How to Calculate Beam Size Using Beam Design Formula: A Comprehensive Guide

How to Calculate Beam Size Using Beam Design Formula: A Comprehensive Guide

When designing a structure, one of the most critical elements to consider is the beam. Beams are horizontal or slanted structural components that transfer loads from slabs, walls, and floors to columns, which then transfer the load to the foundation. Properly calculating the size of a beam is essential to ensure the stability and safety of a building. In this guide, we’ll walk you through the process of calculating beam size using beam design formulas, along with examples and key considerations.

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What is a Beam?

A beam is a structural element designed to carry and distribute loads across a span. It resists bending and shear forces, ensuring the structure remains stable. Beams are used in residential, commercial, and industrial buildings to support floors, roofs, and other loads. The size and type of beam depend on the span, load, and structural requirements.

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Types of Beams

Before diving into calculations, it’s important to understand the different types of beams used in construction:

1. Cantilever Beam: Fixed at one end and free at the other, often used for balconies or sunshades.
2. Simply Supported Beam: Supported at both ends, free to rotate, commonly used in residential buildings.
3. Continuous Beam: Has more than two supports, often used in multi-storey buildings.
4. Overhanging Beam: Extends beyond its supports on one or both ends.
5. Fixed Beam: Rigidly fixed at both ends, preventing rotation.
6. Lintel Beam: Used above doors and windows to support the structure above.
7. Composite Beam: Combines steel and concrete for enhanced strength.
8. L-Beam: Cast monolithically with slabs, forming an "L" shape.

How to Calculate Beam Size

The size of a beam depends on its span, the load it carries, and the type of beam. The following steps outline the process of calculating beam size using beam design formulas:

Step 1: Determine the Effective Depth

The effective depth (d) of a beam is calculated using the formula:

Effective Depth (d) = Span/Basic Value

The basic value depends on the type of beam:

• Simply Supported Beam: 20
• Cantilever Beam: 7
• Continuous Beam: 26

Step 2: Calculate the Total Depth

The total depth (D) of the beam includes the effective depth, half the diameter of the reinforcement bar, and the clear cover:

Total Depth (D) = Effective Depth (d) + (Diameter of Bar/2) + Clear Cover

 

• Clear cover is typically 25 mm for beams.

 

Step 3: Determine the Width of the Beam

The width (b) of the beam is calculated as:

Width (b) = Total Depth (D)/1.5

The width should not be less than 200 mm.

Step 4: Check Width-to-Depth Ratio

As per IS 13920, the width-to-depth ratio should be greater than 0.3:

Width (b)/Total Depth (D) > 0.3

Step 5: Verify Depth Against Span

The depth of the beam should not exceed ¼ of the clear span:

Depth (D) ≤ (1/4) × Span

 

Examples of Beam Size Calculation

Example 1: Simply Supported Beam

• Span: 5 m (5000 mm)
• Effective Depth (d): 5000/20 = 250 mm
• Total Depth (D): 250+162+25 = 283 mm ≈ 285 mm
• Width (b): 285/1.5 = 190 mm (use 200 mm)
• Width-to-Depth Ratio: 200/285 = 0.7>0.3 (Safe)
• Depth Check: 1/4×5000 = 1250 mm > 285 mm (Safe)

 

Example 2: Cantilever Beam

• Span: 2 m (2000 mm)
• Effective Depth (d): 2000/7 = 285 mm
• Total Depth (D): 285+162+25=318 mm ≈ 320 mmm
• Width (b): 320/1.5 = 213 mm (use 230 mm)
• Width-to-Depth Ratio: 230/320 = 0.71 > 0.3 (Safe)
• Depth Check: ¼ × 2000 = 500 mm > 320 mm (Safe)

 

Example 3: Continuous Beam

• Span: 5 m (5000 mm)
• Effective Depth (d): 5000/26 = 192.3 mm≈200 mm
• Total Depth (D): 200+(16/2)+25=233 mm≈235 mm
• Width (b): 235/1.5 = 156.67 mm (use 200 mm)
• Width-to-Depth Ratio: 200/235 = 0.85 > 0.3 (Safe)
• Depth Check: (1/4) × 5000 = 1250 mm>235 mm (Safe)

 

Check for Lateral Stability

To ensure the beam is safe from lateral buckling, use the following formulas:

For Simply Supported or Continuous Beams

Allowable L = min (60b, (250*(b²/d))

If the span is less than the allowable L, the beam is safe.

For Cantilever Beams

Allowable L=min (25b, (100*(b2/d))

 

Thumb Rule for Beam Depth

A quick rule of thumb for beam depth is:

1 foot of span=1 inch of depth

For example, a 16-foot span would require a 16-inch deep beam.

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Lintel Beam

For lintel beams, the minimum thickness should be 150 mm to prevent cracks around doors and windows.

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Conclusion

Calculating beam size is a crucial step in structural design. By following the formulas and steps outlined above, you can ensure that your beams are properly sized to handle the loads they will encounter. Always verify your calculations and adhere to local building codes and standards. If you have any doubts or need further clarification, feel free to reach out or consult a structural engineer.

Happy designing!