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SM 2.4 A 200 mm length rod of steel is shown in figure. The dilatation e and the change in volume of the rod respectively, are

(Take E =200 GPa, n =0 30. )

(A) e=121#10^-⁶, D =v 23 mm³ (B) e=121#10^-⁶, D =v 18.4 mm³ (C) e=242#10^-⁶, D =v 18.4 mm³ (D) e=242#10^-⁶, D =v 13.8 mm³

SM 2.5 For the axial loading shown in figure, the loading is hydrostatic with 70 MPa

x y z

s =s =s =- . The change in height and the change in volume of the brass cylinder respectively, are

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

Common Data For Q. 6 and 7

A fabric is subjected to a biaxial loading that results in normal stresses 120 MPa

s =x and s =z 160 MPa as shown in figure. The properties of the fabric can be approximated as E =87 GPa and n =0 34. .

SM 22 Axial Loading SM 2

GATE MCQ Mechanical Engineering (4-volumes) Fully Solved

SM 2.6 The change in length of sides AB and BC, are

SM 2.8 An aluminium plate is subjected to a centric axial load which causes a normal stress s as shown in figure. Before the loading, a line of slope 2 1 is scribed on : end A. At the other end a small gap of dimension s exists between the end of the bar and a rigid surface. A load P acts 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 P are to be equal in magnitude, what should be the size s of the gap ?

(A) s PLEA

SM 2.10 The T-shaped arm ABC shown in the figure lies in a vertical plane and pivots about a horizontal pin at A. The arm has constant cross-sectional area and total weight W. A vertical spring of stiffness k supports the arm at point B. What will be the elongation d of the spring due to the weight of the arm ?

(A) Wk

d = 2 (B) Wk

34 d =

SM 2 Axial Loading SM 23

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d = (D) Wk

d = 4

SM 2.11 In the figure shown, a cable with a restrainer at the bottom hangs vertically from its upper end. The cable has an effective cross-sectional area A=40 mm² and an effective modulus of elasticity E =130 GPa. A slider of mass M =35 kg drops from a height h =1.0 m onto the restrainer. If the allowable stress in the cable under an impact load is 500 MPa, what is the minimum permissible length L of the cable ?

(A) 7.4 mm (B) 9.25 mm

SM 2.12 In the figure shown, a uniform bar AB of weight W =25 N is supported by two springs. The distance between the springs is L =350 mm and the spring on the right is suspended from a support that is distance h =80 mm below the point of support for the spring on the left. At what distance x from the left-hand spring should a load P =18 N be placed in order to bring the bar to a horizontal the action of the load P is limited to 3c, what will be the maximum permissible load (Pmax) ?

SM 24 Axial Loading SM 2

GATE MCQ Mechanical Engineering (4-volumes) Fully Solved

(A) 2.25 kN (B) 1.8 kN

SM 2.14 The rigid bar shown in figure is supported by the two short white spruce wooden posts (E =9.65 GPa) and a spring. The spring has a stiffness of k =2MN m/ and an unstretched length of 1.02 m. If each of the posts has an unloaded length of 1 m and a cross-sectional area of 600 mm², what will be the vertical displacement of A and B after the load is applied to the bar ?

(A) dA=dB=4.42 mm (B) d =A 4.42 m, d =B 8.84 mm (C) d =A 2.21 mm, d =B 4.42 mm (D) d =A 4.42 m, d =B 2.21 mm

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 Eal =70 GPa )

(A) 1.19 mm (B) 1.58 mm

SM 2.16 The A-36 steel pipe (E =200 GPa) has a 6061-T6 aluminum core (E =68.9 GPa ). It is subjected to a tensile force of 200 kN as shown in figure. The pipe has an outer diameter of 80 mm and an inner diameter of 70 mm. What will be the average normal stress in the aluminium and the steel due to this loading ?

SM 2 Axial Loading SM 25

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(A) s =al 27.5 MPa, s =st 39.9 MPa (B) s =al 79.9 MPa, s =st 27.5 MPa (C) s =al 27.5 MPa, s =st 79.9 MPa (D) s =al 55 MPa, s =st 79.9 MPa

SM 2.17 The column shown in figure, is constructed from high-strength concrete with 25 GPa

Ec= and four A-36 steel reinforcing rods with Est =200 GPa. It is subjected to an axial force of 800 kN. If one-fourth of the load is carried by the steel and three-fourth by the concrete, the required diameter of each rod will be

(A) 16.9 mm (B) 33.9 mm and the modulus of elasticity of the brass is E =100 GPa. If the bar lengthens by 0.12 mm under a tensile load P, what is the maximum stress smax in the bar ?

