Gate Mechanical Sm by Nodia

8/10/2019 Gate Mechanical Sm by Nodia

1/159

CONTENTS VOL 1

ENGINEERING MECHANICS

AM 1 Equilibrium of Forces AM 3

AM 2 Structure AM 40

AM 3 Friction AM 81

AM 4 Virtual Work AM 117

AM 5 Kinematics of Particle AM 128

AM 6 Kinetics of Particles AM 157

AM 7 Plane Kinematics of Rigid body AM 190

AM 8 Plane Kinetics of Rigid body AM 206

STRENGTH OF MATERIALS

SM 1 Stress and Strain SM 3

SM 2 Axial Loading SM 41

SM 3 Torsion SM 86

SM 4 Shear Force and Bending Moment SM 118

SM 5 Transformation of Stress and Strain SM 179SM 6 Design of Beams and Shafts SM 226

SM 7 Deflection of Beams and Shafts SM 270

SM 8 Column SM 315

SM 9 Energy Methods SM 354

THEORY OF MACHINES

TM 1 Analysis of Plane Mechanism TM 3

TM 2 Velocity and Acceleration TM 20

TM 3 Dynamic Analysis of Slider - Crank and Cam TM 38

TM 4 Gear - Trains TM 59

TM 5 Fly Wheel TM 91

TM 6 Vibration TM 109

MACHINES DESIGN

MD 1 Static and Dynamic Loading MD 3

MD 2 Joints MD 22

MD 3 Shaft and Shaft Components MD 54

MD 4 Spur Gears MD 71

MD 5 Bearings MD 88

MD 6 Clutch and Brakes MD 105


2/159

CONTENTS VOL 2

FLUID MECHANICS

FM 1 Basic Concepts and Properties of Fluids FM 3

FM 2 Pressure and Fluid Statics FM 33

FM 3 Fluid Kinematics & Bernouli Equation FM 80

FM 4 Flow Analysis Using Control Volumes FM 124

FM 5 Flow Analysis Using Differential Method FM 172

FM 6 Internal Flow FM 211

FM 7 External Flow FM 253

FM 8 Open Channel Flow FM 289

FM 9 Turbo Machinery FM 328

HEAT TRANSFER

HT 1 Basic Concepts & Modes of Heat-Transfer HT 3

HT 2 Fundamentals of Conduction HT 34

HT 3 Steady Heat Conduction HT 63

HT 4 Transient Heat Conduction HT 94HT 5 Fundamentals of Convection HT 114

HT 6 Free and Force Convection HT 129

HT 7 Radiation Heat Transfer HT 155

HT 8 Heat Exchangers HT 181

THERMODYNAMICS

TD 1 Basic Concepts and Energy Analysis TD 3

TD 2 Properties of Pure Substances TD 28

TD 3 Energy Analysis of Closed System TD 52

TD 4 Mass and Energy Analysis of Control Volume TD 76

TD 5 Second Law of Thermodynamics TD 106

TD 6 Entropy TD 136

TD 7 Gas Power Cycles TD 166

TD 8 Vapor and Combined Power Cycles TD 199

TD 9 Refrigeration and Air Conditioning TD 226

***********


3/159

CONTENTS VOL 3

MANUFACTURING PROCESS

INDUSTRIAL ENGINEERING

OPERATION RESEARCH


4/159

CONTENTS VOL 4

ENGINEERING MATHEMATICS

EM 1 Linear Algebra EM 1

EM 2 Differential Calculus EM 24

EM 3 Integral Calculus EM 46

EM 4 Directional Derivatives EM 67

EM 5 Differential Equation EM 79

EM 6 Complex Variable EM 103

EM 7 Probability and Statistics EM 123

EM 8 Numerical Methods EM 142

VERBAL ANALYSIS

VA 1 Synonyms VA 1

VA 2 Antonyms VA 16

VA 3 Agreement VA 26

VA 4 Sentence Structure VA 37

VA 5 Spellings VA 58VA 6 Sentence Completion VA 87

VA 7 Word Analogy VA 111

VA 8 Reading Comprehension VA 135

VA 9 Verbal Classification VA 148

VA 10 Critical Reasoning VA 153

VA 11 Verbal Deduction VA 168

QUANTITATIVE ANALYSIS

QA 1 Number System QA 1

QA 2 Surds, Indices and Logarithm QA 14

QA 3 Sequences and Series QA 28

QA 4 Average, Mixture and Alligation QA 44

QA 5 Ratio, Proportion and Variation QA 59

QA 6 Percentage QA 75

QA 7 Interest QA 89

QA 8 Time, Speed & Distance QA 99

QA 9 Time, Work & Wages QA 112

QA 10 Data Interpretation QA 126


5/159

QA 11 Number Series QA 145

SOLVED PAPER

SP 1 Engineering Mathematics SP 3

SP 2 Engineering Mechanics SP 65

SP 3 Strength of Materials SP 90

SP 4 Theory of Machines SP 138

SP 5 Machine Design SP 189

SP 6 Fluid Mechanics SP 218

SP 7 Heat Transfer SP 265

SP 8 Thermodynamics SP 303

SP 9 Refrigeration and Air-Conditioning SP 358

SP 10 Manufacturing Engineering SP 375

SP 11 Industrial Engineering SP 448

SP 12 General Aptitude SP 496


6/159

SM 1STRESS AND STRAIN

Common Data For Q. 1 and 2

A long wire of tungsten ( 190 /kN mT3g = ) hangs vertically from a high-altitude

balloon, is shown in figure.

SM 1.1 If the ultimate strength (or breaking strength) is 1500 MPa, the greatest length

that it can have without breaking, is(A) 3950 m (B) 7900 m

(C) 1975 m (D) 790 m

SM 1.2 If the same wire hangs from a ship at sea ( 10 / )kN msea water3g = , the greatest

length is(A) 8300 m (B) 2075m

(C) 7500m (D) 3750m


The 650 Nload is applied along the centroidal axis of the member as shown in

figure. Take 60cq = .

SM 1.3 The resultant internal normal and shear forces in the member at section a a- ,which passes through point A, is(A) N 0= , V 0= (B) 50 NN= , 650 NV=

(C) N 0= , 650 NV= (D) 650 NN= , V 0=


7/159


GATE MCQ Mechanical Engineering (4-volumes) Fully Solved

by NODIA and COMPANY

Buy online at www.nodia.co.in and get maximum available discount

GATE Mechanical Engineering in 4 Volume NODIA Demo Ebook Page 4

SM 1.4 The resultant internal normal and shear forces in the member at section b b- ,

which passes through point A, is(A) 325 NN= , 563 NV= (B) 650 NN= , 563NV=

(C) 563 NN= , 325 NV= (D) 325 NN= , 1126NV=

SM 1.5 In the figure shown, link BCof 6 mmthickness is made of a steel with a 450 MPaultimate strength in tension. If the structure is being designed to support a 20 kNload Pwith a factor of safety of 3, its width wshould be

(A) 13.9 mm (B) 55.6mm

(C) 27.8 mm (D) 41.7 mm

SM 1.6 In figure shown, the two-member frame is subjected to the distributed loading.MemberCBhas a square cross section of 35 mmon each side and take 8 /kN mw=. The average normal stress and average shear stress acting at section b-b , are

(A) 4.41MPas = , 5.88MPat = (B) 11.76 MPas = , 4.41MPat=

(C) 8.82MPas = , 5.88MPat= (D) 5.88MPas = , 4.41MPat=


A solid bar of circular cross section has a hole of diameter /d 4drilled laterally

through the center of the bar as shown in figure below. The allowable average

tensile stress on the net cross section of the bar is allows .

SM 1.7 The formula for the allowable load Pallowthat the bar can carrying in tension, is

(A) . d0 27 allow2

# s (B) . d0 54 allow2

# s

(C) . d0 675 allow2

# s (D) . d0 54 allow# s


8/159


For more GATE Resources, Mock Test and Study material

join the Group

https://www.facebook.com/groups/GateME


SM 1.8 If the bar is made of brass with diameter 40 mmd= and 80MPaallows = , the

value of Pallowis(A) 86.5 kN (B) 70 kN

(C) 172 kN (D) 35 kN

SM 1.9 An axial load Pis supported by a short 250 0.67W # column of cross-sectional

area 8580mmA 2= and is distributed to a concrete foundation by a square plateas shown in figure. If the average normal stress in the column must not exceed150 MPa and the bearing stress on the concrete foundation must not exceed

12.5MPa, the side aof the plate which will provide the most economical and safe

design is

(A) 103 mm (B) 321 mm

(C) 8.6 mm (D) 160 mm

SM 1.10 The column shown in figure, is subjected to an axial force of 8 kNat its top.What is the average normal stress acting at section a-a?

(A) 1.82MPa (B) 3.64 MPa

(C) 0.91MPa (D) 2.73MPa

SM 1.11 A round bar of 10 mmdiameter is made of aluminum alloy, as shown in figure.When the bar is stretched by axial forces P, its diameter decreases by 0.016 mm. The magnitude of the load Pis

(Take 72GPaE= , 0.33n= , 480 MPaYs = )

(A) 27.4 kN (B) 54.8 kN

(C) 13.7 kN (D) . kN37 7

SM 1.12 A steel bar of length 2.5mwith a square cross section 100 mmon each side issubjected to an axial tensile force of 1300 kNas shown in figure. The increase in


9/159






volume of the bar is

(Take 250 MPaYs = , 200 GPaE= , .0 3n= )

(A) 8112 mm3 (B) 4868 mm3

(C) 3245mm3 (D) 6490 mm3

Common Data For Q.14 and 15

Three steel plates, each 16 mmthick, are joined by two 20 mmdiameter rivets asshown in the figure.

