoted by .

Angle - The angle at which the cross-section turns relative to its original position when it is bent and deformed is called the angle and is denoted by .

The values of the deflection equation – both the deflection and the angle of rotation vary with the position of the section. When discussing the problem of bending deformation, it is common to choose that the coordinate axis x is positive to the right and the coordinate axis y is positive downward. When the axes are selected, the deflection at each cross-section of the beam will be a function of the coordinates x of the cross-sectional position, and its expression is called the deflection equation of the beam, i.e. = f(x).

Obviously, the value of the deflection equation at section x is equal to the deflection at that section. (Construction works).

The slope of the deflection curve at coordinates x at the location of the cross-section, or the first derivative of the deflection versus the coordinates x, is equal to the angle of rotation of the cross-section.

Provisions on the positive and negative signs of deflection and rotation angle: In the coordinate system selected in the image above, the upward deflection is positive, and the counterclockwise turning angle is positive.

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A common method used to study the mechanical properties of materials is the stress-strain curve.

It is divided into the following stages.

Elastic transformation stage: This stage of reversible deformation of the material.

Stress and strain are linear.

Plastic deformation stage: This stage in which the material is permanently deformed.

Yield stage: the stress remains basically the same, the strain is increasing, and the material temporarily loses its ability to resist deformation.

Reinforcement stage: The material regains its resistance to deformation, and an external force is required to continue to deform the material.

The maximum amount of stress that occurs during the fracture of a material is called the ultimate strength.

The ultimate strength in the tensile process is the tensile strength.

The ultimate strength during compression is the compressive strength.

The ultimate strength during shearing is the shear strength.

The ultimate strength during bending is the bending strength.

Flexural strength or flexural strength.

The maximum bending moment is: m p (force) a (distance).

The cross-sectional coefficient of the rectangle w a b b 6 2 8 8 6 cm to the 3rd power) The allowable stress of the material is taken as 1550 (kgf cm 2) m w p a p 1550 200 kgf).

Note: From a microscopic point of view, as long as the heavy things will make the steel plate bend and deform, just how much bending deformation is a matter of how much, now you are calculating how much force the steel plate can bear is more realistic.

The bending resistance of the angle steel is calculated by the formula r=(3f*l) (2b*h*h). Where:

f — Breaking load.

l—Span. b—Width.

h—thickness. Test Method:

The flexural strength test is divided into three-point bending and four-point bending. Each point requires more than 5 data (10 data for the standard) average results.

Flexural strength tests are carried out on an in-scale Instron 1195 universal materials testing machine. The test strips used for testing are 3 4 35 (mm*mm*mm). Measured by the three-point bending method, the span is 30mm, and the loading rate is.

5 test strips were tested for each data and then averaged.

ymax = 5ql^4/(384ej).

where: ymax is the maximum deflection (cm) in the beam span

q is the uniform wiring load (kg cm).

e is the modulus of elasticity of the I-beam, for engineering structural steel, e = 2100000 kg cm2

j is the cross-sectional moment of inertia of the I-beam, and the 40B type I-beam can be taken 22800 (cm 4) for the landlord

Deflection is the linear displacement of the axis of the member perpendicular to the axis or the linear displacement of the middle surface of the plate and shell in the direction perpendicular to the midsurface when the force or non-uniform temperature changes.

The deflection of an elongated object, such as a beam or column, is the amount of displacement within the normal plane of the axis at each point on its axis when it is deformed. The deflection of a sheet or shell is the amount of displacement on the normal of the midplane at each point on the midface. The law of the deflection of each point on an object as a function of position and time is called the deflection function or displacement function.

Calculating strain and stress by finding the deflection function is one of the research methods of solid mechanics.

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1. Definition of bending stiffness of reinforced concrete component section.

cross-sectional bending stiffness of elastic homogeneous members;

The change of the bending stiffness of the cross-section of the reinforced concrete flexural member during the whole process of stress;

m—· curve of cross-section of reinforced concrete member;

Definition of bending stiffness of cross-section of reinforced concrete members;

The basic expression for the bending stiffness of a reinforced concrete member section.

