NapurStudents - TGPCET · N KT /K S /17/7287 3 P.T.O b) A solid shaft transmits 300 kw at 200 rpm....

NKT/KS/17/7287 1 P.T.O

B.E.Fourth Semester (Mechanical Engineering) (C.B.S.) Mechanics of Materials

P. Pages : 3 NKT/KS/17/7287

Time : Three Hours Max. Marks : 80

_____________________________________________________________________

Notes : 1. All questions carry marks as indicated.

2. Solve Question 1 OR Questions No. 2.






8. Due credit will be given to neatness and adequate dimensions.

9. Assume suitable data whenever necessary.

10. Illustrate your answers whenever necessary with the help of neat sketches.

11. Use of non programmable calculator is permitted.

12. Use of design data book is permitted.

1. a) A circular steel bar is subjected to various forces as shown in fig. Q. 1 a. Determine the

total elongation in the bar. 25 mm/N102E .

40kN 60mm P30

kN70kN

600mm 800mm 600mm

Fig. Q.1(a)

30mm 40mm

6

b) A steel rod of 30 mm diameter and 200mm long is rigidly held between supports.

Determine the stress induced in the bar when temp. is raised by 70°C if.

i) Supports are rigid.

ii) Supports yield by 0.6 mm 25 mm/N102E , C/1012 6 .

7

OR

2. a) A metallic block of dimensions 300 mm x 200 mm x 100 mm is loaded with 80 kN (T),

100 kN (C), 90 kN (T) along x, y and z direction resp. Determine the volumetric strain

and change in volume 25 mm/N102E,3.0 .

7

b) Define Elastic constant [E] and modulus of rigidity [G] and Poisson's ratio () & Derive

the relation between E, G and .

6

*0512*

NapurStudents.Org

NKT/KS/17/7287 2

3. Draw the shear force and bending moment diagram for the beam shown in fig. Q. 3.

AB C D E

3m 2m 3m 2m

4 kN/m4 kN

Fig. Q.3

14

OR

4. a) Prove the relation

R

E

I

M

y

for simple and pure bending.

7

b) A test beam has square cross-section 30 mm x 30 mm. It is simply supported over a span of

1.2 meter and loaded with a point load at mid span. Failure takes place at load of 800 N.

Using the factor of safety 7.5. Calculate the safe rate of UDL over a simply supported span

of 5 meter if the cross section is 120 mm x 300 mm deep.

7

5. A simply supported beam as shown in fig. Q. 5 carries point loads. Find :

i) Slope and deflection under each load.

ii) Maximum deflection

iii) Point at which maximum deflection occurs.

AB C

D

40 kN 30 kN

3m3m2m

Fig. Q.5

13

OR

6. a) Define the terms principle planes and principle stresses.

2

b) At a point in a strained material, the intensities of tensile stresses on two planes at right

angle to each other are 40 N/mm2 and 20 N/mm2, accompanied by a shear stress of 30

N/mm2. Find the magnitude and direction of principal stresses analytically and verify it

graphically using Mohr's circle.

11

7. a) Deduce the torsion equation

L

C

RJ

T

7

NapurStudents.Org

NKT/KS/17/7287 3 P.T.O

b) A solid shaft transmits 300 kw at 200 rpm. Determine the diameter of the shaft if the shear

stress is not to exceed 50 N/mm2 and twist in a length of 3 m not exceeding 2°, if the

maximum torque is 1.25 times the mean torque C = 1 x 105 N/mm2.

7

OR

8. a) Prove that the crippling load by Euler's formula for a column having one end fixed and

other end free is given by 2

2

4

EIF

l

7

b) A round column of length 3m has both ends fixed. Determine the minimum diameter of

column if it has to carry a permissible load of 300 kN with a factor of safety of 3.

Take 1600

1,mm/N400 2

e in Rankine's formula.

7

9. a) What do you mean by creeping ? Discuss the conditions responsible for crack

propagation.

6

b) Prove that the strain energy stored in a body due to shear stress is given by V

C2U

2

7

OR

10. a) A load of 5 kN falls by 100 mm on a collar rigidly attached to a vertical rod of diameter

20 mm and length 3m. Find the instantaneous expansion of the bar. 25 mm/N102E .

6

b) A 2m long bar of 30 mm diameter is subjected to an axial load of 2 kN. Determine the

maximum stress and strain energy developed in a bar if load is applied -

i) Gradual

ii) Sudden 25 mm/N102E

7

11. a) Determine the suitable size of a bolt subjected to direct tensile load of 45 kN and a shear

force of 25 kN by using two theories of failure. Material of bolt is SAE 1035. The factor

of safety is 3 & Poisson Ratio = 0.3.

