Flat Plate Simply Supported Deflection and Bending Stress Calculator

Beam Deflection and Stress Formula and Calculators
Engineering Calculators

Flat Plate Deflection Calculator

Flat Plates Stress, Deflection and Reactionary Loading Equations and Calculators


  1. The plate is flat, of uniform thickness, and of homogeneous isotropic material;
  2. the thickness is not more than about one quarterof the least transverse dimension, and the maximum deflection
    is not more than about one-half the thickness;
  3. all forces, loads and reactions are normal to the plane of the plate; and
  4. the plate is nowhere stressed beyond the elastic limit. For convenience in discussion, it will be assumed further that the plane of the plate is horizontal. Beams of Uniform Cross Section, Loaded Transversely


The plate deflects. The middle surface (halfway between top and bottom surfaces) remains unstressed; at other points there are biaxial stresses in the plane of the plate. Straight lines in the plate that were originally vertical remain straight but become inclined; therefore the intensity of either principal stress at points on any such line is proportional to the distance from the middle surface.

Flat Plate Simply Supported

Variables Description Input Data
Length a (mm) = inches
Width, b (mm) =
Thickness, t (mm) =
Modulus of elasticity, E (N/mm2) = psi
Poisson ratio, v = -
Uniform over small concentric circle of ro, qo (N/mm2) = psi
Load application radius, ro (mm) inches
Total area mm2 = in2
a/b, aob = -
Uniform loading pressure over entire plate, q (N/mm2) = psi
Total load applied to the plate, W (N) = lbs
Outer radius used in calculation, ro_prime (mm) = in2
Total load applied to center of plate, Wo (N) = lbs
Simply Supported Outer Boundary:
Distributed Load:
Center displacement, dc (mm) = inches
Bending stress at center (N/mm2) = psi
Reaction load at center of long side (N/mm) = lbs/in
Centrally Applied Concentrated Load:
Center displacement, fdc (mm) = inches
Bending stress at center (N/mm2)= psi
References: Roark & Young, Formulas for Stress and Strain, 5th eddition, page 386