STM objective

STRENGTH OF MATERIAL

STRENGTH OF MATERIALS

CLASS WORK, PRACTICE QUESTION & TEST PAPER

CONTENTS

Unit Chapters Page No.
1 Simple Stress & Strain 2 - 25
2 Shear Force & Bending Moment 26 - 49
3 Complex Stress & Strains 50 - 66
4 Theory of Simple Bending 67 - 82
5 Shear Stress Distribution in Beams 83 - 85
6 Torsion & Spring 86 - 100
7 Deflection and Slope 101 - 111
8 Columns and Struts 112 - 116
9 Thin Cylinders 117 - 118

Test Papers Answer Keys 119

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MECHANICAL ENGINEERING

1.1 SIMPLE STRESSES & STRAIN

1. The number of independent elastic constants for a linear elastic isotropic and homogeneous material is

[GATE-2010][CE]

a) 4 b) 3 c) 2 d) 1

2. In terms of Poisson’s ratio () the ratio of Young’s Modulus (E) to Shear Modulus (G) of elastic

materails is [GATE-2004][ME] 1
a) 2(1 + )
b) 2(1 - ) c) (1 + ) d) (1 - )
2

3. A large uniform plate containing a rivet-hole is subjected to uniform uniaxial tension of 95 MPa. The

maximum stress in the plate is  [GATE-1992][ME]



a) 100 MPa 95 MPa 10 cm - - -- - 
b) 285 MPa 
c) 190 MPa  5 cm 
d) Indeterminate -----







4. The maximum value of Poisson’s ratio for an elastic material is [GATE-1991][CE]

a) 0.25 b) 0.5 c) 0.75 d) 1.0

5. The elongation of the bar due to its own weight is.

(a) Wl / 2 AE (b) Wl / AE (c) Wl / b2E (d) 2Wl / AE

6. A steel rod of 2 cm2 area and 1m in height is subjected to a pull of 40,000 N.If Young’s Modulus is

2 x 105 N / mm2, the elongation of the rod in mm will be.

(a) 10 (b) 100 (c) 1 (d) 0.1

7. If all the dimensions of a vertically suspended circular bar are doubled, then the maximum stress

produced in it due to its own weight will .

(a) become half (b) remain unaltered

(c) be doubled (d) be tripled

8. The diameter of a tapering rod varies from ‘D’to ‘D/2’in length of ‘L’m. If it is subjected to an axial

tension of ‘P’ the change in length is . (b) 8 PL /ED2
(a) 4 PL /ED2 (d) None of the above
(c) 2 PL /  ED2

9. If a member is subjected to tensile stress of ‘Px’, compressive stress of ‘Py’ and tensile stress of ‘Pz’

along the x, y and z directions respectively, then the resultant strain ‘ex’along the x -direction would
(E is Young’s modulus of elasticity ‘ ‘ is Poisson’s ratio)

(a) (1/E)(Px + Py -Pz) (b) (1/E)(Px + Py + Pz)
(c) (1/E)(Px- Py + Pz) (d) (1/E)(Px - Py - Pz).

10. A hole to be punched in a plate of 10 mm thick. The allowable crushing stress of the punch is 4 times

the shearing / stress of the plate. The diameter of the smallest hole that can be punched in the plate is

‘mm’ is

(a) 10 mm (b) 20 mm (c) 40mm (d) none

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STRENGTH OF MATERIAL

11. For the compound the bar shown below, the ratio of greatest to the least elongations of different
compnents is,
P 2cm dia 1cm dia 3cm dia  P

20 cm 20 cm 20 cm
12. The axial movement of bottom surface of a compound bar loaded as shown below is .

(a) 1.5 (PL / AE) 2A, LE
(b) 2.0 (PL / AE)
(c) 2.5 (PL / AE) 
(d) 3.0 (PL / AE) 2P A, LE
P

13. The total elongation of the structural element fixed, at one end, free at the other end, and of varying

cross-section as shown in the figure when subjected to a force p at free end is given by

(GATE-1991) (CE)

a) PL/AE A 2A A P
b) 3 PL/AE

c) 2.5 PL/AE

d) 2PL/AE L L

14. Below Fig. shows a rigid bar hinged at Aand supported in a horizontal position by two vertical

identical steel wires. Neglect the weight of the beam. The tension T1 and T2 induced in these wires by

a vertical load P applied as shown are [GATE-1994][ME]

<b < a>---------------------
T2 T1

A

< l >< l>

P P Pbl Pal
b) T1 = , T =
a) T 1 = T 2 = 2 (a2 b2) 2 (a2 + b2)
+
Pal Pbl
d) T = Pal , T = Pbl
c) T1 = (a2 + b2) , T2 = (a2 + b2) 1 2(a2 + b2) 2 2(a2 + b2)

15. A 200 x 100 x 50 mm steel block is subjected to a hydrostatic pressure of 15 MPa. The Young’s

modulus and Poission’s ratio of the material are 200 GPa and 0.3 respectively. The change in the

volume of the block in mm3 is [GATE-2003][ME]

a) 85 b) 90 c) 100 d) 110

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MECHANICAL ENGINEERING

16. For the compound bar shown below, the ratio of stresses in the portions AB:BC:CD will be .

(a) 4 : 1 : 2 A B C D
(b) 1 : 2 : 4
(c) 1 : 4 : 2 d 
(d) 4 : 2 : 1
d  d/2 2F
F  2F 
3F
 
L  L L

17. The ratio of loads shared by parts ‘AB’ and ‘BC’ of the bar shown below is

(a) 1 : 1 A BC
(b) 2 : 1 P
(c) 3 : 1

(d) 1 : 2 2L/3  L/3

18. ABC is rigid bar. It is hinged at ‘A’and suspended at ‘B’and ‘C’by two wires ‘BD’and ‘CE’made

of copper and steel respectively. The bar carries a load of 1 t at ‘F’ midway between ‘B’and ‘C’

Given Ac = 4 cm2 , As = 2 cm2 , Ec = 1 x 106 kg/cm2 , Es = 2 x 106 kg/cm2 . The ratio of forces in

copper and steel wires is. DE
(a) 0.5

(b) 4 A B FC

(c) 0.25 1m  1m 
(d) 2
1t

19. An elastic body is subjected to a direct compressive stress ‘ Px’ in longitudinal direction. If the lateral

strains in the other two directions are prevented by applying ‘Py’ and ‘Pz’ in those directions, then

Py = Pz is equal to ( Poisson’s ratio) (b)  . Px
(a) Px / ( - 1) (d)  . Px / (1-  )
(c) Px /  (1-2)

20. A short cast iron column carries a load of 50 t. If the original dia is 8 cm, E = 1 x 106 kg/sq.cm and

Poisson’s ratio 0.25, the increase in dia of column in ‘cm’would be .

(a) 0.00318 (b) 0.00256

(c) 0.002 (d) 0.00280.

21. Assume that Young’s modulus of steel is twice that of brass. two bars of brass and a bar of steel of

equal cross section form a single tension member with the help of rigid pins as shown in the fig. The

shear in the pin will be . Pin

(a) 0.25 P 
(b) 0.5 P Brass
(c) 0.33 P
(d) 0.4 P Steel  P

Brass

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STRENGTH OF MATERIAL

22. Arigid beamABCD is hinged at D and supported by two springs at Aand B as shown in the fig. The
beam carries a vertical load P at C. The stiffness of spring at A is 2 K and that of B is K. The ratio of
forces of spring at A and that of spring at B is .

(a) 1

(b) 2

(c) 3 A BC D

a a a
(d) 4 P

23. In the given fig,. the wires AB and CD made of the same material are used to suspend a rigid block to
 
which the gradual load ‘W’ is applied in such a way that both the wires get streched by the same

amount. If stresses in wires AB and CD are 1 and 2 respectively . then the ratio 1 / 2 will be.
C

(a) 3 / 2 A 2 6m
(b) 2 / 3 D
(c) 2 3m B 1


(d) 1/ 2  W

Questions 24 and 25 are based on the following data (linked questions)

A steel rod of cross sectional area 2000 mm2 and two brass rods each of 1000mm2 together support

a load 10 kN, Es= 2 x 105 MPa ; Eb = 1 x 105 MPa. 10 kN

24. The ratio of load taken by each steel bar to that of brass bar is . 300mm b sb

(a) 3 / 2 (b) 2 / 3 

(c) 2 / 1 (d) 8 / 1 600mm



25. The stresses developed due to 10 kN in steel and brass in MPa respectively are .

(a) 1.25& 3.75 (b) 3 & 1.5

(c) 2.5 & 2.5 (d) 4 and 1

Questions 26 and 27 are based on the following data (linked questions)

A mild steel rod of 20 mm diameter and 300 mm long is centrally enclosed inside a copper tube of

same length and having external diameter 30 mm and internal diameter 25mm. The ends are brazed

together. The composite bar is subjected to an external tensile force of 40kN.

Es= 200 GPa ; Ecu =100 GPa.
26. The stresses developed in steel and copper respectively in ‘MPa’ are

(a) 150 and 25 (b) 75 and 25 (c) 47 and 37 (d) 95 and 47.

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MECHANICAL ENGINEERING

27. The extension of composite bar in ‘mm’ is

(a) 0 (b) 0.62 (c) 0.142 (d) 0.38

Questions 28 and 29 are based on the following data

Two wires are connected to a rigid bar as shown in the fig. al
If the load of ‘w’ is to be placed on the rigid bar so as to the

wire on the left is of steel and having a cross sectional of 0.1 st 100 cm
cm2 and young’s modulus of 2000,00 MPa. wire on the right 60 cm 30 cm 
is made of aluminium having a cross of 0.2 cm2 and a young’s 
modulus of 66,667 MPa. the bar horizontol , x

28. The distance ‘x’ from the left end.(steel wire end) 10 KN
where this weight should be placed is:

(a) 5.6 cm (b) 8.57 cm (c) 9.21 cm (d) 11.24 cm

29. The stresses developed, in MPa, respectively in steel and aluminium are . 

(a) 23.56 & 12.65 (b) 456.78 & 34.5 (c) 715 & 145 (d) 500 & 250

Questions 30 and 31 are based on the following data

In the above problem if the load is applied at the center of the two wires .

30. The stresses developed, in MPa, respectively in steel and aluminium are .

(a) 23.56 and 12.65 (b) 45.78 & 678.78

(c) 715 and 145 (d) 500 and 250.

31. The angular displacement of rigid bar due to the load at the center of the two wires is .

(a) 0.65(c.w) (b) 0.43(c.w)

(c) 0.65 (anti c.w) (d) 0.43 (anti c.w).

