# RF-CONCRETE Surfaces Version 5

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## RF-CONCRETE Surfaces Version 5

# 2.5.4 Analysis of Concrete Compression Struts

### Analysis of Concrete Compression Struts

To design the concrete compression strut of a shell, it is divided into three surface layers that are subjected to the design membrane forces.

For shells where the applied moment is relatively large in relation to the applied axial force (e_{d}/h > 0.2), the thickness h_{E} of the two outer layers is reduced to 0.35 ⋅ d.
For shells subjected to approximately concentric compression, the surface layer thickness h_{E} is increased to half of the plate thickness h.
If the relative eccentricity of the axial force e_{d}/h is between 0 and 0.2, the surface layer thickness is interpolated.

For e_{d}, the greater value of the quotients of m_{x}/n_{x} and m_{y}/n_{y} is taken.

For the analysis of the concrete compression strut, the strut's compression force n_{strut,+z} to be resisted is compared to the resistant axial force of the surface layer n_{strut,d}.

The resistant axial force n_{strut,d} depends on the thickness h_{E} of the surface layer and the applied concrete strength f_{cd,08}.

The first step to determine the thickness of the surface layer is to determine the provided load eccentricities in x- and y-direction from the internal forces of the linear plate analysis:

${e}_{dx}=\left|\frac{{m}_{x}}{{n}_{x}}\right|=\left|\frac{124.35}{-103.911}\right|=1.197\text{m}$

${e}_{dy}=\left|\frac{{m}_{y}}{{n}_{y}}\right|=\left|\frac{54.36}{-285.386}\right|=0.190\text{m}$

The greater load eccentricity in x-direction is computed as governing.
It can be used to determine the relative load eccentricity e_{d}/h.

$\frac{{e}_{d}}{h}=\frac{1.197}{1.29}=0.9280.2$

Since the relative load eccentricity is greater than 0.2, this is regarded as a shell that is predominantly subjected to bending.
The factor f_{hE} needed for the determination of the surface layer thickness is 0.35.

Thus, the thickness h_{E} of the surface layer is determined as follows:

${h}_{E}={f}_{hE}\xb7h=0.35\xb7129=45.15\text{cm}$

The design value of the concrete compressive strength is reduced to 80 % according to the recommendations from SCHLAICH/SCHÄFER (in: Betonkalender 1993/II, page 378). This recommendation can also be found in EN 1992-1-1, clause 6.5.2, regulating the design of compression struts in strut-and-tie models.

${f}_{cd}=\frac{{f}_{ck}}{{\gamma}_{c}}=\frac{30}{1.5}=20{\text{N/mm}}^{2}$

${f}_{cd,08}=0.8\xb720=16{\text{N/mm}}^{2}$

This value can also be found in the design details (see Figure 2.72).

With this value, it is possible to determine the resisting force of the concrete compression strut n_{strut,d}.

- n
_{strut,d}= b ∙ h_{E}∙ f_{cd,08}= 100 ∙ 45.15 ∙ 16 = 7,224.00 kN/m

The analysis of the concrete compression strut for the top surface is done similarly.