SM 5.1 Consider the given state of stress as shown in figure. By using a method of analysis based on the equilibrium of that element, the normal and shearing stresses exerted on the oblique face of the shaded triangular element, are
(A) s =-0.521 MPa, t =-56.4 MPa (B) s = 0.521 MPa, t =56.4 MPa (C) s =-0 521. MPa, t =56.4 MPa (D) s = 0 521. MPa, t =-56 4. MPa
SM 5.2 In figure shown, the stresses acting on element A in the web of a train rail are found to be 42 MPa tension in the horizontal direction and 140 MPa compression in the vertical direction. The shear stresses of magnitude 60 MPa act in the directions shown. What will be the stresses acting on an element oriented at a counterclockwise angle of 48c from the horizontal ?
(A) s =-x1 118. MPa2 , s =y1 20.2 MPa, tx y1 1=-84.2 MPa (B) s =x1 118. MPa2 , s =y1 20.2 MPa, tx y1 1=-84.2 MPa (C) s =-x1 118. MPa2 , s =-y1 20.2 MPa, tx y1 1=-84.2 MPa (D) s =-x1 118. MPa2 , s =y1 20.2 MPa, tx y1 1=84.2 MPa
SM 5.3 Two members of uniform cross section 50#80 mm are glued together along plane a-a, which forms an angle of 25c with the horizontal. If the allowable stresses for the glued joint are s =800 kPa and t =600 kPa, what will be the largest axial load P ?
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(A) 6.27 kN (B) 7 04. kN
(C) 7 8. kN (D) 3 9. kN
SM 5.4 Consider the state of stress as shown in figure. What will be the principal planes and the principal stresses ?
(A) q =-p 30.96 ,59.04c c, smax=-52 MPa, smin=-84 MPa (B) q =-p 30.96 ,59.04c c, smax=52MPa, smin=-84 MPa (C) q =-p 30.96 ,59.04c c, smax=84 MPa, smin=52 MPa (D) q =p 30.96 ,c -59.04c, smax=52 MPa, smin=-84 MPa
SM 5.5 A rectangular plate of dimensions 100mm#250mm is formed by welding two triangular plates and subjected to a compressive stress of 2.5 MPa in the long direction and a tensile stress of 12.0 MPa in the short direction as shown in figure. What will be the normal stress sw acting perpendicular to the line of the weld and the shear stress tw acting parallel to the weld ?
(A) s =-w 10MPa, t =-w 5MPa (B) s =-w 10. MPa0 , t =w 5. MPa0 (C) s =w 10.0 MPa, t =w 5. MPa0 (D) s =w 10.0 MPa, t =-w 5. MPa0
Common Data For Q. 6 and 7
Two steel plates of uniform cross section 10#80 mm are welded together as shown in figure. The centric forces of 100 kN are applied to the welded plates and the in-plane shearing stress parallel to the weld is 30 MPa.
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SM 5.6 The angle b is
(A) 61 32c. (B) 28 68c.
(C) 14 34c. (D) 75 66c.
SM 5.7 What will be the corresponding normal stress perpendicular to the weld ?
(A) 87.9 MPa (B) 117 3. MPa
(C) 146 7. MPa (D) 73 35. MPa
SM 5.8 Consider the state of plane stress as shown in figure. The value of txy for which the in-plane shearing stress parallel to the weld is zero and the corresponding principal stresses using Mohr’s circle, are
(A) t =xy 2.89 MPa, s =A 12.77 MPa, s =B 1.23 MPa (B) t =-xy 2.89 MPa, s =-A 12.77 MPa, s =B 1.23 MPa (C) t =-xy 2.89 MPa, s =A 12.77 MPa, s =-B 1.23 MPa (D) t =-xy 2.89 MPa, s =A 12.77 MPa, s =B 1.23 MPa
SM 5.9 In figure shown, the grain of a wooden member forms an angle of 15c with the vertical. For the state of stress shown, the in-plane shearing stress parallel to the grain and the normal stress perpendicular to the grain using Mohr’s circle, are
(A) tx yl l=0.3 MPa, s =xl 2.92 MPa (B) tx yl l=0.3 MPa, s =-xl 2.92 MPa (C) tx yl l=-0.3 MPa, s =-xl 2.92 MPa (D) tx yl l=-0.3 MPa, s =xl 2.92 MPa
Common Data For Q. 10 and 11
In figure shown, a propeller shaft subjected to combined torsion and axial thrust is designed to resist a shear stress of 63 MPa and a compressive stress of 90 MPa.
