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MPSC AE CE Mains 2019 Official (Paper 1)

Option 2 : \( \frac{{1 + \sin \left( \phi \right)}}{{1 - \sin \left( \phi \right)}}\)

Building Material & Concrete Technology

15793

20 Questions
20 Marks
25 Mins

__Concept:__

__Coefficient of Active Earth Pressure Coefficient:__

\({K_a} = \frac{{1 - \sin \left( \phi \right)}}{{1 + \sin \left( \phi \right)}} = {\tan ^2}\left( {45 - \frac{\phi }{2}} \right)\;\)

__Coefficient of Passive Earth Pressure Coefficient:__

\({K_p} = \frac{{1 + \sin \left( \phi \right)}}{{1 - \sin \left( \phi \right)}} = {\tan ^2}\left( {45 + \frac{\phi }{2}} \right)\;\)

__Point to be remembered:__

For any value of shearing angle, the product of active earth pressure coefficient and passive earth pressure coefficient will always equal 1.

\({K_a} \times {K_p} = \frac{{1 - \sin \left( \phi \right)}}{{1 + \sin \left( \phi \right)}} \times \frac{{1 + \sin \left( \phi \right)}}{{1 - \sin \left( \phi \right)}} = 1\)