SM 1.13 If the load 50 kNP= , the largest bearing stress acting on the rivets is(A) 39MPa

(B) 156 MPa

(C) 78MPa

(D) 117 MPa

SM 1.14 If the ultimate shear stress for the rivets is 180 ,MPa what force Puis required to

cause the rivets to fail in shear ? (Disregard friction between the plates.)(A) 170 kN (B) 57 kN

(C) 226kN (D) 113 kN

SM 1.15 The small block of 5 mmthickness is shown in figure. If the stress distributionat the support developed by the load varies as shown, the force Fapplied to the

block and the distance dto where it is applied, respectively, are

(A) 220 mm (B) 110 mm(C) 165 mm (D) 55 mm

SM 1.16 The bar has a cross-sectional area of (400 10 )m6 2# - . If it is subjected to a

uniform axial distributed loading along its length and to two concentrated loadsas shown in figure, the average normal stress in the bar as a function of xfor


10/159



join the Group



0 0.5 mx< # , is

(A) . . MPax47 5 20 0-^ h (B) 67.5 MPax(C) . . MPax47 5 20 0+^ h (D) 27.5 MPax


In the figure shown, a hollow box beam ABCof length Lis supported at end

Aby a 20 mmdiameter pin that passes through the beam and its supportingpedestals. The roller support at Bis located at distance /L 3from end A.

SM 1.17 If load Pis equal to 10 kN, the average shear stress in the pin is(A) 15.9 MPa (B) 31.8 MPa

(C) 63.6MPa (D) 7.95MPa

SM 1.18 If the wall thickness of the beam is equal to 12 mm, the average bearing stressbetween the pin and the box beam will be

(A) 41.7 MPa (B) 125.1MPa

(C) 83.4 MPa (D) 20.85MPa

SM 1.19 Rods ABand BCshown in figure, have diameters of 4 mmand 6 mm, respectively.The vertical load of 8 kNis applied to the ring at B. If the average normal stress

in each rod is equivalent then this stress will be


11/159






(A) 237 MPa (B) 316 MPa

(C) 474 MPa (D) 158 MPa

Common Data For Q. 20 amd 21

A steel plate ( /kN m77 3g= ) of dimensions 2.5 1.2 0.1 m# # is hoisted by a

cable sling that has a clevis at each end as shown in figure. The pins through the

clevises are 18 mmin diameter and are located 2.0 mapart. Each half of the cable

is at an angle of 32cto the vertical.

SM 1.20 For above conditions, the average shear stress avert in the pins will be(A) 8.9 MPa (B) 6.7 MPa

(C) 13.4 MPa (D) 26.8MPa

SM 1.21 The average bearing stress bs between the steel plate and the pins is(A) 22.7 MPa (B) . MPa15 2

(C) 7.57 MPa (D) 30.3MPa

SM 1.22 Two solid cylindrical rods ABand BCare welded together at Band loaded as

shown in figure. If the average normal stress must not exceed 150 MPain eitherrod, the smallest allowable values of the diameters d1and d2are


12/159



join the Group



(A) 45.2mmd1 = , 20.1mmd2 = (B) 22.6 mmd1 = , 40.2 mmd2 =

(C) 20.1mmd1 = , 45.2 mmd2 = (D) 40.2 mmd1 = , 22.6mmd2 =

SM 1.23 Members AB and AC of the truss as shown, consist of bars of square crosssection made of the same alloy. It is known that a 20 mmsquare bar of the samealloy was tested to failure and that an ultimate load of 120 kNwas recorded. If a

factor of safety of 3.2 is to be achieved for both bars, the required dimension ofthe cross section of the bar ABis

(A) 27 mma= (B) 12 mma=

(C) 13.5 mma= (D) 6 mma=

SM 1.24 The two steel members are joined together using a 60cscarf weld as shown infigure. The average normal and average shear stress resisted in the plane of the

weld are

(A) 8 MPaavgs = , 4.62MPaavgt = (B) 4.62 MPaavgs = , 8 MPaavgt =

(C) 4.62MPaavgs = , 16MPaavgt = (D) 16MPaavgs = , 4.62MPaavgt =

SM 1.25 A steel pipe of 300 mmouter diameter is fabricated from 6 mmthick plate bywelding along a helix which forms an angle of 25cwith a plane perpendicular to

the axis of the pipe. If a 250 kNaxial force Pis applied to the pipe, the normaland shearing stresses in directions respectively normal and tangential to the weldare


13/159






(A) 18.5MPa- , 17.28 MPa (B) 37.1MPa- , 34.56 MPa

(C) 18.5MPa- , 34.56 MPa (D) 37.1MPa- , 17.28 MPa

SM 1.26 A 6 kNload is supported by two wooden members of 75 125mm mm# uniformrectangular cross section which are joined by the simple glued scarf splice asshown in figure. The normal and shearing stresses in the glued splice respectively,are

(A) 565 kPa, 206 kPa (B) 282 kPa, 206 kPa

(C) 565 kPa, 103 kPa (D) 282 kPa, 103 kPa

SM 1.27 In the figure shown, the wooden members Aand Bare to be joined by plywood

splice plates which will be fully glued on the surface in contact. If the clearancebetween the ends of the members is to be 8 mmand the average shearing stressin the glue is not to exceed 800 kPa, the smallest allowable length Lwill be

(A) 308 mm (B) 150 mm

(C) 300 mm (D) 292 mm


14/159



join the Group



SM 1.28 In the figure shown, the frame is subjected to the distributed loading of 2 /kN m.

What is the required diameter of the pins at Aand Bif the allowable shear stressfor the material is 100 MPaallowt = ? Both pins are subjected to double shear.

(A) 2.6 mmd= (B) 7.8mmd=

(C) 5.2 mmd= (D) 10.4 mmd=

SM 1.29 A specially designed wrench is used to twist a circular shaft by means of a squarekey that fits into slots (or keyways) in the shaft and wrench as shown in thefigure. The shaft has diameter ,dthe key has a square cross section of dimensions

b b# and the length of the key is c. The key fits half into the wrench and halfinto the shaft (i.e., the keyways have a depth equal to /b 2). When a load Pis

applied at distance Lfrom the center of the shaft, the formula for the averageshear stress avert in the key is

( Hints : Disregard the effects of friction, assume that the bearing pressure betweenthe key and the wrench is uniformly distributed)

(A)bc d b

PL2 +

^ h (B)

bc d bPL

22

+

^ h(C)bc d b

PL23

+^ h (D) bc d bPL

24

+^ hSM 1.30 The two wooden members shown in figure supports a 20 kN load, are joined

by plywood splices fully glued on the surface in contact. The ultimate shearingstress in the glue is 2.8 MPaand the clearance between the members is 8 mm. If


15/159






a factor of safety of 3.5 is to be achieved, the required length Lof each splice is

(A) 216 mm (B) 208 mm

(C) 200 mm (D) 104 mm

SM 1.31 A torque T0is transmitted between two flanged shafts by means of four 20 mmbolts as shown in figure. The diameter of the bolt circle is 150 mmd= . If the

allowable shear stress in the bolts is 90MPa, the maximum permissible torquewill be

(A) 16.96 kN m- (B) 8.48 kN m-

(C) 12.72 kN m- (D) 4.24 kN m-

SM 1.32 The cross section of an aluminium tube serving as a compression brace in thefuselage of a small airplane is shown in the figure. The outer diameter of the tubeis 25 mmd= and the wall thickness is 2.5 mmt= . If the factors of safety with

respect to the yield stress and the ultimate stress are 4 and 5 respectively, theallowable compressive force Pallowis

(Take 270 MPaYs = , 310 MPaus = )

(A) 9.5 kN (B) 12.0 kN

(C) 11.0 kN (D) 13.7 kN

SM 1.33 In the figure shown, a long steel wire ( 77.0 /kN m3g = ) hanging from a balloon

carries a weight Wat its lower end. The 4 mmdiameter wire is 25 mlong. Thetensile yield stress for the wire is 350 MPaYs = and a margin of safety againstyielding of 1.5 is desired. The maximum weightWmaxthat can safety be carried is

(Include the weight of the wire in the calculations.)


16/159



join the Group



(A) 1783N (B) 1711N

(C) 1759N (D) 1735N

SM 1.34 What is the smallest dimensions of the circular shaft and circular end cap ifthe load it is required to support is 150 kNP= ? The allowable tensile stress,

bearing stress and shear stress is ( ) 175 MPat allows = , ( ) 275 MPab allows = and115 MPaallowt = .

(A) 15.8mmd1 = , 26.4 mmd3 = , 44.6mmt=

(B) 26.4 mmd1 = , 44.6 mmd3 = , 15.8mmt=

(C) 44.6mmd1 = , 26.4 mmd3 = , 15.8mmt=

(D) 44.6mmd1 = , 15.8 mmd3 = , 26.4 mmt=

SM 1.35 The assembly shown in figure, consists of three disks A, Band Care used tosupport the load of 140 kN. The allowable bearing stress for the material is

( ) 350 MPab allows = and allowable shear stress is 125 MPaallowt = . The smallest

diameter d1of the top disk, the diameter d2within the support space and thediameter d3of the hole in the bottom disk are


17/159






(A) 27.6mmd1 = , 22.6 mmd2 = , 35.7 mmd3 =

(B) 22.6mmd1 = , 35.7 mmd2 = , 27.6mmd3 =

(C) 22.6mmd1 = , 27.6 mmd2 = , 35.7 mmd3 =

(D) 35.7 mmd1 = , 22.6 mmd2 = , 27.6mmd3 =

SM 1.36 In the structure shown, an 8 mmdiameter pin is used at Aand 12 mmdiameterpins are used at B and D. The ultimate shearing stress is 100 MPa at all

connections and the ultimate normal stress is 250 MPain each of the two linksjoining Band D. If an overall factor of safety of 3.0 is desired, the allowable loadPis

(A) 7.7 kN (B) 14.04 kN

(C) 3.97 kN (D) 3.72 kN

SM 1.37 The bar shown in figure, is held in equilibrium by the pin supports at Aand B. The support at Ahas a single leaf and therefore it involves single shear in the

pin and the support at Bhas a double leaf and therefore it involves double shear.The allowable shear stress for both the pins is 125 MPaallowt = . If 1 mx= and

12 /kN mw= , the smallest required diameter of pins Aand Bare (Neglect any

axial force in the bar.)

