Reg. No. :

B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2010

Fourth Semester

Civil Engineering

CE2252 — STRENGTH OF MATERIALS

(Regulation 2008)

Time: Three hours Maximum: 100 Marks

Answer ALL Questions

PART A — (10 × 2 = 20 Marks)

1. A beam of span 4 m is cantilever and subjected to a concentrated load 10 kN at

free end. Find the total strain energy stored. Take the Flexural rigidity is EI.

2. Write down Maxwell’s reciprocal theorem.

3. A fixed beam of span ‘L’ is subjected to UDL throughout w/m. What is end

moments and moment at the centre?

4. Draw BMD for a propped cantilever beam span ‘L’ subjected to UDL

throughout w/m.

5. Define core of a section and draw the same for a circular section.

6. Write Rankine’s equation for column.

7. Define principal plane and principal stress.

8. State the principal stress theory of failure.

9. What is ‘fatigue strength’ and ‘endurance ratio’ in a fatigue testing of material?

10. Write the Winkler-Bach formula for a curved beam.

Question Paper Code: E3047

E 3047 2

PART B — (5 × 16 = 80 Marks)

11. (a) For the beam shown in Fig. 1, find the deflection at C and slope at D

47mm1040I ×=

E = 200 GPa. (16)

Fig. 1

Or

(b) For the truss shown in Fig. 2, find the horizontal movement of the roller

at D AB, BC, CD area = 8 2cm

AD and AC = 16 2cm

E = 5102 × 2mmN . (16)

Fig. 2

12. (a) For the fixed beam shown in Fig. 3, draw the SFD and BMD. (16)

Fig. 3

Or

E 3047 3

(b) For the continuous beam shown in Fig. 4, draw SFD and BMD all the

supports are at same level. (16)

Fig. 4

13. (a) (i) Derive the Euler’s equation for column with two ends fixed. (8)

(ii) A circular bar of uniform section is loaded with a tensile load of

500 kN. The line of action of the load is off the axis of the bar by

10 mm. Determine the diameter of the rod, if permissible stress of

the material of the rod is 140 2mmN . (8)

Or

(b) Find the greatest length of a mild steel rod of 30 mm × 30 mm which can

be used as a compressive member with one end fixed and the other end

hinged. It carries a working load of 40 kN. Factor of safety = 4,

α = 75001 and 300C =σ 2mmN . Compare the result with

Euler. E = 5102 × 2mmN . (16)

14. (a) (i) Briefly explain spherical and deviatory components of stress tensor.

(6)

(ii) Explain the importance of theories of failure. (4)

(iii) For the state of stress shown in Fig. 5, find the principal plane and

principal stress. (6)

Fig. 5

Or

(b) A circular shaft has to take a bending moment of 9000 N.m and torque

6750 N.m. The stress at elastic limit of the material is 610207 × 2mN

both in tension and compression. E = 610207 × KPa and µ = 0.25.

Determine the diameter of the shaft, using octahedral shear stress theory

and the maximum shear stress theory. Factor of safety : 2. (16)

E 3047 4

15. (a) A rectangular simply supported beam is shown in Fig. 6. The plane of

loading makes 30° with the vertical plane of symmetry. Find the

direction of neutral axis and the bending stress at A. (16)

Fig. 6

Or

(b) A curved bar of rectangular section, initially unstressed is subjected to

bending moment of 2000 N.m tends to straighten the bar. The section is

5 cm wide and 6 cm deep in the plane of bending and the mean radius of

curvature is 10 m. Find the position of neutral axis and the stress at the

inner and outer face. (16)

———————

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Reg, No. I

B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/D EEE 2OT.L .Fourth Semester

Civil Engineering

CE 2252 _ STRENGTH OF MATERIAIS

':

Maximum : 100 rEa-rks

Answer ALL.ciiii:etions.