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SM 5.10 What will be the principal stresses ?
(A) s =1 32 4. MPa, s =2 122 4. MPa (B) 32.4 MPas =1 , s =-2 122.4 MPa (C) s =-1 32.4 MPa, s =2 122.4 MPa (D) s =-1 32.4 MPas =-2 122.4 MPa
SM 5.11 The maximum shear stresses and associated normal stresses are (A) s =-ave 77 4. MPa, t =!45MPa
(B) s =ave 45MPa, t =!77. MPa4 (C) s =-ave 45MPat =!77 4. MPa (D) s =ave 77.4 MPa, t =!45 MPa
Common Data For Q. 12 and 13
An element in uniaxial stress is subjected to tensile stresses s =x 55 MPa as shown in the figure. Use Mohr’s circle for further calculation.
SM 5.12 What will be the stresses acting on an element oriented at an angle q =-30c from the x axis (minus means clockwise) ?
(A) s =x1 41.2 MPa, s =y1 27.5 MPa, tx y1 1=23.8 MPa (B) s =x1 41.2 MPa, s =y1 13.8 MPa, tx y1 1=-23.8 MPa (C) s =x1 27.5 MPa, s =y1 13.8 MPa, tx y1 1=23.8 MPa (D) s =x1 13.8 MPa, s =y1 41.2 MPa, tx y1 1=23.8 MPa
SM 5.13 The maximum shear stresses and associated normal stresses are (A) tmax=27.5 MPa, s =avg 13.75 MPa
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SM 5.14 Using Mohr’s circle, the stresses acting on an element oriented at a counterclockwise angle q =22 5c. from the x axis, are
(A) s =-x1 48 28. MPa, s =y1 8 28. MPa, tx y1 1=28. 8 MPa2 (B) s =-x1 20MPa, s =y1 8 28. MPa, tx y1 1=28.28 MPa (C) s =x1 8 28. MPa, s =y1 48 28. MPa, tx y1 1=28.28 MPa (D) s =x1 48 28. MPa, s =-y1 20MPa, tx y1 1=28.28 MPa
SM 5.15 What will be the maximum shear stresses and associated normal stresses using Mohr’s circle ?
(A) tmax=-40 MPa, s =avg 20 MPa (B) tmax=tavg =20 MPa
(C) tmax=tavg =40MPa
(D) tmax=40 MPa, s =-avg 20 MPa
SM 5.16 For the state of stress shown in figure, what will be the range of values of q for which the normal stress sx is equal to or less than 50 MPa ?
(A) 110.085c # q #290.085c (B) 16.524c # q #110.085c (C) 110.085c # q #196.524c (D) 16.524c # q #196.524c
Common Data For Q. 17 and 18
For the state of plane stress shown in figure, consider both in-plane and out-of-plane shearing stresses.
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SM 5.17 The maximum shearing stress when s =y 20 MPa, is
t =xy as shown in figure. The angle q is positive when counterclockwise and negative when clockwise. Using Mohr’s circle, the stresses acting on an element oriented at an angle q = 50c from the x axis, is
(A) s =x1 23.01 MPa, s =-y1 8.99 MPa, tx y1 1=6.31 MPa (B) s =x1 23.01 MPa, s =y1 8.99 MPa, tx y1 1=6.31 MPa (C) s =-x1 8.99 MPa, s =y1 23.01 MPa, tx y1 1=6.31 MPa (D) s =x1 8.99 MPa, s =y1 23.01 MPa, tx y1 1=6.31 MPa
Common Data For Q. 20 and 21
In figure shown, an element in plane stress is subjected to stresses s =x 3100 kPa , s =y 8700 kPa and t =-xy 4500 kPa. Use the Mohr’s circle.
SM 5.20 What will be the principal stresses ?
