GATE - CE - Strength of Materials

7/28/2019 GATE - CE - Strength of Materials

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GATE CE Topic wise Questions

Strength of Materials

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YEAR 2009 ONE MARK

Question. 1

A thin walled cylindrical pressure vessel having a radius of 0.5 m and

wall thickness of 25 mm is subjected to an internal pressure of 700

kPa. The hoop stress developed is

(A) 14 MPa (B) 1.4 MPa

(C) 0.14 MPa (D) 0.014 MPa

Question. 2

The point within the cross sectional plane of a beam through which

the resultant of the external loading on the beam has to pass through

to ensure pure bending without twisting of the cross-section of the

beam is called

(A) moment centre (B) centroid

(C) shear centre (D) elastic center

YEAR 2009 TWO MARK

Question. 3

Consider the following statements :

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


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

Which of the above statements is/are correct ?

(A) 1 and 4 (B) 2 only

(C) 2 and 4 (D) 2 and 3

Question. 4

A hollow circular shaft has an outer diameter of 100 mm and a wall

thickness of 25 mm. The allowable shear stress in the shaft is 125

MPa. The maximum torque the shaft can transmit is

(A) 46 kNm (B) 24.5 kNm

(C) 23 kNm (D) 11.5 kNm

Question. 5

Match List-I (Shear Force Diagrams) beams with List-II (Diagram of

beams with supports and loading) and select the correct answer by

using the codes given below the lists :


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Codes :

a b c d

(A) 3 1 2 4

(B) 3 4 2 1

(C) 2 1 4 3

(D) 2 4 3 1

Statement for Linked Answer Questions 6 & 7 :

In the cantilever beam PQR shown in figure below, the segment PQ

has flexural rigidity EI and the segment QR has infinite flexural

rigidity


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Question. 6

The deflection and slope of the beam at Q are respectively

(A)6

52

3EI

andWLEI

WL3 2 (B)

3 2EIandWL

EIWL3 2

(C)2EI

andWLEI

WL3 2 (D)

3 23

EIandWL

EIWL3 2

Question. 7

The deflection of the beam at R is

(A) 8EIWL3

(B) 56EIWL3

(C)3

7EI

WL3 (D) 86EIWL3

YEAR 2008 ONE MARK

Question. 8

A mild steel specimen is under uniaxial tensile stress. Youngs

modulus and yield stress for mild steel are 2 105# MPa and 250

MPa respectively. The maximum amount of strain energy per unit

volume that can be stored in this specimen without permanent set is

(A) 156 Nmm/mm3 (B) 15.6 Nmm/mm3

(C) 1.56 Nmm/mm3 (D) 0.156 Nmm/mm3

YEAR 2008 TWO MARK

Question. 9

Cross-section of a column consisting to two steel strips, each of

thickness t and width b is shown in the figure below. The critical

loads of the column with perfect bond and without bond between the

strips are P and P0 respectively. The ratio /P P0 is


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(A) 2 (B) 4

(C) 6 (D) 8

Question. 10

A rigid bar GH of length L is supported by a hinge and a spring of

stiffness K as shown in the figure below. The buckling load, Pcr, for

the bar will be

(A) 0.5KL (B) 0.8KL

(C) 1.0KL (D) 1.2KL

Question. 11

The maximum shear stress in a solid shaft of circular cross-section

having diameter d subjected to a subject to a torque T is . If the

torque is increased by four times and the diameter of the shaft is

increased by two times, the maximum shear stress in the shaft will be

(A) 2 (B)

(C) /2 (D) /4

Question. 12

A vertical rod PQ of length L is fixed at its top end P and has a

flange fixed to the bottom end Q. A weight W is dropped vertically

from a height ( )h L< on to the flange. The axial stress in the rod can

be reduced by

(A) increasing the length of the rod


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(B) decreasing the length of the rod

(C) decreasing the area of cross-section of the rod

(D) increasing the modulus of elasticity of the material

Question. 13

The maximum tensile stress at the section X-X shown in the figure

below is

(A)bd

P8 (B)

bdP6

(C)bd

P4 (D)

bdP2

Question. 14

The stepped cantilever is subjected to moments, M as shown in the

figure below. The vertical deflection at the free end (neglecting the

self weight) is

(A)8EIML2

(B)4EIML2

(C)EI

ML2 (D) Zero


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Statement for Linked Answer Questions 15 & 16 :