PARTA-(tO\2=20mafks)

l. State castigliaiot first tt eolJ i '.r1. "'r'.,r,j

2. Calculate t}l.e strain energ5i'itored in the beam shown in f€. 1. EIconstant.

t---+r.- [ +4t

For the flxed beam shown in fig. 2 what is the fixed end moment at A andB.

{Regulation 2008}

Time : Three hours

State any two assumptionslong colurltns.

lr- L' o.'r-Lt2-*Ll2-

Fig. 3

made in the derivation of Euler's formula for

6.

7..

8.

9.

10.

Define 'core' of a sectiott.

State the maximum principal stress tieory.

For the state of stress shovr::r in fig. 4 identify the principal pla'1res'

^ 11nf-'

Fig. 4 i ..:' '., ...l.l.

What is stress concentration?

For the phase section show! in fig. 5 fmd the pioduct Gom€tit of inertiaabout r and / axes. '. i:' .

FiC. 5-

PART B - (5 x 16 = 8O rIrarks)

11. (a) For the beam shown ir hg. 5 fiild the slape alld deflection at 'C'.(8 + 81

{b) (4 For the truss sh6r$4-.ln lig. 7 find the total st ain ener$I stored'lIN B

r E:2x 10s N/mm23 ia Area : AB : 100 mm2tr BC; 100 mm2c AC:80 mm,

Fig. 7

(ii) For tlle trtlss shown in 69. 8 flnd tl1e vertical deflection at C''(1

c Cross sectional area off aI the members : 100

3m mm2

t E=2v 10s N/mm'DJ

Fis. B

2 55241

12 (al A Jixed teo-" tp i: 6 m span and caries a point load 10 kN at 1etrom tefr end. rt also carries a clockwise ;;;;i;i; ilorrr.ichtend,10 kN.m. Draw SFD arld BMD indicating the salient points. (8 + 8)

(b) A continuous beam ABCD in shown in Fig. 9. Draw SID and BMDindicating the salient points. .. d€+l8i

6tn3 ttr/-

"t,,sl& ; ;,,

ta) (i]

tr _t-| i_2 h 2

D

(EI constant tiroughout)

Fig. 9

A rectangular slrur is 25 cIrl x 15 cm. It carries a load of 60 kNat an eccentr.icity of 2 cm in a plale bisecting the thickness.Find the Binimum and .Eaximurlt stresses developed ia thesectron. lE

Derive the Euler's egUation ibr a long cotumn with both endshinged.

(8)

',:.,.'Oi :i' ',:A hollow cylifd?igal cast]..iron {olumn is 3.50 long \rith botherlds fir.ed. Eietermiilef,hc ii&timum diameter of the columlr if ithas to carqr a safe load of 300 kN with a factor of saJety 4.Extemal diarneter is 1.25 times the intemal dia$eter.o = heOO , d. = 550 MN/mr, in RankiDe,s formula. 112)

(ii) D.gfne 'thick cylinder'and draw t}le hoop stress distribution forcylinder.

(ii)

(b) {4

(4t

(a) (0 Slate fl€ shiar strain eners/ theory aid a comment oh it.

I . tt, -for. iastate of shess shown in fig. 10, Iind the principal plarre,pmcrpal stress and maximum shear stress. (L2)i:

.

(4)

3H 5524L

Fis. 10

Or

ln a 4aterial the principal stresses are 50 N/mm'' 40 N/mm' aid

-3o N/rldm,, Caleulate the total strain ener$I' volu(ietric stiair

enersr, shear strain eners/ arld factor of safety on die total €tt

enerry criterion if the material yields at 100 N/mm'! (4 x 4 =

1s. (a) Fig. 11 shows a frame subjected to a load of 3.4 kN fiod,thi:.resulstress at A and B.