8

b) What do you mean by stress concentration suggest suitable remedies to overcome them.

5

12. A pulley is keyed to a shaft midway between two bearings. The shaft is made of SAE

1030. The bending moment at pulley varies from - 100 N.m. to 250 N.m. & the torque on

shaft varies from - 75 N.m. to +150 N.m. Obtain the diameter of shaft for infinite life.

Assume factor of safety of 2 size factor 0.85 and surface finish factor of 0.90.

13

**********

NapurStudents.Org

NKT/KS/17/7287 4

NapurStudents.Org

KNT/KW/16/7287 1 P.T.O

B.E. Fourth Semester (Mechanical Engineering) (C.B.S.) Mechanics of Materials Paper – V

P. Pages : 4 KNT/KW/16/7287


_____________________________________________________________________












12. Use of Design data book is permitted.

1. a) Explain with neat sketch the stress strain curve for a ductile material.

5

b) Find the change in length of the bar ABCD subjected to axial forces as shown in fig 1 (b).

Take E = 200 GPa.

40 kN

0.4

meter

1.5 meter 1.5 meter

80 mm

50 mm

40 kN

fig. 1 (b)

8

2. a) A steel rod of 20 mm diameter passes centrally through a copper tube of 50 mm external

diameter and 40 mm internal diameter. The tube is closed at each end by rigid plate of

negligible thickness. The nuts are tightened lightly home on the projecting parts of rod. If

the temperature of assembly is raised by 65ºC, Calculate the stresses developed in copper

and steel.

Take : GPa100EGPa200E coppersteel

Cº1018αCº1012α 6copper

6steel

8

b) A steel bar of square cross-section 40mm x 40mm, 600 mm long is observed to stretch 0.225

mm under a pull of 120kN. The same bar in single shear test under a force of 125kN shows

the distorsion of original right angle corners by 0.00125 radians. Determine the values of

the four elastic constants (E, G, K, 1/m). of the material.

5

*0151*

NagpurStudents.Org

KNT/KW/16/7287 2

3. Draw the shear force and Bending moment diagram for the beam shown in fig. (3).

Also find the point of contraflexure if any.

10 kN10 kN/meter

AC

1 meter2m 3mB

fig. 3

14

4. a) The chassis of an automobile is made of square hollow (mild steel) pipe. The load on chassis

is shown in figure (4a). Find the cross-section of hollow square pipe if permissible bending

stress is 100 MPa for the maximum bending moment.

10 kN/meter

0.6 meter 3 meter 0.6 meter

fig. 4(a)

10

b) Prove that the maximum shear stress over a rectangular section is 2

3 time the average

shear stress :

averagemax τ2

3τ .

4

5. A I-section shown in fig. 5(i) is loaded as shown in fig. 5 (ii). Using Macaulay's method,

Calculate the slope at 'D' and defection at 'C'.

Take E = 200 GPa.

10mm

10 mm

10 mm

160 mm

80 mm

AC D

E

B

5 kN/m10 kN

1 mm 1 mm 1 mm 1 mm

fig. 5 (i) fig. 5 (ii)

13

NagpurStudents.Org

KNT/KW/16/7287 3 P.T.O

6. a) Determine Analytically the principal stresses and location of principal planes and maximum

shear stress for an element shown in fig. (6). Check the answer by using Mohr's circle

method.

90 MPa

75 MPa

110 MPa

75 MPa

110 MPa

90 MPa Fig (6)

8

b) Derive the differential equation of the deflection curve.

Mdx

ydEI

2

2

5

7. a) A hollow steel shaft 3m long transmits a torque of 24kN.m. The total angle of twist is not

to exceed 2.5º and the allowable shear stress is 90 MPa. Determine the inside and outside

diameter of shaft. G = 85 GPa.

7

b) Define Polar modulus (Zp). And derive the polar modulus values for solid circular bar and

hollow circular section.

6

8. a) A pin jointed strut is 2.5 meter long. It is tubular having inner diameter 30mm and outer

diameter 40mm. Calculate crippling load by Rankine's theory. Assume crushing load 330

MPa and Rankines constant 7500

1a .

8

b) What is equivalent length of a column? Enlist the equivalent length and the corresponding

crippling loads for the various end conditions.

