GATE SOLVED PAPER - ME

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1 YEAR 01 ONE MARK Q. 1 A metric threas of itch mm an threa angle 60c is insecte for its itch iameter using -wire metho. The iameter of the best size wire in mm is (A) (B) (C) 1.15 (D).000 Q. Two threae bolts A an B of same material an length are subjecte to ientical tensile loa. If the elastic strain store in bolt A times of bolt B an the mean iameter of bolt A is 1 mm, the mean iameter of bolt B in mm is (A) 16 (B) (C) 6 (D) 8 YEAR 01 TWO MARKS Common Data For Q. an A single rivete la joint of two similar lates as shown in the figure below has the following geometrical an material etails. with of the late w 00 mm, thickness of the late t 5mm, number of rivets n, iameter of the rivet r 10 mm, iameter of the rivet hole h 11 mm, allowable tensile stress of the late s 00 MPa, allowable shear stress of the rivet s 100 MPa an allowable stress of the rivet s 150 MPa. s Q. If the lates are to be esigne to avoi tearing failure, the maximum ermissible loa P in kn is (A) 8 (B) 15 (C) 167 (D) 501 Q. If the rivets are to be esigne to avoi crushing failure, the maximum ermissible loa P in kn is (A) 750. (B) (C). 50 (D) c

2 YEAR 01 TWO MARKS Q. 5 A fillet wele joint is subjecte to transverse loaing F as shown in the figure. Both legs of the fillets are of 10 mm size an the wel length is 0 mm. If the allowable shear stress of the wel is 9 MPa, consiering the minimum throat area of the wel, the maximum allowable transverse loa in kn is (A) 1. (B) 17.9 (C) 19.9 (D).16 Q. 6 A force of 00 N is alie to the brake rum of 0.5 m iameter in a ban-brake system as shown in the figure, where the wraing angle is 180c. If the coefficient of friction between the rum an the ban is 0.5, the braking torque alie, in Nm is (A) (B) 5. (C).1 (D) 15.7 Q. 7 A soli circular shaft nees to be esigne to transmit a torque of 50 Nm. If the allowable shear stress of the material is 10 MPa, assuming a factor of safety of, the minimum allowable esign iameter is mm is (A) 8 (B) 16 (C) (D) YEAR 011 TWO MARKS Q. 8 Two ientical ball bearings P an Q are oerating at loas 0 kn an 5 kn resectively. The ratio of the life of bearing P to the life of bearing Q is (A) 81 (B) (C) 9 (D) YEAR 010 TWO MARKS Q. 9 A ban brake having ban-with of 80 mm, rum iameter of 50 mm, coefficient of friction of 0.5 an angle of wra of 70 egrees is require to exert a friction torque of 1000 Nm. The maximum tension (in kn) eveloe in the ban is (A) 1.88 (B).56 (C) 6.1 (D) 11.56

3 Q. 10 A bracket (shown in figure) is rigily mounte on wall using four rivets. Each rivet is 6 mm in iameter an has an effective length of 1 mm. Direct shear stress (in MPa) in the most heavily loae rivet is (A). (B) 8.8 (C) 17.6 (D) 5. Q. 11 A lightly loae full journal bearing has journal iameter of 50 mm, bush bore of mm an bush length of 0 mm. If rotational see of journal is 100 rm an average viscosity of liqui lubricant is 0.0 Pa s, the ower loss (in W) will be (A) 7 (B) 7 (C) 118 (D) 7 YEAR 009 TWO MARKS Q. 1 A forge steel link with uniform iameter of 0 mm at the centre is subjecte to an axial force that varies from 0 kn in comression to 160 kn in tension. The tensile ( S u ), yiel ( S y ) an correcte enurance ( S e ) strengths of the steel material are 600 MPa, 0 MPa an 0 MPa resectively. The factor of safety against fatigue enurance as er Soerberg s criterion is (A) 1.6 (B) 1.7 (C) 1.5 (D).00 Common Data For Q. 1 an 1 A 0c full eth involute sur inion of mm moule an 1 teeth is to transmit 15 kw at 960 rm. Its face with is 5 mm. Q. 1 The tangential force transmitte (in N) is (A) 55 (B) 611 (C) 1776 (D) 105 Q. 1 Given that the tooth geometry factor is 0. an the combine effect of ynamic loa an allie factors intensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material is (A).0 (B) (C) 11.0 (D) 7.0