32. A steel bolt having a nominal diameter of 20 mm and a pitch of 2.4 mm is used to connect two plates
of 10 mm thickness each.An aluminium tube of inner diameter 22mm and outer diameter of 44 mm is
separating the plates as shown in fig. The nut is pulled snug (just tight) and then given a one- third
additional turn. Find the resulting stresses in the bolt and the tube neglecting the deformation of the
plates. Young’s modulus of steel and aluminium are 207 x 103 MPa and 67.5 x 103 MPa respectively.
(G-2K)

10 mm

350
mm

10 mm

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

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STRENGTH OF MATERIAL

1.2 THERMAL STRESSES

1. A uniform, slender cylindrical rod is made of a homogenous and isotropic material. The rod rests on a

frictionless surface. The rod is heated uniformly. If the radial and longtudinal thermal stresses are

represented by r and z respectively, then [GATE-2004][ME]

a) r = 0 ,z = 0 b) r  0 ,z = 0 c) r = 0 ,z  0 d) r  0 ,z  0

2. A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of
T. The Young’s modulus is E and the coefficient of linear expansion is ‘’. The thermal stress in the

rod is b)  T c) E T [GATE-2007][ME]
a) 0 d) E TL

3. A cantilever beam of tubular section consists of 2 materails copper as outer cylinder and steel as inner

cylinder. It is subjected to temperature rise of 200C and copper>steel. The stress developed in the

tubes will be [GATE-1991][CE]

a) Compression is steel and tension in copper b) Tension in steel and compression in copper

c) No stress in both d) Tension in both the materials

4. A square plate (a x a) rigidly held at three edges is free to move along the fourth edge. if temperature

of the plate is raised by temperature ‘t’, then the free expansion at the fourth edge will be(coefficient of

thermal expansion of the material is , modulus of elasticity of the material is E and its Poisson’s ratio

is v) (b) a  t (1+ v) (c) a  t + t v. (d) a  t (1 + v)
(a) a  t v

5. A thin steel tyre of diameter ‘d’ is to be shrunk on to slightly large wheel of diameter ‘D’, if ‘E’ is the

modulus of elasticity of steel, the circumferential stress developed :

(a) ((D-d)/ d ) E comp. (b) ((D-d)/ d )E tensile (c) ((D-d)/ D ) E comp. (d) ((D-d)/ D ) E tensile.

6. A steel bar is kept between two copper(parallel) bars and rigidly conneeted at room tcmpcrature. lf

the system is fixed at the ends and cooled suddenly the stresses produced in the bars will be .

(a) tensine in steel & compression in copper

(b) compression in both steel & copper .

(c) tension in both steel & copper

(d) compression in steel & tension in copper

7. A metal bar of length 100 mm is inserted between two rigid supports and its temperature in increased

by 100C. If the coefficient of thermal expansion is 12 x 10-6 per OC and the Young’s modulus is

2 x 105 MPa, the stress in the bar is (GATE 2007) (CE)

a) zero b) 12 MPa c) 24 MPa d) 2400 MPa

8. Determine the temperature rise necessary to induce bucking in a 1m long circular rod of diameter

40 mm shown in the figure below.Assume the rod to be pinned at its ends and the coefficiet of thermal

expansion as 20 x 10-6/0C. Assume uniform heating or the bar. [GATE-1993][ME]

40 mm diameter



< 1m >

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MECHANICAL ENGINEERING

Questions 9 and 10 are based on the following data.(Linked questions)

A composite bar made up of aluminium and steel is held between two rigid supports is shown in fig. The are
stress free at 380C , Es = 200GPa; Ea = 70GPa; s = 11 x 10-6 / 0C ; a = 24 x 10-6 / 0C.,Ls = La = 1m
; As= 100 mm2, Aa = 200 mm2. The temperature is increased to 580C;

100 mm steel aluminium

9. The support reactions in kN are.

(a) 2.34 (b) 5.76 (c) 6.98 (d) 8.96.
(d) none
10. The stresses in steel and aluminium bars respectively in MPa.

(a) 57.65 & 57.65 (b) 57.65 & 28.82 (c)28.82 & 14.41

Questions 11 and 12 are based on the following data.(Linked questions)

A gun metal rod of cross section area 200 mm2 is screwed at ends, passes through a steel tube of

cross sectional area of 100 mm2. The nuts on the rod are screwed tightly home on the ends of the tube.
the temperature is decreased by 200 FEs = 200 GPa ; Egm = 100GPa; s = 6 x 10-6 / 0F,
gm = 10 x 10-6 / 0F, Ls, Lgm= 1.25 m;
11. The temperature thrust due to composite action is , in kN.

(a) 2 (b) 4 (c) 6 (d) 8

12. The temperature stresses in steel and gun metal respectively in MPa are .

(a) 80 & 200 (b) 80 & 40 (c) 40 & 120 (d) 60 & 120

Questions 13 and 14 are based on the following) data.

A rigid block weighing 60kN is supported by three rods symmetrical placed as shown in fig.The lower ends

the rods are assumed to have been at the same level before the block is attached. The cross section of the

rods and the modulus of elasticity of the materials the rods are given as Es = 210GPa; Eb = 98GPa.As = 5
x 10-4 m2; Ab 10 x 10-4 m2, ls = 0.5 m; lb = 1 m;

St Br St
0.5m 1m

60kN

13. The stress in steel rod is

(a) 48.65 MPa (b) 52.35 MPa (c) 60 MPa (d) 40 MPa

14. If the coefficient of thermal expansion for steel and bronze are 11 x 106/ 0C and 19 x 106 / 0C \

respectively, the temperature rise in 0C necessary to cause all the applied load to be supported by the

steel rods is .

(a) 10 (b) 10.58 (c) 15 (d) 28.00

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STRENGTH OF MATERIAL

15. If the rod fitted snugly between the supports as shown in the fig, is heated, the stress induced in it due
to 200c rise temperature will be. [98]
10 mm

0.5 m k = 50 kN/m  = 12.5 x 10 -6/oC
E = 200 GPa

(a) 0.07945 MPa (b) -0.07945 MPa (c) -0.03972 MPa (d) 0.03972 MPa

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

1.1 SIMPLE STRESSES & STRAIN (ANS.) CLASS WORK

1-c, 2-a, 3-c, 4-b, 5-a, 6-c,7-c, 8-b, 9-a, 10-a, 11- 9:1, 12-, 13-c, 14-b, 15-b, 16-c, 17-d, 18-a, 19-d, 20-c, 21-a, 22-c, 23-c, 24-c,

25-c, 26-d, 27-c, 28-b, 29-c, 30-d, 31-b, 32-b = 72.55 N/mm2  = 263.36 N/mm2
r

1.2 THERMAL STRESSES : (ANS) CLASS WORK

1-a, 2-a, 3-b, 4-b, 5-b, 6-d, 7-c, 8-sol, 9-b, 10-b, 11-d, 12-b, 13-a, 14-b, 15-b.

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MECHANICAL ENGINEERING

1. The homogenous state of stress for a mental part undergoing plastic deformation is

(GATE-12)

10 5

T= 0

5 20

Where the stre0ss component values are in MPa. Using von Mises yield criterion, the value of estimated shear yield

stress, in MP0aa is 0

a) 9.50 -10 b) 16.07 c) 28.52 d) 49.41

2. A rod of length L having uniform cross-section area A is subjected to a tensile force P as shown in the figure below.

If the Young’s modulus of the material varies linearly from E1 to E2 along the length of therod, the normal stress

developed at the section-SS at (GATE-2013)

P P(E - E )
a) b) 1 2

A A(E +E )
c) PE2 12

AE PE
1 d) 1

AE2

3. A circular rod of length ‘L’ and area of corss-section ‘A’ has a modulus of elasticity ‘E’ and coefficient of thermal
expansion ‘‘ One end of the rod is fixed and other end is free. If the temperature of the rod is increased by T, then
(a) stress developed in the rod is E T and strain developed in the rod is T (GATE-14)

(b) both stress and strain developed in the rod ate zero
(c) stres developed in the rod is zero and strain developed in the rod is T

(d) stress developed in the rod is E a ?T and strain developed in the rod is zero

4. The stress-strain curve for mild steel is shown in figure given below.Choose the correct option refering

to both figure and table. (GATE-14-Set 3)

Point on the graph Description of the point
P. 1. Upper yield point
Q. 2. Ultimate tensile strength
R. 3. Proportionality limit
S. 4. Elatic limit
T. 5. Lower yield point
U. 6. Failure

a) P-1, Q-2, R-3, S-4, T-5, U-6 b) P-3, Q-1, R-4, S-2, T-6, U-5
c) P-3, Q-4, R-1, S-5, T-2, U-6 d) P-4, Q-1, R-5, S-2, T-3, U-6

5. Which one of the following types of stress-strain relationship best describes the behavior of brittle materials, such

as ceramics and thermosetting plastics. (stress and strain)? (GATE-15-Set 1)

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STRENGTH OF MATERIAL

6. A metallic rod of 500 mm length and 50 mm diameter, when subjected to a tensile force of 100kN at

the ends, experiences an increases in its length by 0.5 mm and a reduction in its diameter by

0.015 mm, The Poisson’s ration of the rod materials is___________ (GATE-14-Set 1)

7. A steel cube, with all faces free to deform, has Young’s moudus, E, Poisson’s  The Pressure (hydrostatic
stress) developed within the cube, when it is subjected to a uniform increass in temperature, T,

is given by (GATE-14-Set 2)

T)E T)E T)E

a) 0 b) c) - d) 3(1 - 2v)
1 - 2v 1 - 2v

8. A thin plate of uniform thickness is subject to pressure as shown in the figure below
(GATE-14-Set 2)

Under the assumption of plane stress, which one of the following is correct?
(a) Normal stress is zero in the z-direcation
(b) Normal stress is tensile in the z-direcation
(c) Normal stress is compressive in the z-direction
(d) Normal stress varies in the z-direcation

9. If the Poisson’s ration of an elastic material is 0.4, the ratio of modulus of rigidity to Young’s modulus

is_____________ (GATE-14-Set 4)

10. The number of independent elastic constants required to define the stress-strain relationship for an

isotropic elastic solid is_____________ (GATE-14-Set 4)

11. The state of stress at a point is given by  = -6 MPa,     Pa, and    Pa. The maximum
x y xy

tonsile stress (in MPa) at the point is______ (GATE-14-Set 1)

12. A 200 mm long, stress free rod at room temerature is held between two immovable rigid walls. The

temperature of the rod is uniformly raised by 2500C. If the Young’s modulus and coefficient of thermal

expansion are 200 GPa and 1 x 10-5/0C, respectively, the magnitude of the tongitudinal stress

(in MPa) developed in the rod is__________ (GATE-14-Set 1)

