Mechanics of Solids Question Papers
Post on 05-Mar-2016
46 Views
Preview:
DESCRIPTION
Transcript
7/21/2019 Mechanics of Solids Question Papers
http://slidepdf.com/reader/full/mechanics-of-solids-question-papers 1/10
'.
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
7/21/2019 Mechanics of Solids Question Papers
http://slidepdf.com/reader/full/mechanics-of-solids-question-papers 2/10
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 .
7/21/2019 Mechanics of Solids Question Papers
http://slidepdf.com/reader/full/mechanics-of-solids-question-papers 3/10
7/21/2019 Mechanics of Solids Question Papers
http://slidepdf.com/reader/full/mechanics-of-solids-question-papers 4/10
7/21/2019 Mechanics of Solids Question Papers
http://slidepdf.com/reader/full/mechanics-of-solids-question-papers 5/10
7/21/2019 Mechanics of Solids Question Papers
http://slidepdf.com/reader/full/mechanics-of-solids-question-papers 6/10
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]
7/21/2019 Mechanics of Solids Question Papers
http://slidepdf.com/reader/full/mechanics-of-solids-question-papers 7/10
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
7/21/2019 Mechanics of Solids Question Papers
http://slidepdf.com/reader/full/mechanics-of-solids-question-papers 8/10
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]
7/21/2019 Mechanics of Solids Question Papers
http://slidepdf.com/reader/full/mechanics-of-solids-question-papers 9/10
7/21/2019 Mechanics of Solids Question Papers
http://slidepdf.com/reader/full/mechanics-of-solids-question-papers 10/10
top related