Beam GHI is supported by three pontoons as shown in the figure

below. The horizontal cross-sectional area of each pontoon is 8 m2,

the flexural rigidity of the beam is 10000 kNm2 and the unit weightof water is 10 kNm3

Question. 15

When the middle pontoon is removed, the deflection at H will be

(A) 0.2 m (B) 0.4 m

(C) 0.6 m (D) 0.8 m

Question. 16

When the middle pontoon is brought back to its position as shown in

the figure above, the reaction at H will be

(A) 8.6 kN (B) 15.7 kN

(C) 19.2 kN (D) 24.2 kN

YEAR 2007 ONE MARK

Question. 17

An axially loaded bar is subjected to a normal stress os 173 MPa.

The stress in the bar is

(A) 75 MPa (B) 86.5 MPa

(C) 100 MPa (D) 122.3 MPa


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Question. 18

A steel column, pinned at both end, has a buckling load of 200 kN. If

the column is restrained against lateral movement at its mid-height,

it buckling load will be

(A) 200 kN (B) 283 kN

(C) 400 kN (D) 800 kN

Question. 19

For an isotropic material, the relationship between the Youngs

modulus (E), shear modulus (G) and Poissons ratio () is given by

(A)( )

G E2 1

=+

(B)( )

E E2 1

=+

(C)( )

GE

1 2=

+(D)

( )G

E2 1 2

=

YEAR 2007 TWO MARK

Question. 20

A metal bar of length 100 mm is inserted between two rigid supports

and its temperature is increased by 10 Cc . If the coefficient of thermal

expansion is 12 10 per C6# c and the Youngs modulus is 2 105#

MPa, the stress in the bar is

(A) zero (B) 12 MPa

(C) 24 MPa (D) 2400 MPa

Question. 21

A rigid bar is suspended by three rods made of the same material as

shown in the figure. The area and length of the central rod are 3 A

and L, respectively while that of the two outer rods are A2 and L2 ,

respectively. If a downward force of 50 kN is applied to the rigid bar,

the forces in the central and each of the outer rods will be


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(A) 16.67 kN each (B) 30 kN and 15 kN

(C) 30 kN and 10 kN (D) 21.4 kN and 14.3 kN

Question. 22

The maximum and minimum shear stresses in a hollow circular shaft

of outer diameter 20 mm and thickness 2 mm, subjected to a torque

of 92.7 Nm will be

(A) 59 MPa and 47.2 MPa (B) 100 MPa and 80 MPa

(C) 118 MPa and 160 MPa (D) 200 MPa and 160 MPa

Question. 23

The shear stress at the neutral axis in a beam of triangular section

with a base of 40 mm and height 20 mm, subjected to a shear force

of 3 kN is

(A) 3 MPa (B) 6 MPa

(C) 10 MPa (D) 20 MPa

Question. 24

U1 and U2 are the strain energies stored in a prismatic bar due to axial

tensile forces P1 and P2, respectively. The strain energy U stored in

the same bar due to combined action ofP1 and P2 will be

(A) U U U1 2= + (B) U U U1 2=

(C) U U U< 1 2+ (D) U U U> 1 2+

YEAR 2006 ONE MARK

Question. 25

Mohrs circle for the state of stress defined by30

0

0

30> H MPa is a circle


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with

(A) centre at (0, 0) and radius 30 MPa

(B) centre at (0, 0) and radius 60 MPa

(C) centre at (30, 0) and radius 30 MPa(D) centre at (30, 0) and zero radius

Question. 26

A long shaft of diameter d is subjected to twisting moment T at its

ends. The maximum normal stress acting at its cross-section is equal

to

(A) zero (B)dT163

(C)dT32 3

(DdT64 3

Question. 27

The buckling load P Pcr= for the column AB in figure, as KT

approaches infinity, becomesLEI2

2

Where is equal to

(A) 0.25 (B) 1.00

(C) 2.05 (D) 4.00

YEAR 2006 TWO MARKS

Question. 28

A thin-walled long cylindrical tank is inside radius r is subjected

simultaneously to internal gas pressure p and axial compressive force

F at its ends. In order to produce pure shear state of stress in the


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wall of the cylinder, F should be equal to

(A) p r2 (B) p r2 2

(C) p r3 2 (D) p r4 2

Question. 29

Consider the beam AB shown in the figure below. Part AC of the

beam is rigid while Part CB has the flexural rigidity EI. Identify the

correct combination of deflection at end B and bending moment at

end A, respectively

(A) ,EI

PL PL3

23

(B) ,EI

PL PL3

3

(C) ,2EIPL

PL38 3

(D) ,EIPL

PL38 3

Question. 30

A simply supported beam AB has the bending moment diagram as

shown in the following figure.