4 YEAR 008 TWO MARKS Q. 15 A journal bearing has a shaft iameter of 0 mm an a length of 0 mm. The shaft is rotating at 0 ra/ s an the viscosity of the lubricant is 0 mpa- s. The clearance is 0.00 mm. The loss of torque ue to the viscosity of the lubricant is aroximately. (A) 0.00 N- m (B) 0.5 Nm - (C) 0.00 N - m (D) 0.65 Nm - Q. 16 A clutch has outer an inner iameters 100 mm an 0 mm resectively. Assuming a uniform ressure of MPa an coefficient of friction of liner material is 0., the torque carrying caacity of the clutch is (A) 18 N - m (B) 196 Nm - (C) 7 N - m (D) 90 Nm - Q. 17 A sur gear has a moule of mm, number of teeth 16, a face with of 6 mm an a ressure angle of 0c. It is transmitting a ower of kw at 0 rev/s. Taking a velocity factor of 1.5 an a form factor of 0., the stress in the gear tooth is about. (A) MPa (B) 6 MPa (C) 58 MPa (D) 70 MPa Q. 18 One tooth of a gear having moule an teeth is shown in the figure. Assume that the gear tooth an the corresoning tooth sace make equal intercets on the itch circumference. The imensions a an b, resectively, are closest to (A) 6.08 mm, mm (C) 6.8 mm,. mm (B) 6.8 mm,. mm (D) 6.8 mm,.1 mm Q. 19 Match the tye of gears with their most aroriate escrition. Tye of gear Descrition P Helical 1. Axes non arallel an non intersecting Q Siral Bevel. Axes arallel an teeth are incline to the axis R Hyoi. Axes arallel an teeth are arallel to the axis S Rack an inion. Axes are erenicular an intersecting, an teeth are incline to the axis. 5. Axes are erenicular an use for large see reuction 6. Axes arallel an one of the gears has infinite raius

5 (A) P-, Q-, R-1, S-6 (B) P-1, Q-, R-5, S-6 (C) P-, Q-6, R-, S- (D) P-6, Q-, R-1, S-5 Common Data For Q. 0 an 1 A steel bar of # mm is cantilevere with two M 1 bolts (P an Q) to suort a static loa of kn as shown in the figure. Q. 0 The rimary an seconary shear loas on bolt P, resectively, are (A) kn, 0 kn (B) 0 kn, kn (C) 0 kn, 0 kn (D) 0 kn, 0 kn Q. 1 The resultant shear stress on bolt P is closest to (A) 1 MPa (B) 159 MPa (C) 178 MPa (D) 195 MPa YEAR 007 ONE MARK Q. A ball bearing oerating at a loa F has 8000 hours of life. The life of the bearing, in hours, when the loa is ouble to F is (A) 8000 (B) 6000 (C) 000 (D) 1000 YEAR 007 TWO MARKS Q. A thin sherical ressure vessel of 00 mm iameter an 1 mm thickness is subjecte to an internal ressure varying form to 8MPa. Assume that the yiel, ultimate an enurance strength of material are 600, 800 an 00 MPa resectively. The factor of safety as er Gooman s relation is (A).0 (B) 1.6 (C) 1. (D) 1. Q. A natural fee journal bearing of iameter 50 mm an length 50 mm oerating at 0 revolution/ secon carries a loa of kn. The lubricant use has a viscosity of 0 mpas. The raial clearance is50 m m. The Sommerfel number for the bearing is (A) 0.06 (B) 0.15 (C) 0.50 (D) 0.785

6 Q. 5 A bolte joint is shown below. The maximum shear stress, in MPa in the bolts at A an B, resectively are (A).6,.5 (B).5,.6 (C).5,.5 (D) 18.75,.6 Q. 6 A block-brake shown below has a face with of 00 mm an a mean co-efficient of friction of 0.5. For an activating force of 00 N, the braking torque in Nm is (A) 0 (B) 0 (C) 5 (D) 60 Q. 7 The iston ro of iameter 0 mm an length 700 mm in a hyraulic cyliner is subjecte to a comressive force of 10 kn ue to the internal ressure. The en conitions for the ro may be assume as guie at the iston en an hinge at the other en. The Young s moulus is 00 GPa. The factor of safety for the iston ro is (A) 0.68 (B).75 (C) 5.6 (D) 11.0

