A simply supported steel beam is one of the most basic structural elements used in construction. It is supported at both ends and is free to bend under applied loads, making it suitable for various applications in buildings, bridges, and other structures. This blog outlines the design steps for a simply supported steel beam, providing a clear guide for engineers, architects, and students. We will also reference relevant Indian Standards (IS codes) to ensure compliance with best practices in structural design.
1. Determine the Loads Acting on the Beam
The first step in designing a simply supported beam is to calculate the loads it will carry. These loads can be categorised into:
- Dead Load: This includes the self-weight of the beam and other permanent fixtures, such as flooring, roofing, or any other non-movable parts of the structure.
- Live Load: These are variable loads such as the weight of people, furniture, and vehicles. The values for live loads depend on the usage of the structure and are provided in IS 875 (Part 2): 1987.
- Other Loads: Consider additional loads such as wind, earthquake, or snow, if applicable, as per IS 875 (Part 3): 1987 and IS 1893: 2016 for seismic loads.
2. Calculate the Maximum Bending Moment
The bending moment is a measure of the bending effect on the beam due to external loads. It is crucial to calculate this accurately to ensure the beam’s safety and stability.
- For a simply supported beam with a uniformly distributed load (UDL), the maximum bending moment (M) is given by:
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where:- ω = uniformly distributed load per unit length (N/m),
- L = span length of the beam (m).
- For a point load (P) at the centre of the beam, the maximum bending moment is:
These formulas can be adapted based on the loading condition of the beam.
3. Calculate the Required Section Modulus
The section modulus (Z) is a geometric property of the beam’s cross-section that indicates its resistance to bending. It is calculated using the formula:
where:
- M = maximum bending moment (N·m),
- f = permissible stress in steel (N/mm²).
For structural steel, the value of fff can be taken from IS 800: 2007, which provides the allowable stresses based on the grade of steel used.
4. Select a Suitable Beam Section
From the calculated section modulus, choose an appropriate beam section from standard tables such as IS 808: 1989, which lists the properties of rolled steel sections like I-beams, H-beams, and channels. It is advisable to select a section with a section modulus slightly greater than the required value for added safety.
- Preference for Deeper Sections: While selecting the section, deeper beams are generally preferred because they offer greater resistance to bending and deflection with a lesser amount of material, making them more economical.
5. Calculate the Maximum Shear Force
The maximum shear force (V) for the beam must be determined to check for shear strength. For a beam with a UDL, the maximum shear force is given by:
For a point load at the centre, the maximum shear force is:
6. Check for Shear Stress
The beam section must be checked for safety against shear stress. The intensity of shear stress (τ) can be calculated using the formula:
where:
- V = maximum shear force (N),
- d = overall depth of the beam (mm),
- t = thickness of the web (mm).
The shear stress should not exceed the permissible shear stress provided in IS 800: 2007.
7. Check for Deflection
Excessive deflection can lead to serviceability issues such as cracking in finishes and misalignment of structural components. The maximum permissible deflection for a simply supported beam is:
where L is the span length. Deflection is calculated using the formula:
where:
- E = modulus of elasticity of steel (usually taken as 2 \times 10^5 N/mm²),
- I = moment of inertia of the section (mm⁴).
If the calculated deflection exceeds the permissible limit, a deeper or stiffer section should be selected.
8. Check for Lateral Stability
Ensure that the beam is laterally stable, as lateral-torsional buckling can cause failure even if the beam is safe in bending and shear. Provide lateral supports at regular intervals, especially for long-span beams, as per the recommendations in IS 800: 2007.
9. Design of Connections
Design the connections, such as end bolts or welds, to transfer the loads safely from the beam to the supports. IS 800: 2007 and IS 9595: 1996 provide detailed guidelines for the design of bolted and welded connections.
10. Detailing and Final Review
Prepare detailed drawings showing the dimensions, reinforcement, and connection details of the beam. Verify the design against all possible failure modes and ensure compliance with all relevant IS codes.
Conclusion
Designing a simply supported steel beam involves a series of steps to ensure that the beam can safely carry the applied loads without excessive deflection or failure. By following the design steps outlined above and adhering to relevant IS codes, such as IS 875 for loads and IS 800 for design and safety, engineers can create safe and economical steel structures. Regular inspections and maintenance will further ensure the long-term performance of the beam in various applications.