33. A rod is subjected to a uni-axial load within linear elastic limit. When the change in the stress is

200 MPa, the change in the strain is 0.001. If the Poisson’s raton of the rod is 0.3 the modulus of

ridrigidity (in GPa) is __________ (GATE-14-Set 2)

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

Ans :
1 - b, 2- a, 3 - c, 4 - c, 5 - d, 6 - 0.3, 7 - a, 8 - a, 9 - 0.357, 10 - sol, 11 - 8.4339 MPa ,12 - 500 MPa, 13 - 76.9230 GPa

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MECHANICAL ENGINEERING

1.1 & 1.2 PRACTICE QUESTIONS

1. The principle of superposition is made use of in structural computations when : [GATE-1990][CE]

a) The geometry of the strucutre changes by a finite amount during the application of the loads

b) The changes in the geometryof the strucuture during the application of the loads is too small and the

strains in the structure are directly proportional to the corresponding stresses

c) The strains in the strucutre are not directly proportional to the correspoinding stresses, even though

the effect of changes in geometry can be neglected.

d) None of the above conditions are met

2. The figure below shows a steel rod of 25mm2 cross sectional area. It is loaded at four points. K, L, M

and N. Assume Esteel = 200 GPa. The total change in length of the rod due to loading is
[GATE-2004][ME]

100 N L 250 N 50 N
K 200 N K L

500 mm 1700 mm 400 mm

<> <>
<
>

a) 1m b) -10m
c) 16m d) - 20m

3. A steel bar of 40 mm x 40 mm square -section is subjected to an axial compressive load of 200 KN.

If the length of the bar is 2m amd E = 200 GPa. The elongation of the bar will be

[GATE-2006][ME]

a) 1.25 mm b) 2.70 mm

c) 4.05 mm d) 5.40 mm

4. A bar having a cross-sectional area of 700 mm2 is subjected to axial loads at the positions indicated.

The value of stress in the segment BC is [GATE-2006][ME]

63kN 35kN 49kN 21kN

a) 40 MPa A B C b)D50 MPa

c) 70 MPa d) 120 MPa

5. The axial movement of top surface of stepped column as shown in figure is [GATE-1989][CE]

P

a) 2.5 PL/AE L AE <<
b) 3 PL/AE L 2AE
c) 1.5 PL/AE
d) 2 PL/AE

6. The stretch in a steel rod of circular section, having a length ‘I’ subjected to a tensile load ‘P’ and

tapering uniformlyfrom a diameter d1 at one end to a diameter d2 at the other end, is given. [95]
(b) P.l /Ed1.d2
(a) P.l /4 Ed1.d2 (d) 4P.l /E.d1.d2

(c) P.l /4E (d1.d2)

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STRENGTH OF MATERIAL

7. The total extension of the bar loaded as shown in the fig is.A= area of cross -section, E = modulus

of elasticity. [95]

10T 3T 2T 9T

10 10 10

(a) 10 x 30/AE (b) 26 x 10/AE

(c) 9 x 30/AE (d) 30 x 22/AE

8. If Poisson’s ratio a material is 0.5, then the elastic modulus for the material is. [95]

(a) three times its shear modulus. (b) for times its shear modulus.

(c) equal to its shear modulus. (d) Interminate.

9. A bar of uniform cross-section of one sq.cm is subjected to a set of five forces as shown in the given

fig. esulting in its equilibrium. the maximum tensile stress (in kgf/cm2) produced in the bar is. [97]

11kgf 1 23 4
2kgf 1kgf 5kgf 5kgf

-----------------------------------------------

-----

A B CD E

1 23 4

(a) 1 (b) 2 (c) 10 (d) 11

10. Match List I (Elastic properties of an isotropic elastic material) with List II (Natural of strain

produced) and select the correct answer using the codes given below the lists : [97]

List- I List - II

A. Young’s modulus - 1. Shear strain.

B. Modulus of rigidity - 2. Normal strain.

C. Bulk modulus - 3. Transverse strain.

D. Poisson’s ratio - 4. Volumetric strain

Codes:

ABCD

(a) 1 2 3 4

(b) 2 1 3 4

(c) 2 1 4 3

(d) 1 2 4 3

11. A 10 cm long and 5 cm diameter steel rod fits snugly between two rigid walls 10 cm a part at room
temperature. Young’s modulus of elasticity and coefficient of linear expansion of steel are 2 x 106kg/
cm2 & 12 x 10-6 / 0C. respectively. The stress developed in the rod due to a 1000C rise in

temperature wall be. [97]

(a) 6 x 10-10 kgf /cm2 (b) 6 x 10-9 kgf /cm2 (c) 2.4 x 103 kgf /cm2 (d) 2.4 x 104 kgf /cm2

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MECHANICAL ENGINEERING

12. For a composite bar consisting of a bar enclosed inside a tube of another material and when

compressed under a load ‘W’as a whole through rigid collars at the end of the bar. The equation of

compatibility is given by (suffixes) 1 and 2 refer to bar and tube respectively) [97]

(a) W1 + W2 = W (b) W1 + W2 = Constant.

(c) W1 W (d) W1 W= 2
A1E 1 =2 A1E 2 A2E 1
A2E 2

13. A tapering bar (diameter of end sections being, d1 and d2) and a bar of uniform cross-section ‘d’ have
the same length and are subjected the same axial pull. Both the bars will have the same extension if ‘d’

is equal to. [98]

(a) d 1 + d 2 (b) d 1 d 2
2

d 1 + d2 (d) d 1 + d 2
(c) 2

2

14. The number of independent elastic constaints required to express the stress-strain relationship for a

linearly elastic isotropic material is. [98]

(a) one (b) two (c) three (d) four.

15. The deformation of a bar under its own weight as compared to that when subjected toa direct axial

load equal to its own weight will be. [98]

(a) the same (b) one fourth

(c) half (d) double.

16. If permissible stress in plates of joint through a pin as shown in the fig. is 200 MPa, then the width

w will be. [98] Pin
(a) 15 mm A

(b) 20 mm 2000N 10mm 2000N
(c) 18 mm 2 mm
(d) 25 mm w

2 mm
B

17. The number of elastic constants for a completely anisotropic elastic material is. [99]

(a) 3 (b) 4

(c) 21 (d) 25

18. A rod of material with E = 200 x 103 MPa and  = 10 -3mm/mmoC is fixed at both the ends.It is

uniformly heated such that the increase in temperature is 300C, The stress developed in the rod is.

[99]

(a) 6000 N/mm2 (tensile) (b) 6000 N/mm2 (compressive)

(c) 2000 N/mm2 (tensile) (d) 2000 N/mm2 (compressive)

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STRENGTH OF MATERIAL

19 The Poisson ratio of a material which has Young’s modulus of 120 GPa and shear modulus of 50 GPa, is. [99]

(a) 0.1 (b) 0.2

(c) 0.3 (d) 0.4

20. For a given material, the modulus of rigidity is 100 GPa and Poisson’s ratio is 0.25. The value of modulus of elasticity

in GPa is.

(a) 125 (b) 150

(c) 200 (d) 250

21. A rigid beam of negligible weight is supported in a horizontal position by two rods of steel and aluminium, 2m and

1m long having values of cross-sectional area 1 cm2 and 2 cm2 and E of 200 GPa and 100 GPa respectively.A load P

is applied as shown in the fig.

2 m steel 1mAluminium

Rigid Beam
P

If the rigid beam is horizontal then.
(a) the forces on both sides should be equal.
(b) the force on aluminium rod should be twice the force on steel.
(c) the force on the steel rod should be twice the force on aluminium.
(d) the force P must be applied at the centre of the beam.

22. A straight bar is fixed at edges A and B.Its elastic modulus is E and cross-section is A. There is a load P =120N acting

at C. Determine the reactions at the ends. B

A

(a) 60 N at A, 60 N at B P = 120 N
(b) 30 N at A, 90 N at B C

(c) 40 N at A, 80 N at B

(d) 80 N at A, 40 N at B

l 2l

23. Toughness for mild steel under uniaxial tensile loading is given by the shaded portion of

the stress-strain diagram as shown in.

(a) (b) 
yL
 
 yu x

x



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MECHANICAL ENGINEERING

(c) UTS (d) Fracture
x x
 



24. The modulus of elasticity for a material is 200 GN/m2 and Poisson’s ratio is 0.25. what is the modulus of rigidity ?

(a) 80 GN/m2 (b) 125 GN/m2

(c) 250 GN/m2 (d) 320 GN/m2

25. A bar of length L tapers uniformly from diameter 1.1 D at one end of 0.9 D at the othere end . The elongation due to

axial pull is computed using mean diameter D. What is the approximate error in computed elongation ?

(a) 10 % (b) 5 %

(c) 1 % (d) 0.5 %

26 A bar of copper and steel form a composite system. They are heated to a temperature of 400C . What type of stress

is in duced in the copper bar ?

(a) Tensle (b) Compressive

(c) Both tensile end compressive (d) Shear

27. A cube with a side length of 1 cm is heated uniformly 10C above the room temperature and all the sides are free to

expand. what will be the increase in volume of the cube? (Given coefficient of thermal expansion is  per 0C)

(a) 3 cm3 (b) 3 cm3

(c) cm3 (d) zero

28 If E,G and K denote Young’s modulus, Modulus of rigidity and Bulk Modulus, respectively, for an elastic material,

then which one of the following can be possible true ?

(a) G = 2K (b) G = E

(c) K = E (d) G = K = E.

29. A soliduniform metal bar of diameter D and length L is hanging vertically from its upper end. The elongation of the

bar due to self weight is.

(a) Proportional to L and inversely proportional to D2 (b) Proportional to L2 and inversely proportional to D2.

(c) Proportional to L but independent of D. (d) Proportional to L2 but independent of D.

30. Two tapering bars of the same material are subjected to a tensile load P, The lengths of both the bars are the same.

The larger diameter of each of the bars is D. The diameter of the bar A at its smaller end is D/2 and that of the bar

B is D/3. What is the ratio of elongation of the bar A to that of the bar B ?

(a) 3 : 2 (b) 2 : 3

(c) 4 : 9 (d) 1 : 3

31. E,G,K and m represent the elastic modulus, shear modulus, bulk modulus and Poisson’s ratio respectively of a

linearly elastic, isotropic and homogenous material. To express the stress strain relations completely for this

material, at least.

(a) E,G and m must be known. (b) E,K and m must be known.

(c) any two of the four must be know (d) All the four must be known.

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32 A metal rod is rigidily fixed at its both ends. The temperature of the rod is increased by 1000c. if the co-efficient of
linear expansion and elastic modulus of the metal rod are 10 x 10-6/oc and 200 GPa respectively, then what is the

stress produced in the rod?