7 Common Data For Q. 8 an 9 A gear set has a inion with 0 teeth an a gear with 0 teeth. The inion runs at 0 rev/s an transmits a ower of 0 kw. The teeth are on the 0c full-eth system an have a moule of 5mm. The length of the line of action is 19 mm. Q. 8 The center istance for the above gear set in mm is (A) 10 (B) 150 (C) 160 (D) 170 Q. 9 The contact ratio of the contacting tooth is (A) 1.1 (B) 1.5 (C) 1.9 (D) 1. Q. 0 The resultant force on the contacting gear tooth in N is (A) 77. (B) 1.0 (C) 58.1 (D) 89. YEAR 006 TWO MARKS Q. 1 A isc clutch is require to transmit 5kW at 000 rm. The isk has a friction lining with coefficient of friction equal to 0.5. Bore raius of friction lining is equal to 5 mm. Assume uniform contact ressure of 1MPa. The value of outsie raius of the friction lining is (A) 9. mm (B) 9.5 mm (C) 97.9 mm (D) 1.9 mm Q. Twenty egree full eth involute rofile 19 tooth inion an 7 tooth gear are in mesh. If the moule is 5 mm, the centre istance between the gear air will be (A) 10 mm (B) 150 mm (C) 80 mm (D) 00 mm Q. A cylinrical shaft is subjecte to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cycles is 90 MPa. If the correcte enurance strength is 70 MPa, estimate shaft life will be (A) 1071 cycles (B) cycles (C) 8191 cycles (D) 986 cycles Q. A 60 mm long an 6mm thick fillet wel carries a steay loa of 15 kn along the wel. The shear strength of the wel material is equal to 00 MPa. The factor of safety is (A). (B). (C).8 (D) 6.8

8 YEAR 005 ONE MARK Q. 5 Which one of the following is criterion in the esign of hyroynamic journal bearings? (A) Sommerfel number (B) Rating life (C) Secific ynamic caacity (D) Rotation factor YEAR 005 TWO MARKS Common Data For Q. 6 an 7 A ban brake consists of a lever attache to one en of the ban. The other en of the ban is fixe to the groun. The wheel has a raius of 00 mm an the wra angle of the ban is 70c. The braking force alie to the lever is limite to 100 N an the coefficient of friction between the ban an the wheel is 0.5. No other information is given. Q. 6 The maximum tension that can be generate in the ban uring braking is (A) 100 N (B) 110 N (C) N (D) 0 N Q. 7 The maximum wheel torque that can be comletely brake is (A) 00 Nm (B) 8 Nm (C) 60 Nm (D) 8 Nm YEAR 00 ONE MARK Q. 8 Two mating sur gears have 0 an 10 teeth resectively. The inion rotates at 100 rm an transmits a torque of 0 Nm. The torque transmitte by the gear is (A) 6.6 Nm (B) 0 Nm (C) 0 Nm (D) 60 Nm Q. 9 In terms of theoretical stress concentration factor ( K t ) an fatigue stress concentration factor ( K f ), the notch sensitivity q is exresse as ( Kf - 1) ( Kf - 1) (A) (B) ( Kt - 1 ) ( Kt + 1 ) ( Kt - 1) ( Kf + 1) (C) (D) ( Kf - 1 ) ( Kt + 1 ) Q. 0 The S-N curve for steel becomes asymtotic nearly at (A) 10 cycles (B) 10 cycles (C) 10 6 cycles (D) 10 9 cycles

9 YEAR 00 TWO MARKS Q. 1 In a bolte joint two members are connecte with an axial tightening force of 00 N. If the bolt use has metric threas of mm itch, the torque require for achieving the tightening force is (A) 0.7 Nm (C) 1. Nm (B) 1.0 Nm (D).8 Nm Q. Match the following Tye of gears Arrangement of shafts P. Bevel gears 1. Non-arallel off-set shafts Q. Worm gears. Non-arallel intersecting shafts R. Herringbone gears. Non-arallel, non-intersecting shafts S. Hyoi gears. Parallel shafts (A) P- Q- R-1 S- (B) P- Q- R- S-1 (C) P- Q- R-1 S- (D) P-1 Q- R- S- YEAR 00 ONE MARK Q. A wire roe is esignate as 6# 19 stanar hoisting. The numbers 6# 19 reresent (A) iameter in millimeter # length in meter (B) iameter in centimeter # length in meter (C) number of strans # numbers of wires in each stran (D) number of wires in each stran # number of strans YEAR 00 TWO MARKS Q. Square key of sie / each an length l is use to transmit torque T from the shaft of iameter to the hub of a ulley. Assuming the length of the key to be equal to the thickness of ulley, the average shear stress eveloe in the key is given by (A) T l (B) (C) 8T l (D) 16T l 16T Q. 5 In a ban brake the ratio of tight sie ban tension to the tension on the slack sie is. If the angle of overla of ban on the rum is 180c, the coefficient of friction require between rum an the ban is (A) 0.0 (B) 0.5 (C) 0.0 (D) 0.5

