Question

Rankine formula is used for calculation of lateral pressure in case of

• A. Shallow bin
• B. Deep bin
• C. Both shallow and deep bin
• D. Ultra deep bin

Hint:

Shallow bin $\rightarrow$ Rankine Coulomb formula.
Deep bin (Silo) $\rightarrow$ Janssen's Airy's formula.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Lateral grain pressure against storage walls depends on the geometry of the bin and the plane of rupture of the granular material.
Key Formula or Approach:
\[ L = \frac{1}{2} w h^2 \left( \frac{1 - \sin \phi}{1 + \sin \phi} \right) \quad \text{(Rankine's Lateral Earth/Grain Pressure)} \]

Step 2: Detailed Explanation:
In grain storage bin mechanics:
1. Shallow Bins: Wall friction does not significantly reduce the vertical floor load because the plane of rupture intersects the top free grain surface before striking the opposite wall. Lateral pressure is calculated using Rankine's or Coulomb's formula.
2. Deep Bins (Silos): Lateral wall friction supports a major portion of the grain weight. Lateral and vertical pressures are computed using Janssen's or Airy's equations.

Step 3: Final Answer:
Hence, Rankine's formula is used for lateral pressure in Shallow bins, corresponding to option (A).