' L2()

(b)

"+Er.,Fig. 11

Or

(b) A beam of T-sectio4-.r(flange : 1o0 x 20 mm, webi 150 mm x 10

in 3 m in lengt.h arrd Li4pb, srilP-olted at eods (Fig. 12). It car

2.2 hN

7

l. *

3m(Beam loaded centrally,Load not shown)

Fig. 12

4

2.2 kN ilclined 20e to'rtIrc ve&a1 and passing tlrrough the ce!of the secdon. Calcq{ate the giaximum tensile stress ajld maxir

compressive stress. Al€,o lilld the position of the neutral axis.(7 +

Beg, No :

B.EJB.TeclL DECIREE melfiNarrOr, NOVEMBER/DECEMBm 2011.

Fouith Semest€r

Ciyil Engineeriag

CE 1252 - SIT.ENGI'II Or MATERIAIS

(Regulatiou 2004)

(CoBmoo to B.E. (patt-Time) Ihird Semestei Regulation 2005)te : Three houre

Anawer ALL questions,

PARTA-(10x2=20Earks)

Maximum : 100 marks

L

L

a

{

a

Define Btlair eEer$r.

State Maxwell'e reeiprocal theorem.

State theoreE of three moments.

DifJrentiate bet\reeE dete.minate and indeterEinate beams-

Statc aesuoptione made ia Euler,s theorem,

Defne 'core' of a section.

Ddae a principal plane.

Ihat do you understaud by etress tensor?

Ilefiae'uasymmetrical bendiq,.

Itat i.s meaot by endurauce limit?

restion Pa Code:38237

PARTB-(6x16=80marks)

11. (e) Calcuate the deflection at B and C of a cautilever beam loaded as ehownin Fig. 1- AssuBe E =zx,oi N I mrn2 and I=21OOxlOAmma.

lo 9.,

6)

Fis'1'Or

Find the Horizontal defleetion at joint Bshown in ffg. 2. Take ,=2x105N1,I,.1l 'ardFor all veltical end Horizortal meii*)ers.

of a portal frame troaded asI=850Ox10'mrnr.

diagram for a three spanEI is coDstant for the entire

Fie'2'

12. (a) Find the reactions and end momeDts of a frxed beaE AB of spaD 6.0 Dfrxed at ends A aad B alrd loaded with two concentrated load ol intensity10.0 LN and 18.0 kN acting at a distaDce of 2.0 m and 4.0 m ftom left endA.

Or(b) Draw shear folce atrd benaling moment

continuous beam loadea as shown in Fig. 3.leDgth of the beal6.

Fig.3.

l,r, t,Jl,tu

13. (a) A solid round bar 4,0 m long and 50 Em diameter !i,as found to extend4.6 mm urdet a teneile load of 50 kN, Ttris bar is used as a strut witherls hiaged. DeterEine the buckling toed for the bar and aleo the safe

loail. Aesuoe a factor of safery of 3,0.

Or

(b) Find tle thickness of metal necesaaty for a cylindrical shell of intemaldiaEeter 160 EB to withstaDd an internal preaaune of 6 N/mml. thehaximum hoop atrcss in the eection is not to exceed 30 N/mm2'

14. (a) At a point io a strained oaterial, the principal 6tre88es are 90 N/rnm2(Iensile) aad ,t0 N/mm2 (compree.eive). DeterEiEe the re8ultant it?efa inmagnitude ald direction on a plane iuclined at 60" to the axis of t}remejor principal Btress. AIso calcutiate the maximuE intensity ol shearstress st thot point.

Or

(b) A steel rod ie 2.06 long and 50 mE in diametet. An axial pull ol 100 kNie suildenly applieil to.the md. Caleulate the inatantsneous Btrcsa

inaluced add al6o the maximum elongation produced in the rod. AasumeYounCe modulus is 2 x 106 N/EE9.

15. {a) A beam of T sectiou haviag alioeneions aa flang! : 100 610 x 20 rBm, web: 150 ad x 10 mm is used as a simply supportod beam. The spao of thebea6 is 3.0 !!. It calries a load of 3.6 LN iacliDed at an angle of 20" to thevertical, aa<l the load lioe ie passiog through the centroid of the section'

Calculate the maxirilutE tensile and comp?esaive 8tre88e8, Young'smodulus ie 2 x 1S N/mm'?.

