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→Stiffness matrix: (''T''·''d'') |
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: <math>K_s=\frac{G\cdot T\cdot d}{a}</math>
Where ''d'' is the distance between springs, ''T'' is the thickness of the element, ''a'' is the length of the representative area, ''E'' is the [[Young modulus]], and ''G'' is the [[shear modulus]] of the material. The above equation indicates that each spring represents the stiffness of an area
To model reinforcement bars embedded in concrete, a spring is placed inside the element at the ___location of the bar; the area
▲To model reinforcement bars embedded in concrete, a spring is placed inside the element at the ___location of the bar; the area <math>(T\cdot d)</math> is replaced by the actual cross section area of the reinforcement bar. Similarly to model embedded [[Steel sections |steel sections]], the area <math>(T\cdot d)</math> may be replaced by the area of the steel section represented by the spring.
Although the element motion moves as a [[Rigid body |rigid body]], its internal [[Deformation (engineering) |deformations]] are represented by the spring deformation around each element. This means the element shape does not change during analysis but the behavior of assembly of elements is deformable.
The two elements are assumed to be connected by only one pair of normal and shear springs. To have a general stiffness matrix, the locations of element and contact springs are assumed in a general position. The stiffness matrix components corresponding to each [[Degrees of freedom (physics and chemistry) |degree of freedom]] are determined by assuming a unit [[Displacement (vector) |displacement]] in the studied direction and by determining forces at the centroid of each element. The 2D element stiffness matrix size is 6 x 6; the components of the upper left quarter of the [[Stiffness matrix |stiffness matrix]] are shown below:
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