Question Bank • QB_APE_STOR_014 NAT • 2 Marks

Section 6: Agricultural Process Engineering

Storage Systems

Subtopic: Godowns, bins and grain silos

Question Statement:

In a shallow grain storage bin, grain with an internal angle of friction $\phi = 26.0^\circ$ exerts lateral pressure on a retaining wall. According to Rankine's earth pressure theory, the ratio of passive lateral earth pressure coefficient ($k_p = \frac{1 + \sin\phi}{1 - \sin\phi}$) to the active lateral earth pressure coefficient ($k_a = \frac{1 - \sin\phi}{1 + \sin\phi}$) is ________ (round off to two decimal places).

Answer Key:

6.56

Step-by-Step Solution & Explanation

Multi-Approach Solution: **Method 1: Direct Ratio Formula** $\sin(26.0^\circ) = 0.43837$ $k_a = \frac{1 - 0.43837}{1 + 0.43837} = \frac{0.56163}{1.43837} = 0.39046$ $k_p = \frac{1 + 0.43837}{1 - 0.43837} = \frac{1.43837}{0.56163} = 2.56106$ $\frac{k_p}{k_a} = \frac{2.56106}{0.39046} = 6.5591 \approx 6.56$ **Method 2: Squared Relationship** $\frac{k_p}{k_a} = \left( \frac{1 + \sin\phi}{1 - \sin\phi} \right)^2 = (2.56106)^2 = 6.5590 \approx 6.56$
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