Calculating the total load on an RCC beam is crucial for structural integrity. Engineers must assess both the beam’s self-weight and the superimposed load from the slab. Let’s break it down step by step.
Given Data for Calculation
- Span of Beam B1 = 4500 mm = 4.5 m
- Span of Beam B2 = 3000 mm = 3.0 m
- Sectional Dimensions = 230 mm × 450 mm = 0.23 m × 0.45 m
Slab Type Identification
To determine the slab type:
Lx / Ly = 4500 mm / 3000 mm = 1.5 < 2
Since the ratio is less than 2, it is a two-way slab.
Load Distribution Over Beams
The slab will transfer load to both B1 and B2 beams. Below is the detailed load calculation for each beam.
Total Load on Beam B1
1. Self-Weight of Beam B1
- Area of Cross-section = 0.23 m × 0.45 m
- Density of RCC = 25 KN/m³
Self-weight calculation:
= 0.23 × 0.45 × 25 = 2.588 KN/m
Factored self-weight:
= 1.5 × 2.588 = 3.88 KN/m
Total factored self-weight over full span:
= 3.88 × 4.5 = 17.46 KN
2. Load Transferred From Slab to Beam B1
The formula used:
= 1/2 × (Lx × Ly – Lx² / 2) × W
Where W = 12.94 KN/m² (from slab load calculations):
= 1/2 × (3 × 4.5 – 3² / 2) × 12.94
= 1/2 × (9) × 12.94
= 58.23 KN
3. Total Factored Load on Beam B1
= 17.46 + 58.23 = 75.69 KN
Total Load on Beam B2
1. Self-Weight of Beam B2
Self-weight calculation:
= 0.23 × 0.45 × 25 = 2.588 KN/m
Factored self-weight:
= 1.5 × 2.588 = 3.88 KN/m
Total factored self-weight over full span:
= 3.88 × 3 = 11.64 KN
2. Load Transferred From Slab to Beam B2
The formula used:
= (Lx² / 4) × W
= (3² / 4) × 12.94
= (9 / 4) × 12.94
= 2.25 × 12.94 = 29.11 KN
3. Total Factored Load on Beam B2
= 11.64 + 29.11 = 40.75 KN
Conclusion
Both B1 and B2 beams carry different total loads due to their spans and positions under a two-way slab. Beam B1 carries 75.69 KN, while Beam B2 carries 40.75 KN. Accurate load calculations ensure safe and efficient structural design.
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