Problem 1: The cantilevered reinforced concrete beam for a domestic building illustrated in Figure 1 is engineered to support vertically distributed loads (w) alongside concentrated vertical forces (live). The dead load G, excluding self-weight, is 6 kN/m, while the live load Q measures 4 kN/m. Additionally, a concentrated vertical load of 12 kN is applied at the cantilever’s end. The beam has a span length of 3 meters. Reinforcement comprises normal class N steel bars (Es = 200,000 MPa; fsy = 500 MPa), with stirrup bar diameter set at 10 mm. Concrete possesses a characteristic compressive strength of 32 MPa. The cover is 20 mm.
Figure 1
DESIGN ACCORDING TO ULTIMATE LIMIT STATE AS3600-2018:
1. Compute the self-weight of the beam.
2. Determine the design bending moment at Ultimate M*u.
3. Calculate the effective depth d in compliance with AS3600-2018 durability stipulations.
4. Design the area of tensile steel Ast.
5. Choose suitable reinforcing bars and spacing. Provide a clear cross-section of the beam, indicating all dimensions, tension reinforcement (number of bars with spacing), and stirrups.
6. Perform the final design checks.
DESIGN ACCORDING TO SERVICE LIMIT STATE AS3600-2018:
7. Compute the total shrinkage strain of concrete and ignore short-term deflection due to concrete shrinkage.
8. Calculate the crack moment Mcr for short-term conditions.
9. Determine the effective moment of inertia Ief and the short-term mid-span deflection of the beam using clause 8.5.3.1 and Equation 8.5.3.1(1). Consider long-term deflection with concrete shrinkage included. Verify Ief using a simplification method.
10. Compute the design service bending moment M*ser for long-term conditions.
11. Calculate the effective moment of inertia Ief using clause 8.5.3.1 and Equation 8.5.3.1(1), along with the long-term mid-span deflection of the beam. Confirm Ief using a simplification method.
12. Deduce the total deflection (short + long terms) and compare it with AS3600 Service Limit State requirements. Does the beam satisfy AS3600-2018 SLS criteria for deflection control?
Problem 2: The reinforced concrete beam shown in Figure 2 is designed to carry vertically uniformly distributed loads (w). The dead load G is 70 kN/m, self-weight included. The live load Q is 90 kN/m. The beam span L is 15 m. The effective depth d is 1030mm and the effective width bef is 1800 mm. The reinforcement is composed of normal class N steel bars (Es = 200000 MPa; fsy = 500 MPa). The characteristic compressive strength of concrete is 40 MPa. The exposure condition of the beam is A1. This beam is domestic structure that located in Tarcoola.
1. Calculate the design bending moment M*u for the maximum loads.
2. Design tensile steel Ast and select the appropriate reinforcing bars.
3. Check total deflection (short + long terms) and compare with AS 3600 Service Limit State.
(Please use clause 8.5.3.1 and Equation 8.5.3.1(1). Note: The effect of concrete shrinkage will be included in long term deflection only.)
4. Design the stirrups required according to AS 3600:2018.
Figure 2
