Worked Examples To Eurocode 2 Volume 2 Instant

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

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 worked examples to eurocode 2 volume 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

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 is a highly regarded, practical guide for structural engineers, offering detailed, step-by-step designs for complex structures like tanks, foundations, and retaining walls. It is praised for bridging theoretical code requirements with practical application, making it an essential, reliable resource for mastering Eurocode 2 design. For more details, visit Eurocodes jrc.ec.europa.eu.

Eurocode 2: Volume 2 (officially BS EN 1992-2) specifically addresses the design of concrete bridges. While Volume 1 focuses on general rules and building design, Volume 2 expands these principles to handle the complex loading and durability requirements unique to bridge engineering. Core Focus Areas in Volume 2 Worked Examples Worked Examples to Eurocode 2 Volume 2: Design

Most comprehensive worked examples for bridges cover several specialized chapters beyond standard beam and column design:

Foundation Design: Includes detailed calculations for spread footings, piled foundations, and the analysis of bridge abutments.

Serviceability Limit States (SLS): Focuses heavily on crack width control, stress limitations, and deflection checks, which are more critical in bridges due to environmental exposure.

Specialized Structures: Examples often include free-standing cantilever retaining walls, underground reservoirs, and water-retaining tanks (cylindrical and rectangular).

Prestressed Concrete: Bridge design frequently involves prestressing. Worked examples demonstrate the calculation of prestress losses and the design of prestressed sections. Comprehensive Professional Resources

For those seeking rigorous, step-by-step calculations, the following publications are industry standards: WORKED EXAMPLES TO EUROCODE 2 VOLUME 2

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

The conference room in the Manchester high-rise smelled of stale coffee and dry-erase markers. Leila Vasquez, a senior structural engineer, stared at the cracked spine of the book on the table: Worked Examples to Eurocode 2 Volume 2. It was her talisman, her anchor in a sea of uncertainty.

Across from her sat two junior engineers, Tom and Priya. Between them was a 3D-printed model of a pedestrian bridge. It was elegant—a single, sweeping concrete arch with a thin, curving deck. The architect, a man with more vision than practical sense, had loved it. The client had loved it.

Leila did not love it. The bridge had "cracking issues" written all over its graceful curves.

"Right," Leila said, flipping the book open to a dog-eared page. "Clause 7.3.1. Deflection control without direct calculation. We can't use the span-to-depth ratios in Table 7.4N. The arch introduces axial tension, and the deck curvature means our effective span is ambiguous."

Tom slumped. "So we're stuck?"

"No," Leila said, tapping the Volume 2 cover. "We're moving to the worked examples. Example 7.2: Crack control in a curved tension member. It's not our bridge, but it's our problem."

She pulled out a notepad and began sketching. "Eurocode 2 gives us the rules, but Volume 2 shows us how to break them safely. Look here—they calculate crack widths for a curved retaining wall with variable curvature. The principle is the same: we find the critical tensile zone, limit the steel stress using Equation 7.9, and check the crack width with 7.8." Eurocode 2: Design of concrete structures - Part

Priya leaned forward. "But our bridge has both bending and axial tension from the arch thrust."

"Exactly," Leila said, a faint smile appearing. "That's why we need the worked example from Chapter 9: 'Beams with axial tension.' The one with the underground car park slab."

She turned to the page, showing a table of iterative calculations. "They don't just give you the answer. They show you where they went wrong first. Look—their initial steel stress was 320 MPa. Cracks failed at 0.45 mm. Then they increased the bar size, reduced spacing to 150 mm, re-ran the calculation. Final crack width: 0.28 mm. Compliant."

Tom took the book, scanning the dense equations. "So we treat the bridge deck as a beam-column? Adjust for tension stiffening?"

"Yes," Leila said. "But there's another twist. The arch's horizontal thrust changes with live load. So we have three load cases: minimum thrust (cracking governs) and maximum thrust (serviceability stress governs)."