(a) 100 MPa (tensile) (b) 200 MPa (tensile)

(c) 200 MPa (compressive) (d) 100 MPa (compressive)

33. What is the phenomenon of progressive extension of the material i.e., strain increasing with the time at a constant

load, called?

(a) Plasticity (b) Yielding

(c) Creeping (d) Breaking.

34. Which one of the following statements is correct ? If a material expands freely due to heating, it will develop

(a) thermal stress (b) tensile stress

(c) compressive stress (d) no stress.

35. Which one of the following expresses the total elongation of a bar of length L with a constant cross-section of A

and modulus of Elasticity E hanging vertically and subject to its own weight W ?

WL WL
(b) 2AE
(a)
(d) WL
AE 4AE

(c) 2WL
AE

36. If he ratio G/E (G= Rigidity modulus, E = Young’s modulus of elasticity) is 0.4, then what is the value of the Poissons

ratio ?

(a) 0.20 (b) 0.25

(c) 0.30 (d) 0.33

37. What are the materials which show direction dependent properties, called?

(a) Homogeneous materials

(b) Viscoelastic materials

(c) Isotropic materials

(d) Anisotropic materials

38. What is the relationship between the linear elastic properties Young’s modulus (E), rigidity modulus (G) and bulk

modulus (K)?

1 93 3 91

(a) = + (b) = +

E KG E KG

9 31 9 13
(d) = +
(c) = + E KG

E KG

39. A 100 mm x 5 mm x 5 mm steel bar free to expand is heated from 150C to 400C. What shall be developed ?
(a) Tensile stress
(b) Compressive stress
(c) Shear stress
(d) No stress.

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MECHANICAL ENGINEERING

40. What is the relationship between elastic constants E,G and K ?

KG 9KG
(a) E= (b) E= K + G

9K + G

(c) E= 9KG (d) E= 9KG
K + 3G 3K + G

41. A bar produces a lateral strain of magnitude - 60 x 10- 5 m/m, when subjected to tensile stress of magnitude 300 MPa

along the axial direction. Find the elastic modulus of the material, if the Poisson’s ratio is 0.3

(a) 100 GPa (b) 150 GPa

(c) 200 GPa (d) 400 GPa

42. A bar of 2m length is fixed at both ends. If E = 2 x 106 kg/cm2. Coefficient of expansion is 1.5 x 10-6 / 0C and the

temperature rise is 200C, the stress developed in the material is .

(a) 60 kg/cm2 (tensile)

(b) 60 kg/cm2 (compressive)

(c) 60 kg/cm2 tensile of one face and 60 kg/cm2 compressive on opposite face .

(d) No stress is developed.
43. Astraight wire 15m long is subjected to tensile stress of 2000 kg /cm2 , E = 2 x 106 kg/cm2 .= 12.5 x 10-6 / 0C.The temp.

change to produce the same elongation as due to 2000 kg/ cm2, tensile stress in the material is .

(a) 40 (b) 80

(c) 120 (d) 160.

44. A straight wire 15m long is subjected to tensile stress of 2000 kgf /cm2 , Elastic modulus is 1.5 x 106 kgf/cm.

Coefficient of linear expansion for the material is 16.66 x 10-6F. The temp. change (in 0F) to produce the same

elongation as due to 2000 kgf /cm2, tensile stress in the material is .

(a) 40 (b) 80

(c) 120 (d) 160.

45. For the cantilever beam as shown in fig. the cross- sectional area of the steel, aluminium and,bronze part is

500 mm2,400 mm2,and 200 mm2. respectively. The maximum P that will not exceed a stress in steel of 140 MPa,

inaluminium of 90 MPa or in Bronze of 100 MPa is .

steel

Aluminium
Bronze

4P  P  2P

(a) 25000N (b) 36030 N

(c) 14000 N (d) 10000 N

46. ABC is a rigid bar. It is hinged at A and suspended at B and C by two wires, BD and CE made of copper and steel

respectively, as shown in the given fig. The bar carries a load of kN at F, midway between B and C. Given that.

Ac = 4cm2, As = 2cm2, Ec = 1 x 105 N/mm2, Es= 2 x 105 N/mm2.

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STRENGTH OF MATERIAL

Subscript c and s stands for copper and steel. If the
extensions in the steel and copper wires are Asand Ac respectively, the rato As / Ac would be

(a) 1/4 DE
(b) 4
(c) 2 Copper Steel 1m
(d) 1 / 2


BF 

10 kN C

1m  1m 
 
47. A block of steel is loaded by a tangential force on its top surface while the bottom surface is held rigidily. The
deformation of the block is due to.

F

(a) shear only (b) bending only

(c) shear and bending (d) torsion

48. A gradually applied load W is suspended by wire ropes AB and CD as shown in the fig. The wires AB and CD, made

of the same material and of the same cross section are connected to a rigid block from which the load W is

suspended in such a way that both the ropes stretch by the same amount. if the stress in AB and CD are p and p
12

respectively, then the ratio p1/p2 will be. A C

(a) 3 / 2 4m A p2 p2 6m
(b) 2 / 3  D 
(c) 9 / 4
(d) 4 / 9  xW

49 Amild steel bar is in three parts, each 20 cm long. The diameters of part AB,CB and CD are 2cm and 3 cm respectively.

The bar is subjected to an axial pull of 4 t as shown in the given fig. If E = 2 x 106 kg/cm2 and the elongation in the

three parts of the bar and A1,A2, and A3.respectively, then the ratio of the greatest to the least of these elongations

will be . 2cm 1 cm 3 cm
(a) 9 B C
(b) 4 A D 4t
(c) 3 4t

(d) 2 20 cm  20 cm   
20 cm

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50. Match the following using the codes given below.

Type of material General value of Poisson’s ratio

A. Concrete - 1. 0

B. Cork - 2. 0.15

C. Rubber - 3. 0.25

D. Isotropic Materials - 4. 0.33

5. 0.5

CODES :

ABCD

(a) 2 1 5 4

(b) 2 1 5 3

(c) 3 1 5 4

(d) 3 5 1 4

51. Match list I with list II and select the correct answer using the codes given below the lists:

List I (Material) List II (Modulus of Elasticity N/mm2)

A. Steel - 1. 0.6 x 105

B. Cast iron - 2. 1 x 105

C. Aluminium - 3. 2 x 105

D. Timber - 4. 0.1 x 105

Codes :-

ABCD

(a 3 2 1 4

(b) 2 3 1 4

(c) 3 2 4 1

(d) 2 3 4 1

52. Consider the following statements :

A : An isotropic material is always homogeneous

B : An isotropic material is one in which all the properties are the same in all the direcions at every point . Of these

statements .

(a) both A and B are true (b) both A and B are false

(c) A is true but B is false (d) A is false but B is true.

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

PRACTICE QUESTIONS (ANS.)
1-b, 2-a, 3-a, 4-a, 5-b, 6-d, 7-b, 8-a, 9-d, 10-c, 11-c, 12-c, 13-b, 14-b, 15-c, 16-a, 17-c, 18-b, 19-b, 20-d, 21-b, 22-d, 23-d, 24-a,
25-c, 26-b, 27-a, 28-c, 29-d, 30-b, 31-c, 32-c, 33-c, 34-d, 35-b, 36-b, 37-d, 38-d, 39-d, 40-d, 41-b, 42-b, 43-b, 44-d, 45-d, 46-d,
47-a, 48-a, 49-a, 50-b, 51-a, 52-d.

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STRENGTH OF MATERIAL

TEST PAPER

UNIT - I

TIME : 90 MINUTES ] [ M.M. : 50 MARKS

----------------------------------------------------------------------------------------------------------

Question 1 to 10 will carry 1 mark each

1. Given that for an element in a body of homogenous isotropic material subjected to plane stresses x,  y and z

are normal strains in x, y and z directions respectively and is the Poisson’s ratio . the magnitude of unit volume

charge of the element is given by (b) x - ( y +  z )
(d) (1 / x) + (1 /  y)+ (1 /  z)
(a) x + y + z
(c)  (  x +  y +  z)

2. A solid metal bar of uniform diameter D and length ‘L’is hung vertically from a ceiling. if the density of the material

of the bar is p and the modulus of elasticity is E, then the total elongation of the bar due to its own weight is .

(a) pL/ 2E (b) pL2 / 2E

(c) pE/ 2L (d) pE/ 2L2.

3. In an experiment it is found that the bulk modulus of a material is equal to its shear modulus. The poisson’s ratio is

(a) 0.125 (b) 0.250 (c) 0.375 (d) 0.500

4. The ability of material to absorb a large amount of energy is :

(a) Ducitlity (b) Hardness

(c) Toughness (d) Resilience

5. For metals which do not have a well- define yield point, the proof stress is determined by drawing a line parallel to

he initial tangent at an offset of m :

(a) 0.2 % (b) 0.5 % (c) 1.0 % (d) 2.0 %

6. Match list - I (Mechanical property) with list - II (Feature) and select the correct answer using the codes given below

the lists:

List - I List - II

A. Creep - 1. Amenability to go through changes of shape without rupture.

B. Tenacity - 2. Susceptibility to deform with the time under sustained loading.

C. Ductility - 3. Ultimate tensile strength

D. Brittleness - 4. Susceptibility to fail suddenly without warning.

Codes :

ABCD

(a) 4 1 3 2

(b) 2 3 1 4

(c) 4 3 1 2

(d) 2 1 3 4

7. Match list - I with list - II and select the correct answer using codes given below the lists:

List- I (Materials) List - II (characteristic)

A. Inelastic material - 1. No plastic zone

B. Rigid plastic material - 2. Large plastic zone

C. Ductile material - 3. Strain is not recovered after unloading

D. Brittle material - 4. Strain is zero upto a stress level and then stress remains constant.

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Codes : MECHANICAL ENGINEERING
A
BCD
(a) 3 421
(b) 3 412
(c) 4 321
(d) 4 312

8. Match list -I with list - II and select the correct answer using the codes given below the lists:

List- I (Property) List- II (characteristic)

A. Fatigue - 1. Material continues to deform with time under sustained loadings.

B. Creep - 2. Decreased resistance of material to repeated reversals of stress.

C. Plasticity - 3. Material has a high probability of not failing under reversals of stress of magnitude

below the lists:

D. Endurance limit- 4. Material continues to deform without any further increase in stress.

Codes :

ABCD

(a) 2 1 4 3

(b) 2 1 3 4

(c) 1 2 4 3

(d) 1 2 3 4

9. Match list-I wiht list-II and select the correct answer using the codes given below:

List - I List-II

(various test stages) (Observation)

A. I stage - 1. Yield point

B. II stage - 2. Limit of proportionality

C. III stage - 3. Breaking stress

D. IV stage - 4. Ultimate stress

Codes :

ABCD

(a) 2 1 3 4

(b) 2 1 4 3

(c) 1 2 4 3

(d) 1 2 3 4

10. Which of the following statement is false ?
(a) The stress dependent part of the plastic deformation is referred to as creep, and the time dependent part which
is also influenced by the temperature as slip.
(b) In case of ductile material possessing a well-defined yield point, the proportional limit almost coincides.
(c) A fatigue failure is of a brittle nature even for materials which are normally ductile .
(d) The endurance limit for machined and polished specimens is higher than for rolled or fogged components

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STRENGTH OF MATERIAL

Question 11 to 30 will carry 2 marks each

11. Two bars of same size but of different materials are subjected to same tensile force. If the bars have their elongation

in the ratio of 4 : 6, then the ratio of modulus of elasticity of the two materials would be .