(A) 957 mmdA = , 20.6mmdB= (B) 10.3 mmdA = , 9.57 mmdB=

(C) 19.14 mmdA = , 10.3 mmdB= (D) 9.57 mmdA = , 10.3 mmdB=

SM 1.38 Two plates, each 3 mmthick, are used to splice a plastic strip as shown below. Ifthe ultimate shearing stress of the bonding between the surface is 900 kPaand

1500NP= , the factor of safety with respect to shear will be

(A) 2 (B) 3.6

(C) 5.4 (D) 1.8


18/159



join the Group



SM 1.39 The cable shown in figure has a specific weight g(weight/volume) and cross-

sectional area A. If the sag sis small, so that its length is approximately Landits weight can be distributed uniformly along the horizontal axis, the average

normal stress in the cable at its lowest point Cis

(A)sL2

2

s g

= (B)sL

8s

g=

(C)sL8

2

s g

= (D)sL4

2

s g

=

SM 1.40 An elastomeric bearing pad consisting of two steel plates bonded to a chloropreneelastomer, is subjected to a shear force Vduring a static loading test as shown in

figure. The pad has dimensions 150 mma= , 250 mmb = and the elastomer hasthickness 50 mmt= . When the force Vequals 12 kN, the top plate is found tohave displaced laterally 8.0mmwith respect to the bottom plate.

The shear modulus of elasticity Gof the chloroprene is(A) 0.5 MPa (B) 1MPa

(C) 4 MPa (D) 2 MPa

SM 1.41 A metal bar ABof weight Wis suspended by a system of steel wires arranged asshown in the figure. The diameter of the wire is 2 mmand the yield stress of thesteel is 450 MPa. The maximum permissible weightWmaxfor a factor of safety of1.9 with respect to yielding, is


19/159






(A) N685 (B) 10 N28

(C) 1370N (D) 2740N


In figure shown below, link BDconsists of a single bar 30 mmwide and 12 mm

thick. Each pin has a 10 mmdiameter.

SM 1.42 If 0cq = , the maximum value of the average normal stress in link BDis

(A) zero (B) 72MPa

(C) 24MPa (D) 48MPa

SM 1.43 If 90cq = , the maximum value of the average normal stress in link BDis

(A) 83MPa (B) 125 MPa

(C) 42MPa (D) 44.5MPa

SM 1.44 The rigid beam ACshown in figure, is supported by a pin at Aand wires BDand CE. If the load Pon the beam causes the end Cto be displaced 10 mm

downward, the normal strain developed in wires CEand BDare

(A) .0 00025CEe = , 0.0107BDe = (B) .0 0025CEe = , .0 00107BDe =

(C) .0 025CEe = , 0.0107BDe = (D) .0 00107CEe = , .0 0025BDe =

SM 1.45 The rigid beam shown in figure, is supported by a pin at Aand wires BDand

CE. If the load Pon the beam is displaced 10 mmdownward, the normal strain

developed in wires CEand BDare


20/159



join the Group



(A) .1 43 10CE3

#e = - , .3 58 10BD

3#e = -

(B) .1 43 10CE3

#e = - , .1 79 10BD

3#e = -

(C) .1 79 10CE3

#e = - , .1 43 10BD

3#e = -

(D) .2 86 10CE3

#e = - , .1 79 10BD

3#e = -

SM 1.46 A steel pipe is to carry an axial compressive load 1200 kNP= as shown in figure.A factor of safety of 1.8 against yielding is to be used. If the thickness tof the pipeis to be one-eighth of its outer diameter, the minimum required outer diameter

dminis (Take 270 MPaYs = )

.

(A) 153 mm (B) 76.5mm

(C) 114.75mm (D) 38.25 mm


A circular aluminum tube of length 400 mmL = is loaded in compression by

forces Pas shown in figure. The out-side and inside diameters are 60 mmand

50 mm, respectively. A strain gage is placed on the outside of the bar to measure

normal strains in the longitudinal direction.

.

SM 1.47 If the measured strain is 550 10 6#e = - , the shortening dof the bar is

(A) 0.220 mm (B) 2.20 mm

(C) 0.022 mm (D) 1.10 mm

SM 1.48 If the compressive stress in the bar is intended to be 40MPa, the load Pshould be(A) 17.35 kN (B) 34.6 kN

(C) 69.4 kN (D) 52.0 kN


21/159







A suspender on a suspension bridge consists of a cable that passes over the main

cable is shown in figure and supports the bridge deck, which is far below. The

suspender is held in position by a metal tie that is prevented from sliding downward

by clamps around the suspender cable. Let Prepresent the load in each part of the

suspender cable and qrepresent the angle of the suspender cable just above the tie.

Also, let allows represent the allowable tensile stress in the metal tie.

SM 1.49 The minimum required cross-section area of the tie is

(A) tanA Pminallows q= (B) /tanA P2

min allowq s=

(C) /cotA P2min allowq s= (D)cot

A P

minallows

q=

SM 1.50 If 130 kNP= , 75cq = and 80MPaallows = , the minimum area will be(A) 6064 mm2 (B) 12130 mm2

(C) 435 mm2 (D) 870 mm2

SM 1.51 An elastomeric bearing pad consisting of two steel plates bonded to a chloropreneelastomer, is subjected to a shear forceVduring a static loading test as shown infigure. The pad has dimensions 150 mma= , 250 mmb = and the elastomer has

thickness 50 mmt= . When the force Vequals 12 kN, the top plate is found tohave displaced laterally 8.0mmwith respect to the bottom plate.

The shear modulus of elasticity Gof the chloroprene is(A) 0.5 MPa (B) 1MPa

(C) 4 MPa (D) 2 MPa

SM 1.52 Part of a control linkage for an airplane consists of a rigid member CBDand a


22/159



join the Group



flexible cable AB. Originally the cable is unstretched. If a force is applied to the

end Dof the member and causes a normal strain in the cable of 0.0035 /mm mm, the displacement of point Dis

(A) 21.9 mm (B) 4.38mm

(C) 43.8 mm (D) 8.76 mm


The material distorts into the dashed position is shown in figure.

SM 1.53 The average normal strains xe , ye and the shear strain xyg at Aare

(A) 0x ye e= = , 0.0798 radxyg =(B) 0xe = , .0 00319ye = , 0.0798 radxyg =

(C) .0 00319xe = , 0ye = , 0.0798 radxyg =

(D) .0 00319x ye e= = , 0.0798 radxyg =

SM 1.54 The average normal strain along line BEis(A) 0.179 /mm mm- (B) 0.0179 /mm mm

(C) 0.0179 /mm mm- (D) 0.179 /mm mm

SM 1.55 In the figure shown, the bar is originally 300 mm long when it is flat. It is

subjected to a shear strain defined by . x0 02xyg = , where xis in millimeters. Itis distorted into the shape shown, where no elongation of the bar occurs in the xdirection. The displacement yD at the end of its bottom edge will be


23/159


24/159

SM 2AXIAL LOADING

Common Data For Linked Q. 1 and 2

A 15 mmdiameter rod is subjected to a 3.5 kNtensile force as shown in figure.An elongation of 11mmand a decrease in diameter of 0.62mmare observed ina 120 mmgage length.

SM 2.1 What will be the modulus of elasticity of the material ?(A) 216 MPa (B) 270 MPa

(C) 162 MPa (D) 108 MPa

SM 2.2 The Poissons ratio and Modulus of rigidity of the material respectively, are(A) .0 15, 93.125MPa (B) .0 90, 36.75 MPa

(C) .0 60, 55.8MPa (D) .0 45, 74.5MPa

SM 2.3 An elastomeric bearing with 220 mmb = and 30 mma= is shown in figure. Fora maximum lateral load 19 kNP= and a maximum displacement 12 mmd= , the

shearing modulus Gand the shear stress trespectively, are

(A) 1.08MPa, 43 kPa2 (B) 0.54 MPa, 431 kPa

(C) 1.08MPa, 862 kPa (D) 1.08MPa, 6 kPa21


25/159



join the Group



SM 2.4 A 200 mmlength rod of steel is shown in figure. The dilatation eand the change

in volume of the rod respectively, are

(Take 200 GPaE= , .0 30n= )

(A) e 121 10 6#= - , 23 mmv 3D = (B) e 121 10 6#=

- , 18.4 mmv 3D =

(C) e 242 10 6#= - , 18.4 mmv 3D = (D) e 242 10 6#=

- , 13.8 mmv 3D =

SM 2.5 For the axial loading shown in figure, the loading is hydrostatic with

70MPax y zs s s= = =- . The change in height and the change in volume of the

brass cylinder respectively, are

(A) 0.031mm3, 521 mm (B) 0.031mm- , 521 mm3-

(C) 0.031mm, 521 mm3 (D) 0.031mm3- , 521mm-


A fabric is subjected to a biaxial loading that results in normal stresses120 MPaxs = and 160 MPazs = as shown in figure. The properties of the fabric

can be approximated as 87GPaE= and .0 34n= .