Ot

O) Derive Winkler Bach theory applicablo for beams curved il plaa.

8323?

I

I

I

Reg. No. :

M 0454

B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 201r

FOURTH SEMESTER

CN'IL ENGINEERING

CET255 STRENGTH OI MATERIAI"S - [

. (REGIII,ATION 2OO?)

Time : Three hours Maximum : 100 marks

Anlwer ALL queotions.

. PART A - (10 x 2 = 20 marks)

l. State Maxwell's leciprccal theore&.

2. What is fleant by Btrain enelgy?

3. How will you find th€ reactioa at the plop of a cantilewr bean propped at thefree end?

4. State the advaltages of a frted bean ovel simply supported beam?

5- What is neent by equivalent length of s columrl?

6. Sketch the core of a circular section of diameter 'd',

7. Name the important theories offailures.

. 8. Define the term voludetric etlain.

9. Write down the expreeeion for Wiol<ler'Bach foroula.

10. Defiie endurance limit.

PARTB-(5 x 16 = 80 marks)

ll. U8ing Caetigliano's tbeoreo, dete.mine the Elope and d€flection at theoverhanging enl4 C of a sirnply suppoded beaE AB of span 'U with a ovelharg

IBc oflensth ! iubiect to a clockwise moloent ofM at the &ee end C.-3

Or

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14.

12. A tension bar 5 m long is made up of two parts. 3 m of its length has a crosssectional area of 1000 mm2 while the remaining 2 m has a cross aectional areaof 2000 mm2. An axial load of 100 kN is gradually applied. Find the total strainenergy stored in the bar and cornpare this value with that.obtained in a

uniform bar of same length and hsving the same volume under the same load.TakeE=200kN/mmr.

13. Draw the shear folce and bending moment diagtam for a ffxed beam AB ofspan 6m carrying a urrifoimly distributed load of 6 kN/m over the left half o{the spa[.

Or

A continuous beam ABC of uniform section has the span AB = BC = 6 m. It ishxed at A and simply supported at C. TTre beam is carrying a uniformlydistdbuted load of 6 kN/m throughout the span AB and a concentrated load of20 kN at the mid span of BC. Analyee the beam by the theorem of tbreemoments and draw the shear force and bending moment diagram.

A hollow circular short column of 250 mm exte![al diameter and 200 mminternal diameter carries an axial load of 200 kN. It also carries a load of150 kN on a bracket whose line of action is 200 mm from the axis of thecolumn. Determine the maximum and minirnum stresses at the base of thesection.

Or

16. Determine the crippling load ofa T section 100 mm x 100 mm x 20 Em and oflength 5.5 m when it is used as a strut with both the ends hinged.TakeE=2x10tMPa.

1?. Determine the diameter of a bolt which is subjected to an axial pull of 5 kNtogether with a transverse shear force of 5 kN using the maximum principalstress theory and the maximum pdncipal strain theory.

Or

18. ln a two dimensional stress system, the direct stresses, on t\4'o mutually' perpendicular planes are 120 MPa and o MPa. These planes also carry a

shear stress of 40 MPa. Find the value of d when the shear stlain energy isminimum.

19. A beam of rectangular section 75 mm wide and 125 mm deep i8 subjected to sbending moment of 15 kNm. The. trace of the plane of loading is inclined ati5 degree to Yy axis of the section. Locate the neutral axis of the section andcalculate the maximum bending stress induced in the section.

Or

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20. A central horizontal section of a hook is a symmetrical trapezium 60 mln deep.the inner width being 60 mm and the outer \I/iatfl SO rn_.--p"ii_ot"" tfr"extreme intensitie€ of stress when the hool carries a load of B0 Urt iir" f""aline passing 40 mrn from the inside eclge of the .u"ti"n ^"a-tiu'"".,i"" otcurvaturc being in the load line. ,Also plot the stress ai"t.it"tio"-^".o".. tfl"

secl ion.

