7/21/2019 Mechanics of Solids Question Papers http://slidepdf.com/reader/full/mechanics-of-solids-question-papers 1/10 '. C.40942" Pages: 2) Na me ....................................... ... Reg. ••... .........•........ ..••.••• FOURTHSEMESTER 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 thevolumetric sttain ofabody thealgebraicsumofhelinearstrainsinthreemutually perpendiculardirections: 2. Derive expressionforthe shear stressproducedinacircularshaftsubjectedtotorsion. 3. Statetheassumptionsinvolvedinthetheoryofsimplebending. 4; Defineandexplainprincipalplanesandprincip'alstre"sses. 5. ·Write the assumptionsmade in Ewer'stheoryofcolumns.Alsomentionitslimitations (5x2=':10 marks) ·Part Answer any four questions 1. • Definestress,strainandelasticity;DerivearelatioI1betweenstressand strain ofanelasticbody. . 2. Show that thevolumetricstrainofabodyisthealgebraicsumoftheiinearstrainsinthreemutually perpendiculardIrections. 3. Derive an xpressi ~m forthe shear stressproducedinacircularshaftwhichissubjectedtotorsion. Whataretheassumptionsmadeintheabovederivatiori? . .' . . Themaximumshearstressexperiencedbyashaftofdiameter70 mmis 70 MPa.Computeshear stress at a pOintwhere the radius of35 mm. 5. ExplainMaximumprincipal strain theory,Maximumstrainenergytheoryoffailure that governs thedesign of astressedsystem. 6.. DerivetheEulersformulaforacolumnhinged at bothends .. (4)(5= 20marks) parte 1. ThreebarsmadeofCopper,ZincandAluminum are equal'len\tth and havecross-sectionalareas of400,800arid1200 mm 2 respectively.Theyarerigidlyconnected at their ends. If compound • memberissubjectedtoalongitudinalpullof350kN,.estimatetheproportionofloadcarried by each bar and induced stresses. Take elastic'moduli of Copper,Zinc and Aluminumto be 1.2 x 105 mm 2 1.0)( 105 N mm2 and0.89)( 105 mm 2 respectively. Or Turn over
Calicut University Mechanics of Solid Question Papers
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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
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•