Second, the short-term bending stiffness BS of the cross-section

Average cross-section bending stiffness concept;

Strain inhomogeneity coefficient of reinforcement between cracks ;

the average strain of the concrete at the edge of the compression zone;

The formula for calculating the short-term stiffness BS of a cross-section.

3. The long-term bending stiffness of the cross-section BL

Reasons for the slow increase in deflection over time;

Short-term and long-term effects of loads;

Calculation method of long-term bending stiffness BL of cross-section;

Deflection increase factor.

Fourth, the deflection of flexural components.

the principle of minimum stiffness;

Methods for checking deflection;

the span-to-height ratio of beams and slabs;

The main factors influencing the bending stiffness of a cross-section.

It is calculated by the formula r=(3f*l) (2b*h*h).

The formula for the three-point test bending resistance is: r=(3f*l) (2b*h*h); F is the failure load, L is the span, B is the width, and H is the thickness.

The three-point bending test or four-point test method is used to evaluate, in which the four-point test requires two loading forces, which is more complicated; The three-point test is the most commonly used, and its value is proportional to the maximum pressure withstanding, and the average result is more than 5 data (10 data for the standard) at each point.

The model does not represent the size of different side thicknesses in the same model, so the side width and side thickness of the angle steel should be filled in on the contract and other documents to avoid being represented by the model alone. The specification of hot-rolled equilateral angle steel is 2. Angle steel can be composed of various different stressed components according to the different needs of the structure, and can also be used as a connector between components.

Flexural bearing capacity, expressed by the formula of flexural strength, the formula in the pure plane is f=m w, (unit n mm); Bending deformation varies according to the type of support, e.g. simply supported, uniform load = 5ql 4 384（mm）。

Angle steel is a rolled steel, which is a homogeneous, isotropic, close to ideal material, and its cross-section is calculated by applying the material mechanics formula; Its elastic modulus e is very high, and it is relatively fixed with different materials; Its cross-sectional shape is asymmetrical, and the mechanical parameters of the cross-section (cross-sectional moment w, moment of inertia i, rotation radius r) are very troublesome to calculate.

1. Angle steel is rolled steel, which is homogeneous, isotropic and close to ideal material, and its cross-section is calculated by applying the material mechanics formula; Its elastic modulus e is very high, and it is relatively fixed with different materials;

2. Its cross-sectional shape is asymmetrical, and the mechanical parameters of the cross-section (cross-sectional moment w, moment of inertia i, and radius r) are very troublesome to calculate.

3. Its flexural bearing capacity is expressed by the formula of flexural strength, and the formula in the pure plane is f=m w, (unit n mm).

4. Bending deformation, depending on the type of support, such as simply supported, evenly distributed under load = 5ql 4 384（mm）。

In the mechanical design manual, there are diagrams and calculation formulas for the forces of various beams, and diagrams and calculation formulas for the moments of inertia and polar moments of inertia of various cross-sections.

1.Determine the standard value of the load.

2.Calculate the maximum mid-span moment of the member under the standard combination of loads. (according to the theory of elasticity) 3The short-term bending stiffness bs of the component cross-section (at the maximum bending moment) is calculated and the stiffness b is calculated considering the long-term increase.

4.The deflection is calculated according to the deflection formula of the static calculation manual according to the support situation and load nature.

All are calculated according to the formulas and steps in the section of the serviceability limit state of the specification GB50010-2002.

1. Determine the load (dead load, live load) of the flexural member

2. Determine the form of the support and know the formula for calculating the deflection.

3. Calculate the deflection according to the calculation formula.

The deflection of the solid belly steel beam is calculated according to the formula of the "Building Structure Static Calculation Manual" directly checked according to its support type. The manual contains formulas for the maximum deflection for various support types and common load distributions. That's the correct result of the hard work of the seniors, and it is left to the younger generations to enjoy!

For example, the maximum deflection in the span of a simply supported beam under uniform load is f=5ql 4 384eie is the modulus of elasticity of the material and i is the moment of inertia of the cross-section.