Worked Examples To Eurocode 2 Volume 2
[ v_Ed = \fracV_Ed \cdot \betau_1 \cdot d ] For internal column with unbalanced moment small, ( \beta \approx 1.15 ). [ v_Ed = \frac850 \times 10^3 \times 1.154239 \times 210 = \frac977,500890,190 \approx 1.10 \text MPa ]
Volume 1 often deals with one-way spanning slabs. Volume 2 tackles punching shear at internal, edge, and corner columns. A classic worked example includes:
Volume 2 often includes a failed example—showing what happens if you ignore the maximum shear stress limit (v_Rd,max).
Worked Examples to Eurocode 2: Volume 2 is a technical publication designed to assist structural engineers in applying EN 1992 (Eurocode 2)
for the design of concrete structures. While Volume 1 typically covers general rules and building design, Volume 2 focuses on more complex or specialized applications, such as (EN 1992-2) or liquid-retaining structures. Key Content & Purpose
The primary goal of this write-up is to bridge the gap between theoretical code clauses and practical application. You will typically find: Detailed Design Scenarios
: Step-by-step calculations for specific structural elements like continuous beams, slabs, and columns. Bridge Engineering Focus
: If following the standard division, Volume 2 often specifically addresses Eurocode 2: Part 2 (Bridges) , covering deck design, piers, and abutments. National Annex Integration : It illustrates how to apply specific parameters from National Annexes
(e.g., UK or Irish versions), which are crucial for localized safety factors and material properties. Core Structural Elements Covered
A "proper" write-up or manual of these examples usually includes: Material Properties : Determination of characteristic strengths ( f sub c k end-sub ) and design values for concrete and reinforcement. Limit State Checks : Demonstrations of Ultimate Limit State (ULS) for bending, shear, and torsion, as well as Serviceability Limit State (SLS) for cracking and deflection. Reinforcement Detailing
: Worked solutions for minimum/maximum reinforcement areas and spacing requirements. EurocodeApplied.com Where to Find Official Resources
For a formal and accurate reference, you should consult recognized engineering bodies: The Concrete Centre : Provides extensive guides and for Eurocode 2 design. CEN (European Committee for Standardization) : The official source for the full text of Academic/Professional Repositories : Sites like Eurocode Applied
Mastering Concrete Design: Exploring Eurocode 2 Volume 2 Worked Examples
For structural engineers, the transition to Eurocode 2 (EN 1992) often represents a shift toward more advanced, performance-based design. While Part 1-1 covers general rules, Volume 2: Worked Examples serves as a vital bridge between theoretical clauses and real-world application.
Whether you are a senior professional or a student, these worked examples provide the clarity needed to design economic and innovative concrete structures with confidence. Why Volume 2 Matters
Unlike general manuals, Volume 2 focuses on complex design scenarios and durability considerations. It moves beyond basic beam theory to address:
Aggressive Environments: Specific design approaches for structures requiring enhanced durability.
Seismic Design: Implementation of seismic principles for concrete structures.
Specialized Structures: Guidance for underwater or highly durable structural types. Key Topics and Examples
The worked examples in this volume provide step-by-step calculations for essential structural elements: Worked Examples To Eurocode 2 Volume 2
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. worked examples to eurocode 2 volume 2
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
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 [ v_Ed = \fracV_Ed \cdot \betau_1 \cdot d
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
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
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
Worked Examples to Eurocode 2, Volume 2 primarily focuses on the practical application of , which covers the design of concrete bridges Volume 2 often includes a failed example —showing
. This volume is a critical resource for engineers transitioning from national standards like BS 8110 to the Eurocode framework. Core Content and Themes
Volume 2 extends the general principles of Part 1-1 to the specific complexities of civil engineering works, notably bridges. Key topics typically included are: Worked Examples To Eurocode 2 | PDF - Scribd
This guide outlines the structure and key focus areas of Worked Examples to Eurocode 2: Volume 2, which serves as a practical companion for engineers applying EN 1992-1-1 and EN 1992-1-2 to concrete structures. While Volume 1 focuses on building framing elements like slabs and beams, Volume 2 addresses more specialized design tasks. Core Focus Areas
Volume 2 typically covers advanced structural components and specific limit states that are critical for final design compliance:
Foundations: Detailed calculations for various foundation types, including pad footings, raft foundations, and piled foundations for multi-storey buildings.
Serviceability Limit State (SLS): Comprehensive checks for deflection and crack width to ensure long-term durability and functionality.
Structural Fire Design: Application of EN 1992-1-2 rules to verify the fire resistance of reinforced concrete elements.
Retaining Walls: Specific examples for the design of free-standing cantilever and earth-retaining structures.
Specialized Structures: Some editions also include public utility structures such as underground service reservoirs and various tank types (rectangular and cylindrical). Guide Structure and Methodology
The worked examples are designed to bridge the gap between the general clauses of the Eurocode and the specific needs of practicing engineers.
Step-by-Step Verification: Examples follow a logical progression from conceptual design and structural analysis to ultimate limit state (ULS) and serviceability limit state (SLS) verifications.
Clause Referencing: Every calculation step is cross-referenced with the corresponding Eurocode 2 clause, helping users navigate the code effectively.
National Annex Integration: The guide demonstrates how to apply Nationally Determined Parameters (NDPs), often using the UK National Annex as a primary reference for values like partial safety factors and load arrangements.
Practical Design Aids: Includes derived formulae and design charts to simplify routine calculations for column slenderness, reinforcement areas, and shear capacity. Worked Example to Eurocode 2 Vol. - Academia.edu
This is a draft proposal and content outline for a publication titled “Worked Examples to Eurocode 2: Volume 2” .
Since Volume 1 typically covers basic elements (beams, slabs, columns, foundations), Volume 2 should focus on advanced structures, unusual geometries, robustness, and fire/durability.
Here is a professional draft you can use for a book proposal, a course syllabus, or a publisher’s table of contents.
Beyond calculations, Volume 2’s examples shine in detailing drawings. For every solved problem, it includes:
| Component | Key Detailing Rule from Example | | --- | --- | | Bridge deck | Minimum 50mm cover to avoid spalling; secondary transverse bars at 35% of main reinforcement | | Pile cap | 180° hooks on bottom ties if anchorage length exceeds available space | | Retaining wall | Starter bars from footing to stem must be lapped in low-stress zone (above 0.5m from base) | | Prestressed beam | Debonding of strands near ends to avoid end splitting |
If Volume 1 introduced prestress as a force, Volume 2 calculates losses. Expect worked examples covering:
Each worked example follows a 5-step process:
The publication is structured to follow the lifecycle of a structural element, moving from basic material properties to complex structural analysis. Key sections include: