Mechanics of Solids Question Papers

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'.

C.40942"

Pages: 2) Name .......................................

...

Reg. ••... .........•........ ..••.•••

FOURTH SEMESTER

B.TEeH.

(ENGINEERING) DEGREE EXAMINATION

APRIL 2013

ME

09 403/PTME 09 402-MECHANICS OFSOLIDS

'.

(2009 Scheme)

[Regular

I

i n p r ~ m e n t

I Supplementary]

Time:ThreeHours

Maximum:

70

Marks

'.

~

Part A

Answer ali questions

1.

Show

that

thevolumetricsttain ofabody thealgebraicsumofhelinearstrainsinthreemutually

perpendiculardirections:

2. Derive expressionforthe

shear

stressproducedinacircularshaftsubjectedtotorsion.

3. Statetheassumptionsinvolvedinthetheoryofsimplebending.

4;

Defineandexplainprincipalplanesandprincip'alstre"sses.

5.

·Writethe assumptionsmadein Ewer'stheoryofcolumns.Alsomentionitslimitations

(5x2=':10marks)

·Pa r t

Answer any

four

questions

1. •Definestress,strain andelasticity;DerivearelatioI1betweenstressandstrain ofanelasticbody.

. 2. Show

that

thevolumetricstrainofabodyis thealgebraicsumoftheiinearstrainsinthreemutually

perpendiculardIrections.

3. Derive

an x p r e s s i ~ m

forthe

shear

stressproducedinacircularshaftwhichissubjectedtotorsion.

Whataretheassumptionsmadeintheabovederivatiori?

. .'

.

. Themaximumshearstressexperiencedbyashaftofdiameter70mmis70MPa.Computeshear

stressat a

pOint

wherethe radiusof35 mm.

5. ExplainMaximumprincipal

strain

theory,Maximumstrainenergytheoryoffailure

that

governs

thedesignof astressedsystem.

6.. DerivetheEulersformulafor acolumnhingedat bothends

..

(4)(5= 20marks)

par te

1. ThreebarsmadeofCopper,ZincandAluminumare equal'len\tthand havecross-sectionalareas

of400,800arid1200mm

2

respectively.Theyarerigidlyconnectedat their ends. I f compound •

memberissubjectedtoalongitudinalpullof350kN,.estimatetheproportionofloadcarried

by

each

bar

and induced

stresses. Take

elastic'moduliof Copper,Zinc

and

Aluminumto be

1.2x

105

mm

2

1.0)(

105N mm2

and0.89)(

105 mm

2

respectively.

Or

Turn over



2

C40942

2. ,Themodulus

of

rigidityof amaterial is0.8x 105 N/mm

2

.When a6

mm

x 6mm rodofthis material

.was subjectedto an'axial pullof 3600N itwasfo\lnd that the lateral dimensionof the rod changed

L

.

to

5.9991mm

)(

5:9991mm'

Findthe

Poisson'sratio and the modulus of elasticity.

'.

3. Asolidcircular

h a f t

transmits 75KW

at 2OO.r

.p.m.Calculate

the

shaft

diameter if

the twist

in the

shaft isnot exceed10 in 2metres length

ofshaft and the

shearing

t r e s s

is limitedto 50N/mm

2

;

Take

C

=

1',JtOSNhmil

2

•

. . .

Or

4. Drawshear forcebenctin.

g

moment diagramsfor

the

cantilever beam shownin,Fig.1

.

II

...

tO

.

Fig.I,

.

5; Two,wooden

planks

·150mm x

50mm

each are connected

to

formaT-section of abeam. f

the

·movementof 3.4 kNm

is

appliedaround the horizontalneutral axis,inducingtension belowthe

neutral

axis,· find the

stresses

at the extreme fibersof the cross-section.Alsocalculate·the

total

.

tensileforceon thecross-section. ' .

Or

6. A steel girder o f ~ u n i f o r m section, 14 metres long is simply

supported

at its ends. t carries

concentratedJoadsol'90'kNand 60

kN.at

twopoints3metres and 24.5

meters

fromthe twoends

respectively.Calculate:

(a)

The

def1eetion

ofgirder at the

pointsunder

the

twoloads;

(b) The

maximum

e ~ t i o n

Take

E

=

200GNIm2.

7. TheArectangular block ofmaterial issubjectedto atensile stress of looN mm

ona

one plane

and

atensilestress of 50 ~ ona

plane

at

right

angles,Wgetherwith shear stresses of SOpaon

the

sameplanes. .

·

Find:

(a)

The

directionofthe principalplanes

(b) The·magnitude of the principalstress.

.

(c) , The magnitude of the

greatest shear

stress.

Or

, 8.

A

coluinn with one end hingedand·other end fixed hasa

length

of 5m.

and

ahollowcircular

r o s s ~ s e t i o n

of

outer diameter

100IIiIn and wallthickness10nun.

