SM 4.1 For the beam with overhangs as shown in figure, if one load acts downward and the other upward, the shear force V and bending moment M at the midpoint of the beam will be
(A) V= 2bP ML , =0 (B) V =2bP ML , = 2b PL2 (C) V=bP M2L, =0 (D) V bP ML, b PL
2 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 the steel is 150 MPa, the section modulus of the beam is
(A) ^45#103hmm3 (B) ^90#103hmm3 (C) ^180#103hmm3 (D) ^135#103hmm3
SM 4.3 In figure shown, the beam is subjected to the load P at its center. What will be the placement a of the supports for maximum moment and the absolute maximum bending stress in the beam ?
(A) 0,
SM 52 Shear Force and Bending Moment SM 4
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at the end of a vertical arm and a vertical force P2=8.0 kN acting at the end of the overhang. If the widths of the beam and vertical arm are neglected, the shear force V and bending moment M, at a cross section located 3.0 m from the left-hand support using centerline dimensions, will be
(A) V =-1 0. kN,M=-7 0. kN m- (B) V=1 0. kN,M=7 0. kN m -(C) V=1 0. kN,M=-7 0. kN m- (D) V=-1 0. kN,M=7 0. kN m
-SM 4.5 Consider the beam and loading of the S 01 0#1 .1 5 rolled steel section as shown in figure. If the section modulus is S=49 6. #10 m-6 3, the maximum normal stress due to bending will be
(A) 19 35. MPa (B) 9 65. MPa
(C) 38 7. MPa (D) 29 03. MPa
SM 4.6 For the beam and loading shown in figure, if the grade of timber used has an allowable normal stress of 12 MPa, the width b of the beam is
(A) 96mm (B) 24mm
(C) 32mm (D) 48mm
SM 4.7 In figure shown, the beam AB supports a uniformly distributed load of 2kN m / and two concentrated loads P and Q. The normal stress due to bending on the bottom edge of the beam is -56.9 MPa at A and -29.9 MPa at C. What will be the magnitudes of the loads P and Q ?
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(A) P=250 ,N Q=500N (B) P=500N,Q=250N (C) P=1000N,Q=500N (D) P=500N,Q=1000N
SM 4.8 What will be the equations of the shear force and bending-moment curves for the beam and loading shown in figure ?
(A) V w Lcos , sin
Beams AB, BC and CD have the cross sections as shown in the figure and are pin-connected at B and C. The allowable normal stress is 110 MPa in tension and
150 MPa
- in compression.
SM 4.9 If beam BC is not to be over stressed, what will be the largest permissible value of P ?
(A) 4 01. kN (B) 5 02. kN
(C) 3.01 kN (D) 8 02. kN
SM 4.10 What will be the corresponding maximum distance a for which the cantilever beams AB and CD are not to be over stressed ?
(A) 2.45 m (B) 6 54. m
(C) 4 09. m (D) 3 27. m
SM 4.11 Consider a timber beam of length L =16 m and width b =75 mm as shown in figure. The dead load carried by each beam, including the estimated weight of the beam, is a uniformly distributed load wD=350 /N m. The live loads can be represented by a uniformly distributed load wL=600 /N m. If a 6 kN concentrated load P applied at the midpoint C of each beam, what will be the minimum allowable depth h of the beams using LRFD (Load and Resistance Factor Design)
?
: 50 , 1.2, 1.6 .
Use Data sU = MPa gD= gL= andf=0 9
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(A) 312.72 mm (B) 383. mm0 (C) 541 64. mm (D) 270 82. mm
SM 4.12 In figure shown, the aluminium machine part is subjected to a moment of 75 N m
M = - . What will be the bending stress created at points B and C on the cross section ?
(A) sB=3.61MPa,sC =1 55. MPa (B) sB=-3.61MPa,sC=1.55MPa (C) sB=3.61MPa,sC =-1.55MPa (D) sB=1.55MPa,sC =3.61MPa
SM 4.13 The aluminium strut has a cross-sectional area as shown in figure. If it is subjected to a moment M=8 kN m- , the bending stress acting at points A and B are
(A) sA=4 49. MPa,sB=49 4. MPa (B) sA=-4.49MPa,sB=49.4MPa (C) sA=4 .49 MPa,sB=-4. 94 MPa (D) sA=4 .49 MPa,sB=4. 94 MPa
SM 4.14 The member shown in the figure is subjected to an internal bending moment of 40 kN m
M = - . What will be the largest bending stress developed in it ?