5

9. a) A vertical steel bar 55 mm in diameter and 3 meter long has to transmit shock energy of

100 Joule. Calculate the maximum instantaneous stress induced and the maximum

elongation? Take E = 200 GPa.

8

b) Prove that the strain energy stored in a body due to shear stress is given by

ν.C2

τU

τ shear stress; C modulus of rigidity ν volume of the body.

5

10. a) What is creep? Explain in brief how fracture occurs due to creep with the help of creep

curve.

6

b) An unknown weight falls by 30 mm on to a collar rigidly attached to the lower end of a

vertical bar 4 meter long and 1000 mm2 in cross-section. If the maximum instantaneous

extension is found to 3.75mm, find the corresponding stress and the value of unknown

weight. Take E = 200 GPa.

7

NagpurStudents.Org

KNT/KW/16/7287 4

11. a) Define and draw stress-time curve for fluctuating stress; repeated stress and reversed stress.

6

b) A shaft shown in fig. 11 (b) is subjected to bending load of 4kN, pure torque of 1250 N.m

and an axial pulling force of 18kN. Calculate the stresses at points P and Q.

60 mm

300 mm

1250 N.m.

18 kN

4 kN

P

Q

Fig. 11 (b)

8

12. A shaft made of Annealed SAE 1040 is subjected to a torsional moment that varies from

330 N.m clockwise to 110 N.m. counter clockwise and an applied bending moment at a

critical section varies from 440 N.m to -220 N.m. The shaft is of uniform cross-section and

no key-way is present at the critical section. Determine the required shaft diameter. Take

facter of safety '2'; size factor of 0.85 and a surface finish factor of 0.62. The expected

reliability is 95%; temperature factor is 1.

*********

14

NagpurStudents.Org

TKN/KS/16/7375 1 P.T.O

B.E. (Mechanical Engineering) Fourth Semester (C.B.S.) Mechanics of Materials Paper - V

P. Pages : 4 TKN/KS/16/7375


_____________________________________________________________________












12. Use of Design Data Book is Permitted.

1. a) Define various elastic constants. And Derive relation between modulus of Elasticity &

Modulus of Rigidity.

6

b) A steel plate having dimensions 360mm x 220mm x 30mm is subjected to bi-axial normal

stresses as shown in fig 1(b). Assuming E=200GPa and Poisson ratio = 0.3.

Calculate

i) Strain in 3-directions

ii) Volumetric strain

iii) Change in volume

iv) Bulk Modulus

220 mm

360 mm

140 MPa

140 MPa

140 MPa

140 MPa

Fig. 1 (b)

7

OR

2. a) A steel tube of 30mm external diameter and 25mm internal diameter encloses a gun metal

rod of 20mm diameter, to which it is rigidly joined at each end. If at a temperature of 30ºC

there is no longitudinal stress, Calculate the stresses in rod and tube when temperature is

raised to 120ºC.

.C/º1020C/º1012

GPa100E,GPa200E

6GM

6st

GMst

7

*0783*

NagpurStudents.Org

TKN/KS/16/7375 2

b) Member ABCD subjected to point loads as shown in figure 2 (b). Calculate 2P necessary

for equilibrium, if kN130PandkN450P,kN45P 431 . Determine total elongation

Take 25 mmN101.2E .

P1

625 mm2

2500 mm21250

mm2

P2 P3

P4

80 cm200 cm120 cm

Fig. 2 (b)

6

3. Draw shear force and Bending Moment diagram for the overhang Beam shown in fig (3).

Find the point of contraflexure if any the couple is acting at Pt. 'B'.

A

7 kN/mtr 5 kN.m

C

D

20 kN

B

5 m 2 m 3 m

Fig. 3

13

OR

4. a) For a circular cross section beam. Show that maximum shear stress eragecovT34

max .

6

b) A cast iron beam of 25mmx25mm in section and 1 meter long and supported at the ends

tails when a centre load of 1000N is applied. What uniformly distributed load will break a

cantilever of same material 60mm wide 100mm deep and 1.5 meter long.

8

5. A beam of span 8m is simply supported at the ends. It carries a udl of 30 kN/m over its

entire length & a concentrated Load of 60kN at 3m from left support. Determine the

maximum deflection in the beam & its Location. 44 m1080I&GPa200E .

13

OR

6. a) A block 100mmx50mmx7.5mm. Thick is subjected to uniformly distributed stress field as

shown in fig 6 (A) Compute normal stress and shear stress developed along BD Plane.