(A) 23 MPa (B) 69 MPa

SM 2.19 The 10 mm diameter 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 is 10 mm. If the yield stress for the steel is ( )sY st =6 0 MPa4 and for the bronze ( )sY br=520 MPa, what will be the magnitude of the largest elastic load P that can be applied to the assembly ?

(Take Est =200 GPa and Ebr=100 GPa)

SM 26 Axial Loading SM 2

GATE MCQ Mechanical Engineering (4-volumes) Fully Solved

(A) 122 kN (B) 82 kN

SM 2.20 In the figure shown, the joint is made from three A-36 steel plates that are bonded together at their seams. Each plates has a thickness of 5 mm and E =200 GPa. What will be the displacement of end A with respect to end B when the joint is subjected to the axial loads as shown ?

(A) 2.45 mm (B) 4.91 mm

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 a between the plane of the joint and the faces of the boards must be between 10c and 40c. Under a tensile load P, the normal stress in the boards is 4.9 MPa.

SM 2.21 What are the normal and shear stresses acting on the glued joint if a = 20c ? (A) s =q 0.57 MPa, t =q 0.79 MPa (B) s =q 0.57 MPa, t =q 1.58 MPa (C) s =q 1.58 MPa, t =q 0.57 MPa (D) s =q 1.14 MPa, t =q 1.58 MPa

SM 2.22 If the allowable shear stress on the joint is 2.25 MPa, what is the largest permissible value of the angle a ?

(A) 22 2c. (B) 44 4c.

SM 2 Axial Loading SM 27

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SM 2.23 For what angle a will the shear stress on the glued joint be numerically equal to twice the normal stress on the joint ?

(A) 19.9c (B) 16.6c

Common Data For Q. 24 and 25.

In the shown figure, a 15 mm diameter steel shaft AC is supported by a rigid collar, which is fixed to the shaft at B. It is subjected to an axial load of 80 kN at its end.

SM 2.24 The uniform pressure distribution p on the collar required for the equilibrium, is

(A) 10.9 MPa (B) 21.8 MPa lengths but different diameters is shown in figure. Segment AB and BC have diameters d1=100 mm and d2=60 mm, respectively. Both segments have length

/2 0.6 m

L = . A longitudinal hole of diameter d is drilled through segment AB for one-half of its length (distance L/4=0.3 m). Compressive loads P =110 kN act at the ends of the bar. If the shortening of the bar is limited to 8.0 mm, what is the maximum allowable diameter dmax of the hole ?

(A) 11.9 mm (B) 7.96 mm

SM 28 Axial Loading SM 2

GATE MCQ Mechanical Engineering (4-volumes) Fully Solved

Common Data For Linked Q. 27 and 28

The elastoplastic rods AB and BC are made of mild steel with E =200 GPa and 345 MPa

s =Y 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 P is

(A) 332 kN (B) 415 kN

SM 2.28 What will be the permanent set measured at point A and B after the force has been removed ?

(A) d =A 0, d =B 6.37 mm (B) dA=dB=6.37 mm (C) d =A 0, d =B 0 (D) d =A 6.37 mm, d =B 0

SM 2.29 A post AB is tapered uniformly throughout its height H as shown in figure.

The cross sections of the post are square with dimensions b#b at the top and . b . b

1 5 #1 5 at the base. Assume that the angle of taper is small and disregard the weight of the post itself. The shortening d of the post due to the compressive load P acting at the top is

SM 2 Axial Loading SM 29

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SM 2.30 A rectangular bar of length L has a slot in the middle half of its length as shown in figure. The bar has width b, thickness t and modulus of elasticity E. The slot has width of b 4. What will be the expression for the elongation d/ of the bar due to the axial load P ?

(A) d=8sL E/7 (B) d=7sL E/4 (C) d=7sL E/6 (D) d=7sL E/8

SM 2.31 A long slender bar in the shape of a right circular cone with length L and base diameter d hangs vertically under the action of its own weight is shown in figure.

The weight of the cone is W and the modulus of elasticity of the material is E. Assume that the angle of taper of the cone is small. What will be the expression for the increase in the length of the bar due to its own weight ?

(A) d=2WL dE/p (B) d=2WL d E/p ² (C) d=WL/2pd E² (D) d=4WL d E/p ²

Common Data For Linked Q. 32 and 33

In the figure shown, rod AB consists of two cylindrical portions AC and BC, each with a cross-sectional area of 1750 mm². Portion AC is made of mild steel with E =200 GPa, s =Y 250 MPa and portion BC is made of high-strength steel with E =200 GPa, s =Y 345 MPa. A load P is applied at point C. Assume both steels to be elastoplastic.

