# Gauss point

## Gauss point

[′gau̇s ‚pȯint] (geodesy)

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(geodesy)

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Eight node continuum elements with one Gauss point and hourglass control are used for concrete in the FE model.

There are five types of smoothing elements ((i) split smoothing element: there is one Gauss point on each boundary segment for split smoothing element; (ii) split-blending smoothing element: one Gauss point on each boundary segment is sufficient; (iii) tip smoothing element: five Gauss points on a segment of smoothing element are sufficient; (iv) tip-blending smoothing element: five Gauss points on each boundary segment are sufficient; (v) standard smoothing element: one Gauss point on each boundary segment is sufficient) being used for numerical integration as mentioned in [41].

In practical work, some Gauss point has the same nodes as some neighboring computational points.

As we explained in previous sections, the RKEM shape functions are piecewise rational shape functions, therefore, we need to use many Gauss point to evaluate the integrals such that we can obtain a well conditioned, non singular system of equations (15).

The values of principal stress obtained from Gauss point of element were [[sigma].sub.11][member of] (-l17,21.2)MPa and [[sigma].sub.22][member of] ( -120, 4.14) MPa.

It can produce a graph between variables like, load and deflection, stress and strain, convergence details, single and multiple Gauss point state.

[[sigma].sup.c.sub.ij] is the concrete stress distribution along the thickness, [[sigma].sup.sk.sub.ij] represents the steel stress of a layer placed at [x.sub.3sk], while [A.sub.sk] represents the steel bar cross section, being [N.sub.s] the reinforced layer number and [[delta].sub.ij] the Kronecker delta, [[xi].sub.IG] is the Gauss point homogenous co-ordinate.

where [[psi].sub.m] is the value of [[psi].sub.m] of the NI-th Gauss point; [c.sub.pi,r]=1 is the value of [c.sub.pi,r]=1 of the NI-th Gauss point; Wt(NI) is the weight value of the NI-th Gauss point; GJ is the proportion factor of the integral transformation, and GJ=dz/d[zeta]=[h.sub.e]/2.

Positions of Gauss Points. Gauss Point (/) 1 2 3 4 5 6 [y.sub.l] (= [y.sub.l]/h) 0.013 0.067 0.160 0.283 0.426 0.574 Gauss Point (/) 7 8 9 10 [y.sub.l] (= [y.sub.l]/h) 0.717 0.840 0.933 0.987

The results shown were calculated at the Gauss point just above the center-line.

So the direction cosines [[lambda].sub.x'], [[lambda].sub.yx'], and [[lambda].sub.z'] of the local coordinate system established at different Gauss point with respect to the global coordinate system are different with each other.

At each element, the smoothed value for each stress component considered is obtained computing the average of the corresponding Gauss point values at FS line and PS line, respectively.

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