The beam is possibly under the action of following loads

(A) Couples ofM 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 2 /M L at D

(D) Concentrated load of /M L at C and couple of 2M at D


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Question. 31

A beam with the cross-section given is subjected to a positive bending

moment (causing compression at the top) of 16 kNm acting around

the horizontal axis. The tensile force acting on the hatched area ofthe cross-section is

(A) zero (B) 5.9 kN

(C) 8.9 kN (D) 17.8 kN

Question. 32

If a beam of rectangular cross-section is subjected to a vertical shear

force V, the shear force carried by the upper one-third of the cross-

section is

(A) zero (B) V277

(C) V278

(D) V3

Question. 33

For the section shown below, second moment of the area about an

axis /d 4 distance above the bottom of the area is

(A) bd48

3

(B) bd12

3


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(C) bd48

7 3 (D) bd

3

3

Question. 34

I-section of a beam is formed by gluing wooden planks as shown in

the figure below. If this beam transmits a constant vertical shear

force of 3000 N, the glue at any of the four joint will be subjected to

a shear force (in kN per meter length) of

(A) 3.0 (B) 4.0

(C) 8.0 (D) 10.7

Common data for questions 35 & 36 :

Consider a propped cantilever beam ABC under two leads of

magnitude P each as shown in the figure below. Flexural rigidity of

the beam is EI.

Question. 35

The reaction at C is

(A) ( )L

Pa169 upwards (B) ( )

LPa

169 downwards


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(C) ( )L

Pa89 upwards (D) ( )

LPa89 downwards

Question. 36

The rotation at B is

(A) ( )EI

PLa165 clockwise (B) ( )

EIPLa

165 anticlockwise

(C) ( )EI

PLa1659 clockwise (D) ( )

EIPLa

1659 anticlockwise

YEAR 2005 ONE MARK

Question. 37

The symmetry of stress tensor at a point in the body under equilibrium

is obtained from

(A) conserved of mass

(B) force equilibrium equations

(C) moment equilibrium equations

(D) conservation of energy

Question. 38

The components of strain tensor at a point in the plane strain case can

be obtained by measuring longitudinal strain in following directions

(A) along any two arbitrary directions

(B) along any three arbitrary directions

(C) along two mutually orthogonal directions

(D) along any arbitrary direction

YEAR 2005 TWO MARK

Question. 39

If principal stresses in a two-dimensional case are 10 MPa and 20

MPa respectively, then maximum shear stress at the point is

(A) 10 MPa (B) 15 MPa

(C) 20 MPa (D) 30 MPa


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Question. 40

The bending moment diagram for a beam is given below :

