The discussion revolves around the deformation of a spring and a beam structure when impacted by an object moving at a constant velocity. Participants explore the calculations involved in determining the deformation and the forces at play, considering both springs and beams under various conditions.
Participants express various viewpoints on the calculations and assumptions necessary for determining deformation in both springs and beams. There is no consensus on the specific methods or assumptions to be used, indicating that multiple competing views remain.
Limitations include assumptions about the rigidity of the impacting object, the elastic limits of the beam, and the applicability of Hooke's Law. The discussion also highlights the need to consider gravitational effects in certain scenarios.
As a minimum, it depends on the material ( E = Young Modulus), and beam geometry (Area Moment of Inertia, I), and length between supports (L), impact speed, etc. Equivalent stiffness (k) of a simply supported beam subject to point loading at midpoint is 48EI/L^3, in units of force/length (N/m in SI).andrestander said:What if I have a simple beam structure and the object impacts in the middle of the beam? By how much the beam will deform and bend?
andrestander said:so 0.5mv^2=0.5kx^2
Where k is the equivalent stiffness matrix for the beam?
PhanthomJay said:Yes, as I see it, but with a lot of assumptions, like the moving object is rigid and the beam remains within its elastic limit and obeys Hooke's Law when deforming. Also, if the moving object is is subject to gravity forces like for the case where it is moving straight down upon impact, then you must include its change in potential energy as well, that is, 0.5mv^2=0.5kx^2 -mgx.