Question

Airy’s formula is used for calculation of lateral pressure in
A. CAP structure
B. Deep bins
C. Shallow bins
D. Pusa bins
E. Morai structure
Choose the correct answer from the options given below:

• A. A only
• B. B only
• C. B and C only
• D. D and E only

Hint:

Remember the applications of grain pressure theories:
- Janssen's theory \(\rightarrow\) Deep bins only.
- Airy's theory \(\rightarrow\) Both deep and shallow bins.
- Rankine's theory \(\rightarrow\) Retaining walls and shallow bins (assuming zero wall friction).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Granular materials stored in bulk structures exert both lateral and vertical pressures.
These pressures are calculated using different equations depending on the dimensions of the storage structure (classified as deep bins or shallow bins).

Step 2: Detailed Explanation:
Let us review the classification of bins and the formulas used to calculate their pressures:
- Shallow Bins vs. Deep Bins:
According to Rankine's theory, a bin is classified as shallow if the plane of rupture (plane of shear) intersects the top free surface of the grain before it hits the opposite wall.
If the plane of rupture intersects the opposite wall, the bin is classified as deep.
- Pressure Formulas:
1. Janssen's Formula: This is the standard equation used to calculate lateral and vertical pressures in deep bins (silos). It assumes that a portion of the grain weight is supported by friction against the side walls.
2. Airy's Formula: This is a more comprehensive analytical method used to calculate pressures in both shallow bins and deep bins. It is based on the wedge theory of soil mechanics and takes into account the friction between the grain and the wall, as well as internal grain-on-grain friction.
Therefore, Airy's formula is applicable to both deep bins (B) and shallow bins (C).

Step 3: Final Answer:
The correct option is (C).