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Spring stiffnesses for joints assigned between lines
A spring stiffness is sometimes required in the definition of a joint
assigned between line features, or a support attribute assigned to a line
feature in LUSAS.
Spring stiffness, k, is as defined in Hooke's law, viz. F=k*x where F is an applied force and x is the resulting displacement. It follows that where a
known displacement (x) for a known force (F) is available, the spring stiffness entered in the dialog box, k = F/x (typical units
kN/m, N/mm etc).
When assigned to line features, which have a length, forces are
per unit length and spring stiffnesses should be likewise (typical units therefore
kN/m², N/mm² etc).
Engineering theory can be used to derive equations for k based on the structural member which the spring is intended to model e.g. If we assume the supporting
member to behave as a 2D continuum:
Perpendicular to joint: Kx = EA/l based on in-plane ("axial") deformation. Since Kx will
normally be defined "per unit length" and assigned to a
line feature, in the usual way A=thickness, t.
Parallel to joint: Ky = Gt/L based on shear deformation. For isotropic elastic materials, Shear modulus G=E/[2(1+v)].
Parallel to joint: Kz = 3EI/l³ based on flexural deformation of slab (minor bending axis). Since
Kz will normally be "per unit length" and assigned to a
line feature, in the usual way 't' should be divided through.
Sometimes it is necessary to use a joint element to model a "fixed"
or "free" condition (e.g. to mimic the action of a tension-only member).
However:
- For a "fixed" condition, you cannot enter a stiffness of infinity, so you should use a high stiffness.
- For a "free" condition, you may not be able to enter a stiffness of zero, so you may use a low stiffness. Zero may be entered but may cause numerical instability, depending on the solution method selected.
In a case where the stiffness specified is to model a "fixed" or
"free" condition, in principle, the stiffnesses should be high or low relative
to the rest of the structure, in particular adjacent members. A good starting point for the estimation of a suitable spring stiffness
might therefore be:
- For a "fixed" condition, input spring
stiffnesses:
Perpendicular: Kx = 1000*Et/l, Parallel: Ky = 1000*Gt/L,
Lateral: Kz = 1000*3EI/tl³
based on the most stiff adjacent element
- For a "free" condition, input spring
stiffnesses:
Perpendicular: Kx = 0.001*Et/l, Parallel: Ky = 0.001*Gt/L,
Lateral: Kz = 0.001*3EI/tl³
based on the least stiff adjacent element
Lift off supports, shell type models: First
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