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tnriian F;-.ieSf .... u.,• I D-VSF-L-PRA I
-CIVIL ENGINEERING
Paper I
I Time Allowed Three Hours! !Maximum Marks: 200!
INSTRUCTIONS
Candidates should aUempt Questions No. I and
5 which are compulsory, and any THREE of the
remaining questions, selecting at least ONE
question from each Sect_ion.
Assume suitable data, if considered necessary,
and indicate the same' clearly.
Standard notations are given in the questions
and these notations have their usual meanings,
unless otherwise indicated.
All questions have equal marks.
Marks allotted to each part/subpart of a
question are indicated against each.
Answers must be .wriUen in ENGLISH only •
D-VSF-L-PRA 1 !Contd.l

SECTION A
1. Attempt any four of the following 10x4=40
rigid bar AD is pinned at A and attached to
the bars BC and ED as shown in the figure. The
entire system is initially stress free and the
weights of all bars are negligible.The
temperature of the bar BC is lowered 25°C and
that of bar ED is raised 25°C. Neglecting any
possibility of lateral buckling, find .the normal
stress in bars BC and ED. For BC, which is
brass, assume E 90 GPa, alpha 20 x 10-6/degC and
for ED, which is steel, take E 200 GPa and
alpha= 12x10-6/deg C. The cross-sectional area of BC
is 500 mm2 and of ED is 250 mm2. 10

<img src='./qimages/1369-1a.jpg'>

Two long wooden planks form a T-section of a
beam, as shown in figure. If this beam transmits
a constant vertical shear of 3000 find the
necessary spacing of the nails between the two
planks to make the beam act as a unit. Assume
that the allowable shear force per nail is 700N. 10

<img src='./qimages/1369-1b.jpg'>

(c)The L-shaped bar shown in figure is of uniform
cross-section 60 mm x 120 mm. Calculate the
total strain energy.
Take E 2x105 MPa and G 0·8 x 105 MPa
<img src='./qimages/1369-1c.jpg'>

(d)Two pipes A and B are connected in parallel
between two reservoirs M and N. The details of
the two pipes are as follows
<img src='./qimages/1369-1d.jpg'>

What difference in the water surface elevations of
the reservoirs M and N would produce a flow of
0·30 m3/s of water from the higher reservoir to
the lower one Neglect minor losses. 10
(e)The time period T of water surface wave is
known to depend on the wavelength lamda, depth of
flow density of the fluid row, acceleration due to
gravity g and the surface tension sigma. Using
Buckingham's pie-theorem, obtain the
dimensionless form of functional relationship. 10

2.(a)The cross-sectional area of each member of
the truss shown below is A 400mm2 and
E 200GPa.
(i)Determine the vertical displacement of
joint C if a 4 kN force is applied to the
truss at C.
(ii)If no loads act on the truss, what would be
the vertical displacement of joint C if
member AB were 5 mm too short Use
unit load method.
<img src='./qimages/1369-2a2.jpg'>

(b)Draw the influence line diagram for the truss
shown below for member BG. Determine the
maximum compressive force developed in
member BG of the truss due to wheel loads
crossing the truss. Assume the loads are applied
directly to the truss and move from left to right.
Support A is hinge and Support E is roller. 15
<img src='./qimages/1369-2b.jpg'>

a certain point in a piece of elastic material
there are normal stresses of 30 MPa, tension
and 20 MPa, compression on two planes at right
angles to one another, together with shearing
stresses of 15 MPa on the same planes. If the
loading on the material is increased so that the
stresses reach values of K times those given,
find the maximum values of Kif the maximum
direct stress in the material is not to exceed 80
MPa, and the maximum shear is not to exceed
50 MPa. 10
Find the collapse load for the given frame. Use
kinematic method.
<img src='./qimages/1369-3a.jpg'>

(b)The truss shown below carries a vertical load of
100 kN at A. Determine the displacement of
joint A. Also,calculate. the member forces in
members AB and AC. Use stiffness method only. 8
<img src='./qimages/1369-3b.jpg'>

pipeline carrying water has a 60° reducing
bend in a horizontal plane. The cross-sectional
areas at inlet and outlet of the bend are 1·0 m2
and 0·5 m2 respectively. The pressures at
inlet and outlet of the bend are 40 kN/m2 and
30 kN/m2 respectively. The discharge in the pipe
is measured as 10 m3/s. Calculate the magnitude
and direction of the force required to hold the
bend in position. Take the density of water as
1000 kg/m3. 10
(d)Water flows at a steady and uniform depth of
2·5m in an open channel of rectangnlar
cross-section having base width equal to 4m
and laid at a slope 1 in 1000. It is desired to
obtain critical flow in the channel by providing a
hump in the bed. Calculate the minimum height
of the hump. Also sketch the flow profile and
label salient features. Consider the value of
Manning's coefficient n=0·02 for the channel
surface.
4.(a)A highly viscous oil is to be transported
through a pipe in laminar mode. The discharge
is 30 litres/s and the energy gradient is limited
to 0·02. Estimate the smallest diameter of the
pipe for this purpose. If this diameter is used,
what would be (i)the Reynolds number and
power required per kilometer of the
pipeline Take density and dynamic viscosity.
of oil as 960 kg/m3 and 0·98 kg/m. respectively. 10

rectangular lined canal 0·016) of 4·0m
width has a bottom slope of 0·0009. It carries a
discharge of 15 m3/s and the normal depth is
known to be 2·0m. The flow is non-uniform in a
certain reach. If the depth of flow at section A in
this reach is 2·6m,
(i)Calculate the depth of flow at a section B
which is 500m downstream of section A.
Use direct step method by taking two
steps; one step to depth 2·8m and another
to depth 2·88m.
(ii)Classify the gradually varied flow profile
between A and B. 20
Kaplan turbine has the following features
Outer diameter of the runner 4·5m
Hub diameter 2·0m
Guide vane angle at outer edge of blades 59° ·
Inlet blade angle at the blade tip 19°