(a) 4 : 6 (b) 6 : 4

(c) 4 : 10 (d) 16 : 36

12. A mild steel bar is 40 cm long. The lengths of parts AB and BC of the bar 20 cm each. it is loaded as shown in the
given fig. The ratio of the stresses 1 in part AB to 2 in part BC is. P1 = 1000 kg, P2 = 1000 kg.

(a) 2 A

(b) 0.5 dia - 2 cm 20cm 
(c) 4
(d) 0.25  B
20cm
dia - 2 cm  
P

C
P2

13. The volumetric strain of a cylindrical shell with an internal pressure is equal to.

(a) 2 longitudinal strain net circumferential strain.

(b) 2 longitudinal strain 1/2 net circumferential strain.

(c) 1/2 longitudinal strain 1/2 net circumferential strain.

(d) longitudinal strain 2 net circumferential strain.

14. A steel cube of volume 8000 cc is subjected to all round stress of 1330 kg/cm2. The bulk modulus of the material is
1.33 x 106 kg/cm2. The volumetric change is.

(a) 8 cc (b) 6 cc

(c) 0.8 cc (d) 103cc

15. An elastic bar of length ‘L’, cross- sectional area A, young’s modulus of elasticity E and self-weight W is hanging

vertically. It is subjected to a load P applied axially at the bottom end. The total elongation of the bar is given by.

(a) WL / AE + PL / AE (b) WL / 2AE + PL / AE

(c) WL / 2AE + PL / 2AE (d) WL / AE + PL /2 AE.

16. A prismatic bar of volume ‘V’is subjected to a compressive force in the longitudinal direction. if the Poisson’s ratio

of the material of the bar is and the longitudinal strain is ‘e’ then the final volume of the bar will be .

(a) (1 + e) (1- )2 V. (b) (1 - e2) (1 +  e) V.

(c) (1 + e) (1 +  e)2 V. (d) (1 - e) (1 + e )2 V.

17. A square bar of certain material with 4 cm side, is subjected to a pull of 16 T, where by the extension is 0.1cm in a

length of 200 cm. If the Poisson’s ratio is 1/4, the rigidity modulus of the material in kg / cm2 .
(a) 2 x 106
(b) 1.6 x 106
(c) 1.8 x 106
(d) 0.8 x 106

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MECHANICAL ENGINEERING

18. A cylindrical bar fo 20 mm diameter and 1 m length is sub jected to a tensile test. its longitudinal strain is 4 times
that of its lateral strain. if the modulus of elasticity is 2 x 105 N / mm2. then its modulus of rigidity will be.
(a) 8 x 106 N / mm2
(b) 8 x 105 N / mm2
(c) 0.8 x 104 N / mm2
(d) 0.8 x 105 N / mm2.

19. A round bar made of same material consists of 3 parts each of 100 mm length having diameters of 40mm, 50mm and
60 mm respectively. If the bar is subjected to an axial load of 10kN, the modulus elasticity E is given in kN/ mm2 . the

change n length of the bar in ‘mm’ is .
(a) (0.4 /E) (1/16 + 1/25 + 1/36) mm
(b) (4 /E) (1/16 + 1/25 + 1/36) mm
(c) (0.4 /E) (1/16 + 1/25 + 1/36) mm
(d) (40 /E) (1/16 + 1/25 + 1/36) mm.

20. The shear modulus of most materials with respect to the module of elasticity is.

(a) More than half

(b) Less than half

(c) Equal to half

(d) Unrelated

21. A plate of 1 mm thick and 5 cm wide has a rivet hole of diameter 1 cm as shown in fig. It is subjected to a load of

1000 N. the maximum tensile stress in the plate is approximately .

(a) 20 MPa 1000 N 1000 N
(b) 25 MPa
(c) 60 MPa 
(d) 75 MPa

22. A steel rod of circular section tapers from 2 cm diameter to 1 cm diameter diameter over a length of 50 cm. If the

modulus of elasiticity of the material is 2 x 106 kg/cm2, then the increase the length under a pull of 3000 kg will be.

(a) 0.3/2cm (b) 30 / cm

(c) 300 /  (d) 750 cm

23. A square bar of certain material with 4 cm side, is subjected to a pull of 16 T, where by the extension is 0.1cm in a

length of 200 cm. If the Poisson’s ratio is 1/4, the rigidity modulus of the material in kg / cm2 .

(a) 2 x 106 (b) 1.6 x 106 (c) 1.8 x 106 (d) 0.8 x 106

24. A bar 4 cm in diameter is subjected to an axial load of 4 t . The extension of the bar over a gauge length of 20 cm is

0.03 cm. The decrease in dia is 0.0018 cm. The poisson’s ratio is

(a) 0.25 (b) 0.30 (c) 0.33 (d) 0.35

25. A free bar of length 1 is uniformly heated from 00C to a temprerature 10C.  is the coefficient of linear expansion and

E the nodulus of elasticity. The stress in the bar is [GATE-1992][ME]
a) tE
b) tE/2

c) zero d) none of these

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STRENGTH OF MATERIAL

26. Two indentical circular rods of same diameter and same length are subjected to same magnitude or axial tensile
force. One of the rod is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out
of cast iron having the modulus of elasticity of 10 GPa. Assume both the materials to be homogeneous and isotropic
and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are with in
the proportional limit of the respective materails. Which of the following observations is correct ? [GATE-03][ME]
a) Both rods elongate by the ssame amount
b) Mild steel rod elongates more than the cast iron
c) Cast iron rod elongates more than the mild steel rod
d) As the stresses are equal strains are also equal in both the rods

27. If a steel tyre is heated and struck on a rigid wheel after cooling the tyre will de subjected to .

(a) normal compression (b) normal tension (c) Hoop compression (d) Hoop tension

28. A steel frame is fitted with an equal length of an aluminium rod at room temp. (total area of steel = area of aluminum

200mm2 ).When fitted they are in stress free state. Given Es = 210GPa; Ea= 70 GPa; s = 12.5 x 10-6 / 0C,
a = 25 x 10-6 / 0C, for a temperature rise of 800C the load in the aluminium bar is .

(a) 21.0kN (b) 18kN (c) 15.8 kN (d) 10.5 kN

29. A steel bar of 2m length is fixed at both ends at 200, The coef ficient of thermal expansion is 11 x 106 / 0C and the

modulus of elasticity is 2 x 106 kg / cm2. If the temperature is changed to 180C, then the bar will experience a stress

of .

(a) 22 kg / cm2 (tensile) (b) 22 kg / cm2 (compressive)

(c) 44 kg / cm2 (compressive) (d) 44 kg / cm2 (tensile)

30. A 600 mm long and 50 mm diameter rod of steel (E = 200 GPa, =12 x 106 / 0C) is attached at the ends to

unyielding supports. When the temperature is 300C there is no stress in the rod. After the temperature of the rod

drops to 200C, the axial stress in the rod will be.

(a) 24 MPa (tensile) (b) 72 MPa (compressive) (c) 120 MPa (tensile) (d) 144 MPa (compressive).

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

“Sucess is not measured by what one brings,
but rather by what one leaves.”

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MECHANICAL ENGINEERING

2 SHEAR FORCE AND BENDING MOMENT

1. The bending moment diagram shown in fig. shown corresponds to the shear force diagram in.
[IES - 99]

(b)
(a)

(c) (d)

2. For the simply supported beam of length L, subjected to a uniformly distributed moment M kN-m per
unit length as shown in the figure, the bending moment (in kN-m) at the mid-spam of the beam is
[GATE 2010][CE]

M kN-m per unit length

L

a) zero b) M c) ML d) M/L

3. Consider the following statements : [IES - 2003]

In a cantilever subjected to a concentrated load at free end.

1. The bending stress is maximum at the free end.

2. The maximum shear stress is constant along the length of the beam.

3. The slope of the elastic curve is zero at the fixed end .

Which of these statements are correct?

(a) 1,2 and 3 (b) 2 and 3

(c) 1 and 3 (d) 1 and 2

4. A simply supported beam of span l is subjected to a uniformlyvarying load having zero intensity at the

left support and w N/m at the right support. The reaction at the right support is. [IES - 2003]

(a) wl/2 (b) wl/5

(c) wl/4 (d) wl/3

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STRENGTH OF MATERIAL

5. Match List-I with List-II and select the correct answer. [IES - 2009]

List- I

A. Bending moment is constant

B. Bending moment is maximum or minimum.

C. Bending moment is zero.

D. Loading is constant.

List - II

1. Point of contraflexure

2. Shear force changes sign

3. Slope of shear force diagram is zero over the portion of the beam

4. Shear force is zero over the portion of the beam.

Codes:

ABCD

(a) 4 1 2 3

(b) 3 2 1 4

(c) 4 2 1 3

(d) 3 1 2 4

6. List - I shows different loads acting on a beam and List - II shows different bending moment

distributions.Match the load with the corresponding bending moment diagram. [GATE 2003][CE]

List - I List - II

A. 1.
2.
<

B.

C. 3.

D. 4.

5.

Codes :

ABCD

a) 4 2 1 3

b) 5 4 1 3

c) 2 5 3 1

d) 2 4 1 3

7. A cantilever beam of 2m length supports a triangularly distributed load over its entire length, the

maximum of which is at the free end. The total load is 37.5kN. What is the bending moment at the

fixed end ? [IES - 2009]
(a) 50 x 106 Nmm
(c) 100 x 106 Nmm (b) 12.5 x 106 Nmm
(d) 25 x 106 Nmm

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MECHANICAL ENGINEERING

8. A cantilever beam having 5m length is so loaded that it develops a shear force of 20 T and a bending

moment of 20T-m at a section 2m from the free end. Max shearing force and max bending moment

developed in the beam under this load, are respectively 50 T and 125 T-m.The load on the beam is

. [IES - 95]

(a) 25T concentrated load at free end

(b) 20T concentrated load at free end

(c) 5T concentrated load at free end 2 T/m load over entire length.

