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Reinforcement calculation in surfaces

For bending moment

The elastic analysis will result in values for Mxx, Mzz and Mxz in each mesh node. When calculating reinforcement, the twisting couple Mxz cannot be neglected.

At any point in the plate, there exists a pair of orthogonal directions (the principal directions) where the twisting moment Mxz vanishes ( Mxz =0). In those directions, the bending moments are the principal moments M1 and M2​.

    \[M_{1,2}= \frac{1}{2} (M_{xx} + M_{zz} \pm \sqrt{(M_{xx} - M_{zz})^{2}+ 4\cdot M_{xz}^{2}})$\]

The angle \theta​ between the x’-axis and the direction of M1​ is:

    \[tan(2\theta)=\frac{2M_{xz}}{M_{xx}-M_{zz}}\]

You could use the principal moments M1 and M2 to calculate the required reinforcement in the plate, but it will lead to reinforcement on a curved path. Which makes it impractical in real life.

Diamonds calculates the reinforcement using Wood-Armer moments. This results in an orthogonal reinforcement mesh: the reinforcement is always parallel to the local x’ and y’ axes of the surface.

(ENV 1992-1-1 §A2.8)

Notes:

  • More info on the Wood-Armer moments in: R. H. WOOD, The reinforcement of slabs in accordance with a pre-determined fiel of moments (original paper), feb 1968
  • For reinforcement calculations according to NEN 6720, Diamonds will use the following reinforcement moments:

        \[M_{u,dx}=M_{xx} \pm \left| M_{xz} \right| \text{ and } M'_{u,dx}=M_{zz} \pm \left| M_{xz} \right|\]

For axial force

Analogous to moment, the reinforcement forces are determined based on the internal forces Nxx, Nzz, Nxz.

(Source: ENV 1992-1-1 §A2.9)

On this page

  • For bending moment
  • For axial force