56-CS/11 Civil Eng,lneering

Paper-1

Time : 3 hours

Full Maries : 300

The figures in the ｲｩｧｨｴＭｨ｡ｾ､＠ margin indicate marks.

Candidates should attempt Q. No. 1 from Section -A and Q. No. 5 from Section- B which are compulsory and THREE of the

'. remaining questions, selecting at least ONE from ·each ｓ･｣ｴｩｯｮｾ＠

SECTION-A ·

1. Answer any three .of the following : 20x3 = 60 . .

(a) . The beam ABC having depth 80 mm and Width 40 mm is loaded as shown in Figure 1. Find the slope at A and deflection at C if E = 2 x. ＱＮｾＵ＠ N/mm2 using Conjugate .beam

method.

20kN 10kN B

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ｙｑｾＲＱＯＶ＠ (Turnover)

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(b) A shaft of 100mm diameter is subjected. to a bending moment of 8 kN-m and a twisting moment of 12kN-m at a .certain cross-section . Calculate the maximum direct stress induced in the section and specify the position of the plane on which it acts. Taking v = 0.3, find the stress -which acting alone, will produce,the same maximum strain. .

(c) Design a thick walled cylinder of a 100mm internal diameter for an internal pressure of 55MPa such as to provide a factor of safety of 2 against any yielding in the cylinder. The

·yield stress of steel tension is 250MPa. (d) Compute and show the shear flow on the thin

walled channel section in Figure 2, if the vertical shear fo·rce is 8.0kN,· also locate the position of shear center.

8 ｾ＠ ＴＰｭｭｾ ﾭ

ｊｊｾｾＱＪｾ］］］］］］ｾﾷ＠ A

100mm -

:-+

c . --- ·---··-+1mm

" ,!; . . ｾＭ｢］］］］］ＺＺｴｊ＠ T ·1 mm D E

Figure 2 ·

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• • • Iii ｾ＠

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. 2. (a) Analyze the frame shown in Figure 3. Draw

the bending moment diagram. 30

-200kN B C -

El co·nstant 6m

D A 5m

Figure3 . . . (b) A unifo1111ly distributed load of intensity 2kNI

m, 5m long crosses a simply supported

gi-rder of span 20m from left to right._

Determine the maximum positive and

ｮｾ｡ｴｩｶ･ Ｎ＠ shear force and bending moment

at a section am· from··-left hand support.

Using Influence line diagram, calculate the

absolute maximum shear force and·

. maximum bending moment. - 30

(c) Analyse the continuous beam (Figure 4) of

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varying cross-section using displacement

method of analysis.

20kN/m 80kN

2m (I)

I ｾＫＴＭＭＭＭ 6m -. ---...1---. - 4m -__....•I · Figure 4

: 3. (a) Design a beam-column welded ｣ｯｮｮ･｣ｴｩｾｮ＠

for a· moment of 120 kN from a beam ISMB ·

500 to a column ISSC 200 ｵｳｩｾｧ＠ moment

plates ·and web angles. The properties of

ISMS 500 are as follows.

Mass= 86.9kglm, sectional area= 111 an2,_

Breadth of flange = 180 mm, thickness of

flange· = 17.2 mm, thickness of web=. ·

ＱＰ Ｎ ｾ＠ mm, lxx = 45200-cm4, lyy.= 1370'cm4,

Zxx = 1810 cm3, Zyy = 152 an3, rx = 20.2 em,

ry = 3.52 em. the ーｾｯｰ･ｲｴｩ･ｳ＠ of ISSC 200

·are as follows .

. . Mass= 60.3 kg/m, sectional area= 76.8

cm2, Breadth of flange = ··2000·· mm,

thickness of flange = .15 mm, thickness of

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.

web= 9.0 m·m, lxx = 5330 cm4 , lyy = 1370

cm4 , Zxx = 553 cm3 , Zyy = 153 cm3 • rx =;

8.48 em, ry = 4.46 em. 20

(b) Design a built up ｢･ｾｭ＠ by providing a flange

·plate only on the compression flange of

·ISMB-400 using ｳｴ･ｾｬ＠ of grade fy = 250 MPa.

The-effective -span of the beam is 6.0 m and

is subjected to a uniformly distributed ｾｯ｡､ Ｎ＠

of 45 kN/m. The Compression flange is

restrained laterally. ｣ｾ＠ for ｾ･ｦｬ･｣ｴｩｯｮＮ＠ The

· propetties of ISMB 400 are as follows.