10 Common Data For Q. 6 an 7 The overall gear ratio in a stage see reuction gear box (with all sur gears) is 1. The inut an outut shafts of the gear box are collinear. The counter shaft which is arallel to the inut an outut shafts has a gear (Z teeth) an inion ( Z 15 teeth) to mesh with inion ( Z 1 16 teeth) on the inut shaft an gear (Z teeth) on the outut shaft resectively. It was ecie to use a gear ratio of with moule in the first stage an moule in the secon stage. Q. 6 Z an Z are (A) 6 an 5 (B) 5 an 6 (C) 8 an 60 (D) 60 an 8 Q. 7 The centre istance in the secon stage is (A) 90 mm (B) 10 mm (C) 160 mm (D) 0 mm YEAR 00 ONE MARK Q. 8 The minimum number of teeth on the inion to oerate without interference in stanar full height involute teeth gear mechanism with 0c ressure angle is (A) 1 (B) 1 (C) 18 (D) YEAR 00 TWO MARKS Q. 9 The couling use to connect two shafts with large angular misalignment is (A) a flange couling (B) an Olham s couling (C) a flexible bush couling (D) a Hooke s joint Q. 50 A static loa is mounte at the centre of a shaft rotating at uniform angular velocity. This shaft will be esigne for (A) the maximum comressive stress (static) (B) the maximum tensile (static) (C) the maximum bening moment (static) (D) fatigue loaing Q. 51 Large see reuctions (greater than 0) in one stage of a gear train are ossible through (A) sur gearing (B) worm gearing (C) bevel gearing (D) helical gearing Q. 5 If the wire iameter of a close coil helical sring subjecte to comressive loa is increase from 1cm to cm, other arameters remaining same, the eflection will ecrease by a factor of (A) 16 (B) 8 (C) (D)

11 YEAR 001 ONE MARK Q. 5 Bars AB an BC, each of negligible mass, suort loa P as shown in the figure. In this arrangement, (A) bar AB is subjecte to bening but bar BC is not subjecte to bening. (B) bar AB is not subjecte to bening but bar BC is subjecte to bening. (C) neither bar AB nor bar BC is subjecte to bening. (D) both bars AB an BC are subjecte to bening. YEAR 001 TWO MARKS Q. 5 Two helical tensile srings of the same material an also having ientical mean coil iameter an weight, have wire iameters an /. The ratio of their stiffness is (A) 1 (B) (C) 6 (D) 18 *********

12 SOLUTION Otion (C) is correct. For -wire metho, the iameter of the best size wire is given by a cos where itch mm, a 60c Hence D 1.15 mm cos 0c Stain Energy is given by U s E V Given U A U B FALA FBLB A E A E A A F # A B B AL E FL AE Since bolts of same material an length an subjecte to ientical tensile loa, i.e. EA EB, LA LB, FA FB So that 1 A A AB 1 A A B or B A or B A # 1 mm Otion (C) is correct. If the rivets are to be esigne to avoi crushing failure, maximum ermissible loa P s # A where for crushing failure A ^w-hole h# t So that P ^w- hole h# t#s ^00 - # 11h # 5 # N 167 kn Otion (C) is correct. For Design against tearing failure, maximum ermissible loa P n. rivet # t#sc # 10 # 5 # N.5 kn Otion (C) is correct. Given : With of fillets s 10 mm, l 0 mm, t 9 MPa

13 The shear strength of the joint for single arallel fillet wel is, P Throat Area # Allowable stress t# l#t From figure t ssin 5c s P # s# l#t #( 0. 01) #( 0. 0) #( 9 # 10 6 ) 1997 N or 19.9 kn Given : T 1 00 N, m 0.5, q 180c 180 c # ra. 180c D 0.5 m, r D 0.5 m For the ban brake, the limiting ratio of the tension is given by the relation, T T 1 e mq 00 T e 05. #.19 T N 19. For Ban-rum brake, Braking Torque is T B ( T1-T )# r ( ) # Nm, 5. Nm FOS.. Allowable shear stress Design shear stress Design shear stress for soli circular shaft t 16T 16 # 50 # 10 From T J Therefore FOS.. 10 # 16 # 50 # 10 or, 10 # 16 # 50 # 10 # 16# 50# # 15.8 mm, 16 mm Given : W P 0 kn, W Q 5 kn Life of bearing, L 10 W C k 6 b l # revolutions r t