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(A) 161.25 MPa (B) 96 75. MPa
(C) 129 0. MPa (D) 80 63. MPa
SM 4.15 The smooth pin of 20 mm diameter is supported by two leaves A and B and subjected to a compressive load of 0.4 kN as shown in figure. What will be the absolute maximum bending stress in the pin ?
(A) 248.25 kPa (B) 331.0 kPa
(C) 413 75. kPa (D) 206 85. kPa
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 M=50 N m- .
SM 4.16 What will be the maximum bending stress developed in the material using the flexure formula, where Iz = 41p(0.08 )(0.04 )m m 3 ?
(A) 372.75 kPa (B) 310 65. kPa
(C) 621 25. kPa (D) 497 0. kPa
SM 4.17 What will be the maximum bending stress developed in the material using integration ?
(A) 621 25. kPa (B) 497 0. kPa
(C) 310 65. kPa (D) 372.75 kPa
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Common Data For Q. 18 and 19
For the beam and loading of the S310#52 rolled steel shape as shown in figure, the section modulus is S=625#10 m-6 3.
SM 4.18 What will be the magnitude and location of the maximum bending moment, respectively using singularity functions ?
(A) -18kN m- ,1.94m (B) 28 28. kN m- ,1.94m (C) -27kN m- ,1.94m (D) 18kN m- ,1.94m
SM 4.19 The maximum normal stress due to bending is
(A) 56.5 MPa (B) 33 9. MPa
(C) 45 2. MPa (D) 28 25. MPa
Common Data For Q. 20 and 21
A timber beam is supported and loaded as shown in figure. The available stock consists of beams with a 12 MPa allowable stress and a rectangular cross section of 30 mm width and depth h varying from 80 to 160 mm in 10 mm increments.
SM 4.20 What will be the magnitude and location of the maximum bending moment, respectively for the beam and loading using singularity functions ?
(A) 0 872. kN m- ,4.0m
Common Data For Q. 22 and 23
In the figure shown, a beam is made of a material that has a modulus of elasticity Ec in compression and Et in tension.
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SM 4.22 The location c of the neutral axis, is
SM 4.23 If it is subjected to the bending moment M, an expression for the maximum tensile stress in the beam having the dimensions shown, will be
(A) bhM
SM 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 A and B do not exert an axial force on the shaft, the absolute maximum bending stress developed in the shaft will be
(A) 203.75 MPa (B) 163 0. MPa
(C) 101 85. MPa (D) 122 25. MPa
Common Data For Q. 25 and 26
The composite beam as shown in figure, is made of aluminium ( )A and red brass ( )B . Take Eal =68.9 GPa and Ebr=101 GPa.
SM 4.25 What will be the dimension h of the brass strip so that the neutral axis of the beam is located at the seam of the two metals ?
(A) 82.6 mm (B) 413mm
(C) 41 3. mm (D) 4 13. mm
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SM 4.26 If the allowable bending stress for the aluminium is (sallow al) =128 MPa and for the brass is (sallow br) =35 MPa, what maximum moment will this beam support ? (A) 6 60. kN m- (B) 36 5. kN m
-(C) 29.2 kN m- (D) 43 8. kN m
-Common Data For Q. 27 and 28
A beam AB consists of a cast-aluminium plate of uniform thickness b and 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 of x, L and the maximum stress developed in the wood (Ew =13.1 GPa) and steel are
(A) sst=4 55. MPa,sw=0 30. MPa (B) sst=4.55MPa,sw =2 28. MPa (C) sst =2 28. MPa,sw=0.60MPa (D) sst=0 60. MPa,sw =0.30MPa
SM 4.30 The cantilever beam AB consisting of a cast-iron plate of uniform thickness b and length L, is to support the distributed load w x( ) as shown in figure. If the beam is of constant strength, the expression for h in terms of x, L and h0 will be
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(A) h h Lx / compression and s =t 120 MPa is in tension. What will be the greatest magnitude of the applied forces P ?