26/159






SM 2.6 The change in length of sides ABand BC, are

(A) 0.103 mmABd = , 0.075 mmBCd = (B) 0.075 mmABd = , 0.103 mmBCd =

(C) 0.075 mmABd = , 0.206 mmBCd = (D) 0.150 mmABd = , 0.103 mmBCd =

SM 2.7 The change in length of diagonal AC, is(A) 0.61mm (B) 1.22mm

(C) 0.122 mm (D) 0.244 mm

SM 2.8 An aluminium plate is subjected to a centric axial load which causes a normalstress s as shown in figure. Before the loading, a line of slope :2 1is scribed on

the plate. When 125 MPas = , the slope of the line is

(Take 74GPaE= , .0 33n= )

(A) .1 995 (B) .19 95

(C) .0 1995 (D) .3 99

SM 2.9 In the figure shown, a bar ABhaving length Land axial rigidity EAis fixed atend A. At the other end a small gap of dimension sexists between the end of the

bar and a rigid surface. A load Pacts on the bar at point C, which is two-third

of the length from the fixed end. If the support reactions produced by the load Pare to be equal in magnitude, what should be the size sof the gap ?

(A) sEAPL4

= (B) sEAPL3

=

(C) s EA

PL

6= (D) s EA

PL

9=

SM 2.10 The T-shaped arm ABCshown in the figure lies in a vertical plane and pivotsabout a horizontal pin at A. The arm has constant cross-sectional area and total

weight W. A vertical spring of stiffness ksupports the arm at point B. What willbe the elongation dof the spring due to the weight of the arm ?

(A)k

W2

d= (B)kW43d=


27/159



join the Group



(C)kW34d= (D)

kW4

d=

SM 2.11

In the figure shown, a cable with a restrainer at the bottom hangs vertically fromits upper end. The cable has an effective cross-sectional area 40 mmA 2= and aneffective modulus of elasticity 130 GPaE= . A slider of mass 35 kgM= drops

from a height 1.0 mh= onto the restrainer. If the allowable stress in the cableunder an impact load is 500 MPa, what is the minimum permissible length Lofthe cable ?

(A) 7.4 mm (B) 9.25mm

(C) 11.1mm (D) 5.55mm

SM 2.12 In the figure shown, a uniform bar ABof weight 25 NW= is supported by twosprings. The distance between the springs is 350 mmL = and the spring on theright is suspended from a support that is distance 80 mmh= below the point

of support for the spring on the left. At what distance x from the left-handspring should a load 18 NP= be placed in order to bring the bar to a horizontalposition ?

(A) 67.5 mm (B) 135 mm

(C) 270 mm (D) 202.5 mm

SM 2.13 A rigid bar ABCDis pinned at point Band supported by springs at Aand D. Aload Pacts at point Cis shown in figure. If the angle of rotation of the bar due to

the action of the load Pis limited to 3c, what will be the maximum permissibleload (Pmax) ?


28/159






(A) 2.25 kN (B) 1.8 kN

(C) 1.35 kN (D) 0.9 kN

SM 2.14 The rigid bar shown in figure is supported by the two short white spruce wooden

posts ( 9.65 GPaE= ) and a spring. The spring has a stiffness of 2 /MN mk= andan unstretched length of 1.02m. If each of the posts has an unloaded length of

1 mand a cross-sectional area of 600 mm2

, what will be the vertical displacementof Aand Bafter the load is applied to the bar ?

(A) 4.42mmA Bd d= = (B) 4.42mAd = , 8.84 mmBd =

(C) 2.21mmAd = , 4.42mmBd = (D) 4.42mAd = , 2.21mmBd =

SM 2.15 The aluminium strap as shown in figure, is subjected to an axial force of 30 kN.What is the elongation of the strap ?

(Take 70GPaEal= )

(A) 1.19 mm (B) 1.58mm

(C) 0.79mm (D) 2.37 mm

SM 2.16 The A-36 steel pipe ( 200 GPaE= ) has a 6061-T6 aluminum core ( 68.9 GPaE=). It is subjected to a tensile force of 200 kNas shown in figure. The pipe has

an outer diameter of 80 mmand an inner diameter of 70 mm. What will be theaverage normal stress in the aluminium and the steel due to this loading ?


29/159



join the Group



(A) 27.5MPaals = , 39.9 MPasts =

(B) 79.9MPaals = , 27.5MPasts =

(C) 27.5MPaals = , 79.9 MPasts =

(D) 55MPaals = , 79.9 MPasts =

SM 2.17 The column shown in figure, is constructed from high-strength concrete with

25GPaEc= and four A-36 steel reinforcing rods with 200 GPaEst= . It is

subjected to an axial force of 800 kN. If one-fourth of the load is carried by thesteel and three-fourth by the concrete, the required diameter of each rod will be

(A) 16.9 mm (B) 33.9mm

(C) 11.3 mm (D) 28.2mm

SM 2.18 In the figure shown, a round brass bar of diameter 20 mmd1 = has upset ends ofdiameter 26 mmd2 = . The lengths of the segments of the bar are 0.3 mL1 = and

0.1mL2 = . Quarter-circular fillets ( .K 1 6. ) are used at the shoulders of the barand the modulus of elasticity of the brass is 100 GPaE= . If the bar lengthens

by 0.12mmunder a tensile load P, what is the maximum stress maxs in the bar ?

(A) 23MPa (B) 69MPa

(C) 46MPa (D) 34.5MPa

SM 2.19 The 10 mmdiameter steel bolt is surrounded by a bronze sleeve as shown in

figure. The outer diameter of this sleeve is 20 mm and its inner diameter is10 mm. If the yield stress for the steel is ( ) 6 0 MPa4Y sts = and for the bronze

( ) 520 MPaY brs = , what will be the magnitude of the largest elastic load Pthat

can be applied to the assembly ?

(Take 200 GPaEst= and 100 GPaEbr= )


30/159






(A) 122 kN (B) 82 kN

(C) 126kN (D) 204 kN

SM 2.20 In the figure shown, the joint is made from three A-36 steel plates that are bondedtogether at their seams. Each plates has a thickness of 5 mmand 200 GPaE= .

What will be the displacement of end Awith respect to end Bwhen the joint issubjected to the axial loads as shown ?

(A) 2.45mm (B) 4.91mm

(C) 0.0491mm (D) 0.491mm

Common Data For Q. 21 to 23

Two boards are joined by gluing along a scarf joint, as shown in figure. For

purpose of cutting and gluing, the angle abetween the plane of the joint and thefaces of the boards must be between 10cand 40c. Under a tensile load P, thenormal stress in the boards is 4.9 MPa.

SM 2.21 What are the normal and shear stresses acting on the glued joint if 20ca = ?(A) 0.57 MPas =q , 0.79MPat =q (B) 0.57 MPas =q , 1.58MPat =q

(C) 1.58MPas =q , 0.57 MPat =q (D) 1.14 MPas =q , 1.58MPat =q

SM 2.22 If the allowable shear stress on the joint is 2.25MPa, what is the largest permissiblevalue of the angle a?(A) .22 2c (B) .44 4c

(C) .33 3c (D) .27 8c


31/159



join the Group



SM 2.23 For what angle awill the shear stress on the glued joint be numerically equal to

twice the normal stress on the joint ?(A) 19.9c (B) 16.6c

(C) 33.2c (D) 26.6c

Common Data For Q. 24 and 25.

In the shown figure, a 15 mmdiameter steel shaft ACis supported by a rigid

collar, which is fixed to the shaft at B. It is subjected to an axial load of 80 kNat its end.

SM 2.24

The uniform pressure distribution pon the collar required for the equilibrium, is(A) 10.9 MPa (B) 21.8MPa

(C) 14.54 MPa (D) 32.7 MPa

SM 2.25 What is the elongation on segment BCand segment BA?(A) 1.13mmBC BAd d= =

(B) 0BCd = , 1.13mmBAd =

(C) 1.13mmBCd = , 0BAd =

(D) 0BC BAd d= =

SM 2.26 A plastic bar ABC ( 4.0 GPaE= ) of length L consists of two parts of equallengths but different diameters is shown in figure. Segment ABand BChavediameters 100 mmd1 = and 60 mmd2 = , respectively. Both segments have length

/2 0.6 mL = . A longitudinal hole of diameter dis drilled through segment ABfor

one-half of its length (distance /4 0.3 mL = ). Compressive loads 110 kNP= actat the ends of the bar. If the shortening of the bar is limited to 8.0 mm, what isthe maximum allowable diameter dmaxof the hole ?

(A) 11.9 mm (B) 7.96mm

(C) 23.9 mm (D) 2.39mm


32/159







The elastoplastic rods ABand BCare made of mild steel with 200 GPaE= and

345 MPaYs = is shown in figure. The rods are stretched until end has moved

down 9 mm. Neglect the stress concentrations.