The shear force at sections aal and bbl respectively are of the

magnitude

(A) 100 kN, 150 kN (B) zero, 100 kN

(C) zero, 50 kN (D) 100 kN, 100 kN

Question. 41

A circular shaft shown in the figure is subjected to torsion T at two

point A and B. The torsional rigidity of portions CA and BD is GJ1

and that of portion AB is GJ2. The rotations of shaft at points A and

B are 1 and 2 . The rotation 1 is

(A)GJ GJ

TL1 2+

(B)GJTL

1

(C) GJTL

2 (D) GJ GJ TL1 2

YEAR 2004 ONE MARK

Question. 42

For linear elastic systems, the type of displacement function for the

strain energy is


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(A) linear (B) quadratic

(C) cubic (D) quartic

YEAR 2004 TWO MARK

Question. 43

In a two dimensional stress analysis, the state of stress at a point

is shown below. If 120 MPa = and 70 MPa = , andx y , are

respectively,

(A) 26.7 MPa and 172.5 MPa (B) 54 MPa and 128 MPa

(C) 67.5 MPa and 213.3 MPa (D) 16 MPa and 138 MPa

Question. 44

For the linear elastic beam shown in the figure, the flexural rigidity,

EI is 781250 kNm2. When 10w kN/m= , the vertical reaction RA at

A is 50 kN. The value ofRA for 100w kN/m= is

(A) 500 kN (B) 425 kN

(C) 250 kN (D) 75 kN


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Question. 45

A homogeneous, simply supported prismatic beam of width B, depth

D and span L is subjected to a concentrated load of magnitude P

. The load can be placed anywhere along the span of the beam. Themaximum flexural stress developed in beam is

(A)BDPL

32

2 (B) BDPL

43

2

(C)BDPL

34

2 (D) BDPL

23

2

Question. 46

A circular solid shaft of span 5L m= is fixed at one end and freeat other end. A twisting moment 100T kNm= is applied at the free

end. The torsional rigidity GH is 50000 kNm /rad2 .

Following statements are made for this shaft :

1. The maximum rotation is 0.01 rad

2. The torsional strain energy is 1 kNm

With reference to the above statements, which of the following applies

?

(A) Both statements are true

(B) Statement 2 is true but 2 is false

(C) Statement 2 is true but 1 is false

(D) Both the statements are false

Common Data for Question 47 & 48 :

A three-span continuous beam has an internal hinge at B. Section B

is at the mid-span of AC. Section E is at the mid-span of CG. The

20 kN load is applied at section B whereas 10 kN loads are applied

at sections D and F as shown in the figure. Span GH is subjected

to uniformly distributed 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 hogging moment at section E is 10.31 kNm


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Question. 47

The magnitude of the shear force immediate to the left and immediate

to the right of section B are respectively

(A) 0 and 20 kN (B) 10 kN and 10 kN

(C) 20 kN and 0 (D) 9.84 kN and 10.16 kN

Question. 48

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

YEAR 2003 ONE MARK

Question. 49

A bar of varying square cross-section is loaded symmetrically as

shown in the figure. Loads shown are placed on one of the axes of

symmetry of cross-section. Ignoring self weight, the maximum tensile

stress in N/mm2 anywhere is


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(A) 16.0 (B) 20.0

(C) 25.0 (D) 30.0

Question. 50

A curved member with a straight vertical leg is carrying a vertical

load at Z, as shown in the figure. The stress resultants in the XY

segment are

(A) bending moment, shear force and axial force

(B) bending moment and axial force only

(C) bending moment and shear force only

(D) axial force only

YEAR 2003 TWO MARK

Question. 51

The state of two dimensional stresses acting on a concrete lamina

consists of a direct tensile stress, 1.5 N/mmx2 = , and shear stress,

1.20 N/mm2 = , which cause cracking of concrete. Then the tensile

strength of the concrete in N/mm2 is

(A) 1.50 (B) 2.08

(C) 2.17 (D) 2.29

Question. 52

A " "H shaped frame of uniform flexural rigidity EI is located as

shown in the figure. The relative outward displacement between

points K and O is


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(A)EI

RLh2 (B)

EIRL h2

(C)

EI

RLh

3

2

(D)

EI

RL h

3

2

Question. 53

A simply supported beam of uniform rectangular cross-section of

width b and depth h is subjected to linear temperature gradient 0c at

the top and Tc at the bottom, as shown in the figure. The coefficient

of linear expansion of the beam material is . The resulting vertical

deflection at the mid-span of the beam is

(A)L

Th8

upward2

(B)h

TL8

upward2

(C)L

Th8

downward2

(D)h

TL8

downward2

Question. 54

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.


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Codes :

A B C D

(A) 4 2 1 3

(B) 5 4 1 3

(C) 2 5 3 1

(D) 2 4 1 3

Question. 55

A long structural column (length L= ) with both ends hinged is actedupon by an axial compressive load, P. The differential equation

governing the bending of column is given by :

EIdx

d y2

2

Py=

Where y is the structural lateral deflection and EI is the flexural

rigidity. The first critical load on column responsible for its buckling


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is given by

(A)LEI2

2 (B)

LEI2

2

2

(C) LEI2 22

(D) LEI4 22

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GATE - CE - Strength of Materials