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2025-02-28

VE0034 | Torsion of Thin Plate

Description

A thin plate is fixed on one side (φz=0) and loaded by means of the distributed torque on the other side. First, the plate is modeled as a planar surface. Furthermore, the plate is modeled as one-quarter of the cylinder surface. The planar model's width is equal to the length of one-quarter of the circle of the curved model. The curved model has thus almost equal torsional constant J as the planar model. Determine the maximum rotation of the plate φz,max for both geometrical models and compare the results using both the Kichhoff and the Mindlin plate theory.

Material Steel Modulus of Elasticity E 210000.000 MPa
Poisson's Ratio ν 0.300 -
Geometry Curved Model Radius r 100.000 mm
Planar Model Width s 157.080 mm
Plate Thickness h 200.000 mm
Plate Height t 3.000 mm
Load Distributed Torque m 1268.720 Nm/m
Torsion of Thin Plate
Torsion of Thin Plate

Analytical Solution

The torsional constant for the planar plate (rectangular cross-section) can be calculated according to the the following formula:

J=st33=1413.720 mm4
Torsional Constant for Planar Plate

Considering the same width of the planar and curved plate the identical torsional constant can be used. The width of the planar plate is the same as length of one quarter of the circle of the curved model: s=πr/2. The torsional constants of the planar plate and curved plate are compared also using program SHAPE-THIN: Jp=1396,710 mm4, Jc=1392.670 mm4. Using torsional constant, which is calculated in above mentioned formula, the maximum rotation on the top of the plate (z=h) can be determined as follows:

φz,max=mshGJ=0.349 rad=20.000°
Maximum Rotation on Top of Plate

RFEM Settings

  • Modeled in RFEM 5.26 and RRFEM 6.06
  • The element size is lFE= 0.002 m
  • Geometrically linear analysis is considered
  • The number of increments is 5
  • Plate entity is used
  • Quadrangular elements are used

Results

Model Analytical Solution RFEM 6 RFEM 5
φz,max [°] φz,max [°] Ratio [-] φz,max [°] Ratio [-]
Planar, Kirchhoff 20.000 20.163 1.008 20.163 1.008
Curved, Kirchhoff 20.163 1.008 20.163 1.008
Planar, Mindlin 20.666 1.033 20.733 1.037
Curved, Mindlin 20.797 1.040 20.863 1.044
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