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Structural Design: A reinforced concrete beam with a rectangular cross - section of width 3 0 0 mm and depth 5 0 0 mm is

Structural Design:
A reinforced concrete beam with a rectangular cross-section of width 300 mm and depth 500 mm is reinforced with 4 steel bars of diameter 20 mm. The grade of concrete is M25, and the steel is Fe500. Calculate the ultimate moment capacity of the beam.
Geotechnical Engineering:
A retaining wall is 5 meters high and retains a granular backfill with a unit weight of 18 kN/m^3 and an internal friction angle of 30. Calculate the lateral earth pressure at the base of the wall using Rankines theory.
Hydrology:
A catchment area of 50 km^2 receives a uniform rainfall of 20 mm/hr for 5 hours. Calculate the total runoff volume if the runoff coefficient is 0.6.
Structural Analysis:
A propped cantilever beam of length 6 meters is subjected to a uniformly distributed load of 15 kN/m. Calculate the reactions at the supports and the bending moment at the fixed end.
Environmental Engineering:
A trickling filter in a wastewater treatment plant treats an influent with a BOD of 200 mg/L. The filter has a volume of 1000 m^3 and the hydraulic loading rate is 10 m^3/m^2.day. Calculate the BOD removal efficiency if the filter media has a specific surface area of 120 m^2/m^3.
Transportation Engineering:
Design a vertical curve connecting two road gradients of +3% and -2%. The design speed is 80 km/h, and the minimum sight distance required is 160 meters. Calculate the length of the vertical curve.
Water Supply Engineering:
A water distribution system has a pipeline of diameter 300 mm and length 2 km. The head loss due to friction is 15 meters. Calculate the flow rate using the Darcy-Weisbach equation. Assume the friction factor
f is 0.02.
Concrete Technology:
A concrete mix requires a compressive strength of 40 MPa at 28 days. If the standard deviation of the mix is 5 MPa, calculate the required mean strength of the concrete using a factor of safety of 1.65.
Foundation Engineering:
A circular footing with a diameter of 1.5 meters is to be constructed on a clayey soil with an undrained shear strength of 100 kN/m^2. Calculate the bearing capacity of the footing using Terzaghis bearing capacity equation.
Fluid Mechanics:
A venturi meter with a throat diameter of 100 mm is installed in a pipeline of diameter 200 mm carrying water. The differential pressure head is 0.5 meters. Calculate the flow rate through the pipeline. Assume the coefficient of discharge is 0.98.
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