SM 2.27 The maximum value of the force Pis(A) 332 kN (B) 415 kN

(C) 166kN (D) 249 kN

SM 2.28 What will be the permanent set measured at point Aand Bafter the force hasbeen removed ?(A) 0Ad = , 6.37 mmBd = (B) 6.37 mmA Bd d= =

(C) 0Ad = , 0Bd = (D) 6.37 mmAd = , 0Bd =

SM 2.29 A post AB is tapered uniformly throughout its height Has shown in figure.The cross sections of the post are square with dimensions b b# at the top and

. .b b1 5 1 5# at the base. Assume that the angle of taper is small and disregardthe weight of the post itself. The shortening dof the post due to the compressiveload Pacting at the top is

(A)EbPH

32

2d= (B) EbPH

23

2d=

(C)EbPH

43

2d= (D) EbPH

52

2d=


33/159



join the Group



SM 2.30 A rectangular bar of length Lhas a slot in the middle half of its length as shown

in figure. The bar has width b , thickness tand modulus of elasticity E. The slothas width of /b 4. What will be the expression for the elongation dof the bar due

to the axial load P?

(A) /L E8 7d s= (B) 7 /4L Ed s=

(C) /L E7 6d s= (D) 7 /8L Ed s=

SM 2.31 A long slender bar in the shape of a right circular cone with length Land base

diameter dhangs vertically under the action of its own weight is shown in figure.The weight of the cone is Wand the modulus of elasticity of the material is E.Assume that the angle of taper of the cone is small. What will be the expressionfor the increase in the length of the bar due to its own weight ?

(A) /WL dE2d p= (B) /WL d E2 2d p=

(C) /WL d E 2 2d p= (D) /WL d E4 2d p=


In the figure shown, rod ABconsists of two cylindrical portions ACand BC,

each with a cross-sectional area of 1750 mm2. Portion ACis made of mild steelwith 200 GPaE= , 250 MPaYs = and portion BCis made of high-strength steelwith 200 GPaE= , 345 MPaYs = . A load Pis applied at point C. Assume bothsteels to be elastoplastic.


34/159


35/159



join the Group



200 mmL1 = . The middle segment has cross-sectional area 1260 mmA22=

and length 250 mmL2 = . Loads PBand PCare equal to 25.5 kNand 17.0 kN,respectively. What will be the compressive axial force FBCin the middle segment

of the bar ?

(A) 22.5 kN (B) 30 kN

(C) 15 kN (D) 7.5 kN

SM 2.38 The rod ABCconsist of two portions is shown in figure. Both portions are made

of aluminium for which 70GPaE= and the magnitude of Pis 4 kN. For zerodeflection at A, the value of Qis

(A) 16.67 kN (B) 65.6 kN

(C) 21.87 kN (D) 32.8 kN

SM 2.39 A composite bar of square cross section with dimensions b b2 2# is constructedof two different metals having moduli of elasticity E1and E2as shown in figureThe two parts of the bar have the same cross-sectional dimensions. The bar is

compressed by forces Pacting through rigid end plates. The line of action of theloads has an eccentricity eof such magnitude that each part of the bar is stresseduniformly in compression. What will be the eccentricity eof the loads ?

(A) eE E

b E E

2 2 1

2 1=

+

-

^^

hh (B) e

E E

b E E

2 2 1

2 1=

-

+

^^

hh

(C) eE E

b E E

2 1 2

1 2=

-

+

^^

hh (D) e

E E

b E E

2 1 2

1 2=

+

-

^^

hh


36/159






SM 2.40 A rigid bar of weight 800 NW= hangs from three equally spaced vertical wires,

two of steel and one of aluminum is shown in figure. The wires also support a loadPacting at the midpoint of the bar. The diameter of the steel wires is 2 mmand

the diameter of the aluminium wire is 4 mm. If the allowable stress in the steelwires is 220 MPaand that is 80MPain the aluminum wire, what load Pallowcan

be supported ?

(Take 210 GPaEst= , 70GPaEal= )

(A) 3.0 kN (B) 1.5 kN

(C) 2.25 kN (D) 4.5 kN

SM 2.41 A plastic cylinder is held snugly between a rigid plate and a foundation by twosteel bolts as shown in figure. Data for the assembly are as follows :Length 200 mmL = , pitch of the bolt threads 1.0mmp = , modulus of elasticity

for steel 200 GPaEs= , modulus of elasticity for the plastic 7.5 GPaEp = , cross-

sectional area of one bolt 36.0 mmAs2

= , 1n= and cross-sectional area of theplastic cylinder 960 mmAp2= .

What will be the compressive stress ps in the plastic when the nuts on the steel

bolts are tightened by one complete turn ?

(A) 31.25MPa (B) 18.75MPa

(C) 25MPa (D) 15.63MPa

SM 2.42 The uniform wire ABCof unstretched length l2 , is attached to the supports asshown in figure and a vertical load Pis applied at the midpoint B. The cross-sectional area of the wire is denoted by Aand the modulus of elasticity is by E.

For l


37/159



join the Group



(A) /l P AE2 /1 3d= ^ h (B) l AEP/1 2

d=b l(C) l

AE

P /1 3d=

b l (D) l

AE

P /2 3d=

b lSM 2.43 A nylon thread is subjected to a 8.5 N tensile force. If 3.3 GPaE= and thelength of the thread increases by . %1 1 , the diameter of the thread and the stressin the thread respectively, are(A) 5.46 mm, 36MPa (B) 0.36mm, 54.6 MPa

(C) 0.546 mm, 36MPa (D) 3.6 mm, 546 MPa

SM 2.44 In the figure shown, the 4 mm diameter cable BC is made of steel with200 GPaE= . If the maximum stress in the cable and the elongation of the cable

must not exceed 190 MPaand 6 mmrespectively, the maximum load Pcan be

(A) 9.94 kN (B) 1.988 kN

(C) 0.994 kN (D) 19.88 kN

SM 2.45 The rigid bar is supported by the pin-connected rod CBof cross-sectional area of

14 mm2as shown in figure and is made from 6061-T6 aluminium ( 68.9 GPaE=). What will be the vertical deflection of the bar at Dwhen the distributed loadis applied ?

(A) 12.97 mm (B) 21.63 mm

(C) 17.3 mm (D) 6.48mm

SM 2.46 In the figure shown, the distributed loading is supported by the three suspenderbars AB, EF and CD. The bars AB and EF are made from aluminium (

70GPaEal= ) and CDis made from steel ( 200 GPaFst= ). Each bar has a cross-

sectional area of 450 mm2

. If allowable stress of ( ) 180 MPaallow sts = in the steeland ( ) 94 MPaallow als = in the aluminium is not exceeded, the maximum intensitywof the distributed loading will be


38/159






(A) 28.35 /kN m (B) 45.9 /kN m

(C) 120.8 /kN m (D) 68.5 /kN m

SM 2.47

The links ABand CDare made of aluminium ( 75 )GPaE= and has a cross-sectional area of 125 mm2each. If they support the rigid member BCas shown infigure, the deflection of point E, is

(A) 0.055 mm (B) 1.10mm(C) 0.110 mm (D) 0.55mm

SM 2.48 An axial force of 60 kNis applied to the assembly as shown by means of rigid endplates. The normal stress in the brass shell and the corresponding deformation ofthe assembly respectively, are

(A) 47.5MPa, 0.113 mm (B) 47.5MPa, 0.226 mm

(C) 22.6 MPa, 0.475 mm (D) 11.3MPa, 0.475 mmSM 2.49 The rigid beam as shown in figure, is supported by the three posts A, Band

C. Posts Aand Chave a diameter of 60 mmand are made of aluminium, forwhich 70GPaEal= and ( ) 20 MPaY als = . Post B is made of brass, for which

100 GPaEbr= and ( ) 590 MPaY brs = . If 130 kNP= , the largest diameter of post

Bso that all the post yield at the same time, is


39/159



join the Group



(A) 3.56mm (B) 1.78mm

(C) 8.9 mm (D) 17.8mm


Three steel rods ( 200 )GPaE= supports a 36 kNload Pas shown in figure. Each

of the rod ABand CDhas a 200 mm2cross-sectional area and rod EFhas a625 mm2cross-sectional area.

SM 2.50 The change in length of rod EFis(A) 0.762 mm (B) 0.0762mm

(C) 0.1524 mm (D) 7.62mm

SM 2.51 What will be the stresses in rods ABand EF?(A) 30.5MPaABs = , 38.1MPaEFs = (B) 15.25MPaABs = , 38.1MPaEFs =

(C) 30.5MPaABs = , 19.05MPaEFs = (D) 38.1MPaABs = , 30.5MPaEFs =


Consider the figure shown.

SM 2.52 What will be the compressive force in the bars shown, after a temperature rise


40/159






of 96 Cc ?

(A) 162.75 kN (B) 217.3 kN6

(C) 271.25 kN (D) 108.5 kN

SM 2.53 The corresponding change in length of the bronze bar is(A) 0.1823mm (B) 0.1215mm

(C) 0.24 mm25 (D) 0.081mm

SM 2.54 In the figure shown, a bar ABof length Lis held between rigid supports andheated non-uniformly in such a manner that the temperature increase TD at

distance x from end A. The temperature increase is given by the expression/T T x LB

3 3D D= , where TBD is the increase in temperature at end Bof the bar.If the material has modulus of elasticity Eand coefficient of thermal expansion

a, What is the expression for the compressive stress cs in the bar ?

(A)E T

8cB

s a D

= ^ h

(B)E T

2cB

s a D

= ^ h

(C) E T6c

Bs a D= ^ h (D) E T4c Bs a D= ^ h

SM 2.55 Five bars, each having a diameter of 10 mmsupport a load Pis shown in figure.If the material is elastoplastic with yield stress 250 MPaYs = , the plastic loadPpis

(A) 55 kN (B) 82.5 kN

(C) 110 kN (D) 41.25 kN

***********


41/159

SM 3TORSION

SM 3.1 The torque which may be applied to a solid shaft of 90 mm outer diameterwithout exceeding an allowable shearing stress of 75 MPa, is(A) 21.6 kN m- (B) 10.8 kN m-

(C) 16.3 kN m- (D) 5.4 kN m-

SM 3.2 In the figure shown, the link acts as part of the elevator control for a airplane. The

attached aluminum tube has an inner diameter of 25 mm and a wall thickness of5 mm. What will be the maximum shear stress in the tube when the cable forceof 600 N is applied to the cables ?

