Effective Depth Calculation
To determine the effective depth (d) of the beam, we first need to calculate it using the given dimensions and effective cover.
- Total depth of the beam = 500 mm
- Effective cover = 50 mm
- Diameter of main steel bars (assume 20 mm for calculation) = 20 mm
Effective depth (d) = Total depth - Effective cover - (Diameter of bars / 2)
d = 500 - 50 - (20 / 2) = 500 - 50 - 10 = 440 mm
Design Moment Capacity
The design moment capacity (Mu) is given as 170 kNm. Using the formula for the moment capacity of a singly reinforced beam:
Mu = 0.138 * fck * b * d^2
Where:
- fck = characteristic strength of concrete (M20 = 20 MPa)
- b = width of beam = 250 mm
- d = effective depth = 440 mm
Now, converting units:
Mu = 0.138 * 20 * 250 * (440)^2 / 10^6
Mu = 0.138 * 20 * 250 * 193600 / 10^6
Mu = 1.06 kNm (approx)
Area of Steel Required
Using the equation for the area of steel (Ast):
Ast = Mu / (0.87 * fy * lever arm)
Assuming lever arm (z) = 0.95 * d:
z = 0.95 * 440 = 418 mm
Using fy = 415 MPa:
Ast = (170 * 10^3) / (0.87 * 415 * 418 / 10^6)
Ast = (170 * 10^3) / (0.87 * 0.415 * 418)
Ast = 446.56 mm²
Final Steel Area
To ensure sufficient reinforcement, we will round up and use:
- Minimum required steel area = 450 mm²
Hence, use 2 bars of 16 mm diameter or equivalent.
This design ensures the beam can safely withstand the applied moments while adhering to structural integrity standards.