(A) s =1 5300 kPa, s =2 5900 kPa (B) s =1 600 kPa, s =2 11200 kPa (C) s =1 11200 kPa, s =2 600 kPa (D) s =1 11200 kPa, s =2 5300 kPa
SM 5.21 The maximum shear stresses and associated normal stresses are
(A) tmax=-5300 kPa, s =avg 5900 kPa (B) tmax=5300 kPa, s =avg 5900 kPa (C) tmax=avg = 5300 kPa (D) tmax=avg = 5900 kPa
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SM 5.22 A rectangular steel plate with thickness t =10 mm is subjected to uniform normal stresses sx and sy as shown in figure. Strain gauges A and B oriented in the x and y directions, respectively, are attached to the plate. The gauge readings are
480 10
x 6
e = # - (elongation) and y 130 10 6
e = # - (elongation). What will be the stresses sx and sy and the change in the thickness Dt of the plate ?
(Take E =200 GPa, n =0.30)
(A) s =x 60.2 MPa, s =y 114.1 MPa, Dt=2610#10 mm-6 (B) s =x 114.1 MPa, s =y 60.2 MPa, Dt=2610#10 mm-6 (C) s =x 60.2 MPa, s =y 114.1 MPa, Dt=2610#10 mm-6 (D) s =x 114.1 MPa, s =y 60.2 MPa, Dt=-2610#10 mm-6
SM 5.23 A brass cube 50 mm on each edge is compressed in two perpendicular directions by forces P =175 kN as shown in figure. The change Dv in the volume of the cube and the strain energy U stored in the cube respectively, are
(Take E =100 GPa, n =0 34. )
(A) -56 mm3, 4. 4 J0 (B) -56 mm3, 2 2.0 J (C) -56 mm3, 8 8.0 J (D) 56 mm3, 4.04 J
Common Data For Q. 24 and 25
A circle of diameter d =200 mm is etched on a brass plate as shown in figure.
The plate has dimensions 400#400#20 mm. Forces are applied to the plate, producing uniformly distributed normal stresses s =x 42 MPa and s =y 14 MPa.
(Take E =100 GPa and n =0 34. )
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SM 5.24 The change in length Dac of diameter ac and Dbd of diameter bd, are plate and the strain energy U stored in the plate respectively, are
(A) 0.00381 mm, -573 mm3, 25 J (B) -0.00381 mm, 573 mm3, 25 J (C) -0.00381 mm, 573 mm3, 50 J (D) 0.00381 mm, -573 mm3, 50 J
Common Data For Q. 26 and 27
In figure shown, a cube of granite (E =60 GPa, n =0 25. ) with sides of length 75 mm
a = is subjected under triaxial stress. The compressive strains in the material are x 720 10 6
(Hint: Use the maximum shearing stress criterion)
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(A) 717 N m- (B) 896N m
-(C) 538N m- (D) 448N m
-SM 5.30 A spherical steel pressure vessel has a diameter of 250 mm and a wall thickness of 6 mm. The maximum gauge pressure is 8 MPa in the vessel. If the ultimate stress in the steel used is s =U 400 MPa, the factor of safety with respect to tensile failure is
(A) 7 56 (B) . 5 04.
(C) 10 08 (D) . 2 52.
SM 5.31 In the figure shown, a cylindrical portion of the compressed air tank is fabricated of 6 mm thick plate, welded along a helix forming an angle b =30c with the horizontal. If the shearing stress parallel to the weld is 30 MPa, what will be the gage pressure ?
(A) 3.41 MPa (B) 4 26. MPa
(C) 2 56. MPa (D) 2 31. MPa
SM 5.32 In the figure shown, the tank has a 180 mm inside diameter and a 12 mm wall thickness. If the tank contains compressed air under a pressure of 8 MPa, what will be the magnitude T of the applied torque for which the maximum normal stress in the tank is 75 MPa ?
(A) 21 36. kN m- (B) 12 76. kN m -(C) 17 06. kN m- (D) 1 .0 68kN m
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Common Data For Q. 33 and 34.
A brass ring of 160 mm outside diameter fits exactly inside a steel ring of 160 mm inside diameter as shown in figure, when the temperature of both rings is 5 Cc . The temperature of the rings is then raised to 55 Cc .