(A) 7.25MPa (B) 20.6MPa

(C) 10.3MPa (D) . MPa14 5

SM 3.3 The solid rod BChas a diameter of 30 mm and is made of aluminum for which

the allowable shearing stress is 25 MPa. Rod AB is hollow and has an outerdiameter of 25 mm. It is made of brass for which the allowable shearing stress is50 MPa. Which of the following is the largest inner diameter of rod ABfor whichthe factor of safety is the same for each rod ?

(A) 11.39 mm (B) 7.59mm

(C) 5.7 mm (D) 15.18 mm


The steel shaft of a socket wrench has a diameter of 8.0 mm and a length of 200mm is shown in figure. The allowable stress in shear is 60MPaand 78GPaG= .


42/159

SM 38 Torsion SM 3





SM 3.4 What is the maximum permissible torque Tmax that may be exerted with thewrench?

(A) 6.03 N m- (B) 7.53 N m-

(C) 4.53 N m- (D) 3.76 N m-

SM 3.5 Through what angle fwill the shaft twist under the action of the maximumtorque? (Disregard any bending of the shaft.)(A) 2.75c (B) 1.65c

(C) 2.20c (D) 1.37c

SM 3.6 The solid brass rod ( 39 )GPaAB G= is bonded to the solid aluminum rod

( 27 )GPaBC G= as shown in figure. The angle of twist at Aand Bare

(A) 0.741 , 1.573A Bc cf f= = (B) 0.831 , 0.741A Bc cf f= =

(C) 0.741 , 0.831A Bc cf f= =

(D) 1.573 , 0.741A Bc cf f= =

SM 3.7 A plastic bar of diameter 50 mmis to be twisted by torques Tas shown in figure,

until the angle of rotation between the ends of the bar is .5 0c. If the allowableshear strain in the plastic is 0.012 rad, what is the minimum permissible lengthof the bar?

(A) 113.75mm (B) 136.5 mm(C) 182 mm (D) 227.5 mm


An aluminum bar of solid circular cross section is twisted by torques Tacting at


43/159

SM 3 Torsion SM 39


join the Group



the ends as shown in figure. The dimensions and shear modulus of elasticity are

as follows: 1.2 mL = , 30 mmd= and 28GPaG= .

SM 3.8 The torsional stiffness of the bar is(A) 1860 N m- (B) 1395 N m-

(C) 2325 N m- (D) 1163 N m-

SM 3.9 The design specifications of a 2 m long solid circular transmission shaft requirethat the angle of twist of the shaft not exceed 3 when a torque of 9 kN-m is

applied. Which of the following is the required diameter of the shaft if the shaftis made of a steel with an allowable shearing stress of 90 MPa and a modulus ofrigidity of 77 GPa ?(A) 41.06 mm (B) 79.9 mm

(C) 39.9mm (D) 82.1mm


A circular tube of outer diameter 70 mmd3 = and inner diameter 60 mmd2 = iswelded at the right-hand end to a fixed plate and at the left-hand end to a rigid

end plates as shown in figure. A solid circular bar of diameter 40 mmd1 = isinside of and concentric with the tube. The bar passes through a hole in the fixedplate and is welded to the rigid end plate.

The bar is 1.0 m long and the tube is half as long as the bar. A torque 1000 N mT -=

acts at end Aof the bar. Also, both the bar and tube are made of an aluminum

alloy with shear modulus of elasticity 27GPaG= .

SM 3.10 The maximum shear stresses in both the bar and tube are(A) 79.6 , 64.6MPa MPabar tube t t= =

(B) 32.3 , 79.6MPa MPabar tube t t= =(C) 79.6 , 32.3MPa MPabar tube t t= =

(D) 39.8 , 32.3MPa MPabar tube t t= =

SM 3.11 The angle of twist at end Aof the bar is(A) 7.07c (B) 9.43c


44/159

SM 40 Torsion SM 3





(C) 11.79c (D) 5.89c

SM 3.12 The composite shaft as shown is to be twisted by applying a torque Tat end A.

The modulus of rigidity is 77 GPa for the steel and 27 GPa for the aluminum. Ifthe allowable stresses are not to be exceeded 60MPasteelt = and 45MPaaluminumt =,the largest angle through which end Amay be rotated, is

(A) 4.13c (B) 1.65c

(C) 2.65c (D) 6.63c

SM 3.13 The torques TAand TB as shown, are exerted on pulleys A and B which areattached to solid circular shafts ABand BC. In order to reduce the total massof the assembly, which of the following is the smallest diameter of shaft BCfor

which the largest shearing stress in the assembly is not increased ?

(A) 29.9 mm (B) 39.8 mm(C) 49.7 mm (D) 24.9mm

SM 3.14 A uniformly tapered tube ABof hollow circular cross section is shown in the figure.The tube has constant wall thickness tand length L. The average diameters at

the ends are dAand d d2B A= . The polar moment of inertia is represented by theapproximate formula /4J d t3. p .

What will be the angle of twist fof the tube when it is subjected to torques T

acting at the ends ?

.

(A)GtdTL

23

A4f p

= (B)GtdTL

43

A3f p

=


45/159

SM 3 Torsion SM 41


join the Group



(C)GtdTL

43

A4f p

= (D)GtdTL

23

A3f p

=

SM 3.15

For a given allowable stress, which of the following is the ratio T/wof the maximumallowable torque Tand the weight per unit length wfor the hollow shaft shown ?

(A) ccc

21all2

2212

gt

-c m (B) 2c cc1all2

2212

gt

+c m(C)

2c

cc1all1

2212

gt

+c m (D) 2c cc1all1

2212

gt

-c mSM 3.16 A prismatic bar ABof length Land solid circular cross section of diameter dis

loaded by a distributed torque of constant intensity tper unit distance as shownin figure. What will be the angle of twist fbetween the ends of the bar ?

(A)GdtL4

4

2

fp

= (B)GdtL16

4

2

fp

=

(C)GdtL12

4

2

fp

= (D)GdtL8

4

2

fp

=

SM 3.17 A solid circular bar of diameter 50 mmd= shown in figure, is twisted by a torque500N mT -= . At this value of torque, a strain gage oriented at 45cto the axis

of the bar gives a reading 339 106

e #= -

. What is the shear modulus Gof thematerial?

(A) 22.5 GPa (B) GPa30

(C) . GPa37 5 (D) GPa45

SM 3.18 The drive shaft for a truck of outer diameter 60d mm2 = and inner diameter40d mm1 = is running at 2500 rpm as shown in figure. If the shaft transmits 150

kW, what is the maximum shear stress in the shaft?


46/159

SM 42 Torsion SM 3





(A) 10.5MPa (B) . MPa12 6

(C) . MPa16 8 (D) MPa21


The solid aluminum shaft has a diameter of 50 mm and an allowable shear stress

of 6 MPaallowt = . The largest torque T1 is applied to the shaft and it is alsosubjected to the other torsional loadings. It is required that T1act in the directionshown.

SM 3.19 What will be the largest torque T1?(A) 215 N m- (B) 2 N m58 -

(C) N m172 - (D) N m129 -

SM 3.20 The maximum shear stress within regions CDand DE are(A) 2 MPaCDt = , 2. MPa58DEt = (B) 2.58MPaCDt = , 2 MPaDEt =

(C) MPa4CDt = , 2. MPa58DEt = (D) . MPa5 16CDt = , MPa4DEt =

SM 3.21 The 60 mm diameter solid shaft is subjected to the distributed and concentratedtorsional loadings as shown in figure. The shear stress at points Aand Bare

(A) . MPa18 86At = , . MPa14 1Bt = (B) . MPa9 43At = , . MPa14 1Bt =

(C) . MPa9 43At = , . MPa7 05Bt = (D) . MPa18 86At = , . MPa7 05Bt =

SM 3.22 The steel shafts are connected together using a fillet weld as shown in figure. Ifthe torque applied to the shafts is 60 N mT -= , the average shear stress in theweld along the critical section a-ais


47/159

SM 3 Torsion SM 43


join the Group



(A) 1.17 MPa (B) . MPa0 87

(C) 1. 7 MPa4 (D) . MPa0 735

SM 3.23 The propellers of a ship are connected to a solid steel ( 75GPaG= ) shaft that is60 m long and has an outer diameter of 340 mm and inner diameter of 260 mm.If the power output is 4.5 MW when the shaft rotates at 20 rad/s, the maximumtorsional stress in the shaft and its angle of twist respectively, are

(A) 22.15 , .MPa 11 9c (B) 22.15 , .9MPa 5 6c

(C) . , .9MPa44 3 5 6c (D) . , 11.9MPa44 3 c

SM 3.24 The 8 mm diameter bolt with 75GPaG= is screwed tightly into a block at Aas shown in figure. What will be the couple force Fthat should be applied to the

rigid wrench and the corresponding displacement of each force F, needed to cause18MPaof maximum shear stress in the bolt ?

