Tutorial-2
Concrete Design (48353)
Tutorial 2 – ULS Design
Problem 2.1
The cantilever under-reinforced beam of a balcony, shown in Figure 1, carries a live load of 6
kN/m and a superimposed dead load of 3 kN/m, in addition to its self-weight (density is 2400
kg/m3). The width and the total depth of the beam are 150 mm and 200 mm respectively. The
beam span L is equal to 1.4m. The reinforcement is composed of normal class steel bars (Es =
200000 MPa; fsy = 500 MPa). The exposure condition of the beam is A1. The characteristic
compressive strength of concrete is 32 MPa. Steel bars in the compressive zone will not be
accounted for in the ULS design. Both stirrup bar diameter and bars in the compressive zone
200 mm
diameter are 8 mm.
8mm diameter bar
8mm diameter bar
150 mm
B
A
L
Figure 1: Cantilever beam subject to uniform distributed permanent and live loads.
1: Calculate the self-weight (s.w.) of the beam.
2: Calculate the design bending moment at Ultimate M*u.
3: Calculate the effective depth d according to AS3600 durability requirements.
4: Calculate concrete elastic modulus Ec.
5: Design the tensile steel area Ast.
6: Select appropriate reinforcing bars and spacing.
7: Carry out the final design checks (1 marks).
Problem 2.2
The reinforced concrete beam shown in the Figure below is designed to carry vertically
uniformly distributed loads (w). The dead load G is 50 kN/m over the whole beam, self-weight
included. The live load is Q is 55 kN/m. The beam cross-section width b = 800 mm and the
beam cross-section depth h = 400 mm. The concrete cover c = 20 mm. Both bending and shear
reinforcement are composed of normal class steel bars (Es = 200000 MPa; fsy = 500 MPa). The
characteristic compressive strength of concrete is 32 MPa.
B
C
w
D
E
400 mm
A
800 mm
Ultimate Limit State (ULS) design
1. Calculate the design bending moments (positive and negative) at Ultimate. For the
positive design bending moment M*u+, consider that Q is applied only over the span
BCD. For the negative design bending moment M*u-, consider that Q is applied over
the whole beam ABCDE.
2. Calculate the effective depth d assuming that stirrups bar diameter is 12 mm and tensile
bars are N28 for positive design bending moment and N24 for negative design bending
moment.
3. Design the tensile steel area Ast for both moments M*u+ and M*u- and select appropriate
reinforcing bars and spacing.
Problem 2.3