Solved Previous Paper Civil Engg. (GATE) 2008

A continuous beam is loaded as shown in the figure below. Assuming a plastic moment capacity equal to M_P, the minimum load at which the beam would collapse is

The Young's modulus of a wire of of length L and radius r is Y Nm². If the length is reduced to L/2, and radius r/2, its Young's modulus will be

In the design of a reinforced concrete bean the requirement for bond is not getting satisfied. The economical option to satisfy the requirement for bond is by

A person standing on the bank of a canal drops a stone on the water surface. He notices that the disturbance on the water is not traveling up-stream. This is because the flow in the canal is

A stable channel is to be designed for a discharge of Q m³/s with silt factor f as per Lacey’s method. The mean flow velocity (m/s) in the channel is obtained by

The capacities of “One-way 1.5 m wide sidewalk (persons per hour)” and “One-way 2-lane urban road (PCU per hour, with no frontage access, no standing vehicles and very little cross traffic)” are respectively

A combined value of flakiness and elongation index is to be determined for a sample of aggregates. The sequence in which the two tests are conducted is

Three values of x and y are to be fitted in a straight line in the form y = a + bx by the method of least squares. Given: ^{$\sum x= 6, \sum y=21, \sum x^2\ and\ \sum xy = 46,$} the values of a and b are respectively

The equation ^{$k_x\frac{\partial^2h}{\partial x^2} + k_z \frac{\partial ^2h}{\partial z^2} = 0$}can be transformed to^{$\frac{\partial^2h}{\partial x_1^2} + \frac{\partial ^2h}{\partial z^2} = 0$}by substituting

If probability density function of a random variable X is
f(x) = x² for – 1_^$\le$ x_^$\le$1, and
= 0 for any other value of x
Then, the percentage probability ^{$p \left(}

• \dfrac{1}{3} \le x \le \dfrac{1}{3}
  \right) $is

A vertical PQ of length L is fixed at its top end P and has a flange to the bottom end Q. A weight W is dropped vertically from a height h (<L) on to the flange.
The axial stress in the rod can be reduced by

The base width of an elementary profile of gravity dam of height H is b. The specific gravity of the material of the dam is G and uplift pressure coefficient is K. The correct relationship for no tension at the heel is given by

Unfactored maximum bending moments at a section of a reinforced concrete beam resulting from a frame analysis are 50, 80, 120 and 180 kNm under dead, live, wind and earthquake loads respectively. The design moment (kNm) as per IS: 456- 2000 for the limit state of collapse (flexure) is

A rigid bar GH of length L is supported by a hinge and a spring of stiffness K as shown in the figure below. The buckling load (P_cr) for the bar will be

The maximum shear stress in a solid shaft of circular cross section having diameter subjected to a torque T is $\tau$ . If the torque is increased by four times and the diameter of the shaft is increased by two times, the maximum shear stress in the shaft will be

The members EJ and IJ of a steel truss (shown in the figure below) are subjected to a temperature rise of 30^oC. The coefficient of thermal expansion of steel is 0.000012 per ^oC per unit length. The displacement (mm) of joint E relative to joint H along the direction HE of the truss is

A reinforced concrete column contains longitudinal steel equal to 1 percent of net cross sectional area of the column. Assume modular ratio as 10. The loads carried (using the elastic theory) by the longitudinal steel and the net area of concrete are P_s and P_c respectively. The ratio P_s/P_c expressed as percent is

Cross section of a column consisting of two steel strips, each of thickness t and width b is shown in the figure below. The critical loads of the column with perfect bond and without bond between the strips are P and P₀ respectively. The ratio P/P_o is

The stepped cantilever is subjected to movements, M as shown in the figure below. The vertical deflection at the free end (neglecting the self weight) is

A pile of 0.50 m diameter and length 10 m is embedded in a deposit of clay. The undrained strength parameters of the clay are cohesion = 60 kN/m² and the angle in internal friction = 0. The skin friction capacity (kN) of the pile for an adhesion factor of 0.6, is

A footing 2 m x 1 m exerts a uniform pressure of 150 kN/mm² on the soil.
Assuming a load dispersion of 2 vertical to 1 horizontal, the average vertical stress (kN/m²) at 1.0 m below the footing is

A saturated clay stratum draining both at the top and bottom undergoes 50 percent consolidation in 16 years under an applied load. If an additional drainage layer were present at the middle of the clay stratum, 50 percent consolidation would occur in

A weir on a permeable foundation with down stream sheet pile is shown in the figure below. The exit gradient as per Khosla’s method is

A test plate 30 cm x 30 cm resting on a sand deposit settles by 10 mm under a certain loading intensity. A footing 150 cm x 200 cm resting on the same sand deposit and loaded to the same load intensity settles by

Water emerges from an ogee spillway with velocity = 13.72 m/s and depth = 0.3 m at its toe. The tail water depth required to form a hydraulic jump at the toe is