14 For ball bearing, k. Thus C Basic ynamic loa rating Constant L 10 W C 6 b l # revolutions These are the ientical bearings. So for the Life of P an Q. LP WQ cl m c Q W m b P 0 5 l b l 7 8 Otion (D) is correct. Given : b 80 mm, 50 mm, m 05., q 70c, T B 1000 N-m Let, T 1 " Tension in the tight sie of the ban (Maximum Tension) T " Tension in the slack sie of the ban (Minimum Tension) Braking torque on the rum, T B ( T1-T) r T1- T T B 1000 r N...(i) 0 15 We know that limiting ratio of the tension is given by, T T 1 e mq a e 05. # 180 #70k. 6 T Ṭ1 6 Substitute T in equation (i), we get T T &.6T1- T T & T kn. 6 Given : 6mm, l 1 mm, P 1000 N Each rivets have same iameter, So equal Loa is carrie by each rivet. Primary or irect force on each rivet, F P N Shear area of each rivet is, A ^ # h # 10 mm Direct shear stress on each rivet, t F A # MPa 8. 6 # 10 Otion (A) is correct. Given : 50 mm, D mm, l 0 mm, N 100 rm, m 0.0 Pa s Tangential velocity of shaft, - u N. 1 # 50 # 10 # m/ sec An Raial clearance, y D mm Shear stress from the Newton s law of viscosity, t m u # y # Nm / # 10 Shear force on the shaft, F t # A 768 #( # # l)

15 768 #. 1 # 50 # 10 # 0 # Torque, T F # # # N - m We know that ower loss, P NT #. 1 # 100 # W - 7 W 11.8 N Otion (A) is correct. Given : S u or s u 600 MPa, S y or s y 0 MPa, S e or s e 0 MPa, 0 mm F max 160 kn (Tension), F min - 0 kn (Comression) Maximum stress, s F max max 160 # 10 A ( ) MPa Minimum stress, s F min min - 0 # MPa A ( 0) # max min Mean stress, s m s + s MPa max min Variable stress, s v s - s (-56. 6) MPa From the Soerberg s criterion, 1 m v s + s FS.. sy se FS So, FS Otion (A) is correct. Given : m mm, Z 1, P 15 kw 15 # 10 W N 960 rm b 5 mm, f 0c Pitch circle iameter, D mz # 1 8mm Tangential Force is given by, F T T...(i) r Power transmitte, P NT & T N P Then F T 60 N P # r 1 r Pitch circle raius 60 # 15 # # - # # # N - 55 N From Lewis equation F T s FT b by b# y# m m m 1 c # 10 # 0. # # 10 s b 111 MPa Minimum allowable (working stress)

16 s W s b# Cv 111 # MPa Otion (A) is correct. Given : 0 mm, l 0 mm, w 0 ra/ sec - Z( m ) 0 mpa -s 0 # 10 Pa -s, cy ( ) 0.00 mm Shear stress, t m u From the Newton s law of viscosity...(i) y u rw # 0 0. m/ sec - t 0 # 10 # Nm / # 10 Shear force is generate ue to this shear stress, F t A t# l A l Area of shaft 00 #. 1 # # N Loss of torque, T F# r # N - m N-m Given : mm & r 1 50 mm, 0 mm & r 1 0 mm 6 MPa # 10 Pa, n 0. When the ressure is uniformly istribute over the entire area of the friction faces, then total frictional torque acting on the friction surface or on the clutch is given by, ( ) ( ) T r 1 - r m ; E ( 50) ( 0) 10 # # # # N - m N-m Given : m mm, Z 16, b 6 mm, f 0c, P kw N 0 rev/ sec 0 # 60 rm 100 rm, C v 1.5, y 0. Moule, m D Z D m# Z # 16 8 mm Power, P NT 60 T 60 N P 60 # # 10 #. 1 # N-m.88 # 10 N-mm Tangential loa, W T T R D T #. 88# N 8 From the lewis equation Bening stress (Beam strength of Gear teeth) s b WP T W T P by bym : P m m 1 C D # 10 # 0. # # 10 s b # 10 Pa 0.70 MPa. # 10 Permissible working stress s W s b# Cv 0.70 # MPa, 6 MPa

17 Otion (D) is correct. Given : m, Z, Tooth sace Tooth thickness a We know that, m D Z Pitch circle iameter, D mz # 18 mm An for circular itch, P c m.1 # 1.56 mm We also know that circular itch, P c Tooth sace + Tooth thickness a+ a a a Pc mm From the figure, b aenum + PR or PQ a/ sin f 1. OQ f sin (. 0 09). 81c OP 6 cos. 81c 6.9 mm PR OR - OP mm OR Pitch circle raius An b m+ PR mm Therefore, a 6.8 mm an b.1 mm Otion (A) is correct. Tyes of Gear Descrition P. Helical. Axes arallel an teeth are incline to the axis Q. Siral Bevel. Axes are erenicular an intersecting, an teeth are incline to the axis R. Hyoi 1. Axes non arallel an non-intersecting S. Rack an inion 6. Axes are arallel an one of the gear has infinite raius So, correct airs are P-, Q-, R-1, S-6 Otion (A) is correct. In given figure W S reresent the rimary shear loa whereas W S1 an W S reresent the seconary shear loas. Given : A 10 # 50 mm, n, W kn # 10 N We know that rimary shear loa on each bolt acting vertically ownwars, W s W kn kn n Since both the bolts are at equal istances from the centre of gravity G of the two

