For directly supported concrete beams with loads applied at the top, EN 1992-1-1 clause 6.2.3 (5) allows you to design shear reinforcement (stirrups) using the minimum design shear force, VEd, within a length interval.
\text{l} = \text{z} \cdot \text{cot(}\theta\text{)}In PolyBeam the design shear force (commonly denoted V2) are shown by a dotted line.
When the load is applied in the middle or bottom of the concrete section there are 2 different methods to design the shear reinforcement.
- The length interval is changed to account for the load position. \begin{array}{cc}\text{l} = 0.5 \cdot \text{z} \cdot \text{cot(}\theta\text{)} & \text{load attack point – middle} \end{array} \begin{array}{cc}\text{l} = 0 \cdot \text{z} \cdot \text{cot(}\theta\text{)} & \text{load attack point – bottom} \end{array}
- The load is transferred to the top with some additional reinforcement. The design shear force V2, is determined based on the original length interval (for load applied at the top). These two contributions are summed to find the required shear reinforcement.
Example
A simply supported beam with a span of 5m.
\begin{array}{ccc}\text{z} = 512\text{mm} & \text{cot(}\theta\text{)} = 2 & \text{l} = \text{z} \cdot \text{cot(}\theta\text{)} = 1024\text{mm}\end{array}
| Load attack point | Length interval | Largest shear force, V₂ |
|---|---|---|
| Top | l = z ⋅ cot(θ) = 1024mm | V₂ = 73.8kN |
| Middle | l = 0.5 ⋅ z ⋅ cot(θ) = 512mm | V₂ = 99.4kN |
| Bottom | l = 0 ⋅ z ⋅ cot(θ) = 0mm | V₂ = 125kN |
Using method 2, the shear reinforcement for load applied at the bottom could be designed with an additional reinforcement to transfer the load from the bottom to the top, and then using the V2-curve for load applied at the top. This would result in:
\text{V₂} = 73.8\text{kN} \text{V}_\text{additional} = \text{l} \cdot 50 \text{kN/m} = 1024\text{mm} \cdot 50 \text{kN/m} = 51.2 \text{kN} \text{V}_\text{total} =\text{V₂} +\text{V}_\text{additional} = 125\text{kN}It is seen that both using method 1 and method 2 will result in a requirement for the shear reinforcement of 125kN, when the load is applied at the bottom.
Concentrated loads applied at the bottom
For larger concentrated loads applied at the bottom of the concrete section an additional reinforcement must be provided to transfer the load, P, from the bottom of the section to the top. This reinforcement is a supplemental reinforcement to the regular shear reinforcement.
Below is an example of the detail for a concentrated load P.