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Fourth Semester

I . Question Paper Code: 91225.

B.E.IE.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2014.

Civil Engineering

CE 2252/GE 431OS0100019/101l1 CE 403 - STRENGTH OF MATERIALS

. (Regulation 200S/2010)

(Common to 10111 CE 403 - Strength of Materials for B.E. (Part-Time)Second Semester Civil Engineering - Regulation 2010)

Time: Three hours Maximum : 100 marks

Answer ALL questions.

PART A - (10 x 2 = 20 marks) .

1. A bar of 2 m long, 50 mm wide and 40 'mm height. When it is subjected to ate.nsile load of 60 KN. Calculate the strain energy stored in the bar. Take Er asconstant.

2. Write the principle of virtual work.

3. A cantilever beam 4 m long carries a gradually varied load. Zero starts at freeend to 3 KNIM at the fixed end. Draw the SFD and BMD for the beam.

4. Give the two stages to draw BMD for a continuous beam under any system ofloading.

5. State the middle third rule.

6. What is known as crippling load?

7. Define 'stress tensor'.

S. What is principal strain?

9. Give the reasons for unsymmetrical bending.

10. Write Winkler Bach formula ..

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PART B - (5 x 16 = 80 marks)

11. (a) A bar of uniform cross section A and length L hangs vertically, subjectedto its own weight. Prove that the strain energy stored within the bar is. Axp2xL3

gIven by u = ---'----6E

Or

(b) A simply supported beam having 8 m span and carries UDL of 40 kNIMas shown in fig. (a). Determine the deflection of the beam at its midpointand also the position of maximum deflection and maximum deflection.Take E = 2 X 105 Nzmm- and I = 4.3 X 108 mm+,

Figure (a)

12. (a) A continuous beam ABC of uniform section, with span AB and BC as 6 m.each, -is1ixed at-A and supported a Band C. Span AB-carciea. UDL of __

/" 2 KN/m arid BC having a midpoint of 12 KN. Find the support momentsand the reactions. Also draw the SFD and BMD of the beam.

~ /' Or/"

(b) What is the Clapeyron's theorem of three moments? Derive an expressionfor Clapeyron's theorem of three moments.

Or

13. (a) State the Euler's assumption in column theory. And derive a relation forthe Euler's crippling load for a columns with both ends hinged.

(b) A short length of tube having internal diameter and external diameterare 4 cm and 5 cm respectively, which failed in compression at a load of250 KN. When a 1.8m length of the same tube was tested as a strut withfixed ends, the load failure was 160 kN. Assuming that ere in Rankin's

formula is given by the first test, find the value of the constant a in thesame formula. What will be the crippling load of this tube if it is used asa strut 2.8 m long with one end fixed and the other hinged?

2 91225

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14. (a) A mild steel shaft is subjected to an end thrust producing a stress of120 MPa and the maximum shearing stress on the surface arising from:torsion is 90 MPa. The ·yield point of the material in simple tension wasfound to be 450 MPa. Calculate the factor of safety of the shaftaccording to

(i) Maximum shear stress theory and

. (ii) Maximum distortion energy theory.

Or

(b) State the Haigh's theory. Also explain the maximum strain energytheory .

. 15. (a) A beam of rectangular section 20 mm x 40 mm has its centre line curvedto a radius of 50 mm. The beam is subjected rto a bending moment of4 x 105 N.mm. Determine the intensity of maximum stresses in the beam.Also plot the bending stress across the section.

Or

(b) A water main of 500 mm internal diameter and 20 mm thick is runningfull. The water main is of cast iron and is supported at two points 10 mapart. If, the cast iron and water weigh 72000 N/m3 and 10000 N/m3

respectively. Find the maximum stress in the metal.

3 91225

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