·Mass= 61.5 kg/m, sectional area= 78.4

an2, Breadth of flange= 140 mm, thickness

of flange = 16.0 mm, thickness of web = .8.9 mm, lxx = 20500 cm4, lyy. = 622 cm4,

Zxx = 1020 an3, Zyy = 88.9 an3, rx = 16.2 ｾﾷ＠

. ry = 2.82 em. . · 20

(c) _ .Design a simply supported ·welded plate

girder · over a span of 16 m to carry ·an

superimposed UDL of 40 kN/m and two . .

concentrated loads of 200 kN at 4m from

｢ｯｾ＠ sides. Design. the section and ·stiffners

required for the girder. 20

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4. (a) A rectangular column of effective height of 4.0 m is subjected to a cf:laracteristic .axial load of 800 kN and bending ｭｯｭ･ｮｾ＠ of 1 00 kNm about the major axis of column. Design a suitable section for.the column so

that the width should not exceed 400 mm. Use the minimum percentage ·of longitudinal

steel. Assume fy = 415 Nlmm2 and fck = · . 20 N/mm2. 20

(b) A dog-logged staircase for a ｾ･ｳｩ､･ｮｴｩ｡ｬ＠ flat ·

consists of 18 steps, each of 300 mm tread

and 180 mm rise, with an intermediate

landing 1.2 m in width at the middle. The · width of staircase is also 1.2 m. If the flights

are equal number of steps, ｾ･ｳｩｧｮ＠ the staircase and detail the steel, Assume fy = 415 N/mm2 and fd< = 2.0 Nimm2. . . 20

(c) A concrete beam of symmetricall-sedion·

spanning 8m has the width and thickness of

flanges equals to 200 and 60 mm respectivelY. The overall depth of beam is 400 mm. The thickness of web is 80 mm·.

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The beam is pre-stressed by a ｰ｡ｾ｡ ﾷ ｢ｯｬｩ｣＠

cable with an eccentricity of 150 mm at the -center and ·zero at the supports with an

effective force of 100 kN. The live load .on the ·beam is 2 kN/m. Draw the stress . .

disbibution diagram at the central section for : (i) Pre-stressed + self weight (Considering density of cor:-tcrete = 24 kNJm3). (ii} Pre-stressed + self vveight + live load. 20

SECTION-S • . .

5. Attempt any three of the following :

(a) A cylindrical empty bucket 450. mm ·in diameter and 750 mm long is forced with it r

open end first into water until its lower edge is 6m below the surface. Determine the force required to maintain position,

· ｾｳｳｵｭｩ Ｍ ｮｧ＠ ｴｨｾ＠ trapp.ed air remains at constant temperature ､ｾｲｩｮｧ＠ the whole operation. Atmospheric pressure = 1.01 bar. ;:The WiiU thickness and-weight of the buCket may be COO$idered as negligible. 20

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.... .! >.

(b) (i) Define and dJfferentiate between Local

and Convective acceler.ations with

reference to fluid kinematics.

· (ii) ·In an incompressible flow, the velocity

vector is given by :

v = Ｈｾ＠ + yZ2)i + (3t + xy2)j + (xy-2xyZ-

6tz)k

Verify whether the continuity equatio11-is

satisfied. Determine the acceleration vector

at point having coordinates {2,2,2) at t= 2.0 .

. 6+14 = 20 . .

.(c) An open cylindrical ｶ･ｳｳｾｾ＠ 180 mm in . . .

diameter and 450 mm deep is filled with /

water upto the top .. E;stimate ｾ Ｎ ｶｯｬｵｭｾ ｟ ｯｦ＠

water left in the vessel when· it is rotated ·

about its vertical axis :. (i) with a speed ·of

200 r.p.m and (ii) with a speed of 400 r.p.m.

8+12 = 20

(d) Derive ｾ＠ Heuygen-Poiseuilla Equation for

flow ·of :viscous fluid in circular pipes.

mentioning all assumptions. · · 20

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ｳ ｾ＠ · (a) (i) . What -is _meant by "most economica-l

,_

· aection _·of a channeV'·? Derive the

｣ｯｮ､ｩｾｩｯｮ＠ ｾｯｲ＠ a trapezoidal channel .

section . .

(ii) Design a concrete lined channel to carry

a disc.harge of 500m3/s at a slope of 1

in 4000. The side slopes of channel

may be taken as 1·:1. The Manning's

coefficient for the lining is 0.014.

