Sub: Structural Analysis

STRUCTURAL ANALYSIS____________________________________________________________________________________________________________

.

1. A truss, as shown in the figure, is carrying 180 kN load at node L2. The force in the diagonal member M2U4 will be

(a) 100kN tension                                  (b) 100 kN compression            (c) 80 kN tension                                      (d) 80 kN compression

2. For the plane truss shown in the figure, the number of zero force members for the given loading is

(a) 4  (b)    8   (c)    11     (d)        13

3. A truss is shown in the figure. Members are to equal cross section A and same modulus of elasticity E. A vertical force P is applied at point C.

 A)  Force in the member AB of the truss is

(a) P

√2       (b) 

P

√3    (c)   P/2    (d)        P

 B)   Deflection of the point C is

(a)  (2√2+1 )

2PLEA

         (b)   √ 2PLEA

    

    

(c) (2√2+1 ) PLEA

      (d) (√2+1 ) PLEA

   

      4. For the truss shown in the figure. the force

in the member QR is

(A) zero (B) P/√2(C) P (D) √2P

5. The pin-jointed 2-D truss is loaded with a horizontal force of 15 kN at joint S and another 15 kN vertical force at joint U, as shown. Find the force in member RS (in kN ) and report your answer taking tension as positive and compression as negative.

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6. three-hinged parabolic arch ABC has a span of 20 m and a central rise of 4 m. The arch has hinges at the ends at the centre. A train of two point loads of 20 kN and 10 kN, 5 m apart, crosses this arch from left to right, with 20 kN load leading. The maximum thrust induced at the supports is

(a)  25.00 kN  (b)  28.13 kN(c)   31.25 kN   (d)        32.81 kN

7. A three hinged parabolic arch having a span of 20 m and a rise of 5 m carries a point load of 10 kN at quarter span from the left end as shown in the figure. The resultant reaction at the left support and its inclination with the horizontal are respectively

(A) 9.01 kN and 56.31° (B) 9.01 kN and 33.69° (C) 7.50 kN and 56.31°(D) 2.50 kN and 33.69°8. A symmetric frame PQR consists of two

inclined members PQ and QR, connected at ‘Q’ with a rigid joint, and hinged at ‘P’ and ‘R’. The horizontal length PR is l. If a weight W is suspended at ‘Q’, the bending moment at ‘Q’ is

(A) Wl2

(B) ) Wl4

(C) ) Wl8

(D) zero

9. Consider the beam AB shown in the figure below. Part AC of the beam is rigid while Part CB has the flexural rigidity EI. Identify the correct combination of deflection at end B and bending moment.

(a)   P L3

3 EI,2 PL     (b)    

P L3

3 EI, PL      

(c)  8 P L3

3 EI,2 PL    (d)   

8 P L3

3 EI,PL     

10. The stepped cantilever is subjected to movements, M as shown in the figure below. The vertical deflection at the free end (neglecting the self weight) is

   

(A)  M L2

8 EI      (B)  

M L2

4 EI    (C) 

M L2

2 EI  (

D) Zero

11. A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of 'k') at points' l' and '2', and an inclined load acts at '2', as shown. Q.52 Which of the following options represents the deflections δ 1 and δ 2 at points' l' and '2'?

(A)δ 1=25 ( 2 P

k )∧δ2=45 ( 2P

k )(B) δ 1=

25 ( P

√2 k )∧δ2=45 ( P

√2 k )(C) δ 1=

25 ( P

k )∧δ 2=45 ( P

k )(D) δ 1=

25 (√2 P

k )∧δ2=45 (√2 P

k )

a) If the load P equals 100 kN, which of the following options represents forces R1

and R2 in the springs at points' l' and '2'?

(A) R1 = 20 kN and R2= 40 kN

(B) R1= 50 kN and R2 = 50 kN

(C) R1 = 30 kN and R2 = 60 kN

(D) R1 = 40 kN and R2 = 80 kN

12. A simply supported beam is subjected to a uniformly distributed load of intensity w per unit length, on half of the span from one end. The length of the span and the flexural stiffness are denoted as l and EI, respectively. The deflection at mid-span of the beam is

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(A) 5

6144w l 4

EI (B)

5768

w l4

EI

(C) 5

384w l 4

EI(D)

5192

w l4

EI

13. A parabolic cable is held between two supports at the same level. The horizontal span between the supports is L. The sag at the mid-span is h. The equation of the

parabola is y=4 hx2

L2 .where x is the

horizontal coordinate and y is the vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is

(A) ∫0

L

√1+64h2 x2

L4dx

(B) 2∫0

L/2

√1+64h3 x2

L4dx

(C) ∫0

L/2

√1+64h2 x2

L4dx

(D) 2∫0

L/2

√1+64h2 x2

L4dx

14. A 35 m cable is supported at ends A and B which are at the same horizontal level and are 25 m apart. A vertical level load of 25 KN is acting at point C which is at distance of 9 m from A. find the horizontal reaction at A and dip at C?

