Worked Examples to Eurocode 2 Volume 2: Design of Concrete Structures
Eurocode 2 (EC2) is a widely used European standard for the design of concrete structures. It provides a comprehensive framework for the design of buildings and civil engineering works, ensuring their safety, durability, and sustainability. To facilitate the application of EC2, several worked examples have been developed to illustrate its practical use. This article presents a selection of worked examples from Volume 2 of the Eurocode 2 series, covering various aspects of concrete structure design.
Example 1: Design of a Reinforced Concrete Beam
A rectangular beam with a span of 6 meters and a cross-sectional area of 0.3 x 0.6 meters is subjected to a permanent load of 10 kN/m and a variable load of 5 kN/m. The beam is reinforced with 4 longitudinal bars of 16 mm diameter and 2 stirrups of 8 mm diameter.
Using EC2, the design bending moment is calculated as:
MEd = 1.35 x (10 x 6^2 / 8) + 1.5 x (5 x 6^2 / 8) = 63.9 kNm
The required reinforcement area is calculated as:
As = 0.0013 x 0.3 x 0.6 x 500 = 117 mm^2
The provided reinforcement area is:
As.provided = 4 x π x (16/2)^2 = 804 mm^2
The beam is checked for shear resistance:
VRd,c = 0.12 x (1 + (0.6/0.3)) x 0.3 x 0.6 x 25 = 45.9 kN
The design shear force is:
VEd = 1.35 x (10 x 6 / 2) + 1.5 x (5 x 6 / 2) = 54.5 kN worked examples to eurocode 2 volume 2
The beam requires additional shear reinforcement.
Example 2: Design of a Concrete Column
A square column with a side length of 0.4 meters and a height of 3 meters is subjected to a permanent axial load of 500 kN and a variable axial load of 200 kN. The column is reinforced with 4 longitudinal bars of 20 mm diameter.
Using EC2, the design axial load is calculated as:
NEd = 1.35 x 500 + 1.5 x 200 = 847.5 kN
The required reinforcement area is calculated as:
As = 0.01 x 0.4 x 0.4 x 500 = 800 mm^2
The provided reinforcement area is:
As.provided = 4 x π x (20/2)^2 = 1256 mm^2
The column is checked for buckling:
λ = 3 / 0.4 = 7.5
The critical buckling load is:
Ncr = π^2 x 25 x 0.4^4 / (3^2) = 2761 kN Worked Examples to Eurocode 2 Volume 2: Design
The column is stable.
Example 3: Design of a Concrete Slab
A rectangular slab with a span of 4 meters and a thickness of 0.2 meters is subjected to a permanent load of 2 kN/m^2 and a variable load of 1.5 kN/m^2. The slab is reinforced with a mesh of 10 mm diameter bars at 200 mm spacing.
Using EC2, the design bending moment is calculated as:
MEd = 1.35 x (2 x 4^2 / 8) + 1.5 x (1.5 x 4^2 / 8) = 18.9 kNm
The required reinforcement area is calculated as:
As = 0.0013 x 0.2 x 1 x 500 = 130 mm^2
The provided reinforcement area is:
As.provided = (π x (10/2)^2) / 0.2 = 392 mm^2
The slab is checked for punching shear:
VEd = 1.35 x (2 x 4 / 2) + 1.5 x (1.5 x 4 / 2) = 18.5 kN
The design punching shear resistance is:
VRd,c = 0.12 x (1 + (0.6/0.2)) x 0.2 x 1 x 25 = 12.5 kN Eurocode 2: Design of concrete structures - Part
The slab requires additional shear reinforcement.
These worked examples illustrate the application of Eurocode 2 to various concrete structure design scenarios. They demonstrate the importance of careful consideration of loads, material properties, and reinforcement requirements to ensure the safety and durability of concrete structures.
References
This guide is structured as a practical companion for structural engineers. It assumes the reader has a copy of BS EN 1992-1-1 (and the UK National Annex where applicable) and focuses on the more complex design scenarios typically covered in a second volume (e.g., punching shear, torsion, serviceability, fire, and detailing).
Advanced foundation design rarely appears in introductory texts. Volume 2 typically provides a full calculation for:
The Scenario: A 6m high retaining wall, backfilled with granular soil, surcharge load of 10 kPa, groundwater at 1.5m depth.
Key Eurocode 2 Clauses applied: 2.4 (Combinations of actions), EN 1997-1 (Geotechnical interaction), plus EC2 detailing.
Why this is a classic: Retaining walls sit at the intersection of EC7 (geotechnical) and EC2 (structural). Volume 2 handles the handshake perfectly.
The Worked Solution Highlights:
Takeaway: Volume 2 teaches you to draw bending moment diagrams for both sides of the wall stem.
No resource is perfect. Volume 2 has two notable limitations:
Additionally, some examples assume proprietary software for analysis (e.g., for bridge moving loads). This is acceptable, but the book should have included a manual influence line check.