a) To calculate the earth pressure on the cut, we can use the Rankine's theory of earth pressure. The equation for the active earth pressure is given by:
P = Ka * γ * H^2
Where P is the earth pressure, Ka is the active earth pressure coefficient, γ is the unit weight of the sand, and H is the height of the cut.
To calculate Ka, we can use the equation:
Ka = (1 - sin(φ')) / (1 + sin(φ'))
Where φ' is the effective angle of internal friction. Given that φ' = 32° = 0.559 radians, we can calculate Ka as:
Ka = (1 - sin(0.559)) / (1 + sin(0.559)) = 0.19
Substituting the given values, we have:
P = (0.19) * (18.6 kN/m²) * (6m)^2 = 115.03 kN/m
Therefore, the earth pressure on the cut is 115.03 kN/m.
b) To calculate the strut load at different levels, we need to determine the horizontal force acting on each strut.
At level A:
The horizontal force acting on each strut is equal to half of the earth pressure on the cut since the struts are located at 3m center to center in plan. Therefore, the strut load at level A is:
Load_A = (115.03 kN/m) / 2 = 57.515 kN/m
At level B:
The horizontal force acting on each strut is equal to the earth pressure on the cut since the struts are at the corners of the cut. Therefore, the strut load at level B is:
Load_B = 115.03 kN/m
At level C:
The horizontal force acting on each strut is again equal to half of the earth pressure on the cut since the struts are located at 3m center to center in plan. Therefore, the strut load at level C is:
Load_C = (115.03 kN/m) / 2 = 57.515 kN/m
c) To calculate the required section of the struts, we can use the equation for the axial stress:
σ = P / A
Where σ is the axial stress, P is the strut load, and A is the cross-sectional area of the strut. Rearranging the equation, we have:
A = P / σ
Given that the permissible axial or bending stress is 200 x 10^3 Pa, we can calculate the required section of the struts. Substituting the values, we have:
Section = (57.515 kN/m) / (200 x 10^3 Pa) = 287.58 x 10^-3 m²
Therefore, the required section of the strut is 287.58 x 10^-3 m².
d) To calculate the required section of the wales at level A, we can use the same equation as before:
Section = (Load_A) / (210 x 10^3 Pa) = (57.515 kN/m) / (210 x 10^3 Pa)
Simplifying, we have:
Section = 0.27389 x 10^-3 m²
Therefore, the required section of the wales at level A is 0.27389 x 10^-3 m².
A braced cut (or excavation) is made in a deposit of sand to a depth of 6m and width of 4m. The braced cut is supported by horizontal struts as shown in Figure Q4. The angle of internal friction of sand is 32° while the unit weight is 18.6kN/m². If the struts are located at 3m center to center in plan. Calculate: - a) The earth pressure envelope on the cut (7 marks) b) The struts load at level A, B and C. (3 marks) c) The strut section if the permissible axial (axial or bending) stress is 200 x 10 kPa. (8 marks) d) The required section of the wales at level A, if the axial (axial or bending) stress is 210 x 103 kPa (2 marks) 4m 1m А ЧЕ 2 m B 2m с 1m
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