Der all,

I am working on a case study and I am required to design machine elements with a maximum displacement of 1/1000.

As a "proof of concept" i have taken a sheet metal and calculated the maximum expected force on its surface.

I need to determine the maximum span between beam members for a given sheet metal.

I have chosen a 5mm cold rolled sheet metal:

- 5mm thick
- 1220mm wide

To determine the vertical deflection, I need to obtain first the Second moment of inertia, which is Ix = (1220 x 5^3) / 12 = 12,708

To determinate now the deflection, I have used the following equation for equal distributed force:

y=(5 x F x L^3) / (384 x E x Ix) = (5 x 2.36kN x 200mm^3) / (384 x 200 x 12,708) = 0.097mm

To simulate the same I took SimulationXpress and created a part as described above and applied the same force to it.

However, when I create the report, the maximum displacement is not near the calculated value of 0.097mm, it is shown on page 7 with 0.021mm. I have attached the generated report for your reference.

Do you have any idea what I am missing?

Note: I am working with the current Student Edition.

Thank you, Frank

Both ends are effectively fixed in the simulation which will impart extra stiffness when compared to the simply supported assumption. Perhaps a better hand calculation to match the simulation would be to use a beam bending calculation for a beam fixed at both ends with uniform loading. The equation for maximum deflection in that case is ( F*L^3 ) / (384*E*I) or a factor of 5 less than the simply supported beam equation you posted.

That being said you should question which boundary condition is more representative of the real world application.