(d) 10 T/m udl over entire length.

9. A simply supported beam PQ is loaded by a moment of 1 kN-m at the mid-spam of the beam as

shown in the figure. The reaction forces RY and RQ at supports P and Q respectively are
[GATE 2011][ME]

1kN-m Q

P

V

< 1m >

a) 1kN downward, 1kN upward b) 0.5 kN upward, 0.5 kN downward

c) 0.5 kN downward, 0.5kN upward d) 1kN downward, 1 kN upward

10. Two bars AB and BC are connected by a friction less hinge at B. The assembly is supported and

loaded as shown in fig. Draw the shear force and bending moment diagrams for the combined beam,

AC, clearly labelling the important values.Also indicate your sign convention. (GATE-96)

AB 100 kN 100 kN

DE

C

oo

1.5m 2 m 1m 1 m

11. A 2m long beam BC carries a single concentrated load at its mid-span and is simply supported at

ends by two cantilevers AB 1m long and CD 2m long as shown in the fig. [IES - 97]

The shear force at endAof the cantilever AB will be.

100 kgf

A BC D

1m 2m 3m

(a) 0 (b) 40 kgf (c) 50 kgf (d) 60 kgf

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STRENGTH OF MATERIAL

12. A simply supported beam carries a load ‘P’ through a bracket, as in shown in fig. The maximum

bending moment in the beam is. l/2 a (GATE-2K)
(a) pl / 2
(b) pl / 2 + aP / 2 

(c) (pl / 2 +ap)/2  l 
(d) pl / 2 - aP 

13. A concentrated load of P acts on a simply supported beam of span L at a distance L / 3 from the left

support. The bending moment at the point of application of the load is given by. (GATE-03)

(a) PL / 3 (b) 2PL / 3 (c) PL / 9 (d) 2PL/ 9

14. A lever is supported on two hinges at A and C. it carries a force of 3kN as shown in the above fig.

The bending moment at B will be. [IES - 98]
3kN

1m BC
A

1m 1m 1m

(a) 3kN-m (b) 2 kN-m (c) 1 kN-m (d) zero

15. A mass of 35 kg is suspended from a weightless barAB which is supported by a cable CB and a pin

at A as shown in Fig. The pin reactions atA on the barAB are [GATE 2003][CE]

a) Rx = 343.4 N C
Ry = 755.4 N
125 mm < > <
b) Rx = 343.4 N
Ry = 0 AB

c) R = 755.4 N < >
x
Ry = 343.4 N  275 mm

d) Rx = 755.4 N
Ry = 0

16. A frameABCD is supported by a roller at Aand is on a hinge at C as shown below :

The reaction at the other Ais given by [GATE 2000][CE]

a) P b) 2P L/2 L/2 L/2
c) P d) zero
< >< >< >
2
B PG p
D

L



<>

A

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MECHANICAL ENGINEERING

17. [IES - 2009]
2kN 6kN

A C
1m 1m
B

2m 1m

An over hanging beam ABC is supported at points A and B, as shown in the above fig. Find the
maximum bending moment and the point where it occurs.
(a) 6 kN-m at the right support
(b) 6 kN-m at the left support.
(c) 4.5 kN-m at the right support
(d) 4.5 kN-m at the midpoint between the supports.
18. A horizontal beam carrying uniformly distributed load is supported with equal overhang as shown in
the given fig. resultant bending moment at the mid span shall be zero if a /b is. [IES - 2002]

a b a
(b) 2 / 3 (c) 1 / 2
(a) 3 / 4 (d) 1 / 3

19. Which one of the given bending moment diagrams correctly represents that of the loaded beam shown

in fig.  P
2I
I

L/2  L/2 


(a) (b) (c) (d)

20. Two people weighing W each are sitting on a plank of length Lfloating on water at L/4 from either end.
Neglecting the weight of the plank, the bending moment at the centre of the plank is
[GATE 2009][CE]

WL WL WL d) zero
a) 8 b) 16 c) 32

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STRENGTH OF MATERIAL

21. Abeam subjected to a load P is shown in the given fig. The bending moment at the supportAAof the

beam will be. L/2 L/2 [IES - 97]

(a) PL A
(b) PL/2 A
(c) 2PL
(d) 0 L/2

P

L/2

22. The bending memenet diagram for a beam is given below [GATE 2005][CE]

---------- b 200 kN-m
--------------------
a

100 kN-m

a’ b’

 

0.5m 0.5m 1m 1m

The shear force at sections aa’ and bb’ respectively are of the magnitude

a) 100 kN, 150 kN b ) zero 100 kN c) zero, 50 kN d) 100 kN, 100 kN

Questions 23 and 24 are based on the given fig.
23. The bending moment at ABC and D respectively in kN-m.

(a) 40,90,130 and 150 D 3 C
(b) 20, 0, 30 & 20 A m D
(c) 20, 0 , 40 & 40 B
(d) 0, 20, 30 & 40
20 KN 2.5
E m

2 (d) 0,20,0

m

24. The axial thrust in the members AC,CD and DE in kN respectively.

(a) 20,20,20 (b) 0,0,20 (c) 0,20,20

Questions 25 and 26 are based on the given fig.
A simply supported beam with overhang in one side is loaded, as shown, with one of the diagonals of
the square cross section of the beam is kept horizontal

25. Shear force in kN at P is 100 kN

(a) 21.2 (b) 41.4 0. 25m 25 kN/
P m

(c) 61.6 (d) 81.8 SQ

26. The bending moment, kN-m, at S is 21
m m 1 1. 5 m

m

(a) 29.23 (b) 39.23 (c) 49.2 (d) 59.23

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MECHANICAL ENGINEERING

27. Asimplysupported beamAB has the bending moment diagram as shown in the following figure :

M [GATE 2006][CE]
A C DB

MM

L L L

The beam is possibly under the action of following loads
a) Couples of M at C and 2M at D
b) Couples of 2M at C and M at D
c) Concentrated loads of M/L at C and 2M/L at D
d) Concentrated load of M/L at C and couple of 2M at D
28. The shear force diagram of a loaded beam is shown in the following fig.
The maximum bending moment in the beam is

14
kN

(a) 16kN-m 2 kN
(b) 11kN-m
(c) 28kN-m A C B
(d) 8kN-m 2
1
m m

- 16 kN

29. With reference to following fig. match list-I with list -II and select the correct answer by using codes
given below the lists:

37 kg C 16 kg/m D
AB 4m

2m 3m

List - I List - II

A. S.F. at A is : C 16 kg
B. S.F. at B is : 3 58 kg
C. S.F. at C is : 2 43 kg
D. S.F. at D is : 1 48 kg
Codes: 1
D
AB 4
(a) 1 2 1
(b) 3 4 2
(c) 3 1 3
(d) 2 4

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STRENGTH OF MATERIAL

30. A simply supported beam with equal overhang on both sides is loaded as shown in the fig. If the
bending moment at mind span is zero, then the percentage over hang on each side will be.

(a) 33.3
(b) 25
(c) 20
(d) 15

l

Date for Q : 31 - 32 are given below. Solve the problems and choose the correct answers,

Athree-span continuous beam has an internal hinge at B, Section B is at the mid-spam ofAC. Section

E is at the mid-spam of CG. The 20 kN load is applied at section B whereas 10kN loads are applied

at sections D and F as shown in the figure. Spam GH is subjected to uniformly distributetd load of

magnitude 5 kN/m. For the loading shown, shear force immediate to the right of Section E is 9.84 kN

upwards and the sagging moment at section E is 10.31 kN-m. [GATE 2002][CE]

kN 10 kN 10 kN

D F
  20 5 kN/m

E 

B In the figure

CD = DE = EF = FG = 1m

AC G H



4m 4m 4m

31. The magnitude of the shear force immediate to the left and immediate to the right of section B are,

respectively

a) 0 and 20kN b) 10 kN and 10 kN

c) 20 kN and 0 d) 9.84 kN and 10.19 kN

32. The vertical reaction at support H is

a) 15 kN upward b) 9.84 kN upward

c) 15 kN downward d) 9.84 kN downward

33. A simply supported beam of length L is subjected to a varying distributed load sin (3x/L) Nm-1

where the distance x is measured from the left support. The magnitude of the vertical reaction force in

N at the support is (GATE-13)

(a) Zero (b) L/3 (c) L/ d2L/

 Acantilever beam OP is connected to another beam PQ with a pin joint as shown in the figureAload

of 10 kN is applied at the mid-point of PQ. The magnitude of bending moment (in kN-m) at fixed end

O is __________ (GATE-15-Set 2)

(a) 2.5
(b) 5
(c) 10
(d) 25

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MECHANICAL ENGINEERING

35. For the overhanging beam shown in figure the magnitude of maximum bending moment (in kN-m)

is______ (GATE-15-Set 3)

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

SHEAR FORCE AND BENDING MOMENT (ANS.)
1-b, 2-a, 3-b, 4-d, 5-c, 6-d, 7-a, 8-d, 9-a, 10 : R = 100kN, R = 200 kN, 11-c, 12-c, 13-d, 14-c,

BC

15-d, 16-d, 17-a, 18-c, 19-b, 20-d, 21-b, 22-c, 23-c, 24-d, 25-b, 26-c, 27-a, 28-a, 29-c, 30-b,
31-a, 32-b, 33 - b, 34 - c, 35 - 40.

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STRENGTH OF MATERIAL

PRACTICE QUESTIONS

1. Consider the following statements:

If at section distant from one of the ends of the beam, M represents the bending moment V the shear force

and w the intensity of loading, then. [IES-95]

1. dM/dx = V

2. dV/dx = w

3. dw/dx = y (the deflection of the beam at the section)

of these statements .

(a) 1 and 3 are correct (b) 1 and 2 are correct

(c) 2 and 3 are correct (d) 1,2 and 3 are correct

2. If the shear force acting at every section of a beam is of the same magnitude and of the same direction

then it represents a . [IES-96]

(a) simply supported beam with a concentrated load at the centre.

(b) overhanging beam having equal overhung at both supports and carrying equal concentrated loads

acting in the same direction at the free ends.

(c) cantilever subjected to concentrated load at the free end.

(d) simply supported beam having concentrated loads of equal magnitude and in the same direction acting

at equal distances from the supports.

3. The given fig shows the shear force diagram for the beam ABCD bending moment in the portion BC of the

beam. CD [IES-96]

AB

(a) is a non zero constant (b) is zero

(c) varies linearly form B to C. (d) varies parabolically from B to C.