IfE

= 1.S

x

105

N mm

2

•

and

crushingstrengthf= 350N/mm2 findthe loadthat

the

columnmay·carry with afactorof safety

· of2.5 acCording

to

Euler theory and Rankine-Gordontheory. Take a =114500.

(4x

10

=40 marks)

r .



4. (a) (i) Find the shear deflection, bending def lection and total d eflection for an edge loaded

cantilever beam of r ectangular cr oss-section.

(7 mark s)

(ii) In an attempt to make a beam which combines light weight with high stiffness, 6 mm.

steel plates ar e r ivetted to the top and bottom of an aluminium alloy I beam for whichIxx = 2375 cm.4 By what r atio is the stif f ness of the I beam increased by the addition of

steel plates and what is the ratio of the bending stress in steel and aluminium?

E t 1= 2 x 106 kgf/cm.2, EA}= 0.667 x 106 kgf /cm.2see .

Analyse the bending of a cantilever beam with a point load at the free end for stresses and

compare the solutions with those obtained using elementary str ength of materials approach.

(15 marks)

(6 mark s)

1000, 720 and 600 ~cm!cm.

Explain the "Theory of columns and buck ling".

In a three element d ata rosette, the strain readings ar e

respectively. Find the pr incipal strains.

5. (a) (i)

(ii)

( b) Deter mine the Euler's cr ippling load f or a hollow cylindrical steel column of 38 mm. exter nal

d iameter and 33 mm internal diameter . The length of the column is 2.4 m. and is hinged

at both end s. Also determine the buckling load by R ankine's f ormula. Use

constants: 320 N/mm.2 and 1/7500, E = 205 GPa.

(15 mark s)

[4 x 15 = 60 marks]



THIRD SEMESTER B.TECH. (ENGINEERING) DEGREE

EXAMINATION, JUNE 2009

MEIAM 04 304-MECHANICS OF SOLIDS

Answer all quest ions.

1. (a) Define Poisson's ratio, Hookes Law and bulk modules of elasticity.

(c) State and ex plain theor y of tor sion.

(d) Draw the bend ing moment and shear f orce d iagrams for the cantilever loaded at its free

(e) Discuss the moment area method f or d eflection, stating the relevant theorems.

(f ) Explain: Shear formula from eq uations of equilibrium of beams.

(g) Explain the secant for mula for columns with eccentric loading.

(h) In a three element data rosette, the strain readings ar e 1000, 720 and 600 ~ em. /

r espectively. Find the principles str ains.

2. (a) (i) Write a short note on :

Saint Venant's pr inciple.

(ii) What is the necessity of stress-strain relations? What is their minimum number necess

f or the complete solution of a general problem in elasticity?

(b) (i) A sleeve of brass is just ste pped over another sleeve of steel at a temper ature of 65°C

now, the assembly cools to room temperature of 26°C, find the str ess in br ass and s

and mutual pressure between the two sleeves. Mean diameters and thicknessof brass and steel sleeves are 51.25 cm., 47.5 cm. and 1.25 cm. and 2.5 cm E &a for s

= 2 x 106 kgf / cm2. and 12 x 10-6 / DC. E & a for br ass = 9 x 105 kgf / cm2•

9 x 10-6 1°C .

(10 mar

(5 mar



3. (a) Wr ite a short note on :

(i) Singularity functions and their uses.

(ii) Sign conventions for bend ing moment and shear force.

(iii) Torsion of thin hollow sections.

(5 mark s)

(5 mark s)

(5 marks)

( b) A solid shaf t is req uired to tr ansmit 330 k W at 120 r . p.m. The shear str esses in the mater ial

should not exceed 80 MPa. Find the d iameter r equired. If the shaft is r e placed by a hollow

shaft with a diameter ratio 3 : 5, maximum shear str ess r emaining the same, calculate the

percentage saving in weight that could be obtained .

4. (a) (i) Ex plain the two reasons because of which unsymmetrical bending may take place, with

exam ples.

(ii) Find the shear deflection, bending deflection and total d eflection for an edge load ed

cantilever of rectangular cr oss-section.

-(b) A steel beam of symmetr ical I section 150 mm. d eep has flanges 80 mm. wide and 10 mm

thick and 6 mm. thick . Compar e its f lexur al strength with that of a beam of r ectangular

section of same weight, the depth being twice its bread th.

5. (a) At a point in a str ained mater ial, the resultant intensity of stress across a plane is 50 MPa

tensile, inclined at 45° to the nor mal. The nor mal component of intensity of stress across a

plane at right angles to it is 40 MPa. tensile. Find the princi pal stresses and princi pal planes.

Locate also the plane of maximum shear str ess and the magnitude of maximum shear stress.

(15 mar k s)

(6 marks)

(ii) Derive the f ormula f or valid ity limit of Euler 's formula in ter ms of yield str ess and VI

r atio.

(9 mar k s)

[4 x 15 = 60 mar k s]

Mechanics of Solids Question Papers

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