The hydraulic and overall efficiencies are 0·92
and 0·90 respectively If the discharge through
the turbine is 120 determine the (i)speed
and (ii)power developed by the turbine. The
discharge at the outlet of the runner can be
taken as axial. Take unit weight of water as
gaama= 9·79 kN/m3. 10

SECTION B
5.Attempt any four of the following 10x4=40
member consisting of two ISA 90 x 90 x 10 mm
back-to-hack welded on one face of a gusset plate
are tack welded at 1000 mm spacing. The
assembly is subjected to tension. Determine
the tension capacity of the member and weld
requirement. Area of cross-section of one
ISA 90 x 90 x 10 is 1703 mm2. Use 8 mm thick
weld in calculations.
<img src='./qimages/1369-5a.jpg'>

(b)Design the shear reinforcement for a factored
shear force of 100 kN. The cross-section iS
250 mm x 400 mm. Assume M 20 grade.
concrete and Fe415 reinforcement. Effective
cover is 35 mm. The shear strength of concrete
(torque is 0·73 MPa corresponding to the
longitudinal steel. Adopt 8 mm diameter as web
reinforcement.

(c)The mass specific gravity of a saturated
specimen of clay is 1·84 when the water content
is 38%. On oven drying, the mass specific
gravity falls to 1·70. Determine the specific
gravity of solids and shrinkage limit of the clay. 10
footing 3 m x 2 m in size, transmits a
pressure of 140kN/m2 on a soil having
E 5 x 104 kN/m2 and mew 0·50. Find the
immediate settlement for the footing at the
centre, assuming it to be flexible footing,
(ii)rigid footing.
For L/B 1·5, Influence factor 1·36 for flexible
and 1·06 for rigid footing.

(e)Undisturbed soil sample of 2m thick stratum,
was tested in the laboratory and the average
value of co-efficient of consolidation was found
to be 2 x 10-4 cm2/sec. If a building is
constructed on this stratum, how long will it
take to attain half the ultimate settlement. Soil
stratum is having double drainage.

An RC beam 300 mm wide and 500 mm deep
overall is reinforced with 4 nos. of 16 mm
diameter on tension face. The effective cover to
centre of reinforcement is 50 mm. Find the
moment of resistance and the safely distributed
load the beam can carry. The span is 5m. 15
Take
fck 20 MPa (Grade of concrete),
fy 415 MPa (Grade of steel) and
unit weight of concrete 25 kN/m3.
(b)Analyze the beam described below using load
balancing concept.
Span of the beam 10·0m
Cross-section 400 x 600 mm (rectangular)
External load 30 kN/m
Unit weight of concrete 24 kN/m3
Prestressing force 1800 kN
Cable profile parabolic
Eccentricity at mid cross-section 155mm
Eccentricity at support section 0 mm

(c)Determine the dimensions of an isolated footing
subject to a factored axial load Pu 1000 kN and
a factored uniaxial moment Mu 120kNm (with
respect to the major axis) at the column base.
Assume that moment is reversible. The safe
bearing capacity of the soil may be taken as
200 kN/m2 at a depth of 1·5m. One side of
footing width is restricted to 2·0m. Assume M 20
concrete and Fe 415 steel.
Calculate the footing depth from one way shear
and two way shear considerations. Shear stress
of concrete is limited to 1·12 MPa.
(Design of reinforcement not necessary). 15
7.(a)The following figure shows a section of a girder
where the bending moment is 2500 kNm and
shear is 600 kN. Design a triple plate shear
splice using 22 mm diameter power driven shop
rivets. Adopt allowable tensile stress of 142 MPa. 20
<img src='./qimages/1369-7a.jpg'>

Area of cross-section of ISA 130 x 130 x 12=29·82 cm2
Double shear strength of rivet 100 MPa.
Bearing strength 236 MPa.
Limit allowable flexural compressive/tensile
stress to 94·5 MPa.

1s Quick Sand Phenomenon
Calculate critical hydraulic gradient for a
coarse grained soil having voids ratio 0·7
and specific gravity 2·70. Discuss the
result. 10
concentrated load of 2000 kg acts on the
surface of homogeneous soil of large extent.
Find the stress intensity at a depth of 15m
(i)directly under load, (ii)at a distance of
7·5m (horizontal). Use Boussinesq
equation. 10
8.(a)An unconfined compression test was conducted
on an undisturbed sample of clay. The sample
had a diameter of 37·5 mm and was 80 mm
long. The load at failure measured by the
proving ring was 28 N and the axial deformation
of the sample at failure was 13 mm. Determine
UCS and Cu of the clay. 10
saturated soil has a compression index of 0·25.
Its void ratio at a stress of 10 kN/m2 is 2·02 and
its permeability is 3·4 x 10-7mm/s.
Compute
(i)Change in void ratio if the stress 1s
increased to 19 kN/m2.
(ii)Settlement if stratum is 5m thick.
(iii)Time required for 40% consolidation if
drainage is two way. 20
Design a square pile group to carry 400 kN in
clay with an unconfined compression strength
of 60kN/m2. The piles are 30cm diameter and
6m long. Adhesion factor may be taken as 0.6. 10