4. The maximum bending moment in a simply supported beam of length L loaded by a concentrated load

W at the mid point is given by. [IES-96]

(a) WL (b) WL/2

(c) WL/4 (d) WL/8

5. If a beam is subject to a constant bending moment along its length then the shear force will.

(a) also have a constant value everywhere along its length. [IES-97]

(b) be zero at all sections along the beam.

(c) be maximum at the centre and zero at the ends.

(d) zero at the centre and maximum at the ends.

6. For the beam shown in the above fig. the elastic curve between the supports B and C will be.

PP [IES-98]

BC

a 2b a

(a) circular (b) parabolic (c) elliptic (d) a straight line

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MECHANICAL ENGINEERING

7. A loaded beam is shown in the below fig. The bending moment diagram of the beam is best represented

as. [IES-2000]

W W W
L

L 2L L

(a) (b)

(c) (d)

8. At a certain section at a distance ‘x’ from one of the supports of a simply supported beam, the intensity

of loading , bending moment and shear force are Wx ,Mx and Vx respectively. If the intensity of loading
is varying continuously along the length of the beam, then the in valid relation is. [IES-2000]

(a) Slope Qx= Mx / Vx (b) Vx= d Mx / dx
(c) Wx= d2Mx / dx2 (d) Wx= dVx / dx

9. The shear force diagram is shown above for a loaded beam. The corresponding bending moment diagram

is represented by. [IES-2003]

++

--

+ +

(a) - (b) - -

-

+ (d) +
- --
(c)

-

10. A beam of length 4L is simply supported on two supports with equal overhangs of L on either sides and

carries three equal loads, one each at free ends and the third at the diagrams represents correct

distribution of shearing force on the beam? [IES-2004]

(a) (b)

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STRENGTH OF MATERIAL

(c) (d)

11. The point of contraflexure is a point where: [IES-2009]

(a) Shear force changes sign (b) Bending moment changes sign

(c) Shear force is maximum (d) Bending moment is maximum

12. A uniformly distributed load w (in kN/m) is acting over the entire length of a 3m long cantilever beam. if the

shear force at the mid point of cantilever is 6 kN. What is the value of w ? [IES-2009]

(a) 2 (b) 3 (c) 4 (d) 5

13. For a simply supporting beam on two end supports the Bending Moment is maximum : [GATE 1989][ME]

a) usually on the supports b) always at mid span

c) where there is not shear Force d) where the deflection is maximum

14. A block of steel is loaded by atngential force on its top surface while the bottom surface is held rigidly. The

deformation of the block is due to F [GATE 1992][ME]
a) shear only >

b) bending only

c) shear and bending

d) torsion

15. The number of points of contraflexure in a simply supported beam subjected to eccentric load at an intermediate

point is.

(a) 0 (b) 1 (c) 2 (d) 3

16. W W

A ............. C ............. D L/3 B
L/3

L

Consider the simply supported beam AB subjected to the point loads of equal magnitude as shown in the

above diagram:

Which one of the following statements is correct?

The portion CD of the beam is

(1) In pure bending

(2) in pure shear

(3) having maximum bending moment

(4) having maximum shear force

a) 1 & 2 are correct b) 1 & 3 are correct

c) 2 & 3 are correct d) all are correct

17. In a simply supported beam of length L with a triangular load W varying from zero at one end to the

maximum value at the other end, the maximum bending moment is

(a) WL/3 (b) 2WL / 93 (c) WL/4 (d) WL/93

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MECHANICAL ENGINEERING

18. If the beam is supported so that there are only three unknown reactive elements at the supports. These

can be determined by using the following fundamental equation of statics.
(a)H = 0
(b) V = 0
(c) H = 0; V = 0
(d) H = 0; V = 0; M = 0
19. For a simply supported beam of length L, the bending moment M is described as, M = a (x -x3/L2),
0  x < L; where a is a constant. The shear force will be zero at

(a) The supports (b) X = L/2
(c) x = L/3 (d) x = L/3

Directions : The following items consists of two statements; one labeled as ' Assertion (A)' and their other

as 'Reason (R)' Select the correct answer to these items using the codes given below.

Codes:

(a)Both A andR are true and R is the correct explanationof A

(b)Both A and R aretrue and R is not a correct explanationof A

(c) A is true but R is false

(d) A is false but R is true

20. Assertion (A): Bending moment in a beam is maximum at a section where shear force is zero.

Reason (R): Shear force at a section is given by the rate of change of bending moment.

21. Assertion (A): The maximum bending moment occurs where the shear force is either zero or changes

sign.

Reason (R) : If the shear force diagram line between the two, points is horizontal. The BM diagram line is

inclined. But if the SF diagram is inclined, the BM diagram is a parabola of second degree.

22 With reference to following fig. match list-I with list -II and select the correct answer by using codes given

below the lists:

37 kg 16 kg/m D
AB C

2m 3m 4m

List - I List - II
16 kg
A. S.F. at A is : 58 kg
43 kg
B. S.F. at B is : 48 kg

C. S.F. at C is : D
4
D. S.F. at D is : 1
2
Codes: 3

AB C
3
(a) 1 2 2
1
(b) 3 4 1

(c) 3 1

(d) 2 4

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STRENGTH OF MATERIAL

23. Match list-I (Beams) with list-II (Shear force diagrams) and select the correct answer using the codes

given below the list

List - I List - II

P FT PQ R S T

A. 1.

QR S

P QR ST PQ R ST

B 2
zero value
M
PQ R S T
P QR ST
3
CM

P QR ST

D F FF 4 ST
ST
F PQ R

5 QR

P

ABCD

(a) 4 2 5 3

(b) 1 4 5 3

(c) 1 4 3 5

(d) 4 2 3 5

24. The B.M. at ‘A’ of structure shown a side is .

(a) 4t.m 2t 1t

(b) 2t.m 12
mm
(c) 3t.m
A
(d) 0

25. Bending moment distribution in a built beam is shown in the given fig. [IES - 2001]

C

AE
BD

The shear force distribution in the beam is represented by.

AC E

(a) (b) A E

AC A E
(c) E
(d) C

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MECHANICAL ENGINEERING

26.

M B
+
A

-
M

1/2 1/2

Figure shown above represents the BM diagram for a simply supported beam. The beam is subjected to which

one of the following ?

(a) A concentrated load at its mid - length. (b) A uniformly distributed load over its length.

(c) A couple at its mid - length. (d) Couple at 1/4 of the span from each end.

27. In the bending moment diagram for simply supported beam is of the form given below then the load acting

on the beam is.

(a) A concentrated force at C. AC B
(b) A uniformly distributed load

over the whole length of the beam.

(c) Equal and opposite moments applied at A and B

(d) A moment applied at C.

28. A cantilever is loaded as shown in the above fig. The bending moment along the length is .

(a) uniform P



(b) uniformly varying l a 
(c) zero
(d) concentrated at the free end P

29. A member is loaded by a set of loads shown in fig. the member is subjected to .

(a) a purely axial load

(b) shear force and BM

(c) shear force and axial load

(d) shear, BM and Axial force

30. The shear force diagram of a loaded beam is shown in the following fig.

The maximum bending moment in the beam is

(a) 16kN-m 14
(b) 11kN-m kN

(c) 28kN-m 2 kN
(d) 8kN-m
A C B
2
1
m m

- 16 kN

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STRENGTH OF MATERIAL

31. Two bars AB and BC are connected by a frictionless hinge at B. The assembly is supported and loaded as
shown in fig. For the combined beam AC the maximum BM and SF will be.

WW

B C
Internal hinge

1. 2 11

5 m mm

32. The given fig shows the shear force diagram for the beam ABCD bending moment in the portion BC of the

beam.

(a) is a non zero constant CD

(b) is zero AB

(c) varies linearly from B to C

(d) varies parabolically from B to CTwo Marks Questions

33. The given fig.shows a beam BC simply supported at C and hinged at B(Free end) of a cantilever AB. The

beam and the cantilever carry forces of 100 kg and 200 kg respectively. The bending moment at B is

(a) 0

(b) 100 kg-m AC B D
(c) 150 kg-m

(d) 200 kg-m

34. If the shear force acting at every section of a beam is of the same magnitude and of the same direction

then represents a

a. simply supported beam with a concentrated load at the center

b. overhang beam having equal overhang at both supported and carrying equal concentrated loads acting

in the same direction at the free ends

c. cantilever subjected to concentrated load at the free end

d. simply supported beam having concentrated loads of equal magnitude and in the same direction acting

at equal distances from the supports.

35. The bending moment diagram shown in fig (1) corresponds tothe shear force diagram in.

(a) (b)
(c) (d)

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MECHANICAL ENGINEERING

36. Which one of the following portions of the loaded beam shown in fig. is subjected to pure bending?

(a) AB

(b) DE

(c) AE A BC D E
(d) BD

37. In case of a cantilever carrying uniformly varying load, the ratio of maximum bending moment at free end

when the load increases from zero at fixed end to W at free end and that when the load increases from zero

at free end to W at fixed end is

(a) 1 (b) 2

(c) 1/2 (d) 1/4

38. A simply supported beam with equal overhang on both sides is loaded as shown in the fig. If the bending

moment at mind span is zero, then the percentage over hang on each side will be.

(a) 33.3

(b) 25

(c) 20

(d) 15 l

39. A beam of length L carries a udl of ‘w’ per meter. The beam is supported on two simple supports with equal

distance ‘a’ from the ends. its value for the bending moment in the beam is as small as possible will be.

(a) 0.207L (d) 0.707L

(c) 1.414 (d) not possible to determine

40. A beam of length 10m carries a udl of 20 kN/m over its entire length and rests on two simle supports. In

order that the maximum BM produced in the beam is the least possible, the supports must be placed from

the ends at a distance of.

(a) 5.86 m (b) 4.14 (c) 2.93 (d) 2.07 m

41. A cantilever carrying a uniformly distributed load is shown in fig. L select the correct B.M. diagram of the

cantilever.

(a) (b)

(c) (d)

42. Which of the following statements are correct:

1. Bending moment may be defined as the algebraic sum of the moments of all forces on either side of the

section

2. The rate of change of bending moment is equal to shear force at the section .

(a) 1 only (b) 2 only

(c) 1 and 2 (d) none

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STRENGTH OF MATERIAL

43. Which one of the following fig. represents the correct shear force diagram for the loaded beam shown in the

given fig I ? WW

a

(a) (b)

(c) (d)

44. A simply supported beam has equal overhanging lengths and carries equal concentrated loads P at ends.

Bending moment over the length between the supports. [IES-2003]

(a) is zero (b) is a non zero constant.