50mm

35 kN

35 kN

25 kN25 kN

A B

CD

100 mm Fig. 6 (A)

6

NagpurStudents.Org

TKN/KS/16/7375 3 P.T.O

b) On a mild steel plate, a circle of 50mm diameter is drawn before the plate is stressed as

shown in figure 6 (b). Find the length of major & Minor axes of an ellipse formed as a result

of deformation of the circle marked. 25.0&GP200Em1 .

80 MPa

40 MPa

40 MPa

40 MPa

40 MPa

80 MPa

80 MPa

80 MPa

Fig. 6 (b)

7

7. a) Derive the torsional equation for a solid circular shaft with usual notations.

6

b) A solid shaft is required to transmit 300kW at 110rpm, the maximum torque being 20%

greater than mean torque. Determine the diameter 'd' of the shaft so that the torsional shear

stress should not exceed 63MPa & angle of twist not exceed 1.5º in a length of 3m.

Take G=84 GPa.

7

OR

8. a) Prove that Crippling Load by Euler's formula for column having both ends hinged, is given

by,

2L

IE2

crF

5

b) A 1.5m long column has circular cross section of 50mm diameter. One end is fixed while

other end is free. Calculate Safe Load using F.S=3 by

i) Euler's Formula – 25 mmN102.1E

ii) Rankine's formula, 1600

1c &MPa560 .

8

9. a) Show that strain energy stored in a body when the load is applied gradually is given by,

VUE2

2 .

5

b) A Wagon Weighing 35KN is attached to a wire rope & moving on level track at a speed of

3.6Km/hr, When the rope Jams & the Wagon is suddenly brought to rest. If the length of

the rope is 60m at the time of Sudden Stoppage, Calculate the maximum instantaneous

stress & Max. Instantaneous elongation produced. Diameter of rope = 30mm 2m/GN200E .

8

OR

NagpurStudents.Org

TKN/KS/16/7375 4

10. a) Explain the Creep Phenomenon.

5

b) A steel bar 25mm diameter and 2.5m length is fixed at the top end and hangs vertically with

rigid collar at its lower end. Find the maximum instantaneous stress developed in the rod &

deformation if a weight of 200KN falls on collar through 300mm height. Take E = 204 GPa.

8

11. a) Explain in brief the S-N diagram.

4

b) What do you understand by stress concentration ? Explain in brief methods of reducing its

effect.

5

c) Explain in brief different theories of failure.

5

OR

12. A hot rolled steel shaft is subjected to torsional load that varies from 300N-m C.W. to 100

N-m C.C.W & bending moment that varies from +400 N-m to -100 N-m. The shaft is of

uniform Cross-Section & having no stress raiser present at critical section. Determine the

required diameter of shaft. Assume FS=1.5. The material properties are.

MPa290Seb;MPa410Syt;MPa550Sut

Surface finish factor = 0.9, Size factor = 0.8, Reliability = 0.9.

14

************

NagpurStudents.Org

Scanned by CamScanner

NagpurStudents.Org

Special Thanks to Abhijith Alolickal

NJR/KS/18/4427 1 P.T.O

B.E. (Mechanical Engineering) Fourth Semester (C.B.S.) Mechanics of Materials

P. Pages : 4 NJR/KS/18/4427


_____________________________________________________________________











11. Use of design data book is permitted.

1. a) Plot a tensile test diagram for steel. Explain it's salient features.

5

b) Find the change in length of the stepped bar [composite] ABCDEF subjected to tensile

load of 40kN. as shown in fig. 1 [b].

P

A B

C D

E F

P

100mm

Steel

0mm

Br

mm

Br

80 mm 70 mm 60 mm 70 mm 80 mm

0mm100mm

SteelBr

StE 200GPa P 40kN= =

BrE 90GPa= Fig. 1[b]

8

2. a) Find the stresses in the wires of the system shown in fig. 2 (a). The cross-sectional area of

wires is 100 mm2. and the temperature of the system rises by 50ºC.

Copper Steel Copper

20 kN

rigid plate

St

c

6St

6c

E 200GPa

E 110GPa

º12 10 / C

º18 10 / C

−

−

=

=

=

=

Fig. 2 (a)

6

*0771*

NagpurStudents.Org

NJR/KS/18/4427 2

b) An axial load of 56kN is applied to a bar of 36mm diameter and 1 m. length. The

extension of the bar is measured to be 0.265 mm. where as the reduction in the diameter is

0.003 mm. Calculate the Poisson's ratio and the values of the three moduli [E, G, & K].

