Also, from equation (b), 8.421EID = -0.122 - 4.211EIC
Hence, 4.211EID = -0.061 – 2.106EIC (4)
Substitute equation (3) into equation (1), and equation (4) into equation (2):
12.469EIB + 3.077EIC = 0.013 (5)
3.077EIB + 12.469EIC = -0.013 (6)
Solving equations (5) and (6) simultaneously gives:
EIB = 0.001384
EIC = -0.001384
From equation (3), EIA = 0.01379
EID = -0.01379
MAB = 0, MBA = 0.204kNm, MBC = -0.204kNm,
MCB = 0.204kNm, MCD = -0.204kNm, MDC = 0.
These moments are illustrated on Figure B3. From the figure, it can be seen that they are end-moments. Hence, it is important to determine the maximum moment that would act along the span of each member, about a point, using the principles of static equilibrium.
Provide Y10@150mm (main and distribution bars respectively) in accordance with the provisions of clause 188.8.131.52.3.
Detailing and Bar-Bending Schedule
The detailed drawing for the drainage channel is illustrated in Figure B4. From this, the bar-bending schedule for the entire channel’s length (including the irregular section) is produced as shown on Table B1.
The loading diagram of the retaining wall is illustrated in Figure C1. From the figure, it can be seen that the load diagrams have different shapes for different loads. Moreover, it clearly shows the backfill and frontfill sides.
M = Net moment about the base bottom of all forces (due to both horizontal and vertical forces)
e = eccentricity
equilibrium distance, x = (Mresisting – Moverturning) ÷ N = (80.5 – 10.53) ÷ 71.49
x = 0.979m from A.
e = 0.5D – x = 0.9m – 0.979m = -0.079m
|e| = 0.08m
emax = D ÷ 6 = 0.3m
|e| < emax. Hence, middle third rule is satisfied.
P1, 2 = (71.49/1.8) [1 ± (6 * 0.08m ÷ 1.8m)]
P1 = 50.32kN/m2
P2 = 29.11kN/m2
Maximum bearing pressure on soil is 50.32kN/m2 (< the allowable bearing capacity of 60kN/m2).
A factor of safety of 1.4 is applied to the horizontal forces on the wall. Then, moments of the horizontal forces are taken about the centreline of the base. This is because cantilever walls, generally, fail by rotation about a point some ways above the toe.
Provide Y10@200mm c/c longitudinal and transverse on both I.F. and O.F. From experience, being the larger unit, the reinforcement information of the wall is suitable for the base. A trial convinced the trainee!
The reinforcement detailing for the cross-section of the retaining wall is as shown on Figure C3. From this figure, the bar-bending schedule is extracted as tabulated in Table C1.
Figure C3 Detailing of the Cross-section of the Cantilever Retaining Wall
Table C1 Bar Bending Schedule for the Cantilever Retaining Wall
1 NTU means Nephthelometric Turbidity Unit. It is used as a unit in determining the intensity of the turbidity of any water sample.
2 Prestressed concrete is a concrete to which an internal compressive stress has been applied by means of wires or tendons, so that a tensile stress equal to the compressive stress can be applied in service (as live loads) such that the net stress is then zero.
3 Slenderness ratio is the ratio of the effective height of a wall to its thickness, i.e. le/h.
4Adverse partial factor is applied to any loads that tend to produce a more critical design condition at the section considered.
5 Beneficial partial factor is applied to any loads that tend to produce a less critical design condition at the section considered.
6Statical determinate structure is one in which the equations of static equilibrium are sufficient to analyse the structure, i.e. ∑Fx=0, ∑Fy=0, ∑M=0
7 Statically indeterminate structure is one in which the equations of static equilibrium are not sufficient to analyse the structure.
8 FEM are the moments at the support of a fixed section (say, beam) that are produced due to lateral or
9 BS 4466: 1969 – Bending, Dimensioning and Scheduling of Bars for the Reinforcement of Concrete.
10 Latitude is one of the axes of an imaginary coordinate system of the Earth to determine the distance of a point from the equator. It is actually the degree of the angle formed between a line from the point to the centre of the Earth and a line from the equator to the centre of the Earth.
11 Longitude is the other axis in the imaginary coordinate system of the Earth. It is the degree of the angle formed between a line from the point to the centre of the Earth and a line from the prime meridian to the centre of the Earth.