18 bolts, therefore the seconary shear loa on each bolt is same. For seconary shear loa, taking the moment about oint G, Ws1# r1+ Ws# r W# e r 1 r an Ws1 Ws So, rw 1 s1 # 10 #( ) # 0. # Ws1 # 10 # W s1 8# # 0. # 0 kn From the figure, resultant Force on bolt P is F Ws - Ws 0-18 kn Shear stress on bolt P is, t F 18 # 10 Area - ( 1 10 ) # # Otion (D) is correct. Given : W 1 F, W F, L hr We know that, life of bearing is given by L k W C 6 b l # 10 revolution 159. MPa MPa For ball bearing, k, L W C 6 b l # 10 revolution For initial conition life is, L C 6 1 b 10 F l # 8000 hr C 6 b 10 F l #...(i) For final loa, L C C 6 bf l # 10 8 # bf l # 1 (8000 hr) 1000 hr From equation (i) 8 Given : 00 mm, t 1mm, s u 800 MPa, s e 00 MPa Circumferential stress inuce in sherical ressure vessel is, r 100 s # # 50 MPa t # 1 Given that, ressure vessel is subject to an internal ressure varying from to 8MPa. So, s min 50 # 00 MPa

19 Mean stress, s max 50 # 8 00 MPa min max s m s + s MPa max min Variable stress, s v s - s MPa From the Gooman metho, 1 m v s + s FS.. su se & FS Given : 50 mm, l 50 mm, N 0 rs, - Z 0 mpa -sec 0 # 10 Pa -sec - Raial clearance 50 mm 50 # 10 mm, Loa kn We know that, Bearing Pressure on the rojecte bearing area Loa on the journal l# 0.8 Nmm / 50 # # 10 Nm / # Sommerfel Number ZN c iameteral clearance b c l # raial clearance - SN.. 0 # 10 # # 08. # 10 b # 10 l # # 6 # # 10 b l # Otion (A) is correct. Given : Diameter of bolt 10 mm, F 10 kn, No. of bolts n Direct or Primary shear loa of each rivet F P F 10 # 10 N. N n The centre of gravity of the bolt grou lies at O (ue to symmetry of figure). e 150 mm (eccentricity given) Turning moment rouce by the loa F ue to eccentricity F# e 10 # 10 # # 10 N-mm Seconary shear loa on bolts from fig. r r 0 mm an r 0 A C B

20 We know that F# e FA [( r ) ( r ) ( r A + B + C) ] r A FA [ ( ra) ] r # (ra rc an rb 0) A 1500 # 10 FA [ 0 ( ) ] 80F 0 # F A 1500 # N 80 F B 0 ( r 0) F C F rc A # r # N A 0 From fig we fin that angle between F A an F P q A 90c F B an F P q B 90c F C an F P q C 90c Resultant loa on bolt A, R A ( FP) + ( FA) + FP# FAcosqA (. ) + ( 18750) + #. # # cos90c R A 190 N Maximum shear stress at A t A RA 190 ( ) ( ) 10.6 MPa Resultant loa on Bolt B, RB FP. N ( FB 0) Maximum shear stress at B, t RB B..5 MPa ( ) # (10) Otion (C) is correct. A B Given : P 00 N, r 00 mm 150 mm, l 600 mm x 00 mm, m 0.5 an q 5c Let, R N " Normal force ressing the brake block on the wheel F t "Tangential braking force or the frictional force acting at the contact surface of the block & the wheel. Here the line of action of tangential braking force F t asses through the fulcrum O of the lever an brake wheel rotates clockwise. Then for equilibrium, Taking

21 the moment about the fulcrum O, RN # x P# l R N P# l 00 # N x 0. Tangential braking force on the wheel, F t mr N Braking Torque, T B Ft # r mrn # r 0. 5 # 100 # N - m Otion (C) is correct. Given : 0 mm, l 700 mm, 9 E 00 GPa 00 # 10 N/ m 00 # 10 N/ mm Comressive or working Loa 10 kn Accoring to Euler s theory, the criling or buckling loa ( W cr ) uner various en conitions is given by the general equation, W c EI cr...(i) l Given that one en is guie at the iston en an hinge at the other en. So, c From equation (i), W EI cr E # I l l # # # # ( 0) ( 700) 6 # N 6.86 kn We know that, factor of safety (FOS) Criling Loa FOS Working Loa 10 The most aroriate otion is (C). Given : Z P 0, Z G 0, N P 0 rev/ sec, P 0 kw 0 # 10 W, m 5mm Moule, m D DP DG Z ZP ZG D P m# Z P 5# mm or, D G m# Z G 5# 0 00 mm Centre istance for the gear set, L DP DG mm Otion (C) is correct. Given : Length of line of action, L 19 mm Pressure angle, f 0c Length of ath of contact( L) Length of arc of contact cos f mm cos 0c