7

3. Draw the shear force and bending moment diagram for the beam shown in fig. (3).

10 kN/m 8 kN/m25 kN

A B C D E

5m 2m 2m 2m

Fig. (3)

13

4. a) A simply supported beam with overhang is loaded as shown in fig. 4 (a). The beam is

hollow circular section with outer diameter 100 mm and inner diameter 70 mm. Calculate

the maximum tensile and compressive stress due to bending.

25 kN

1.5 m 1.5 m 1 m

20 kN/m

Fig. 4 (a)

70 mm

100 mm

8

b) Derive the governing relation used to find shear stress in beam given by

Ay

FIb

=

→ shear stress

A → c/s area of beam

I → MI about neutral axis

b → width of beam

y → distance between CG of area and neutral axis

5

5. A beam is loaded as shown in fig. (5). Using Macaulay's method calculate the Slope at A

and C and deflection at B and C Take E = 200 GPa & I = 6 4160 10 mm

10 kN 15 kN/m

A

1m 1m 2.5 m

D

Fig (5)

CB

14

NagpurStudents.Org

NJR/KS/18/4427 3 P.T.O

6. a) A plane element is subjected to stresses as shown in fig. 6 (a). Determine analytically

i) The principal stresses and their directions

ii) The max. shear stress and their directions

Fig 6 (a)

30 MPa52 MPa

70 MPa

30 MPa

52 MPa

70 MPa

8

b) Derive the differential equation of deflection curve

2

d2yEI M

dx=

6

7. a) Design the diameter of solid circular shaft to transmit 50kW power, rotating at 240 RPM.

The maximum torque is likely to exceed mean torque by 50%. The maximum shear stress

permissible = 60MPa Also calculate the angle of first for a length of 2 meter. Take

G = 80 GPa

7

b) Derive the torsion equation for a member of circular cross – section given.

T G

GR J L

= =

→ shear stress

R → radius of curvature

T → Torque

J → Polar M. I.

G → Modulus of rigidity

Q → Angle of first

L → Length of shaft

6

8. a) What is meant by equivalent length of columns? What are its value for different end

conditions of column.

5

b) For a hollow cast iron column with outside diameter 250 mm and thickness 25 mm length

4 meter with both ends fixed; Calculate the safe load by Rankine's formula using factor of

safety 4. Also calculate the slenderness ratio and ratio of Euler's to Rankine load. Take 1

c 1600550MPa & = = .

8

9. a) A 2 – meter long bar of 125 mm diameter is subjected to an axial load of 1.5kN. Determine

the maximum stress and the strain energy developed in the bar if the load applied is

i) gradual ii) sudden

iii) falls through a height of 30mm, E = 200 GPa.

7

b) What is strain energy of a material? Derive the expression for strain energy when load is

applied gradually.

6

NagpurStudents.Org

NJR/KS/18/4427 4

10 a) Define creep. Discuss in brief the various stages of creep with neat sketch.

6

b) a simply supported beam of length 'L' meter carrier a uniformly distributed load of

intensity WkN/meter over it's entire length. Find the strain energy stored by the beam.

7

11. a) A shaft made of SAE 1030 is subjected to different loads as shown in fig. 11 (a). Find the

diameter of shaft by maximum normal stress theory and maximum shear stress theory.

Assume factor of safety = 2.

1000 mm

1250 mm

20 kN

50 kN.m

Fig. 11 (a)

11

b) Explain in brief the stress concentration along with suitable remedies to overcome it's

effect.

3

12. A hollow shaft of SAE 1030 is subjected to varying bending moment from – 150 N.m to +

400 N.m along with varying torque from 330N-m clockwise to 110N.m anti-clockwise.

The ratio of DoDi

1.5= .

Obtain the hollow shaft diameter (Do & Di) for infinite life. The stress concentration

factor in bending and torsion are 1.6 and 1.3 respectively Take factor of safety as 2.5; size

factor = 0.85 and surface finish factor 0.65. notch sensitivity factor = 0.90.

Reliability factor = 0.897

Temperature factor KO = 1.

14

*********

NagpurStudents.Org

NapurStudents - TGPCET · N KT /K S /17/7287 3 P.T.O b) A solid shaft transmits 300 kw at 200 rpm....

Documents

Transcript of NapurStudents - TGPCET · N KT /K S /17/7287 3 P.T.O b) A solid shaft transmits 300 kw at 200 rpm....