PAPER · I
SECTION A
l. Attempt any four of the following:
body of mass 20 kg (homogeneously spread) rests on a plane inclined at 60 degree with the horizontal The body is acted upon by a hurizootnl force p1, passing through its centre of gravity. What is the maximum value of P so that tho body will not slide down? Take mew as 0.2). 10)
A ball thrown from the top of a50 m high building with a horizontal velocity of 6.25 m.p.s.hits the ground, rebounds and hits the ground a second time, and so on. What are the horizontal distances from the point of the throw where the first and second hits on the ground take place? Take coefficient of restitution as 0.6 10)
A smooth rectangular plate of 0.8m width and 25 m length, when towed through water(v=10m2/s. and p=9998 kg/m3). experiences a drag of 1540 N on both sides together. Consider Cj tO be between 0.001 and 0 455/(log10 re)2.52 (the applicability of which must also be checked, determine the velocity of towing of the platc.
A bullet of mass 6gm, cross-sectional area 18mm2 and cd=0.43, is fired horizontally at an initial velocity of 300 m/s. determine after what flight distancc horizontally will the bullet's velocity reduce lo 120 m/s due to air resistance, without any added mass effect Take mass density of air as 1.208 kg/m3.
A triangular channel with central angle of 120degrees has a critical depth of 0.4 m. What is the corresponding discharge?
Sketch the mohr's circle for the following data: sigma 1 30 MPA;sigma 30mpa. Also, determine the maximum shear stress.
two point loads of 160 KN {leading) and 80 kN (following), spaced 6 m apart, roll from left to right over a symmetrical three- hinged parabolic arch. Find the horizontal thrust, the bending moment and shear force at a section 6m from the left-end hinge when the lending load is over the central hinge. Span and rise of the arch are '24m and 6m. respectively.
A trussed.frame designed and supported as shown (with ED= DC 6m. each) carries three vertical loads as indicated. Determine the forcece in each member.
<img src='./qimages/1459-2b.jpg'>
3.(a)flow in a wide rectangular channel is controlled by a vertical siuice gate, with depth of flow upstream and downstream of the gate being 1.6m and 0.4 respectively,if the gate is suddenly dropped so as to completely stop the follow to the downstream, what would be the height of the resulting surge?
Oil of mass density 8:50kg/m3 and dynamic viscosity 0.023 poise flows through a 50mm
diameter pipe of length 400m at the rate of 0.18I/s Determine.
the Reynolds' number of the flow:
the pressure gradient
iii) the wall shear stress:and
the power required to maintain the flow:
4. simply supported beam 20 m long has properties I at the outer quarters 21 in the inner half,
and uniform E throughout, as shown in the figure. it carries a concentrated load of 10kn
at mid-span determine the mid-span deflection by the ConJugate-beam method.
<img src='./qimages/1459-4a.jpg'>
A thick cylinder of 100 mm internal diameter is SubJected to an lnternal pressure of 80- Mpa if the maximum shear stress is to be restricted to 150 MPa. what should be thickness of the wall of the cylinder?
Determine the u-component of velocity distribution to satisfy continuity condition given that
u=ax2-by3+cz; and w=bx3+cy=2azx.
A centrifugal pump with outer impeller diameter of 300mm and inner impeller diameter of 150mm runs at 850 r.p.m radial velocity of water through the pump is 2m/s. the vanes are set back at 30degrees to the outer rim. determine the velocity of water at the outlet.

SECTION B
5. Attempt any four of the following(4xl0 40)
A masonry retaining wall with earth retained on its vertical face to its top level without any
surcharge, has top and bottom widths of 1.2 m and 4m. respectively. ond is 6 m high.
Properties of the retained soil are;

unit weight 16 kN/m3, coeficient of friction at the base+0.45.
Find the facor of safety a gainst
overturning and
sliding
wt. of of mosonry 20 kN/m3

concrete mix has w/c ratio of 0.47 and water content of 185 kg/m3· The weight of coarse
aggregate is 992 kg/m3 Air content is 2 per cent find the weight of fine aggregate to be used
per m3 of the mix. take density of cement-3.15, Coarse aggregate-2.70. fine aggregate
2.65. Also determine the unit weight of the mix.
unconfined compressive strength of clay in a rogion is 70kN/m2 the denSity of this soil is 20kn/m3 and its pie=o, What is the maximum depth of cutting with side slope 2h to 1v (for which the stability number is o.17) with a factor of safety of 1.57 l fpto whot slope angle would this d¢p!h value hold good?

A cylindrical specimen of saturated soil fails under an axial stress of 110 kN/m2 in an unconfined compreSSion test. with the failure plane making an angle of 500 to the horizontal. Calculate the cohesion and angle of internal friction of the soil.
A pile group of 9piles. placed in 3 rows l m apart between rows, with 1m spacing in the perpendicular direction between adjacent piles. carries a pointed column load of 2000 kN with eccentricities of 400 mm ond 200 mm with reference to the principnl central directions. Find the maximum and minimum loads carried by the respective candidate piles, and identify these piles on a diagram Also, taking the column to be 500mm 500mm, determine the BM and SF at the column faces.(10)
A M20 concrete beam of rectangular cross-section 250mm wide. 400mm deep overall is reinforced with Fe 415 high-strength deformed bars, It is to b designed to support a limit-state collapse bending moment of 120 Design the reinforcement.
A simply supported welded plale girder. 12m span, is made up of two flange plates each 300
mm=12mm. and a web plate 500mm .8mm. with overall depth of 524mm in the form of
symmetrical I section Assuming that the compression chord is laterally restranined. determine
the safe u.d.I. admissible, given that permissible flexural stress is 150MPA nd Eis 200 OPa. also
design the welded connection between the flange and the web:and
check for adequacy critcrion for deflection.
Adopt 100 MP AS the permissible shear.
A normally consolidated clay layer is 7.4 in thick had an initial in-situ void ratio of 0.986. Consolidation test at mid-height of the layer recorded the following data: Moist mass of soil specimen -20.7 kg: volume of the specimen before drying-o.o11m3 dried mass of the specimen-16.3 kg; specific gravity of soil grains- 2.68. Estimate the consolidation settlement.
A strap foundotion supports two columns, A and 5.4 m apart. transmitting 750 kN and 1050 k.N, respectively. inclusive of weight of their square footings also. The outer edge of the footing under column A is 0.5 in from the axis of the column. Pressure below both the footings has to be uniform. Compute the needed dimensions of the footing (in plan view only) assuming SBC of soil as 150 kN/m2 Also draw the bending moment diogram for the strap beam.
A RCC circular underground water tank is shown in section with dimensions as shown,
together with W.T. location w.r.T G.L What should be the diameter of the base slab to be
safe against uplift? (Take pie 28° and unit weight as 16kN/m3 for the soil). Also. determine the intensity
of horizontal carth pressure at the top and bottom levels of the base slab.
<img src='./qimages/1459-8a.jpg'>

A simply supported pre-stressed rectangular beam.300 mm wide. 720 mm deep overall. 10 in
span, supports a u.d. l. of 6 exclusive of self-weight.it is provided with a single linear
prestressing cable with effective prestressing force of 420 KN at a maximum cccemricity of
281 mm at mid-span and .a minimum eccentricity of 120 mm at supports. Find the. maximum
fibre stresses at
quarter span and
mid-span