SM 5.33 The pressure exerted by the brass ring on the steel ring is
(A) 1.75 MPa (B) 1. MPa4
(C) 2 8. MPa (D) 1 05. MPa
SM 5.34 The tensile stress in the steel ring is
(A) 28 MPa (B) 21MPa
(C) 35MPa (D) 17 5. MPa
SM 5.35 A solid steel sphere of diameter d = 150 mm is subjected to hydrostatic pressure p such that its volume is reduced by 0.4%. What will be the pressure p, the volume modulus of elasticity K for the steel and the strain energy U stored in the sphere ? (Take E =210 GPa, n =0.3) (A) p =350 MPa, K =175 GPa, U =2470 J
(B) p =700 MPa, K =350 GPa, U = 2470 J (C) p =700 MPa, K =175 GPa, U =2470 J (D) p =700 MPa, K =175 GPa, U = 1235 J
SM 5.36 In the figure shown, an element of material subjected to plane strain, has strains as follows: x 220 10 6
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SM 5.37 An aluminum plate is loaded in biaxial stress by normal stresses s =x 86.4 MPa and sy as shown in figure. A strain gauge is bonded to the plate at an angle
Common Data For Q. 38 and 39
The rosette shown in figure, has been used to determine the following strains at a point on the surface of a crane hook :
1 420m
e =+ , e =-2 45m, e =+4 165m
SM 5.38 What should be the reading of gauge 3 ?
(A) -300 m (B) 300 m
(C) 255 m (D) 210 m
SM 5.39 The principal strains and the maximum in-plane shearing strain are (A) e =a 435m, e =-b 315m, gmax=750m
(B) e =a 435m, e =b 315m, gmax=750m (C) e =-a 435m, e =-b 315m, gmax=750m (D) e =a 435m, e =-b 315m, gmax=-750m
SM 5.40 Consider the figure shown. What will be the sum of the three strain measurements (e1+ +e2 e3) made with a 60c rosette which is independent to the orientation of the rosette ? Here eave is the abscissa of the centre of the corresponding Mohr’s circle for strain.
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(A) eave (B) 6eave
(C) 3eave (D) 2eave
SM 5.41 A single strain gauge is cemented to a solid 96 mm diameter aluminium shaft at an angle b =20c with a line parallel to the axis of the shaft as shown in figure. If
27 GPa
G = , the torque T corresponding to a gauge reading of 400 m, is
(A) 7 3. kN m- (B) 5 84. kN m
-(C) 3 65. kN m- (D) 4 38. kN m
-SM 5.42 In figure shown, the beam is subjected to a shear of V = 15 kN and has width of 125 mm
w = . What will be the web’s shear stress at A and B ?
(A) t =A 1.99 MPa, t =B 3 3. MPa (B) t =A 1.65MPa t =B 1.99 MPa (C) t =A 1.99 MPa, t =B 1.65 MPa (D) t =A 3 98. MPa, t =B 1.65 MPa
SM 5.43 The strut shown in figure, is subjected to a vertical shear of V =130 kN. Which of the following is the resultant shear force developed in the vertical segment AB ?
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(A) 50.3 kN (B) 62 9. kN
(C) 37 7. kN (D) 25 15. kN
SM 5.44 The T-beam is subjected to the loading as shown in figure. What will be the maximum transverse shear stress in the beam at the critical section ?
(A) 29.4 MPa (B) 18 37. MPa
(C) 7 35. MPa (D) 14 7. MPa
SM 5.45 What will be the smallest allowable diameter of the solid shaft ABCD of figure shown when t =all 60 MPa and the radius of disk B is r =120 mm ?
(A) 19.6 mm (B) 39 2. mm
(C) 196 mm (D) 3 92. mm
SM 5.46 Member AB has a uniform rectangular cross section of 10#24 mm. For the loading shown in figure, the normal and shearing stresses at point H, are
(A) s =x 32.5 MPa, t =xy 14.06 MPa (B) s =-x 32.5 MPa, t =xy 14.06 MPa (C) s =x 32.5 MPa, t =-xy 14.06 MPa (D) s =-x 32.5 MPa, t =-xy 14.06 MPa
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SM 5.47 The beam is made from three polystyrene strips that are glued together as shown in figure. If the glue has a shear strength of 80 kPa, the maximum load P that can be applied without causing the glue to lose its bond, is
(A) 357 N (B) 178 5. N
(C) 238N (D) 297 5. N
SM 5.48 In the figure shown, a 13 kN force is applied to the 60 mm diameter cast-iron post ABD. At point H, the principal stresses and the maximum shearing stresses are
(A) s =A 4.3 MPa, s =-B 93.4 MPa, t =-48 9. MPa (B) s =-A 4.3 MPa, s =-B 93.4 MPa, t =48.9 MPa (C) s =A 4.3 MPa, s =B 93.4 MPa, t =48.9 MPa (D) s =A 4.3 MPa, s =-B 93.4 MPa, t =48.9 MPa
SM 5.49 The aluminium strut is 10 mm thick and has the cross section as shown in figure.
