# Displaying Curtailment of Longitudinal Reinforcement and Reinforcement Covering Line

### Technical Article

In the case of a huge amount of reinforcement, it might be useful to grade the longitudinal reinforcement of a beam. The grading corresponds to the tensile force distribution. Using RF-CONCRETE Members and CONCRETE, you can specify the curtailment of the reinforcement, which is considered in the automatically proposed reinforcement for the longitudinal reinforcement. When determining this reinforcement proposal, it is necessary to ensure that the envelope of the acting tensile force can be absorbed.

#### Curtailment of Longitudinal Tension Reinforcement

The design of the curtailment of the longitudinal tension reinforcement ensures that the envelope of the acting tensile force F_{Sd} can be absorbed by the provided reinforcement. 9.2.1.3(2) of EN 1992‑1‑1 [1] requires to also consider the additional tensile force ΔF_{td} due to the shear force. For structural components with shear reinforcement, this additional tensile force ΔF_{td }can be calculated according to 6.2.3 (7) of EN 1992‑1‑1 [1]. The tensile force F_{Sd} is calculated from the following equation:

$\begin{array}{l}{\mathrm F}_\mathrm{sd}\;\;=\;\;\left(\frac{{\mathrm M}_\mathrm{Eds}}{\mathrm z}\;+\;{\mathrm N}_\mathrm{Ed}\right)\;+\;{\mathrm{ΔF}}_\mathrm{td}\\\mathrm{where}\\{\mathrm{ΔF}}_\mathrm{td}\;=\;0.5\;\cdot\;{\mathrm V}_\mathrm{Ed}\;\;\cdot\;(\cot\;\mathrm\theta\;–\;\cot\;\mathrm\alpha)\end{array}$

For structural components without shear reinforcement, the tensile force ΔF_{td} may be taken into account by shifting the tensile force curve from $\left(\frac{{\mathrm M}_\mathrm{Eds}}{\mathrm z}\;+\;{\mathrm N}_\mathrm{Ed}\right)$ about a distance of a_{l} = d in the unfavourable direction. This approach may also be used as an alternative to the approach for structural components with shear reinforcement mentioned above. In this case, this 'shift rule' is determined according to the formula ${\mathrm a}_\mathrm l\;=\;0.5\;\cdot\;\mathrm z\;\cdot\;(\cot\;\mathrm\Phi\;-\;\cot\;\mathrm\alpha)$.

Figure 01 - Curtailment of Longitudinal Reinforcement from [1]

The resistant tensile force F_{Rs }of the provided reinforcement is determined within the anchorage lengths l_{bd}.

#### Graphical Display of Reinforcement Covering Line / Curtailment of Longitudinal Reinforcement

If the tensile force of the curtailment of longitudinal reinforcement is divided by the design stiffness f_{yd }of the reinforcing steel, a reinforcement covering line is obtained. In RF-CONCRETE Members and CONCRETE, the distribution of the required tension reinforcement A_{s} (the first result diagram in Figure 02) is shifted by the shift rule a_{1} in order to obtain the envelope of the required reinforcement (the second result diagram in Figure 02). You can display these shifted required reinforcement envelopes graphically by selecting 'Detailed results' under 'Provided Reinforcement' in the result navigator (see Figure 02).

If the envelope of the required reinforcement (red), the shifted envelope of the required reinforcement (green), and the provided reinforcement (blue) are shown graphically together, a reinforcement covering line is obtained (the third result diagram in Figure 02). This diagram corresponds to the curtailment of longitudinal reinforcement in Figure 9.2 of EN 1992‑1‑1.

Figure 02 - Reinforcement Covering Line / Curtailment of Longitudinal Reinforcement

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