Eurocode 8 Capacity Design Calculator

Compute capacity design shear forces and check strong-column–weak-beam hierarchy for beams, columns and joints according to EN 1998‑1.

Capacity Design Tool (EN 1998‑1)

Capacity design factors

Typical 1.1–1.3 (check National Annex).

Use >1.0 for extra conservatism if required.

Beam data

From EN 1992‑1‑1 or EN 1993‑1‑1.

Results

Design actions from capacity design

Enter data and click “Calculate capacity design” to see results.

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Eurocode 8 capacity design – key concepts

Eurocode 8 (EN 1998‑1) is based on capacity design: you deliberately choose where plastic hinges will form during a strong earthquake (typically in beams), and then design all other elements and connections with sufficient overstrength so they remain essentially elastic.

This calculator focuses on the most common capacity design tasks for building structures: beam shear design, column shear design, and beam–column joint checks in ductile frames.

1. Beam capacity design shear

For a beam where plastic hinges are expected at both ends, Eurocode 8 requires the design shear to be based on the overstrength plastic moments at the ends, not on the elastic analysis shear.

For a prismatic beam with clear span \( L_b \):

\( M_{pl,over,left} = \gamma_{Rd} \cdot \gamma_F \cdot M_{pl,Rd,left} \)
\( M_{pl,over,right} = \gamma_{Rd} \cdot \gamma_F \cdot M_{pl,Rd,right} \)

Capacity design shear:
\( V_{Ed,CD} = \dfrac{M_{pl,over,left} + M_{pl,over,right}}{L_b} \)

The beam shear resistance \( V_{Rd} \) from EN 1992‑1‑1 or EN 1993‑1‑1 must satisfy:

\( V_{Rd} \ge V_{Ed,CD} \)

2. Column capacity design shear

For columns, capacity design shear is obtained from the overstrength end moments at top and bottom of the storey:

\( M_{over,top} = \gamma_{Rd} \cdot \gamma_F \cdot M_{top,Rd} \)
\( M_{over,bot} = \gamma_{Rd} \cdot \gamma_F \cdot M_{bot,Rd} \)

\( V_{Ed,CD} = \dfrac{M_{over,top} + M_{over,bot}}{h_c} \)

Again, the column shear resistance must be at least equal to this capacity design shear.

3. Strong-column–weak-beam hierarchy

To avoid storey mechanisms, Eurocode 8 requires that, at each joint, the sum of column flexural capacities exceeds the sum of beam capacities by a certain margin (National Annex dependent). A common requirement is:

\( \sum M_{Rd,column} \ge 1.3 \cdot \sum M_{pl,Rd,beam} \)

The joint mode should be such that beams yield before columns. The calculator reports the ratio:

\( R = \dfrac{\sum M_{Rd,column}}{\sum M_{pl,Rd,beam}} \)

and flags whether the chosen target (e.g. 1.3) is satisfied.

4. Joint shear from capacity design

Beam–column joints must also be checked in shear using the forces associated with the overstrength beam and column moments. A simplified estimate of the joint shear demand is:

\( V_{Ed,j} \approx \dfrac{\sum M_{pl,over,beam}}{h_j} \)

where \( h_j \) is the joint chord length (approximately the column depth in the direction considered). The joint shear resistance \( V_{Rd,j} \) must satisfy:

\( V_{Rd,j} \ge V_{Ed,j} \)

How to interpret the calculator output

  • Design shear VEd,CD – the shear force you must design the element for, based on capacity design.
  • Utilization ratio – the ratio \( V_{Ed,CD} / V_{Rd} \). Values < 1.0 indicate adequate shear capacity.
  • Hierarchy ratio – for joints, the ratio of column to beam moment capacity. Values above the target (e.g. 1.3) indicate a strong-column–weak-beam mechanism.

Limitations and good practice

  • This tool does not perform detailed member or joint design; you must still check all detailing rules in EN 1998‑1 and the relevant material Eurocodes.
  • Always verify the correct values of γRd, behaviour factor q, ductility class and hierarchy factors in your National Annex.
  • Use the calculator for quick iterations and sanity checks; final design should be documented with full hand calculations or validated software.

References

  • EN 1998‑1: Eurocode 8 – Design of structures for earthquake resistance – Part 1: General rules, seismic actions and rules for buildings.
  • EN 1992‑1‑1: Eurocode 2 – Design of concrete structures – Part 1‑1: General rules and rules for buildings.
  • EN 1993‑1‑1: Eurocode 3 – Design of steel structures – Part 1‑1: General rules and rules for buildings.

Eurocode 8 capacity design – FAQ

What is capacity design in Eurocode 8?

Capacity design is a seismic design philosophy where you intentionally allow certain ductile elements (usually beams or specific links) to yield and dissipate energy, while all other elements and connections are designed with sufficient overstrength so they remain elastic. This avoids brittle or unstable failure modes and leads to a predictable global collapse mechanism during strong earthquakes.

Which overstrength factor γRd should I use?

Eurocode 8 suggests overstrength factors typically between 1.1 and 1.3, but the exact value depends on the structural system, ductility class (DCL, DCM, DCH) and National Annex. Many designers start with γRd = 1.2 for preliminary design and then refine the value based on more detailed checks and local practice. Always follow your National Annex and project specifications.

Does this calculator replace a full Eurocode 8 design?

No. The calculator is intended as a quick aid for capacity design shear and hierarchy checks. A complete Eurocode 8 design still requires detailed member and joint design, ductility and detailing checks, verification of global stability, second‑order effects, and compliance with all relevant clauses of EN 1998‑1 and the material Eurocodes (EN 1992, EN 1993, etc.).

Can I use this tool for bridges or only for buildings?

The underlying capacity design principles are general, but this tool is primarily tailored to building‑type elements (beams, columns, beam–column joints) in frames. For bridges, you should refer to Eurocode 8 Part 2 and specialised bridge design guidance. You may use the results here as indicative checks, but they are not a substitute for a full bridge‑specific seismic design.