Reaction Forces of a simply supported thin plate

Click For Summary
SUMMARY

The discussion focuses on calculating reaction forces and moments for a simply supported thin plate measuring 620mm x 620mm, subjected to a uniformly distributed patch load (q0) of 58mm x 58mm. The central deflection is calculated as (3.137 x 10^(-6) q0 (mm)) using the Navier solution, with maximum stress determined to be 64.87q0 (N/m²). The yield strength of the material is 380MPa, leading to a calculated q0 of 5.86MN. The user seeks clarification on whether the reaction forces at the corners differ from those at the edges and the implications of uplift restraint in a simply supported configuration.

PREREQUISITES
  • Understanding of Navier's equations for plate deflection
  • Knowledge of von Mises yield criterion for material strength
  • Familiarity with shear force and moment calculations in structural analysis
  • Concept of simply supported boundary conditions in mechanics
NEXT STEPS
  • Research how to calculate reaction forces for simply supported plates under various loading conditions
  • Learn about the implications of uplift restraint in structural mechanics
  • Explore advanced plate theory for complex loading scenarios
  • Study the effects of corner lifting on reaction forces in thin plates
USEFUL FOR

Structural engineers, mechanical engineers, and students studying plate mechanics who are involved in analyzing reaction forces and moments in thin plates under load.

gemmott
Messages
1
Reaction score
0
I have a square thin plate 620mm*620mm that is simply supported on all four edges and is subjected to a uniformly distributed patch load (q0) over a central area of 58mm*58mm. I have calculated the central deflection to be (3.137x〖10〗^(-6) q0 (mm) via navier solution and the max stress in the plate (64.87q0 (〖N/m〗^2)).
However I am trying to find the reaction forces and moments at the four edges and corners of a thin plate.
Further information:
Material yeilds at 380MPa, by using von mises yield criterion is have calculated q0=5.86MN.

If I calculate the shear force Qx and Qy from
Qx=dMx/dx+dMxy/dy - then as these are the vertical forces then this givse me the reaction forces?

Will the reaction forces in the corners of the plate differ from the reaction forces on the four edges.

Any help would be much appreciated
 
Physics news on Phys.org
Please clarify whether 'simply supported' means uplift is restrained or unrestrained. If corners can lift, what will be the reactions there?
 

Similar threads

Finding the thickness of a plate with a slot, after finding K (SCF)
  • · Replies 6 ·
Replies
6
Views
5K
Dynamic reaction versus Coriolis acceleration of the disk
  • · Replies 1 ·
Replies
1
Views
2K
How Can We Calculate the Fatigue Life of a Simply-Supported Beam?
  • · Replies 6 ·
Replies
6
Views
3K
Statics: Problem about Equilibrium in 3-dimensions
  • · Replies 2 ·
Replies
2
Views
4K
Strength of Materials- Asymmetric, simply supported beam problem
  • · Replies 1 ·
Replies
1
Views
6K
Plate deflection theory vs FEA: same problem, same parameters, different results
  • · Replies 16 ·
Replies
16
Views
9K
Calculating Reaction Forces and Maximum Bending Stress in Simply Supported Beams
  • · Replies 20 ·
Replies
20
Views
13K
Graduate Big Bang Big Schmang, astronomical redshift is an artifact of distance
  • · Replies 1 ·
Replies
1
Views
3K