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.
The deformation of a string refers to the change in its shape or position caused by an external force, such as the impact of an object.
An object with constant velocity exerts a consistent amount of force on the string, resulting in a continuous and gradual deformation.
The amount of deformation in a string is influenced by the mass and velocity of the impacting object, as well as the material and thickness of the string itself.
In most cases, the deformation of a string can be reversed by removing the external force causing it and allowing the string to return to its original shape. However, in some cases, the deformation may be permanent due to the material properties of the string.
The deformation of a string can be measured using various methods, such as using rulers or calipers to measure changes in length or using strain gauges to measure changes in tension. Other methods, such as high-speed cameras, can also be used to visually observe the deformation in real-time.