(A) 12.06 , 0.720N mm (B) 6.03 , 0.720N mm(C) 12.06 , 0.0720N mm (D) 6.03 , 0.0720N mm

SM 3.25 The steel jacket CDhas been attached to the 40 mm diameter steel shaft AE by

means of rigid flanges welded to the jacket and to the rod. The outer diameter ofthe jacket is 80 mm and its wall thickness is 4 mm. If 500 N-m torques are appliedas shown in figure, the maximum shearing stress in the jacket is


48/159

SM 44 Torsion SM 3





(A) 12.24 MPa (B) 7.65MPa

(C) 15.3MPa (D) 9.18MPa

SM 3.26 A hollow shaft is to transmit 250 kWat a frequency of 30 Hz. The shearing stressmust not exceed 50 MPa. What will be the outer diameter of the shaft for whichthe ratio of the inner diameter to the outer diameter is 0.75 ?

(A) 29.12 mm (B) 72.75 mm

(C) 43.65 mm (D) 58.2 mm

SM 3.27 The assembly is made of A-36 steel ( 75GPaG= ) and consists of a solid rod of 15

mm diameter connected to the inside of a tube using a rigid disk at B as shownin figure. If the tube has an outer diameter of 30 mm and wall thickness of 3 mm,the angle of twist at Awill be

(A) 0.90c (B) .2 70c

(C) .3 60c (D) . 01 8 c

SM 3.28

A propeller shaft of solid circular cross section and diameterd,

is spliced by acollar of the same material as shown in figure. The collar is securely bonded toboth parts of the shaft. What should be the minimum outer diameter d1of the

collar in order that the splice can transmit the same power as the solid shaft ?

(A) . d1 49 (B) . d0 819

(C) 1. d221 (D) . d0 794

SM 3.29 A solid circular bar ABCDwith fixed supports, is acted upon by torques T0andT2 0at the locations as shown in the figure. The maximum angle of twist maxf of

the bar is

(A) GJT L3max

0

f = (B) GJT L

43

max0

f =

(C)GJT L

53

max0f = (D)

GJT L

56

max0f =

SM 3.30 A steel pipe of 60 mm outer diameter is to be used to transmit a torque of350 N-m. A series of 60 mm outer-diameter pipes is available for use. The wall


49/159

SM 3 Torsion SM 45


join the Group



thickness of the available pipes varies from 4 mm to 10 mm in 2 mm increments.

If the allowable shearing stress is not to be exceeded 12 MPa , the thickness ofthe pipe will be

(A) 7 mm (B) 8 mm

(C) 6 mm (D) 10 mm

SM 3.31 A steel shaft transmits 150 kW at a speed of 360 rpm and for steel 77GPaG= .If the allowable maximum stress and the angle of twist in a 2.5 m length will notexceed 50 MPa and 3crespectively, the diameter of the shaft will be(A) 35.4 mm (B) 37 mm

(C) 74 mm (D) 70.8mm


In given figure, the shaft is made of red brass with GPaG 37= and has anelliptical cross section. It is subjected to the torsional loading.

.

SM 3.32 The maximum shear stress within regions ACand BC are

(A) 0.955MPaACt = , 1.59MPaBCt = (B) 1.59MPaACt = , 1.91MPaBCt =

(C) 0.795MPaACt = , 0.955MPaBCt =

(D) 1.59 MPaACt = , 0.955MPaBCt =

SM 3.33 The angle of twist of end Brelative to end A is

(A) .0 207c (B) .2 07c

(C) .0 414c (D) .1 04c

SM 3.34 In the figure shown, a solid circular shaft AB of diameter d is fixed against

rotation at both ends and a circular disk is attached to the shaft at the locationshown. If the allowt is the allowable shear stress in the shaft and assume that a b>, what is the largest permissible angle of rotation maxf of the disk ?


50/159

SM 46 Torsion SM 3





(A) /b Gd2max allow3f t= ^ h (B) /b Gd2max allow 2f t= ^ h

(C) /b Gd2max allow4f t= ^ h (D) /b Gd2max allowf t= ^ h


A solid shaft of 54 mm diameter is made of mild steel which is assumed to be

elastoplastic with 145 MPaYt = .

SM 3.35 What will be the maximum shearing stress and the radius of the elastic corerespectively, caused by the application of a torque of magnitude 4 kN-m ?(A) 129.4 , 27MPa mm (B) 129.4 , 54MPa mm

(C) 64.7 , 27MPa mm (D) 64.7 , 54MPa mm

SM 3.36 What will be the maximum shearing stress and the radius of the elastic core

respectively, if a torque of 5 kN-m is applied ?(A) 145 , 46.8MPa mm (B) 145 , 23.4MPa mm

(C) 290 , 23.4MPa mm (D) 290 , 46.8MPa mm

SM 3.37 A hollow steel shaft ACBof outside diameter 50 mm and inside diameter 40 mmis held against rotation at ends Aand Bas shown in figure. Horizontal forces Pare applied at the ends of a vertical arm that is welded to the shaft at point C. Ifthe maximum permissible shear stress in the shaft is 45 MPa, the allowable value

of the forces P will be

(A) 1693.75 N (B) .5 N2032

(C) N2710 (D) . N3387 5

SM 3.38 A high-strength steel symmetric tube, having the mean dimensions is shown infigure and a thickness of 5 mm. If it is subjected to a toque of 40 N mT -= , whatwill be the average shear stress developed at points Aand B?


51/159


52/159

SM 48 Torsion SM 3





(C) . kN m27 9 - (D) . kN m22 3 -

SM 3.42 The solid circular drill rod ABis made of a steel which is assumed to be elastoplastic

with 160 MPaYt = and 77GPaG= as shown in figure. If a torque 5 kN mT -= is applied to the rod and then removed, the maximum residual shearing stress in

the rod is

(A) 44.9 MPa (B) 204 MPa

(C) 43.7 MPa (D) 115 MPa

SM 3.43 A 1.25mlong steel angle has an 127 76 6.4L # # cross section is shown in figure.The thickness of the section is 6.4 mmand its area is 1252mm2. Neglect the effectof stress concentrations. What will be the largest torque Twhich may be applied

and the corresponding angle of twist respectively ?

(Take 60MPaallt = , 77GPaG= )

(A) 157 N m- , 8.72c (B) 196.25 N m- , 5.45c

(C) 117.75 N m- , 10.9c (D) 98.125N m- , 6.54c


A solid shaft has a diameter of 40 mm, length of 1 mand 80GPaG= . It is madefrom an elastic-plastic material having a yield stress of 100 MPaYt = .

SM 3.44 What will be the maximum elastic torque TYand the corresponding angle of twistrespectively ?

(A) 2.52 , .kN m 3 58c- (B) . , .kN m1 26 1 79c-

(C) . , 3.58kN m1 26 c- (D) 2.52 , .kN m 1 79c-

SM 3.45 What is the angle of twist if the torque is increased to .T T1 2 Y= ?

(A) .3 64c (B) .4 86c

(C) .6 08c (D) 3.04c


53/159


54/159

SM 4SHEAR FORCE AND BENDING MOMENT

SM 4.1 For the beam with overhangs as shown in figure, if one load acts downward andthe other upward, the shear force Vand bending moment Mat the midpoint ofthe beam will be

(A) ,VLbP M2 0= = (B) ,V

LbP M

Lb P2 2 2= =

(C) , 0VL

bPM

2= = (D) ,V

LbP

ML

b P2 2

2

= =

SM 4.2 Two metric rolled-steel channels are to be welded along their edges and are used

to support the loading as shown in figure. If the allowable normal stress for thesteel is 150 MPa, the section modulus of the beam is

(A) mm45 103 3#^ h (B) mm90 103 3#^ h(C) mm180 103 3#^ h (D) mm135 103 3#^ h

SM 4.3 In figure shown, the beam is subjected to the load Pat its center. What willbe the placement a of the supports for maximum moment and the absolutemaximum bending stress in the beam ?

(A) 0,bd

PL

2

32

(B) L

4,

bd

PL

3

22

(C) L2

,bdPL

32

3 (D)L43 ,

bdPL

23

3

SM 4.4 In figure shown, the beam ABCis simply supported at Aand B, and has anoverhang from Bto C. The loads consist of a horizontal force 4.0 kNP1 = acting


55/159


56/159



join the Group



(A) 250 , 500N NP Q= = (B) 50 , 50N NP Q0 2= =

(C) , 500N NP Q1000= = (D) 50 , 00N NP Q0 10= =

SM 4.8 What will be the equations of the shear force and bending-moment curves for thebeam and loading shown in figure ?

(A) ,cos sinV w LLx

M w L

Lx0 2

20

2

pp

pp

= =

(B) ,cos sinV w LLx M

w LLx0

20

2

pp

pp= =

(C) ,sin cosV w LLx M

w LLx0 0

2

pp

pp= =

(D) ,sin cosV w LLx

M w L

Lx0 2 0

22

pp

pp

= =


Beams AB, BCand CDhave the cross sections as shown in the figure and are

pin-connected at Band C. The allowable normal stress is 110 MPain tension and150 MPa- in compression.

SM 4.9 If beam BCis not to be over stressed, what will be the largest permissible value

of P ?(A) . kN4 01 (B) . kN5 02

(C) .01 kN3 (D) . kN8 02

SM 4.10 What will be the corresponding maximum distance a for which the cantileverbeams ABand CDare not to be over stressed ?(A) 2.45m (B) . m6 54

(C) . m4 09 (D) . m3 27

SM 4.11 Consider a timber beam of length 16 mL = and width 75 mmb = as shown infigure. The dead load carried by each beam, including the estimated weight of

the beam, is a uniformly distributed load 350 /N mwD= . The live loads can berepresented by a uniformly distributed load 600 /N mwL = . If a 6 kNconcentratedload P applied at the midpoint C of each beam, what will be the minimumallowable depth hof the beams using LRFD (Load and Resistance Factor Design)

? : 50 , 1.2, 1.6 .Use Data MPa and 0 9U D Ls g g f= = = =


57/159


58/159



join the Group



(A) 161.25MPa (B) . MPa96 75

(C) . MPa129 0 (D) . MPa80 63

SM 4.15 The smooth pin of 20 mmdiameter is supported by two leaves Aand Band

subjected to a compressive load of 0.4 kNas shown in figure. What will be theabsolute maximum bending stress in the pin ?

