1. General characteristics#

1.1. Geometry#

The three-point bending beam studied is 5m long. Its section is 0.2x0.5m. Its geometry as well as the positioning of the steels that constitute it are defined on the.

_images/1000000000000368000003CCC6FA11DD0FAE7FD7.png

Figure 1.1-a: plane of the beam.

1.2. Material properties#

  • Concrete:

Young’s module: \(E\mathrm{=}37272\mathit{MPa}\)

Poisson’s ratio: \(\nu =0.2\)

Tensile elasticity threshold: \({\sigma }_{\mathrm{ft}}=3.9\mathrm{MPa}\)

Threshold of elasticity in compression: \({\sigma }_{\mathrm{fc}}=38.3\mathrm{MPa}\)

Threshold of elastic deformation under compression: \({\varepsilon }_{\mathrm{fc}}={\mathrm{2.0.10}}^{-3}\)

Cracking energy \({G}_{f}^{1}\mathrm{=}110J\mathrm{/}\mathit{m²}\)

  • Steel:

Young’s module: \(E=200000\mathrm{MPa}\)

Poisson’s ratio: \(\nu =0.33\)

Elastic limit: \({\sigma }_{e}\mathrm{=}400\mathit{MPa}\)

Tangent module (plastic slope) \({E}_{T}\mathrm{=}3280\mathit{MPa}\)

AND

_images/10000000000000F7000000DEDDD725A2B2B746C2.png

Figure 1.2-a: c stress curve — steel deformation

1.3. Boundary conditions and loads#

Simple press in \(B\): \(\mathit{DY}=0\).

Double press in \(A\): \(\mathit{DX}=\mathit{DY}=\mathit{DZ}=0\) as well as \(\mathit{DRX}=\mathit{DRY}=0\).

Quasi-static loading: monotonic downward displacement \(\mathit{DY}\) applied halfway through \(C\) (3-point flexure test), according to a linear function of time:

\(t\)

\(\mathit{DY}\)

\(\mathrm{0,0}\)

\(\mathrm{0,0}\mathrm{cm}\)

\(\mathrm{3,0}\)

\(\mathrm{-}\mathrm{3,0}\mathit{cm}\)

\(\mathrm{5,0}\)

\(\mathrm{-}\mathrm{5,0}\mathit{cm}\)

The final displacement applied for modeling A is \(\mathrm{-}\mathrm{3,0}\mathit{cm}\).

For the D modeling, the imposed displacement is done according to \(\mathit{DZ}\).

Note: transverse reinforcements are not taken into account in the calculations.