Technology definitions

Chinese name:

Deflection

English name:

Deflection

definition:

The axis or midplane of the structural member causes a linear displacement perpendicular to the axis or midplane due to bending.

Subject:

Hydraulic Science and Technology (Grade 1); Engineering Mechanics, Engineering Structure, Building Materials (Grade 2); Engineering Mechanics (Water Conservancy) (Grade 3)

This content was published by the National Science and Technology Terms Examination and Approval Committee

The

Deflection (German Durchbiegung)—Linear displacement of the cross-section centroid in the direction perpendicular to the axis when bending is called deflection, denoted by y. In short, it refers to the maximum deformation of the flexural members such as beams and trusses under the action of loads. Usually, the y-axis of the vertical direction is the vertical deformation of the component.

Deflection Curve—As shown in the figure, when the plane is bent, the axis of the beam will become a plane curve in the longitudinal symmetry plane of the beam. This curve is called the deflection curve of the beam.

Deflection is related to the size of the load, the size of the cross-section of the component, and the physical properties of the component.

Deflection—Linear displacement of the cross-section centroid in the direction perpendicular to the axis during bending deformation is called deflection and is represented by y.

Corner - The angle at which the cross-section rotates relative to its original position during bending deformation is called the angle of rotation and is denoted by θ.

The deflection curve equations—deflection and rotation angles vary with the cross-sectional position. When discussing the bending deformation problem, it is usually selected that the coordinate axis x is positive to the right and the coordinate axis y is positive. After the axis is selected, the deflection y at each cross-section of the beam will be a function of the cross-sectional position coordinate x, and its expression is called the deflection curve equation of the beam, ie

y = f ( x ).

Obviously, the value of the deflection curve equation at section x is equal to the deflection at that section.

According to the knowledge of calculus, the slope of the deflection curve

Due to the fact that the value of the angle θ of the beam in the actual project is very small, it can be considered as

It can be seen that the slope of the deflection curve at the cross-sectional position coordinate x, or the first derivative of the deflection y with respect to the coordinate x, is equal to the rotation angle of the cross-section.

Deflection and sign of positive and negative sign of rotation: In the coordinate system selected in Figure 6-1, the upward deflection is positive, and the counterclockwise rotation is positive.