Assume the ー･ｲｭｩｳｾｩ｢ｬ ｟ ･＠ velocity in the

section as 2.5mls. 2+6+12 = 20-

(b) A hydraulic jump occurs in a V-shaped

channel-having sides sloping at 45°. Derive

an ｾｵ｡ｴｩｯｮ＠ ｲ･ｾ｡ｴｩｮｧ＠ the two depths and flow rates. If the depths before and after the jump ·

in the -above channel are 0.5m and 1.0m,

detennine the flow rate and Froude numbers·

. before and after the jump. 1 0+4+6 = 20

. ·.·.-.··(c) :::_ (i): · Differentiate between Impulse Turbine

-and ·Reaction Turbine .

. (ii} :The impeller of a· centrifugal pump

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· having-external and intemal ､ｩ｡ｭ･ｾ＠

500 mm and 250 mm respectively,

. width at outlet _50 mm and running at

(9) ＨｔｵｭｾＩ＠

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1200 rpm -works agains.t a head of

48m. The velocity of flow through the

inpeller is ·constant and equal to 3.c:mls.

The vanes are set·back at an angle of ..

40° at outlet. Determ.ine· inlet vane

angle, work done by. the impeller on

water per second,:·and manometric -

efficiency. . ' · 6+14 = 20

7. (a) Prove ｾ＠ the effect of capillary rise in a soil

mass is to increase the effective sbess at all

levels within soil mass.

Also explain the construction of Newmark's

lnftuenoe Chart to esti a ate 1he wrticaJ.stJess

ｾ＠ a loaded area of iregular shape . .

10+10=·20

. · (b) (i) Explain cleady ｾ｡ｮ､･ﾷｳ＠ method . .

to ､ｾ＠ lbe cca:fticient of conso-

lidation.

{ii) A certain layer has ｡ｾ＠ ｯｦｾＭ

con.aldaied, 80 n•1• of selllement had . .

occurred. For a ｾ､｡ｹ＠ and laa:litg

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conditions.-ho\v much-selllcc ne:et would-

occur at the;_end of ｯｮ･Ｍｾｲ＠ and four

years respective1y.: if the thickness of

_::- . : ＼ｾ｟ｮｻＧ Ｚﾷ Ｎ Ｚﾷ＠ ｴｨｩｳ Ｎ ｮ･ｷｴ｡［･ｲ Ｎ ｷ･ｲ･ ｾ ＲＵｭ＿＠ Ｍ ＸＫＱＲｾＲＰ＠

· - (c)"-• (i) What is ｭ･｡ｨｦ｢ｹ ｾ＠ 'direct stw;tar tesr.

. ｾ ﾷ＠ ...

'triaxial stt·ear(test• and 'unconfined

｣ｯｭｰｲ･ｾｳｦ､ｮ Ｍ t.-st• ? What are the

special feab.iteS: *"t uses of each ?

(ii) A consolidated-undrained test was

conducted on a soil sample with cell

pressure 100kNifn2. The deviator sbiESS

· . at failure was observed· to be 60kNfm2. The soil is known to have a cohesion

c' = 0 and angle of shearing resistance

t' = 30° (referred to effective stress)

and undrained cohesion cu = 0 and

angle. ot·shearing 1esistance •u = 13.30

＼ｾｴｯ＠ totar stress>. What was the

8. (a) Fxplakt deady the special considerations ·to

be made while analysing stability of

. ･ｭ｢｡ｮｫｭ･ｾ＠ (i) at the end of· construction

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.·. ｾ ﾷ＠ . .

(ii) at the ·.end ·of:sudden draw down and (iii) after. a' lo·ng ·time, when a state of · equilibrium ｾ ＺＺ ｬ･｡｣ｨ･､Ｎ＠ 20 -

. . Discuss ｴｨ･ ｾ ｴｳ Ｎ ｣ｯ｣ｴ･＠ ·method for estimating the ｢･｡ｲｩｮｧ ｩ Ｙ｡ｰ｡ｾｩｴｹ＠ of soil. Also ､ｪｾｾｳｳ＠... group acti()fl .. 9f, pile". 12+8 = 20

.:_. ·: · (c)· (j) Define and d .ifferentiate between Active

Earth Pressure and Passive Earth . - . . . . . .. . .

Pressure._· ·

(ii) A retaining wall has a vertical back and

7.32 m high. The soil ｩｾ＠ sandy loam having a unit weight 17.3 kNim2,

·cohesion = ·. 12 kN/m2 , .; ］ ﾷ ＲｯｾＮ＠

Neglecting wall friction, determine the

thrust on the waH. The upper surface of the wall is horizontal. 6+14 = 20

. . .

ＭｾＭＭﾷＭＭＭＭ

va.:.21m (100)- .( 12.) 58-CS/11

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