Simple Supported Steel Beam Design: A Comprehensive Eurocode 3 Guide

What is a simple supported beam? Basics and behavior

A simple supported beam is a basic structural element with supports at its ends that allow rotation but prevent vertical movement. Typically, one end is a pinned support (stopping both vertical and horizontal movement but allowing rotation), and the other is a roller support (stopping only vertical movement, allowing horizontal movement and rotation). This setup creates a statically determinate system, meaning reactions, shear forces, and bending moments can be calculated directly from basic equilibrium equations.

Understanding how simple supported beams behave under different loads is important. They mainly deal with bending and shear, and keeping deflections within limits is a key serviceability consideration.

See Beam Analysis for more information on this topic.

Key design considerations for simple supported steel beams (Eurocode 3)

When designing steel beams according to Eurocode 3 (EN 1993-1-1), you need to perform several checks to ensure both strength (ultimate limit state - ULS) and how well it performs in use (serviceability limit state - SLS). Our tool helps simplify these important checks.

1. Beam geometry and material properties

• Beam length (\(L\)): The span of the beam is a main input.
• Camber: This is an intentional upward curve built into the beam to help offset expected sagging under load, making it look and work better.
• Self-weight: The beam its own weight is automatically calculated and added to the permanent loads, which makes the analysis more accurate.
• Steel grade: Choosing the right steel grade (like S235, S275, S355) sets the material its yield strength (\(f_y\)) and ultimate tensile strength (\(f_u\)), which are very important for calculating how much load the beam can resist.

2. Load application and combinations

Accurate modeling of loads is important. Eurocode 3 distinguishes between permanent loads (e.g., self-weight, finishes) and variable loads (e.g., live loads, snow, wind). These are combined using partial factors to derive design loads for ULS and SLS checks. Our tool supports various load types, including point loads and distributed loads, allowing precise definition of their magnitudes and positions. Permanent loads are displayed as G and g for point and distributed loads respectively. And Q and q for variable loads.

3. Stability checks: lateral-torsional buckling (LTB)

For slender steel beams, lateral-torsional buckling (LTB) is a key way they can fail. This happens when the beam buckles sideways and twists at the same time. Eurocode 3 gives ways to check for and design against LTB. Our tool lets you control stability settings in detail:

• Lateral end supports: You can set how the beam ends are held (e.g., fully restrained, bottom flange bolted, or just resting on compression). Do note that a bottom flange bolted with web stiffeners at the supports does count as fully restrained.
• Intermediate lateral restraints: Specify additional restraints along the beam its length (e.g., no restraint, fully restrained, or at specific points you choose).
• Buckling length (\(L_{cr}\)): For certain situations, you can directly enter the effective buckling length.
• Load application point: Where the load is put on the beam (top, middle, or bottom flange) really changes how likely it is to buckle sideways in case it is a free standing load.
• Free standing load: This accounts for loads that can make the beam unstable because they don't offer any side support, which affects the \(C_2\) factor.
• Custom \(C_1\) factor: Allows advanced users to input a custom \(C_1\) factor, which depends on the bending moment diagram shape.

4. Eurocode criteria: ULS and SLS

• Ultimate limit state (ULS): This makes sure the beam can resist failure (like yielding, buckling, or breaking).
  • Consequence class (CC1, CC2, CC3): This affects the partial factors for permanent (\(\gamma_G\)) and variable (\(\gamma_Q\)) loads, showing how serious a failure would be.
  • Partial safety factors (\(\gamma_{M0}, \gamma_{M1}, \gamma_{M2}\)): These factors are used with material strengths to account for things like variations in material properties, manufacturing tolerances, and the accuracy of resistance models.
  • Cross-section class: This groups the beam its cross-section (class 1 to 4) based on its width-to-thickness ratios. This helps figure out how well it can resist local buckling and redistribute forces.
• Serviceability limit state (SLS): Focuses on the beam its performance during normal use, making sure it doesn't deflect too much or vibrate excessively.
  • Beam deflection category: Pick a category (like floor, roof, or cantilever) to automatically apply the right characteristic, frequent, and quasi-permanent deflection limits. You can also set your own custom limits.

Streamline your design: our integrated calculation tool

Our simple supported steel beam calculator is designed to help structural engineers work efficiently and accurately. It offers two different, but related, calculation methods:

• Single beam analysis (design check): Perform a detailed Eurocode 3 check on a specific beam profile (e.g., IPE 300) and steel grade (e.g., S355). Input your chosen beam, and the tool gives you full results, including checks for bending, shear, and buckling, along with deflection analyses.
• Beam optimization (design assistant): This powerful feature acts as your smart design assistant. Set your design rules (e.g., preferred beam types, height/width limits, material grades), and the optimizer will suggest the best beam profiles. You can optimize for different goals, such as minimizing weight (for cost and material efficiency) or making sure a specific unity check limit (UC limit) is met, helping you get an economical and compliant design.

No more wasting time on manual calculations and trying different options. Our tool gives instant feedback, detailed results, and a clear path to a better design.

Frequently asked questions (FAQ)

What is the difference between ULS and SLS in Eurocode 3?

ULS (ultimate limit state) checks the structural integrity and resistance against collapse or failure (e.g., yielding, buckling). SLS (serviceability limit state) checks the performance under normal use, making sure the structure remains functional and comfortable (e.g., limiting deflections, vibrations).

How does the Design Assistant optimize beam selection?

The design assistant allows you to set criteria like desired beam types, height/width ranges, and material grades. It then checks available profiles against these rules and your applied loads, suggesting beams that meet Eurocode 3 requirements while optimizing for things like minimum weight or a specific unity check limit.

Why is lateral-torsional buckling (LTB) important for steel beams?

LTB is important for slender steel beams because it can lead to sudden and serious failure at stresses well below the material its yield strength. It involves the beam its compression flange buckling sideways and the entire cross-section twisting, significantly reducing its bending capacity. Proper design against LTB ensures the beam its stability.

What are partial safety factors (\(\gamma_M\) values) in Eurocode 3?

Partial safety factors (e.g., \(\gamma_{M0}, \gamma_{M1}, \gamma_{M2}\)) are used with material resistances to account for uncertainties in material properties, manufacturing tolerances, and the accuracy of resistance models. They help ensure a sufficient margin of safety in structural design.