# Civil Engineering - GATE 2012 Paper Solution

The estimate of $\int\limits_{0.5}^{1.5}\frac{dx}x$ obtained using Simpson’s rule with three-point function evaluation exceeds the exact value by

The annual precipitation data of a city is normally distributed with mean and standard deviation as 1000 mm and 200 mm, respectively. The probability that the annual precipitation will be more than 1200 mm is

The infinite series corresponds to

The Poisson’s ratio is defined as

The following statements are related to bending of beams:

I   The slope of the bending moment diagram is equal to the shear force.
II  The slope of the shear force diagram is equal to the load intensity.
III The slope of the curvature is equal to the flexural rotation.
IV The second derivative of the deflection is equal to the curvature.

The only FALSE statement is

If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on all faces of the cube is p, then the maximum shear stress developed inside the cube is

As per IS 456:2000, in the Limit State Design of a flexural member, the strain in reinforcing bars under tension at ultimate state should not be less than

Which one of the following is categorised as a long-term loss of prestress in a prestressed concrete member?

In a steel plate with bolted connections, the rupture of the net section is a mode of failure under

The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column with the same dimensions and material, but with pinned ends, is equal to

The effective stress friction angle of a saturated, cohesionless soil is 38$°$. The ratio of shear stress to normal effective stress on the failure plane is

Two series of compaction tests were performed in the laboratory on an inorganic clayey soil employing two different levels of compaction energy per unit volume of soil. With regard to the above tests, the following two statements are made.

I  The optimum moisture content is expected to be more for the tests with higher energy.
II The maximum dry density is expected to be more for the tests with higher energy.

The CORRECT option evaluating the above statements is

As per the Indian Standard soil classification system, a sample of silty clay with liquid limit of 40% and plasticity index of 28% is classified as

A smooth rigid retaining wall moves as shown in the sketch causing the backfill material to fail. The backfill material is homogeneous and isotropic, and obeys the Mohr-Coulomb failure criterion. The major principal stress is

An embankment is to be constructed with a granular soil (bulk unit weight = 20 kN/m3) on a saturated clayey silt deposit (undrained shear strength = 25 kPa). Assuming undrained general shear failure and bearing capacity factor of 5.7, the maximum height (in m) of the embankment at the point of failure is

A trapezoidal channel is 10.0 m wide at the base and has a side slope of 4 horizontal to 3 vertical. The bed slope is 0.002. The channel is lined with smooth concrete (Manning’s n = 0.012). The hydraulic radius (in m) for a depth of flow of 3.0 m is

A rectangular open channel of width 5.0 m is carrying a discharge of 100 m3/s. The Froude number of the flow is 0.8. The depth of flow (in m) in the channel is