22 Contact ratio or number of airs of teeth in contact, Length of arc of contact circular itch ṁ 1. # 5 Otion (C) is correct. Let, T " Torque transmitte in N - m We know that ower transmitte is, P Tw T N # 60 T 60 N P 60 # 0 # N m #. 1 # F T R T Tangential loa on the inion P N From the geometry, total loa ue to ower transmitte, F F Tf N cos cos 0c Otion (A) is correct. Given : P 5kW, N 000 rm, m 0.5, r 5 mm 0.05 m, 1MPa Power transmitte, P NT 60 Torque, T 60 N P 60 # 5 # N m #. 1 # When ressure is uniformly istribute over the entire area of the friction faces, then total frictional torque acting on the friction surface or on the clutch, ( ) ( ) T r 1 - r m ; E # #.1 # 0.5 # 1 # 10 #[ r1 -(0.05) ] r1 - (. 0 05). 885 # 6 #. 1 # 0. 5 # 10 r # # # r 1 ( ) # 6.1 # / - r 1 (. 6 1 # 10 ).9 # 10 m 9. mm Otion (A) is correct. Given : Z P 19, Z G 7, m 5mm Also, m D Z

23 For inion, itch circle iameter is, D P m# Z P 5# mm An itch circle iameter of the gear, D G m# Z G 5# mm Now, centre istance between the gear air (shafts), L DP DG mm Otion (C) is correct. We know that in S-N curve the failure occurs at 10 6 cycles (at enurance strength) We have to make the S-N curve from the given ata, on the scale of log 10. Now equation of line whose en oint co-orinates are 6 ^log101000, log1090h an ^log1010, log1070h or ^,log1090h an ^6,log1070h, y - log1090 log log1090 y- y1 y- y1 x - 6- b x- x1 x - x l 1 y x - y ( x - )...(i) Given, the shaft is subject to an alternating stress of 100 MPa So, y log10100 Substitute this value in equation (i), we get ( x -) x x An log 10 N N The nearest shaft life is 8191 cycles. Given : l 60 mm 0.06 m, s 6 mm m, P 15 kn 15 # 10 N Shear strength 00 MPa We know that, if t is the allowable shear stress for the wel metal, then the shear strength of the joint for single arallel fillet wel, P Throat Area # Allowable shear stress t# l#t P s# l#t t ssin 5 c s

24 t FOS P 15 # MPa # s# l # # Shear strength 00 MPa Allowable shear stress 58.9 MPa Otion (A) is correct. The coefficient of friction for a full lubricate journal bearing is a function of three variables, i.e. m f ZN,, l b c l Here, ZN Bearing characteristic Number, Diameter of the bearing l Length of the bearing, c Diameteral clearance Sommerfel Number ZN b c l It is a imensionless arameter use extensively in the esign of journal bearing. i.e. sommerfel number is also function of ZN, b c l. Therefore otion (A) is correct. Given : r 00 mm 0. m, q 70c 70 raian 180 #, m 0.5 At the time of braking, maximum tension is generate at the fixe en of ban near the wheel. Let, T " Tension in the slack sie of ban T 1 "Tension in the tight sie of ban at the fixe en Taking the moment about the oint O, T # # & T 00 N For the ban brake, the limiting ratio of the tension is given by the relation T T 1 e mq & T 1 T # e. T 1 00 e 05 # # 00 # N N So, maximum tension that can be generate in the ban uring braking is equal mq

25 to 110 N Maximum wheel torque or braking torque is given by, T W ( T1- T) r (110-00) # 0. 8 N - m Otion (D) is correct. Given : Z P 0 teeth, Z G 10 teeth, N P 100 rm, T P 0 N-m Velocity Ratio, Z Z P G N G NG NP ZP NP Z # # 00 rm Power transmitte is same for both inion & Gear. P NPTP NGTG N P T P N G T G T NPTP G 100 NG 00 # 0 60 N-m So, the torque transmitte by the Gear is 60 N - m G Otion (A) is correct. When the notch sensitivity factor q is use in cyclic loaing, then fatigue stress concentration factor may be obtaine from the following relation. K f 1 + qk ( t -1) K f - 1 qk ( t -1) Kf - 1 q K - 1 Otion (C) is correct. The S-N curve for the steel is shown below : t

