Designing a girder, or built-up beam, is a crucial aspect of structural engineering. It involves a series of calculations and checks to ensure the girder can safely support the applied loads without failure. In this blog, we will explore the girder design procedure using a systematic trial-and-error method. This method includes selecting an appropriate section and verifying its strength against bending, shear forces, and deflection criteria. We’ll also reference relevant IS codes to guide the design process according to Indian standards.
What is a Girder?
A girder is a large beam that supports other beams or loads in a structural framework. Girders are typically used in bridges, buildings, and other large structures. The design of girders is not straightforward and involves an iterative process to find the most suitable section that meets all safety and performance criteria.
Step-by-Step Girder Design Procedure
Step 1: Calculate the Bending Moment and Shear Force
The first step in designing a girder is to determine the maximum bending moment (M) and shear force (F) that the beam needs to resist. These values depend on the loads applied and the span of the beam.
Bending Moment (M): The bending moment is calculated using the formula:
M = Load×Span
Shear Force (F): The shear force is calculated based on the load distribution along the beam’s length. For uniformly distributed loads, the maximum shear force can be determined by:
F = Total Load/2
These values are essential for determining the required strength and size of the girder section.
Step 2: Determine the Section Modulus
The section modulus (Z) is a geometric property that measures the strength of the girder’s cross-section. It is calculated using the formula:
Z = M/P
Where:
- M = Maximum Bending Moment (calculated in step 1)
- P = Permissible Bending Stress (as per IS 800:2007)
This step helps in estimating the size of the girder required to resist the bending moment.
Step 3: Select a Rolled Steel Section
Based on the calculated section modulus (Z), select a suitable rolled steel section from standard tables. The section should have a section modulus equal to or greater than the calculated Z.
- If the selected section is insufficient, additional cover plates can be welded to both flanges to achieve the required value of Z. This is often done to enhance the girder’s capacity without changing the section entirely.
Step 4: Check the Girder for Bending Stresses
Once a section is chosen, check it against the maximum bending stresses in the extreme fibres of the girder. The formula for bending stress is:
σ = M/Z
Where:
- M = Maximum Bending Moment
- Z = Section Modulus
Ensure that the calculated bending stress does not exceed the permissible limit specified in IS 800:2007.
Step 5: Verify the Section for Shear Force and Deflection
Shear Force Check: Calculate the shear stress (q) using the formula:
q = Ftw×h
Where:
- F = Maximum Shear Force (calculated in step 1)
- t_w = Thickness of the Web
- h = Depth of the Beam
The value of q should not exceed 94.5 N/mm², as per IS 800:2007.
Deflection Check: Deflection is another critical aspect that must be checked. The permissible deflection (Δ) should not exceed:
Δ = L/325
Where:
- L = Effective Span of the Beam
If the deflection exceeds this limit, the section size must be increased or stiffened to reduce the deflection.
Relevant IS Codes for Girder Design
- IS 800:2007 – General Construction in Steel – Code of Practice: This standard provides guidelines for the design of steel structures, including permissible stresses and deflection limits.
- IS 808:1989 – Dimensions for Hot Rolled Steel Beam, Column, Channel, and Angle Sections: This code lists the standard dimensions for rolled steel sections.
- IS 875 (Part 1 to 5):1987 – Code of Practice for Design Loads (Other than Earthquake) for Buildings and Structures: This code provides the loads to be considered in design calculations.
Key Considerations in Girder Design
- Material Quality: Ensure that the steel used meets the required grade and specifications.
- Fabrication Accuracy: The girder must be fabricated as per the design drawings to ensure it meets the strength and deflection criteria.
- Safety Factors: Apply appropriate safety factors as per IS codes to account for uncertainties in material properties and loading conditions.
Conclusion🎯
The design of a girder involves careful calculation and selection of appropriate sections to ensure the structure’s safety and performance. By following the outlined procedure and adhering to the relevant IS codes, engineers can design girders that efficiently carry loads while maintaining stability and safety. Remember, the key to successful girder design is in the details and ensuring that all factors, including bending, shear, and deflection, are thoroughly checked and verified.