gate mechanical sm by nodia
TRANSCRIPT
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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
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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
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CONTENTS VOL 3
MANUFACTURING PROCESS
INDUSTRIAL ENGINEERING
OPERATION RESEARCH
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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
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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
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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
Common Data For Q. 3 and 4
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=
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SM 4 Stress and Strain SM 1
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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=
Common Data For Q. 8 and 9
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
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SM 1 Stress and Strain SM 5
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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
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SM 6 Stress and Strain SM 1
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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
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SM 1 Stress and Strain SM 7
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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
Common Data For Q. 18 and 19
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
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SM 8 Stress and Strain SM 1
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(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
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SM 1 Stress and Strain SM 9
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(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
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(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
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SM 1 Stress and Strain SM 11
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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
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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.)
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SM 1 Stress and Strain SM 13
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(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
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(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
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SM 1 Stress and Strain SM 15
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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
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(A) N685 (B) 10 N28
(C) 1370N (D) 2740N
Common Data For Q. 42 and 43
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
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SM 1 Stress and Strain SM 17
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(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
Common Data For Q. 47 and 48
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
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Common Data For Q. 49 and 50
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
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SM 1 Stress and Strain SM 19
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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
Common Data For Q. 53 and 54
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
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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
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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-
Common Data For Q. 6 and 7
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= .
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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=
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(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) ?
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(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 ?
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(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= )
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(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
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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
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Common Data For Linked Q. 27 and 28
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=
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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=
Common Data For Linked Q. 32 and 33
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.
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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
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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
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(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
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(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
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(A) 3.56mm (B) 1.78mm
(C) 8.9 mm (D) 17.8mm
Common Data For Q. 50 and 51.
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 =
Common Data For Linked Q. 52 and 53
Consider the figure shown.
SM 2.52 What will be the compressive force in the bars shown, after a temperature rise
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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
***********
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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
Common Data For Q. 4 and 5.
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= .
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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
Common Data For Q. 9 and 10
An aluminum bar of solid circular cross section is twisted by torques Tacting at
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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
Common Data For Q. 10 and 11
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
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(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
=
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(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?
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(A) 10.5MPa (B) . MPa12 6
(C) . MPa16 8 (D) MPa21
Common Data For Q. 19 and 20.
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
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(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
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(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
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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
Common Data For Q. 36 and 37.
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 ?
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(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
Common Data For Q. 35 and 36
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?
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(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
Common Data For Q. 44 and 45
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
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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
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(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
= =
Common Data For Q. 9 and 10
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= = = =
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(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
Common Data For Q. 16 and 17
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
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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
Common Data For Q. 25 and 26
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
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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 -
Common Data For Q. 27 and 28
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
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(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- ?
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(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
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(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
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SM 4.40 For a simple beam ABsupporting two equal concentrated loads Pas shown in
figure, the shear-force and bending-moment diagrams are
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SM 4.41 The shear force and bending-moment diagrams for the beam and loading shownin the figure, are
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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 ?
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Common Data For Q. 43 and 44
Consider the beam and loading as shown in figure.
SM 4.43 The shear force and bending-moment diagrams are
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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
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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?
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SM 4.48 Which of the followings are the required shear force and bending-moment diagramsfor the beam and loading shown in the figure ?
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SM 4.49 Consider the beam and loading as shown in figure. The shear force and bending-moment diagrams for the beam, are
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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
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SM 4.52 For the beam shown in figure, correct representation of the shear force andbending moment diagrams are
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G