26 We can easily see from the S-N curve that, steel becomes asymtotic nearly at 6 10 cycles. Otion (C) is correct. Given : F t 00 N, mm 0.00 m Torque require for achieving the tightening force is, T Ft # r F Pitch t # # 1. N m #. 1 Tye of Gears Arrangement of shafts P. Bevel gears. Non-arallel intersecting shafts Q. Worm gears. Non-arallel, non-intersecting shafts R. Herringbone gears. Parallel shafts S. Hyoi gears 1. Non-arallel off-set shafts So, correct airs are P-, Q-, R-, S-1. Otion (C) is correct. The wire roes are esignate by the number of strans multilie by the number of wires in each stran. Therefore, 6# 19 Number of strans # Number of wires in each stran. Otion (C) is correct. Given : Diameter of shaft Torque transmitte T Length of the key l We know that, with an thickness of a square key are equal. i.e. w t Force acting on circumference of shaft F T T r ( r / ) Shearing Area, A with # length l # Average shear stress, t Force shearing Area l T/ l/ 8T l Otion (D) is correct. Let, T 1 " Tension in the tight sie of the ban, T " Tension in the slack sie of the ban q "Angle of la of the ban on the rum Given : T T 1, q 180 c 180 raian 180 # For ban brake, the limiting ratio of the tension is given by the relation, T T 1 e mq or. log T1 b mq T l. # log() m#. # m # 1. m

27 Otion (A) is correct. Let N 1, N, N an N are the sees of inion 1, gear, inion an gear resectively. Given : Z 1 16 teeth, Z 15 teeth an Z?, Z? Velocity ratio N N 1 Z/ Z1 Z/ Z N \ 1/ Z Z Z 1 Z # 1 Z...(i) But for stage 1, N N 1 Z Z1...(ii) So, Z # 1 Z from eq. (i) Z, Z & Z # 15 5teeth From equation (ii), Z # Z1 # 16 6 teeth Let centre istance in the secon stage is D. D R R D D + + But, D D Z Z m D/ Z moule D # Z # Or, D # Z # So, D mm Otion (C) is correct. In stanar full height involute teeth gear mechanism the arc of aroach is not be less than the circular itch, therefore Maximum length of arc of aroach Circular itch...(i) where Maximum length of the arc of aroach Max. length of the ath of aroach r sin f r tan f cos f cos f Circular itch, P C m Z r m r Z

28 Hence, from equation (i), we get r tan f Z r Z teeth tan f tan 0c Otion (D) is correct. (A) Flange couling :- It is use to connect two shaft having erfect coaxial alignment an no misalignment is allowe between them. (B) Olham s couling :- It is use to join two shafts which have lateral misalignment. (C) Flexible bush couling :- It is use to join the abutting ens of shafts when they are not in exact alignment. (D) Hook s joint :- It is use to connect two shafts with large angular misalignment. Otion (D) is correct. When the shaft rotates, the bening stress at the uer fibre varies from maximum comressive to maximum tensile while the bening stress at the lower fibres varies from maximum tensile to maximum comressive. The secimen subjecte to a comletely reverse stress cycle. This is shown in the figure. When shaft is subjecte to reeate stress, then it will be esigne for fatigue loaing. For a worm gear the velocity ratio ranges between 10 : 1 to 100 : 1. So, Large see reuctions (greater than 0) in one stage of a gear train are ossible through worm gearing. Otion (A) is correct. For Helical sring, eflection is given by, 6PR n 8PD n G G where, P Comressive loa Wire iameter R Coil iameter G Moulus of rigiity From the given conitions \ 1 Given 1 1cm an cm *Shiing Free* Buy Online all GATE Books: sho.noia.co.in *Maximum Discount*

29 1 1 1 b l 1 b l 16 1 So, eflection will ecrease by a factor of Otion (C) is correct. Bars AB an BC have negligible mass. The suort loa P acting at the free en of bars AB an BC. Due to this loa P, In bar AB comressive stress an in bar BC tensile stress are inuce. However, none of these bars will be subjecte to bening because there is no coule acting on the bars. Otion (C) is correct. Let L 1 & L are lengths of the srings an n 1 & n are the number of coils in both the srings. Given : W 1 W mg 1 mg rn 1g rn g m rn A1# L1#r g A# L#rg # D n # D n L Dn # n1 # n D D Given : 1 & 1 # n or, n 1 1 n # n The eflection of helical sring is given by, 8PD n G Sring stiffness, k P G 8Dn From the given conitions, we get k \ n So, k1 1 n k b l # a n k 1 k1 n k c / m # n/ k k # ***********