SM 30 Axial Loading SM 2

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SM 2.32 If P is gradually increased from zero to 975 kN and then reduced back to zero, the maximum deflection of C is

(A) 1.46 mm (B) 0.146 mm

SM 2.33 The permanent deflection of C is

(A) 0.027 mm (B) 0.27 mm

Common Data For Q. 34 and 35

In the figure shown, a plastic rod AB of length L =0.5 m has a diameter d1=30 mm . A plastic sleeve CD of length c =0.3 m and outer diameter d2=45 mm is securely bonded to the rod so that no slippage can occur between the rod and the sleeve. The rod is made of an acrylic with modulus of elasticity E1=3.1 GPa and the sleeve is made of a polyamide with E2=2.5 GPa.

SM 2.34 When the rod is pulled by axial forces P =12 kN, the elongation of the rod is

(A) 1.09 mm (B) 1.91 mm

SM 2.35 What will be the elongations respectively, when

(a) the sleeve is extended for the fully length of the rod and (b) the sleeve is removed ?

(A) 0.68 mm, 0.274 mm (B) 0.136 mm, 1.37 mm (C) 1.36 mm, 2.74 mm (D) 2.72 mm, 0.137 mm

SM 2.36 The specimen as shown in figure has a allowable stress of 140 MPa and K=2 10. . If the raised portions are removed (K=1 0. ) at the ends of the specimen, the percentage change in the maximum allowable magnitude of the centric load P, will be

(A) 90% (B) 110%

SM 2.37 The fixed-end bar ABCD consists of three prismatic segments as shown in the figure. The end segments have cross-sectional area A1=840 mm2 and length

SM 2 Axial Loading SM 31

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200 mm

L1= . The middle segment has cross-sectional area A2=1260 mm2

and length L2=250 mm. Loads PB and PC are equal to 25.5 kN and 17.0 kN, respectively. What will be the compressive axial force FBC in the middle segment of the bar ?

(A) 22.5 kN (B) 30 kN

SM 2.38 The rod ABC consist of two portions is shown in figure. Both portions are made of aluminium for which E =70 GPa and the magnitude of P is 4 kN. For zero deflection at A, the value of Q is

(A) 16.67 kN (B) 65.6 kN

SM 2.39 A composite bar of square cross section with dimensions 2b#2b is constructed of two different metals having moduli of elasticity E1 and E2 as shown in figure The two parts of the bar have the same cross-sectional dimensions. The bar is compressed by forces P acting through rigid end plates. The line of action of the loads has an eccentricity e of such magnitude that each part of the bar is stressed uniformly in compression. What will be the eccentricity e of the loads ?

(A) e

SM 32 Axial Loading SM 2

GATE MCQ Mechanical Engineering (4-volumes) Fully Solved

SM 2.40 A rigid bar of weight W =800 N hangs from three equally spaced vertical wires, two of steel and one of aluminum is shown in figure. The wires also support a load P acting at the midpoint of the bar. The diameter of the steel wires is 2 mm and the diameter of the aluminium wire is 4 mm. If the allowable stress in the steel wires is 220 MPa and that is 80 MPa in the aluminum wire, what load Pallow can be supported ?

(Take Est =210 GPa, Eal =70 GPa)

(A) 3.0 kN (B) 1.5 kN

SM 2.41 A plastic cylinder is held snugly between a rigid plate and a foundation by two steel bolts as shown in figure. Data for the assembly are as follows :

Length L =200 mm, pitch of the bolt threads p =1.0 mm, modulus of elasticity for steel Es=200 GPa, modulus of elasticity for the plastic Ep=7.5 GPa, cross-sectional area of one bolt As =36.0 mm2, n =1 and cross-sectional area of the plastic cylinder Ap=960 mm2.

What will be the compressive stress sp in the plastic when the nuts on the steel bolts are tightened by one complete turn ?

(A) 31.25 MPa (B) 18.75 MPa

SM 2.42 The uniform wire ABC of unstretched length 2l, is attached to the supports as shown in figure and a vertical load P is applied at the midpoint B. The cross-sectional area of the wire is denoted by A and the modulus of elasticity is by E. For d<<l, the deflection at the midpoint B, is

SM 2 Axial Loading SM 33

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(A) d = ^2l P AE/ h^{1 3}^/ (B) l AEP ^{1 2}^/

d = _b _l

SM 2.43 A nylon thread is subjected to a 8.5 N tensile force. If E =3.3 GPa and the length of the thread increases by 1 1. %, the diameter of the thread and the stress in the thread respectively, are

(A) 5.46 mm, 36 MPa (B) 0.36 mm, 54.6 MPa (C) 0.546 mm, 36 MPa (D) 3.6 mm, 546 MPa

SM 2.44 In the figure shown, the 4 mm diameter cable BC is made of steel with 200 GPa

E = . If the maximum stress in the cable and the elongation of the cable must not exceed 190 MPa and 6 mm respectively, the maximum load P can be

(A) 9.94 kN (B) 1.988 kN

SM 2.45 The rigid bar is supported by the pin-connected rod CB of cross-sectional area of 14 mm² as shown in figure and is made from 6061-T6 aluminium (E =68.9 GPa ). What will be the vertical deflection of the bar at D when the distributed load is applied ?