If it is subjected to a shear of V =150 N, the shear flow at points A and B are
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(A) qA=1.39kN m/ , qB=2 50. kN m/ (B) qA=2 79. kN m/ , qA=2 50. kN m/ (C) qA=1.39kN m/ , qB=1.25kN m/ (D) qA=2 78. kN m/ , qB=1.25kN m/
SM 5.50 A beam is constructed from five boards bolted together as shown in figure. If the bolts are spaced s =250 mm apart and the applied shear is V =35 kN, the maximum shear force developed in each bolt is
(A) 6.64 kN (B) 5 31. kN
(C) 10 62. kN (D) 3 98. kN
Common Data For Q. 51 and 52
A force P is applied to a cantilever beam by means of a cable attached to a bolt, located at the center of the free end of the beam as shown in figure. A load P acts in a direction perpendicular to the longitudinal axis of the beam.
SM 5.51 The normal stress at point a in terms of P, b, h, l and b is
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SM 5.53 What will be the location e of the shear center (point O), for the thin-walled member having a slit along its side ?
(A) 52.5 mm (B) 70mm
(C) 87 5. mm (D) 43 75. mm
SM 5.54 Consider an angle of thickness 3 mm and a height of h =100 mm as shown in the figure. If it is subjected to a shear of V = 50 N, the shear flow at point A and the maximum shear flow in the angle are
(A) qA=0, qmax=375N m/ (B) qA=0, qmax=187 5. N m/
(C) qA=187.5 /N m, qmax=375 /N m (D) qA=187.5 /N m, qmax=187 5. N m/
SM 5.55 The stepped support is subjected to the bearing load of 50 kN as shown in figure.
The maximum and minimum compressive stress in the material are
(A) smax=11MPa, smin=5 5. MPa (B) smax=5 5. MPa, smin=0 (C) smax=11 MPa, smin=0 (D) smax=16.5 MPa, smin=0
SM 5.56 Several forces are applied to the pipe assembly as shown in figure. Each section of pipe has inner and outer diameter respectively equal to 36 mm and 42 mm.
What will be the normal and shearing stresses at point H, located at the top of the outer surface of the pipe ?
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(A) s =-H 20 2. MPa, t =H 2 82. MPa (B) s =H 20 2. MPa, t =H 2 82. MPa (C) s =H 20 2. MPa, t =-H 2 82. MPa (D) s =-H 20 2. MPa, t =-H 2 82. MPa
SM 5.57 What will be the magnitude of the load P as shown in figure that will cause a maximum normal stress of smax=200 MPa in the link at section a-a ?
(A) 9.9 kN (B) 13 2. kN
(C) 16 5. kN (D) 8 25. kN
SM 5.58 Consider the assembly shown in figure. Each piston has a radius of 45 mm and the cylinder has a wall thickness of 2 mm. The maximum force P that can be exerted on each of the two pistons so that the circumferential stress component in the cylinder does not exceed 3 MPa, is
(A) 1060 N (B) 636 N
(C) 848 N (D) 530 N
SM 5.59 The cap on the cylindrical tank is bolted to the tank along the flanges as shown in figure. The tank has an inner diameter of 1.5 m and a wall thickness of 18 mm.
If the pressure in the tank is p =120 MPa, what will be the force in the 16 bolts that are used to attach the cap to the tank and also, specify the state of stress in the wall of the tank ?
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(A) s =1 25MPa, s =2 50 MPa, Fb=133 kN (B) s =1 50 MPa, s =2 25MPa, Fb=133 kN (C) s =1 75MPa, s =2 50 MPa, Fb=133 kN (D) s =1 50 MPa, s =2 75MPa, Fb=133 kN
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