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Printed Pages; 4 TME303

(Following Paper ID and Roll No. to be filled in your Answer Book). ~.'

PAPER 10: >4071.' .'

B.Tech(SEM III) QDD SEMESTER THEORY EXAMINATION 2009-10

STRENGTH OF MATERIAL

(a) Derive compatibility equations in Cartesian 10co-ordinat~s.

(b) A solid circular shaft is required to carry 10a torque 40 kNm and a bending moment30 kNm. If yield stress cry in a simpletensile test on a material of the shaft wasfound to be 260 N/mm2, find· the minimumrequired diameter of the shaft according todifferent theories of failure. Take a factorof safety F.S. = 2.5 and Poisson's ratio = 0.3.

(c) The state of stress at a point is given by 10the following array of terms :

[~ ~ ~]Determine the principal stresses and

direction c-asines of maximum principal stress.

Attempt any two parts of the following(a) Mentioning Assumptions involved derive

Bending Equation (Flexural formula).(b) The simply supported beam shown in Fig.l

has a flexural rigidity EI = 8 x 106 Nm 2.

Find deflection at 'C' and '0'.

40kN

BCD·,1m -.j+- 2m -.1+ 1m -./+- 2m

Fig. 1A hollow steel shaft 4 m long is to transmit150 kW power at 150 RPM. The total angleof twist in this length is not to exceed 2.50

and the allowable shear stress 60 N/mm2.Determine the inside and outside diameters,

if N = 0.082 X 106 Nhpm2.

Attempt any two parts of the following(a) Derive critical loads on the basis of Euler's 10

method for column with both ends hinged.(b) A close-coiled helical spring is to have a 10

stifIiless of 100 N/m in compression, withH maximum load of 45 N and a maximumsh'tlring stress of 120 N/mm2. The solidI '11 Ih of the spring (i.e. coils touching) is1\ 111Ill, find :(j) '.I'll' wire diameter(i i) 'l'h' In an coil radius and( j) 'I'll' llU mber of ~oils.~'I'll ( , () 1\ x 105 " /mm2

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(c) A short column of hollow cylindrical section 10has outer diameter 300 rom and inner diameter200 mm and carries a load of 300 kN at adistance of 80 mm from the centre of thecolumn.

(i) Find the extreme stresses and draw thestress diagram.

(i i) What should be the maximum eccentricityso that no tension develops in the column?

Attempt any two parts of the following :

(a) In a thin-walled cylindrical shell, determineHoop stress or circ\Jmferential stress,Longitudinal stress: "ftoop str;in andLongitudinal strain.

(b) A spherical tank has a diameter of 20 m 10and wall thickness 15 mm. If the permissiblestress in the material is 120 MPa, find themaximum pressure at which a gas can bestored in the tank. Find the increase indiameter and volume of the tank due tothe gas pressure. Take E = 200 GPa andPoisson's ratio = 0.3.

(c) A cylindrical pressure vessel of external and 10internal radii 0.3 m and 0.2 m respectivelyis subjected to an internal hydraulic pressureof 20 N/mm2. If E = 2 x 105 N/mm2 andf.l = 0.3, find the stresses at the internal andexternal surtaces and calculate the changein internal and external diameters.

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5 Attempt any two parts of the following :

(a) Describe briefly : 10

(i) Bending of beams with large, initialcurvature

(ii) Unsymmetrical bending.

(b) A curved bar of rectangular cross-section has. 10width 40 mm and depth 60 mm and has aradius of curvature 80 mm about the

~_centroidal axis parallel to width. Find thebending streses at the inner and outer facescaused by a moment of 500 Nm tending toincrease the curvature.

(c) For a channel section shown in Fig. 2, find 10the shear stress at the junction of the flangeand the web and at the centre of the webdue to a shear force of 50 kN. Locate theshear centre.

1.- - - lOmmlOOmm-+j T

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