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GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

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Question : 43 of 65

Marks: +1, -0

A

3 \text{ m} \times 3 \text{ m}

square precast reinforced concrete segments to be installed by pushing them through an existing railway embankment for making an underpass as shown in the figure. A reaction arrangement using precast PCC blocks placed on the ground is to be made for the jacks.

At each stage, the jacks are required to apply a force of

1875 \text{ kN}

to push the segment. The jacks will react against the rigid steel plate placed against the reaction arrangement. The footprint area of reaction arrangement on natural ground are:

c=17 \text{ kPa} ; \varphi=25^{\circ}

\gamma=18 \text{ kN/m}^3

. Assuming that the reaction arrangement has rough interface and has the same properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure is

Your Answer:

Solution:

FOS against shear failure

= \frac{\text{ Strength }}{\text{ Applied load }} = \frac{(c+\sigma \tan \varphi) A}{P}

\sigma = \frac{N}{A} = \frac{4 \text{ kN/m}^2 \times 37.5 \text{ m}^2 \times 7.5 \text{ m}}{37.5 \text{ m}^2}

=24 \times 7.5 \text{ kN/m}^2

\Rightarrow \quad \text{FOS} = \frac{(c+\sigma \tan \varphi) A}{P}

= \frac{(17+24 \times 7.5 \times \tan 25^{\circ}) \times 37.5}{1875}

\text{FOS}=2.0187

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