1. Reference problem

1.1. Geometry

This non-regression test case represents a three-point test of a thick beam. The beam is represented by a rectangular element 7.5 meters long and 4.7 meters high. The element contains a square hopper with a side of 1.5 meters located according to Figure 1.1.-a. A fixed support is placed at the left end of the base of the element and a vertical support is considered to be placed at the right end. A vertical load equal to 3 MN is applied in the direction of gravity at 4.7 meters from the left edge. The geometry, boundary conditions, and material definitions were taken directly from the reference [Shlaich et al., 1987].

P=3 MIN

Image 1.1-1: Sail girder with hopper

1.2. Materials

The reinforced concrete used for plane modeling corresponds to a linear elastic material with the following characteristics:

Concrete:

Young’s modulus	\(E\)	21 GPa
Poisson’s Ratio	\(\nu\)	0.2
Elastic limit	\({f}_{\mathit{cm}}\)	36 MPa

Table 1.2-1

Reinforcing steel:

Young’s modulus	\(E\)	210 GPa
Elastic limit	\({f}_{y}\)	500 MPa

Table 1.2-2

1.3. Boundary conditions and loading

The beam is assumed to have a fixed support at the level of the left side and a carriage-type support (locked in the vertical direction) at the level of the level of the right side. The load and boundary conditions are taken as shown in Figure 1.1-1.

1.4. Characteristics of the mesh

Number of knots: 13504

Number of meshes and types: 13200 meshes QUAD4

1.5. Benchmark solution

1.5.1. Diagram of the Bielles-Tirants truss

One of the solutions proposed in reference [Schlaich et al., 1987] is shown in Figure 2.1-a. The author approaches the problem via an ad hoc definition of the Bielles-Tirants model.

Figure 1.5-1: BT reference model [Shclaich et al., 1987]

1.5.2. Benchmark results

The tie rod sections are shown in the following table:

Pulling	Knot i	Knot j	Force [MN]	Length [m] *	As [m2]*
T2	5	6	1.33	1.33	5.6	0.0024
T1	0	5	1.07	1.07	3	0.0027

Table 1.5-1: Tie rod sections [Shclaich et al. 1897]