She opened the book again, this time to a worked example on second-order effects in slender arches. "Volume 2 doesn't have our exact bridge. But it has pieces of it. Example 4.3 covers non-linear analysis of a slender column under biaxial bending. Example 8.5 covers crack control in partially prestressed members. We just need to combine them."

For the next three hours, the three engineers worked in focused silence. They referenced the book constantly: the simplified stress-strain diagram for concrete (Example 3.1), the calculation of minimum reinforcement area for crack control (Example 7.1), the use of the Nominal Curvature Method for second-order analysis (Example 5.4).

By 6 PM, they had a preliminary design. The deck needed an extra layer of 12 mm bars at 100 mm spacing in the tension zone, and the arch had to be thickened slightly at the springings to reduce tensile stress.

"I thought Eurocode 2 was prescriptive and rigid," Priya said, looking at their final crack width calculation—0.31 mm, just under the 0.35 mm limit for exposure class XC4.

"It is prescriptive," Leila replied, closing Volume 2. "But prescriptive doesn't mean simple. The code gives you the map. This book shows you how to walk the terrain without falling into a ravine. Every worked example is someone else's near-disaster turned into a lesson."

She handed the book to Tom. "Take it home tonight. Read Example 10.6—the one about the water tank that leaked because they forgot to check minimum reinforcement for imposed strains. That's the kind of mistake we can't afford."

Tom nodded, holding the worn volume like a sacred text. Outside, the Manchester evening was turning grey. But on the table, the elegant white model of the bridge no longer looked impossible. It looked like an equation waiting to be solved—and the answer was in the examples.

That night, alone in her flat, Leila opened her own copy of Worked Examples to Eurocode 2 Volume 2. She wasn't checking calculations. She was reading the preface, which she had long ago memorized: "These worked examples have been prepared to assist in the understanding and application of Eurocode 2. They are not a substitute for sound engineering judgment."

She smiled. The bridge would stand. The calculations would hold. And somewhere, in an office or a classroom, another engineer would be learning from the same examples—turning disasters into design, one clause at a time.

Chapter 7: Foundations & Geotechnical Interaction

Step 3: Check

Actual ( \lambda = 57.7 ), ( \lambda_lim = 58.1 ) → Second-order effects may be ignored (just satisfied).

Step 1: Effective wall thickness (for torsion)

[ t_ef = \fracAu \quad \textwhere A = area enclosed by centerline of walls. ] Simplified: ( t_ef \approx 2 \times \textcover + \textlink + \textbar/2 )? No – better use: For solid section, ( t_ef,i = A_ci/u_i ) – but easier: ( t_ef = \textmin(b_w, , 2c_nom + \phi_link + \phi/2) ) for each wall. Assume ( t_ef = 2 \times 35 + 10 + 12.5 = 92.5 \text mm ).

Worked Example 3: Crack Control by Deemed-to-Satisfy (Table 7.2N)

Scenario: Reinforced concrete slab, 200 mm thick.

Step: EN 1992-1-1 Table 7.2N. For ( w_k = 0.3 \text mm ) (XC3 exposure) and ( \sigma_s = 240 \text MPa ):

If stress is 280 MPa → 16 mm max.

Outcome: Use ( \varnothing 20 ) bars @ 150 mm centers → no explicit crack width calc needed.

4.1 Clarity and Methodology

The strength of Volume 2 lies in its step-by-step methodology. Each example begins with clearly defined geometry and loading parameters. The calculations are laid out linearly, referencing specific clauses (e.g., "Cl. 6.2.2") and Equations from the Eurocode. This allows the user to trace the logic from the input data to the final result without ambiguity. The inclusion of design charts (interaction diagrams) within the examples provides a necessary check against hand calculations.

4.3 Deflection Checks

The worked examples for deflection provide excellent contrast between the rigorous calculation method and the "deemed to satisfy" span-to-depth ratio method. The report notes that the volume effectively demonstrates how to adjust the basic span-to-depth ratio using the necessary modification factors ($\rho$, $\rho'$), which is essential for efficient design.