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Roll No. .......................... . ,

Total No. of Questions: 09] ...;.,

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[Total No. of Pages : 03

B.Tech. (Sem. -3rd) SOLID MECHANICS

SUBJECT CODE: CE -207 Paper ID : [A0604]

[Not«: : Please fill subject code and paper ID .onOMR]

Time: 03 Hours

Instruction to Candidates:

1) Section -A is Compulsory. 2) Attempt any Four questions from Section -B. 3) .Attempt any Two questions from Section - C.

Maximum Marks: 60

Section -A
*Ql) (10 *x 2 *=20)
*

a) Define modulus of rigidity.

b) What do principal plane mean?

c) Write the expression for the co-ordinates of the centre ofMoQr's circle in a.two-dimensional stress ~ystein.

d) What is the nature of variation of bending moment dueto a concentrated load?

. e) What do pure bending of a beam? - t) Write .the expression for maximum deflection of a simply supported

beam of span/carrying a UDLof intensity' *W' *per unit 'length.

g) Define torsional rigidity of a shaft.

h) *Two *shafts having same length and material are joined in series. If the
ratio of their diameters is 2, then what is th~ratio oftheir angles of twist? .

What do modulus of resilience in simple bending mean? Define slenderness ratio of a column.

Section - B

i)

j)

(4 x 5 =*20)
Q2) *Discuss briefly the theories of failure for brittle material.

*Q3) *A solid round bar 3 m long and 5cm in diameter is used as a column with
both ends hinged. Determine the percentage change in the Euler's crippling
'load of the column iqhe end conditions are changed to both end fixed. Take
E= 200 GPa.

*M-82 *[1859} *RT. O. *'

*Q4) *A stepped circular section .bar ABCD, figure shown be,low, of steel
(E = 210 GPa) has the partAB (solid, dja= 50mm, length = *60mm), *partBC
(hollow, od = 30mm, length = 50mm) and part CD (solid, dia = 70mm,~-
length = 50mm). What should.be the inner diameter of part BC if the tensile
stress in it is 200 MPa? What is the totaLelongation of the bar ABCD?. .

**A **BCD

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*Q5) *A bronze bar 3m long with a cross-sectional area of320mm2.is placed between

two rigid walls. At a temperature of -20°C, there is a gap of2.5mm, as shown
in figure 'below. Find the temperature at which the compressive stress in the
bar will be 35 MPa. .
Use *a *= 18.0 x 10-6jOCand E = 80-GPa.

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*Q6) *At a point in a strained material, the principal stresses are 13OMPatensile and
50MPa compressive. Find the resultant stress and its direction on a plane
inclined at 45° to the axis of 130MPa stress by Mohr's circle diagram. Also
dete11llinethe maximum intensity of shear stress in the material.

**Section **- C

(2 x ** 10 **=

*20)*

*Q7) *The torques shown in figure 1 given below are exerted on pulleys A, B, C.
Knowing that both shafts are solid and made Qfbrass (G = 39 GPa), dete11lline
the maximum shearing stress in both the shafts and the angle of twist between
pulleys A and C. r

...

*M-82 *2

*Q8)
*

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Draw the shear force and bending moment diagrams for the beam shown in figure 2. Clearly show the values of shear force and bending moment at important "locations. Point out the point(s) of contraflexure if present. AB = FC =CD = 1m,BF= 3m.

A D

c

*Q9) *The simply supp'ortedbeam ABC (figure given below) carries the uniformly
distributed load between its supports and the concentrated load P at end C.
Find the value ofP for which

(a) There is no deflection at C.

(b) The deflection curve at B is horizontal.

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