Question

The lateral pressure exerted by paddy on the bin wall, as computed by Rankine's formula, was \(6000 \text{ kgf/m}^2\) when the pressure coefficient is 0.5. What would be the height of bin if the density of paddy is \(600 \text{ kg/m}^3\)

• A. 30 m
• B. 20 m
• C. 10 m
• D. 5 m

Hint:

Rankine's formula is simple because pressure varies linearly with depth, similar to hydrostatic pressure: \(P = k \rho g h\). Just identify the constant factor (\(k\)) and solve it directly like a fluid pressure problem.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Rankine's theory is used in structural design to estimate the lateral active earth pressure exerted by a granular material against a retaining wall or bin wall. It assumes that the material is dry, cohesionless, and homogeneous.
Key Formula or Approach:
According to Rankine's formula, the lateral active pressure (\(P_L\)) at a depth (\(h\)) is given by: \[ P_L = k \cdot w \cdot h \] where:
\(P_L\) = lateral pressure (\(\text{kgf/m}^2\))

\(k\) = active lateral pressure coefficient

\(w\) = bulk density (or unit weight) of the granular material (\(\text{kgf/m}^3\))

\(h\) = height of the material column (or depth) (\(\text{m}\))

Step 2: Detailed Explanation:
Let us identify the given values:
Lateral pressure, \(P_L = 6000 \text{ kgf/m}^2\)

Pressure coefficient, \(k = 0.5\)

Density of paddy, \(w = 600 \text{ kg/m}^3\) (equivalent to \(600 \text{ kgf/m}^3\) in gravitational units)
Substitute these values into Rankine's formula to solve for height (\(h\)): \[ 6000 = 0.5 \times 600 \times h \] Simplify the calculation: \[ 6000 = 300 \times h \] \[ h = \frac{6000}{300} = 20 \text{ m} \] Thus, the height of the bin is 20 meters.

Step 3: Final Answer:
The height of the bin is 20 m, which corresponds to Option (B).