(c) varies uniformly from one support to the other. (d) s maximum at mid -span

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

“It is always easier to believe than to deny.
Our minds are naturally affirmative”

SHEAR FORCE AND BENDING MOMENT : PRACTICE QUESTIONS (Ans.) :
1-b, 2-c, 3-a, 4-c, 5-b, 6-b, 7-a, 8-a, 9-a, 10-d, 11-b, 12-c, 13-c, 14-c, 15-b, 16-b, 17-b, 18-d, 19-c, 20-a, 21-b, 22-c, 23-d, 24-d,
25-c, 26-d, 27-d, 28-a, 29-a, 30-a, 31-sol, 32-a, 33-a, 34-c, 35-b, 36-d, 37-b, 38-b, 39-a, 40-d, 41-c, 42-c, 43-a, 44-b.

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MECHANICAL ENGINEERING

TEST PAPER

STM : UNIT - II

TIME : 90 MINUTES ] [ M.M. : 50 MARKS

----------------------------------------------------------------------------------------------------------

Question 1 to 10 will carry 1 mark each

1. The bending moment (M) is constant over a length segment /(l) of a beam the shearing force will also be

constant over this length and is given by. [IES-96]

(a) M / I (b) M / 2I (c) M / 4I (d) none of the above

2. [IES-2008]

The shearing force diagram for a beam is shown in the above fig. The bending moment diagram is

represented by which one of the following ?

AB AB

(a) (b)

C C

AB AB

(c) (d)

CC

3. A freely supported beam at its ends carries a centralconcentrated load. and maximum bending moment
is M. If the same load be uniformly distributed over the beam length, then what is the maximum bending

moment ? (b) M / 2 (c) M / 3 [IES-2009]
(a) M (d) 2M

4. A beam having a double attached at mid spam is shown in the figure. The nature of forces in bem ‘ab’ is

P [GATE 1991][CE]
f
a) Bending and shear b
b) Bending, shear and torsion g
c) Pure torsion
d) Torsion and shear a

PC lengths
ed cd = cf
de = fg
ac = cb

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STRENGTH OF MATERIAL

5. The B.M. diagram of the beam shown in fig is

(a) a rectangle A B
(b) a triangle

(c) a trapezium l

(d) a parabola

6. The shape of S.F.D for a cantilever subjected to a couple at its free end is.

(a) No.S.F in any part of beam (b) Rectangular

(c) Linearly varying (d) Parabolic

7. A simply supported beam, as shown in fig, is loaded the maximum shear force in the beam is equal to

(a) wl/2 parabolic
(b) wl/3 loading

(c) wl/4  w
(d) w l

8. The shape of the bending moment diagram for a uniform cantilever beam carrying a uniformly distributed

load over its length is.

(a) a straight line (b) a hyperbola

(c) an ellipse (d) a parabola

9. A beam is simply supported at its ends and is loaded by a couple at its mid-span as shownin the fig A.

Shear force diagram for the beam is given by.

(a) (b)

(c) (d)

10. Match the list -I with list - II and select the correct answer using the codes given below the lists.

List - I List - II

(conditionof beam) (bending movement diagram)

A. Subjected to moment at the end of cantilever - 1. Triangle

B. Cantilever carrying U.D.L over the whole length - 2. Cubic parabola

C. Cantilever carrying linearly varying load from zero at the fixed end to - 3. Parabola

maximum at the support

D. A beam having load the centric and supported at the ends. - 4. Rectangle

ABCD

(a) 4 1 2 3

(b) 4 3 2 1

(c) 3 4 2 1

(d) 3 4 1 2

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MECHANICAL ENGINEERING

Question 2 to 30 will carry 2 marks each

11. Match list - I (Beam with loading) with list-II (B.M. diagram) and select the correct answer using the codes given

below:

List - I List - II

A. 1. B
Hinge A

A Roller
LB
w /m

B. B 2. B
A A B
w /m
C A
A 3

B

DA B 4

Codes:-

ABCD ABC D
2
(a) 3 4 2 1 (c) 1 3 4 3

(b) 1 2 3 4 (d) 2 1 4

12. Match list - I and list - II and select the correct answer using the codes below

List - I List - II

Beam and loading B.M.D

A 1.

B 2.

C 3.

D4

Codes:-
l /A2 B l / 2 C D

(a) 3 4 2 1
(b) 2 3 1 4
(c) 1 3 4 2
(d) 2 1 4 3
13. The ratio of reaction of ‘RA’ and ‘RB’ of the simply supported beam shown in the fig. below is .

(a) 1/2 A 5 kN 2 kN/m 3 kN
(b) 2/3 2m 2m 2m
(c) 3/2 B
(d) 1 2m

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STRENGTH OF MATERIAL

14. In the diagram shown the bending moment at fixed end is (in kN -m)

(a) 0 (b) 10 Hinge 2m 10
(c) 20 (d) 40 1m kN

4m

15. A beam is loaded as shown in fig. The maximum values of axial thrust and bending moment respectively.

(a) P.0.25Pl P
A hinge D 300 B C

(b) 0.25P,0.707Pa a
(c) 0.5P, 0.5Pl b
(d) 0.87P,0.25Pb
l

16. A small narrow barge is loaded as shown in fig. The reaction offered by water will be in the form of.

(a) parabolic concave outwards 3 kN/m 3 0kN
(b) trapezoidal with maximum ordinate at left end

(c) uniformly distributed .........................................

(d) uniformly varying with zero at ends

5 10 5 m 10
m m

17. A simply supported beam is loaded as shown in the fig. The maximum shear force in the beam will be.

(a) zero

(b) W W 2W 3W

(c) 10/4W

(d) 14/4W

18. The bending moment equation,Las a fLunction ofLdistaLnce X measured from the left end, for a simply

supported beam of span L m carrying a uniformly distributed load of intensity (1) N/m will be given by.
a. M = (WL/2)(L-X)-W/2 (L-X)2 N-m
b. M = (WL/2)X - WX2/2 N-m
c. M = (WL/2)(L-X)2 (W/2) (L-X)3 N-m
d. M = WX2/2 - WLX / 2 N-m

19. A simply supported beam as, shown in fig. the at reaction at B is equal to

(a) 2 kN up 4 kN
(b) 2 kN down
(c) 4 kN down 1 m 4 kN
(d) 4 kN up A 1m B

2m 2m

20. The bending moment, in kN units, at the mid span location ‘x’ in the beam with overhangs shown in the fig.

Equal to. 20 10
(a) 0 kN x kN
(b) - 10

(c) - 15 1m 1m 1m 1m
(d) - 20 Spring

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MECHANICAL ENGINEERING

21. A beam subjected to a load P is shown in the given fig. The bending moment at the section AA of the beam

will be. A

(a) PL A
(b) PL/2
(c) 2 PL Lp
(d) 0 L/2

22. An applied couple ‘M’ on a simply supported beam of span ‘L’ as shown. The absolute maximum bending

moment developed in the beam is.

(a) M/2 Mp
(b) M
(c) 3 M/2 l

(d) 2M

23. A unique relation between bending moment (M) and intensity of load (w) acting continuously a beam of

span (L) at a distance (x) along the axis (The flexural rigidity of beam is EI) is given by .

(a) M = wL2 / 12 (b) w = d2M/ dx2

(c) M = EI d2w /dx2 (d) wL2 / 12

24. For the loading given in the fig. below two statements I and II are made . W
I. The member AB carries shear force and bending moment BA

II. The member BC carries axial load and shear force C
Which of the statement is TRUE

a. statement I is true but II is false b. statement I is false and II is true

c. Both I and II are true d. Both I and II are false

25. Consider the following statements : A simply supported beam is subjected to a couple somewhere in the

span. It would produce.

1. a rectangular SF diagram 2. parabolic BM diagrams

3. both +ve and -ve BMs which are maximum at the point of application of the couple.

Of these statements

(a) 1, 2 and 3 correct (b) 1 and 2 are correct

(c) 2 and 3 are correct (d) 1 and 3 are correct

26. The reaction (in kN) at the support ‘A’ for the beam shown in the given fig. is

8 kN 10kN

AB

6  4 5

mm m
 






(a) 18 (b) 1.8 (c) 1.8 (d) 0.8

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STRENGTH OF MATERIAL

27. The beam is loaded as shown in fig-I. Select the correct B.M diagram

(a) (b) .............
.............
............. + ............. ............. +

A.......... B (c) (d)

C ............. ............. + ............. ............. ............. +

28. The shear force diagram (SFD) and Bending moment diagram (BMD) are shown in the fig.

S.F. D

- ve  1
B.M. D tm

The corresponding loading diagram would be.

A 1 1 B
tm B t mA
(a)
(b)

1 1 1
tm
(c) t m (d) t m

29. A simply supported beam is subjected to a distributed loading as shown in the diagram given below:

W N /m [IES-2004]

L

What is the maximum shear force in the beam?

(a) WL / 4 (b) WL / 2 (c) WL / 3 (d) WL / 6

30. A long construction member of uniform section is to be lifted using ropes at C and D as shownin fig. This

causes bending moments due to self-weight as shown. To minimize the peak value of bending moment,

the overhang ‘b’ shall be such that.

(a) M2 = 0 b b B M2
(b) M1 = M2 A CE D M1
(c) M2 = 2 M1
(d) b = 1/4 l

********************** M1

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MECHANICAL ENGINEERING

3 COMPLEX STRESS AND STRAINS

1. Mohr’s circle for the state of stress difiend by 30 0 MPa is a circle with (GATE 2006) (CE)

0 30

a) center at (0, 0) and radius 30 Mpa b) center at (0, 0) and radius 60 Mpa

c) conter at (30, 0) and radius 30 Mpa d) center at (30, 0) and zero radius

2. Consider the following statements : (GATE 2009) (CE)

1. On a principal plane, only normal stress acts

2. On a principal plane, both normal and shear stresses act

3. On a principal plane, only shear stress acts

4. Isotropic state of stress is independent of frame of reference

Whcih of the above statements is /are correct ?

a) 1 and 4 b) 2 only c) 2 and 4 d) 2 and 3

3. In a strained material one of the principal stresses is twice the other. The maximum shear stress in the

same case is  max . Then, what is the value of the maximum principal stress?

(a) max (b) 2max

(c) 4max (d) 8max

4. The figure shows the stress at a certain point in a stressed body. The magnitudes of normal stress in

the x and y directions are 100 MPa and 20 MPa respectively. The radius of Mohr’s stress circle

representing this state of tress is  (GATE 2004) (ME)
y

s) 120 b) 80 
x
c) 60 d) 40 

x

 
y

5. A material element subjected to a plane state of stress such that the maximum shear stress is equal

to the maximum tensile stress, would correspond to.

(a) 1 1  1
(b) 1 1

  1

(c) 1  1 (d) 1 2
1 1

  2
1

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