Plate deflection calculation 50, plate deflection calculation

f=c3(qb^4)/(eh^3)

z =c4q(b/h)^2

x=c5q(b/h)^2

c6q(b/h)^2

Symbolic meaning and units.

q – unit load, n m 2; �

E – modulus of elasticity, GPA;

a - plate length, mm;

b - board width, mm;

h - plate thickness, mm;

z, x - central stress, mpa;

c - rectangular plate coefficient table;

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 the cross-section x is equal to the deflection at that cross-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.

Summary. 1. The maximum deflection under the uniform load is in the span of the beam, and its calculation formula:

ymax = 5ql^4/(384ei)

where: ymax is the maximum deflection in the beam span (mm) q is the standard value of the uniform wiring load (kn m).

e is the modulus of elasticity of the steel, and for engineering structural steel, e = 2,100,000 n mm2

i is the cross-sectional moment of inertia of the steel, which can be found in the section steel table (mm 4) 2, the maximum deflection under a concentrated load in the span of the beam in the span, and its calculation formula.

ymax = 8pl 3 (384ei) = 1pl 3 (48ei) where ymax is the maximum deflection (mm) in the beam span

3. The maximum deflection under two equal concentrated loads is arranged at equal intervals between spans in the span of the beam, and its calculation formula:

ymax =

where: ymax is the maximum deflection in the beam span (mm)4, the maximum deflection under three equal concentrated loads arranged at equal intervals between the spans, and its calculation formula.

ymax = 6

1. The maximum deflection of the car loss under the uniform load is in the span of the beam, and its calculation formula is: ymax = 5QL 4 (384EI) where: ymax is the maximum deflection in the beam span (mm) q is the standard value of the uniform wiring load (kn m) e is the elastic modulus of the steel, for the engineering Chafan Hunger structural steel, e = 2100000 n mm 2i is the cross-sectional moment of inertia of the steel, which can be found in the section steel table (mm 4) 2, the maximum deflection under a concentrated load in the span of the beam, The formula is ymax = 8PL 3 (384EI) = 1PL 3 (48EI), where YMAX is the maximum deflection (mm) in the beam span 3, and the maximum deflection under two equal concentrated loads arranged at equal intervals between the spans is in the span of the beam, and the calculation formula is:

ymax = where: ymax is the maximum deflection in the beam span (mm)4, the maximum deflection under three equal concentrated loads of equal spacing repatriation arrangement between spans, and the calculation formula ymax = 6