(A) 79.75 kN (B) 110 4. kN (C) 159 5. kN (D) 55 2. kN
SM 4.32 A cantilevered machine element of cast aluminium and in the shape of a solid of revolution of variable diameter d, is being designed to support a horizontal distributed load w =20kN m/ as shown in figure. If the machine element is to be of constant strength with sallow=72 MPa and L =300 mm, the smallest allowable value of d0 will be
(A) 503 mm (B) 50.3 mm
(C) 5.03 mm (D) 100 6. mm
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 section a a- ?
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(A) st=1.02MPa,sc=792kPa (B) st=792kPa,sc=1.02MPa (C) st=2.04MPa,sc=792kPa (D) st=1.02MPa,sc=396kPa
SM 4.34 For the tapered beam as shown in the figure, if P =150 kN, what will be the distance x of the transverse section in which the maximum normal stress occurs and the corresponding value of the normal stress ?
(A) xm=0.4 ,m sm=78.15MPa (B) xm=0.2m,sm=156 3. MPa (C) xm=0.4 ,m sm=156 3. MPa (D) xm=0.2m,sm=78.15MPa
SM 4.35 Bar as shown in figure has a thickness of 10 mm. If the maximum bending stress at A B, and C is same and K =1.5, what will be the length L of the center portion of the bar ?
(A) 95 mm (B) 95 mm0
(C) 9.5 mm (D) 19 0. mm
SM 4.36 Consider a machine element of cast aluminium and in the shape of a solid of revolution of variable diameter d to support a distributed load w as shown in figure. If the machine element is to be of constant strength, the expression for d in terms of x L and d, 0 is
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(A) d d Lx
SM 4.37 In the figure shown, the box beam is made of an elastically perfectly plastic material for which s =Y 250 MPa. If the plastic moment Mp is applied and then released, what will be the residual stress in the top and bottom of the beam ?
(A) 317 14. MPa (B) 67 1. MPa
(C) 158 6. MPa (D) 134 2. MPa
SM 4.38 The beam shown in figure, is made of elastic perfectly plastic material. If 50 mm
a = and s =Y 230 MPa, what will be the maximum elastic moment and the plastic moment that can applied to the cross section ?
(A) MY =50.7kN m- ,Mp=86.25kN m -(B) MY =86.25kN m- ,Mp=50.7kN m -(C) MY =101 4. kN m- ,Mp=86 25. kN m -(D) MY =50 7. kN m- ,Mp=43 15. kN m
-SM 4.39 Consider the beam and loading as shown in figure, the shear force and bending moment diagrams for the beam will be
SM 62 Shear Force and Bending Moment SM 4
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SM 4.40 For a simple beam AB supporting two equal concentrated loads P as 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 shown in the figure, are
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SM 4.42 Consider the compound beam as shown in figure. It is supported by a smooth plate at A which slides within the groove and so it cannot support a vertical force, although it can support a moment and axial load. Which of the followings are 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 ABC is loaded by a vertical load P which 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 an overhang BC as shown in figure. The beam is loaded by two same forces P and a clockwise couple of moment Pa that act through the arrangement as shown.
Which of the following options show the required shear-force and bending-moment diagrams for beam ABC ?
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SM 4.48 Which of the followings are the required shear force and bending-moment diagrams for 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-moment diagrams are
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SM 4.52 For the beam shown in figure, correct representation of the shear force and bending moment diagrams are
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SM 4.53 The shear force and bending moment diagrams for the beam shown in the figure, are
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SM 4.54 A cantilever beam AB carries a uniform load of intensity w over one-half of its length as shown in figure. What will be the shear-force and bending-moment diagrams for the beam ?
SM 4.55 In figure shown, the beam ABCD has overhangs that extend in both directions for a distance of 4.2 m from the supports at B and C, which are 1.2 m apart. The shear-force and bending-moment diagrams for this overhanging beam are
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SM 4.56 Two segments of uniform load is supported by a simple beam AB and two horizontal forces acting at the ends of a vertical arm as shown in figure. Which of the followings are the shear-force and bending-moment diagrams for this beam ?
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SM 4.57 In figure shown, a simple beam AB is subjected to a counterclockwise couple of moment M0 acting at distance a from the left-hand support. Which of the followings are the shear-force and bending-moment diagrams for this beam ?
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SM 4.58 The shear force and bending moment diagrams for the beam as shown in figure, are
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