(A) 248.25 kPa (B) 331.0 kPa

(C) . kPa413 75 (D) . kPa206 85


A shaft made of a polymer having an elliptical cross-section is shown in figure. It

resists an internal moment of 50 N mM -= .

SM 4.16 What will be the maximum bending stress developed in the material using theflexure formula, where (0.08 )(0.04 )m mIz 4

1 3p= ?

(A) 372.75 kPa (B) . kPa310 65

(C) . kPa621 25 (D) . kPa497 0

SM 4.17 What will be the maximum bending stress developed in the material using

integration ?(A) . kPa621 25 (B) . kPa497 0

(C) . kPa310 65 (D) 372.75 kPa


59/159


60/159



join the Group



SM 4.22 The location cof the neutral axis, is

(A)E E

h E

t c

c

- (B)

E E

h E

t c

c

+

(C)E E

h E

t c

t

- (D)

E E

h E

t c

t

+

SM 4.23 If it is subjected to the bending moment M, an expression for the maximumtensile stress in the beam having the dimensions shown, will be

(A)bhM

E

E E3

c

t c2

-e o (B)bhM

E

E E3

t

t c2

+e o(C)

bhM

E

E E3

t

t c2

-e o (D)bhM

E

E E3

c

t c2

+e oSM 4.24 The 65 mm diameter steel shaft is subjected to the two loads that act in the

directions as shown in the figure. If the journal bearings at Aand Bdo not exertan axial force on the shaft, the absolute maximum bending stress developed inthe shaft will be

(A) 203.75MPa (B) . MPa163 0

(C) . MPa101 85 (D) . MPa122 25


The composite beam as shown in figure, is made of aluminium ( )A and red brass

( )B. Take 68.9 GPaEal= and 101GPaEbr= .

SM 4.25 What will be the dimension hof the brass strip so that the neutral axis of thebeam is located at the seam of the two metals ?(A) 82.6mm (B) mm413

(C) . mm41 3 (D) . mm4 13


61/159






SM 4.26 If the allowable bending stress for the aluminium is ( ) 128 MPaallow als = and for

the brass is ( ) 35 MPaallow brs = , what maximum moment will this beam support ?(A) . kN m6 60 - (B) . kN m36 5 -

(C) 29.2 kN m- (D) . kN m43 8 -


A beam ABconsists of a cast-aluminium plate of uniform thickness band length

L,is support the load as shown in figure.

SM 4.27 If the beam is to be of constant strength, the expression for h in terms ofx, Landh0for portion ACof the beam will be

(A) h hLx2

0= (B) h h Lx

0=

(C) h hLx20

= (D) h hLx

32

0=

SM 4.28 If 800 mmL = , 200 mmh0 = , 25 mmb = and 72MPaallows = , the maximum

allowable load Pwill be(A) 30 kN (B) 0 kN12

(C) 0 kN6 (D) kN45

SM 4.29 Consider a beam reinforced with A-36 steel straps ( 200 GPaEst= ) at its sides asshown in figure. If the beam is subjected to a bending moment of 4 kN mMz -= ,the maximum stress developed in the wood ( 13.1GPaEw= ) and steel are

(A) . , .MPa MPa4 55 0 30st ws s= =

(B) 4.55 , .MPa MPa2 28st ws s= =

(C) . , 0.MPa MPa2 28 60st ws s= =

(D) . , 0.MPa MPa0 60 30st ws s= =

SM 4.30 The cantilever beam ABconsisting of a cast-iron plate of uniform thickness band

length L, is to support the distributed load ( )w xas shown in figure. If the beamis of constant strength, the expression for h in terms ofx, Land h0will be


62/159



join the Group



(A) h h Lx /

0

2 3

= b l (B) h h Lx /0 5 2= b l(C) h h L

x /0

1 2

= b l (D) h h Lx /0 3 2= b lSM 4.31 For the section shown in figure, the allowable bending stress is 50MPacs = in

compression and 120 MPats = is in tension. What will be the greatest magnitude

of the applied forces P?

(A) 79.75 kN(B) . kN110 4

(C) . kN159 5

(D) . kN55 2

SM 4.32 A cantilevered machine element of cast aluminium and in the shape of a solidof revolution of variable diameter d, is being designed to support a horizontaldistributed load 20 /kN mw= as shown in figure. If the machine element is to be

of constant strength with 72MPaallows = and 300 mmL = , the smallest allowablevalue of d0will be

(A) 503 mm (B) 50.3mm

(C) 5.03mm (D) . mm100 6

SM 4.33 A curved bar of rectangular cross section is subjected to a couple as shown in

figure. What will be the maximum tensile and compressive stress acting at sectiona a- ?


63/159






(A) 1.02 , 792MPa kPat cs s= = (B) 792 , 1.02kPa MPat cs s= =

(C) 2.04 , 792MPa kPat cs s= = (D) 1.02 , 396MPa kPat cs s= =

SM 4.34 For the tapered beam as shown in the figure, if 150 kNP= , what will be thedistance xof the transverse section in which the maximum normal stress occursand the corresponding value of the normal stress ?

(A) 0.4 , 78.15m MPaxm ms= = (B) 0. , .m MPax 2 156 3m ms= =

(C) 0.4 , .m MPax 156 3m ms= = (D) 0. , 78.15m MPax 2m ms= =

SM 4.35 Bar as shown in figure has a thickness of 10 mm. If the maximum bending stressat ,A Band C is same and 1.5K= , what will be the length Lof the center

portion of the bar ?

(A) 95 mm (B) 95 mm0

(C) 9.5 mm (D) . mm19 0

SM 4.36 Consider a machine element of cast aluminium and in the shape of a solid ofrevolution of variable diameter dto support a distributed load was shown in

figure. If the machine element is to be of constant strength, the expression for din terms of ,x Land d0is


64/159



join the Group



(A) d dLx

Lx4 1

/

0

1 3

= +a k& 0 (B) d d Lx Lx2 1 /0 1 3= -a k& 0(C) d d

L

x

L

x4 1/

0

1 3

= -

a k& 0 (D) d d

L

x

L

x2 1/

0

1 3

= +

a k& 0SM 4.37 In the figure shown, the box beam is made of an elastically perfectly plastic

material for which 250 MPaYs = . If the plastic moment Mpis applied and thenreleased, what will be the residual stress in the top and bottom of the beam ?

(A) . MPa317 14 (B) . MPa67 1

(C) . MPa158 6 (D) . MPa134 2

SM 4.38 The beam shown in figure, is made of elastic perfectly plastic material. If

50 mma= and 230 MPaYs = , what will be the maximum elastic moment and

the plastic moment that can applied to the cross section ?

(A) 50.7 , 86.25kN m kN mM MY p- -= =

(B) 86.25 , 50.7kN m kN mM MY p- -= =

(C) . , .kN m kN mM M101 4 86 25Y p- -= =

(D) . , .kN m kN mM M50 7 43 15Y p- -= =

SM 4.39 Consider the beam and loading as shown in figure, the shear force and bending

moment diagrams for the beam will be


65/159






SM 4.40 For a simple beam ABsupporting two equal concentrated loads Pas shown in

figure, the shear-force and bending-moment diagrams are


66/159



join the Group



SM 4.41 The shear force and bending-moment diagrams for the beam and loading shownin the figure, are


67/159






SM 4.42 Consider the compound beam as shown in figure. It is supported by a smoothplate at Awhich slides within the groove and so it cannot support a verticalforce, although it can support a moment and axial load. Which of the followingsare the shear force and bending moment diagrams for this beam ?


68/159



join the Group




Consider the beam and loading as shown in figure.

SM 4.43 The shear force and bending-moment diagrams are


69/159






SM 4.44 The maximum normal stress due to bending is(A) 12.89 MPa (B) 10.75 MPa

(C) 21.49 MPa (D) 17.19 MPa

SM 4.45 In the figure shown, a simply supported beam ABCis loaded by a vertical load

Pwhich is acting at the end of a bracket BDE. The shear-force and bending-moment diagrams for beam ABC, are


70/159



join the Group



SM 4.46 Consider the figure as shown. Which of the followings are the required shear force

and bending-moment diagrams for the beam and loading ?

SM 4.47 Consider a beam ABC, which is simply supported at A and B, and has anoverhang BCas shown in figure. The beam is loaded by two same forces Pand

a clockwise couple of moment Pathat act through the arrangement as shown.Which of the following options show the required shear-force and bending-momentdiagrams for beam ABC?


71/159






SM 4.48 Which of the followings are the required shear force and bending-moment diagramsfor the beam and loading shown in the figure ?


72/159



join the Group



SM 4.49 Consider the beam and loading as shown in figure. The shear force and bending-moment diagrams for the beam, are


73/159






SM 4.50 Which of the followings are the required shear force and bending-moment diagrams

for the beam and loading shown in the figure ?

SM 4.51 For the beam and loading as shown in figure, the shear force and bending-momentdiagrams are


74/159



join the Group



SM 4.52 For the beam shown in figure, correct representation of the shear force andbending moment diagrams are


75/159





G

Documents

Gate Mechanical Sm by Nodia