A volume of 3.0 x 10⁶ m³ of groundwater was pumped out from an unconfined aquifer, uniformly from an area of 5 km². The pumping lowered the water table from initial level of 102 m to 99 m. The specific yield of the aquifer is

A river reach of 2.0 km long with maximum flood discharge of 10000 m³/s is to be physically modeled in the laboratory where maximum available discharge is 0.20 m³/s. For a geometrically similar model based on equality of Froude number, the length of the river reach (m) in the model is

The flow of water (mass density = 1000 kg/m³ and kinematic viscosity = 10^-6 m²/s) in a commercial pipe, having equivalent roughness k_s as 0.12 mm, yields an average shear stress at the pipe boundary = 600 N/m² . The value of k_s / _^$\delta$ (_^$\delta$ being the thickness of aminar sub-layer) for this pipe is

An outlet irrigates an area of 20 ha. The discharge (I/s) required at this outlet to meet the evapotranspiration requirement of 20 mm occurring uniformly in 20 days neglecting other field losses is

Determine the correctness or otherwise of the following Assertion [a] and Reason [r]
Assertion: The crown of the outgoing larger diameter sewer is always matched with the crown of incoming smaller diameter sewer.
Reason: It eliminates backing up of sewage in the incoming smaller diameter sewer.

The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. the area of the reduced plan is measured as 81 cm², the actual (m²) of the survey is

A water treatment plant is required to process 28800 m³/d of raw water (density = 1000 kg/m³, kinematic viscosity = 10^-6m²/s). The rapid mixing tank imparts a velocity gradient of 900 s^-1 to blend 35 mg/I of alum with the flow for a detention time of 2 minutes. The power input (W) required for rapid mixing is

The 5-day BOD of a wastewater sample is obtained as 190mg/I (with k = 0.01h^-1).
The ultimate oxygen demand (mg/I) of the sample will be

A rectangular channel 6.0 m wide carries a discharge of 16.0 m³/s under uniform condition with normal depth of 1.60 m. Manning’s n is 0.015.

The channel width is to be contracted. The minimum width to which the channel can be contracted without affecting the upstream flow condition is

Beam GHI is supported by the pontoons as shown in the figure below. The horizontal cross sectional area of each pontoon is 8 m², the flexural rigidity of the beam is 10000 kN-m² and the unit weight of water is 10 kN-m³.

When the middle pontoon is removed, the deflection at H will be

The ground conditions at a site are shown in the figure below.

The total stress, pore water pressure and effective stress (kN/m²) at the point P are, respectively

A column is supported on a footing as shown in the figure below. The water table is at a depth of 10 m below the base of the footing.

The net ultimate bearing capacity (kN/m²) of the footing based on Terzaghi’s bearing capacity equation is

A rectangular channel 6.0 m wide carries a discharge of 16.0 m³/s under uniform condition with normal depth of 1.60 m. Manning’s n is 0.015.

The longitudinal slope of the channel is

A column is supported on a footing as shown in the figure below. The water table is at a depth of 10 m below the base of the footing.

The safe load (kN) that the footing can carry with a factor of safety 3 is

An automobile with projected area 2.6 m² is running on a road with speed of 120 km per hour. The mass density and the kinematic viscosity of air are 1.2 kg/m³ and 1.5x10^-5 m² /s, respectively. The drag coefficient is 0.30.

The drag force on the automobile is

A rectangular channel 6.0 m wide carries a discharge of 16.0 m³/s under uniform condition with normal depth of 1.60 m. Manning’s n is 0.015.

A hump is to be provided on the channel bed. The maximum height of the hump without affecting the upstream flow condition is

An automobile with projected area 2.6 m² is running on a road with speed of 120 km per hour. The mass density and the kinematic viscosity of air are 1.2 kg/m³ and 1.5x10^-5 m² /s, respectively. The drag coefficient is 0.30.

The metric horse power required to overcome the drag force is

A light house of 120 m height is just visible above the horizon from a ship. The correct distance (m) between the ship and the light house considering combined correction for curvature and refraction, is

A road is provided with a horizontal circular curve having deflection angle 55^o and centre line radius of 250 m. A transition curve is to be provided at each end of the circular curve of such a length that the rate of gain of radial acceleration is 0.3 m/s³ at a curve required at each of the ends is

The length and bearings of a closed traverse PQRSP are given below

The missing length and bearing, respectively of the line SP are

A direct shear test was conducted on a cohesion-less soil (c = 0) specimen under a normal stress of 200 kN/m². The specimen failed at a shear stress of 100 kN/m².
The angle of internal friction of the soil (degrees) is

A pre-tensioned concrete member of section 200 mm × 250 mm contains tendons of area 500 mm² at the centre of gravity of the section. The pre-stress in tendons is 1000 N/mm². Assuming modular ratio as 10, the stress (N/mm²) in concrete is

A reinforced concrete structure has to be constructed along a sea coast. The minimum grade of concrete to be used as per IS: 456-2000 is