(A) 12.97 mm (B) 21.63 mm

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

70 GPa

Eal = ) and CD is made from steel (Fst=200 GPa). Each bar has a cross-sectional area of 450 mm². If allowable stress of (sallow st) =180 MPa in the steel and (sallow al) =94 MPa in the aluminium is not exceeded, the maximum intensity w of the distributed loading will be

SM 34 Axial Loading SM 2

GATE MCQ Mechanical Engineering (4-volumes) Fully Solved

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

SM 2.47 The links AB and CD are made of aluminium (E =75GPa) and has a cross-sectional area of 125 mm² each. If they support the rigid member BCas shown in figure, the deflection of point E, is

(A) 0.055 mm (B) 1.10 mm

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

(A) 47.5 MPa, 0.113 mm (B) 47.5 MPa, 0.226 mm (C) 22.6 MPa, 0.475 mm (D) 11.3 MPa, 0.475 mm

SM 2.49 The rigid beam as shown in figure, is supported by the three posts A, B and C. Posts A and C have a diameter of 60 mm and are made of aluminium, for which Eal =70 GPa and ( )sY al =20 MPa. Post B is made of brass, for which

100 GPa

Ebr= and ( )sY br=590 MPa. If P =130 kN, the largest diameter of post B so that all the post yield at the same time, is

SM 2 Axial Loading SM 35

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(A) 3.56 mm (B) 1.78 mm

Common Data For Q. 50 and 51.

Three steel rods (E =200GPa) supports a 36 kN load P as shown in figure. Each of the rod AB and CD has a 200 mm² cross-sectional area and rod EF has a 625 mm² cross-sectional area.

SM 2.50 The change in length of rod EF is

(A) 0.762 mm (B) 0.0762 mm

SM 2.51 What will be the stresses in rods AB and EF ?

(A) s =AB 30.5 MPa, s =EF 38.1 MPa (B) s =AB 15.25 MPa, s =EF 38.1 MPa (C) s =AB 30.5 MPa, s =EF 19.05 MPa (D) s =AB 38.1 MPa, s =EF 30.5 MPa

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

SM 36 Axial Loading SM 2

GATE MCQ Mechanical Engineering (4-volumes) Fully Solved

of 96 Cc ?

(A) 162.75 kN (B) 217.3 kN6

SM 2.53 The corresponding change in length of the bronze bar is

(A) 0.1823 mm (B) 0.1215 mm

SM 2.54 In the figure shown, a bar AB of length L is held between rigid supports and heated non-uniformly in such a manner that the temperature increase DT at distance x from end A. The temperature increase is given by the expression

/ T T x LB 3 3

D =D , where DTB is the increase in temperature at end B of the bar.

If the material has modulus of elasticity E and coefficient of thermal expansion a, What is the expression for the compressive stress sc in the bar ?

(A) E T

If the material is elastoplastic with yield stress s =Y 250 MPa, the plastic load Pp is

(A) 55 kN (B) 82.5 kN

***********

SM 3

TORSION

SM 3.1 The torque which may be applied to a solid shaft of 90 mm outer diameter without 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 of 5 mm. What will be the maximum shear stress in the tube when the cable force of 600 N is applied to the cables ?

(A) 7.25 MPa (B) 20.6 MPa

SM 3.3 The solid rod BC has 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 outer diameter of 25 mm. It is made of brass for which the allowable shearing stress is 50 MPa. Which of the following is the largest inner diameter of rod AB for which the factor of safety is the same for each rod ?

(A) 11.39 mm (B) 7.59 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 200 mm is shown in figure. The allowable stress in shear is 60 MPa and G =78 GPa.

SM 38 Torsion SM 3

GATE MCQ Mechanical Engineering (4-volumes) Fully Solved

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

(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 f will the shaft twist under the action of the maximum torque? (Disregard any bending of the shaft.)

(A) 2.75c (B) 1.65c

SM 3.6 The solid brass rod AB G =( 39GPa) is bonded to the solid aluminum rod ( 27GPa)

BC G = as shown in figure. The angle of twist at A and B are

(A) fA=0.741 ,c fB=1.573c (B) fA=0.831 ,c fB=0.741c (C) fA=0.741 ,c fB=0.831c (D) fA=1.573 ,c fB=0.741c

SM 3.7 A plastic bar of diameter 50 mm is to be twisted by torques T as shown in figure, until the angle of rotation between the ends of the bar is 5 0c. . If the allowable shear strain in the plastic is 0.012 rad, what is the minimum permissible length

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