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.

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.

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.