Question

When a mass of grain having an angle of internal friction of 30 degrees is stored in a bin, what will be the Rankine's earth pressure coefficient?

• A. 1
• B. 0.5
• C. 0.33
• D. 0.45

Hint:

Recall the formula relating Rankine's lateral pressure coefficient to the angle of internal friction.

Answer 1

The Correct Option is C

Step 1: Grain bins are designed for the lateral pressure exerted by the stored grain mass on the bin wall. Rankine's theory gives the ratio of lateral (horizontal) pressure to vertical pressure as an earth pressure coefficient.

Step 2: Rankine's coefficient of lateral pressure is \[K = \dfrac{1-\sin\phi}{1+\sin\phi}\] where \(\phi\) is the angle of internal friction of the stored material.

Step 3: Here \(\phi = 30^{\circ}\), so \(\sin 30^{\circ} = 0.5\).

Step 4: Substituting, \[K = \dfrac{1-0.5}{1+0.5} = \dfrac{0.5}{1.5} = 0.333\]

Step 5: Rounded to two decimal places, \(K = 0.33\), which matches option 3. The other values, 1, 0.5, and 0.45, do not come from this formula for \(\phi = 30^{\circ}\) and can be ruled out.

Note: the source paper prints the angle as "30 degrees C" by a scanning slip, angle of internal friction is measured in degrees, not degrees Celsius.