A B C 25KN

9m 16mA) 12 kN and 12 mB) 12 kN and 6mC) 6 kN and 12mD) 6 kN and 6 m

15. A light is carrying udl of 30 KN/m. the span of the cable is 77 m, where the supports are at same horizontal level. What will be the percentage change in minimum tension if there is a rise of temperature 350C? coefficient of thermal

expansion of cable material is 12×10−6

C ¿0C. A) 0.8 % decreaseB) 0.8 % increase

C) 1.6 % decreaseD) 1.6 % increase

16. A light cable with span 40m is under udl of 1 KN/m. if the supports are at the same level and the maximum tension allowed in the cable is 30 KN. What is the maximum allowable dip of the cable? A) 6.94 mB) 7.94C) 8.94D) 9.94

17. Find the tension in the cable at point B for the cable shown below.

A B 50kN 5m 20m 10m A) 74.56 kNB) 16.85 kNC) 85.64 kND) 56.86 kN

18. Determine total length of cable as shown in fig.

2.2143 10kN 20kN 2m 3m 2m

A) 7m B) 8.2 mC) 8.5mD) 8.634m

19. Determine the maximum possible span for a cable supported at its two ends (on level supports), if the central sag is limited to 10 percent of the span, and if the permissible tensile stress is 150 MPa. Assume the unit weight of the steel as 78.5 KN/m3. A) 1000 mB) 1162 mC) 1382 mD) 1462 m

20. Determine the tension (kN) in T AB , T BC∧T CD shown below and also find the h (m)? A

h 2m

D B 2m 3kN 8kN

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C 2m 2m 1.5m

A) 6.79, 4.82, 6.9 and 2.74B) 6.9, 4.82, 6.79 and 2.74C) 4.82, 6.79, 6.9 and 2.74D) 4.82, 6.9, 6.79 and 2.74

21. The cable shown supports a girder which weights 12 KN/m. determine the tension in the cable at points A, B and C. 30mA C12m 6m

B

A) 261.4, 154.5 and 214.8B) 261.4, 214.8 and 154.5C) 154.5, 214.8 and 261.4D) 154.5, 261.4 and 214.8

22. A cable is used to support six equal and equidistant loads over a span of 14.7m. the central dip of the cable is 1.5m and the loads are 20 KN each. Find the length of the cable required and its sectional area, if the safe tensile stress is 15 KN/cm2. The distance between the loads is 2.1m.

23. A bridge cable between two piers 100 m apart carries a load of 20 KN/m of span. The tops of the piers are at the same level and the cable at its lowest point sags 10 m below this level. Calculate the max. tension in kN?

A) 269.25B) 279.75C) 285.49D) 253.63

24. A uniform beam weighing 1800 N is supported at E and Fby cable ABCD. Determine the tension (in N) in segment AB of this cable. Assume the cables ABCD, BE and CF to be weightless.

25. Identify the FALSE statement from the following, pertaining to the effects due to a temperature rise ΔT in the bar BD alone in the plane truss shown below:

(A) No reactions develop at supports A and D

(B) The bar BD will be subject to a tensile force

(C) The bar AC will be subject to a compressive force

(D) The bar BC will be subject to a tensile force

26. The degree of static indeterminacy, N s, and the degree of kinematic indeterminacy,N k , for the plane frame shown below, assuming axial deformations to be negligible, given by

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(A) N s=6∧N k=11

(B) N s=6∧N k=6

(C) N s=4∧N k=6

(D) N s=4∧N k=4

27. In the propped cantilever beam carrying a uniformly distributed load of w N/m, shown in the following figure, the reaction at the support B is

(A) 58

w L (B) 38

w L

(C) 12

w L (D) 34

w L

28. For the linear elastic beam shown in the figure, the flexural rigidity. EI, is 781250 kN-m2. When w = 10 kN/m, the vertical reaction RA at A is 50 kN. The value of RA for w = 100 kN/m is

(a) 500 kN     (b) 425 kN              (c) 250 kN   (d) 75 kN

29. For the plane frame with an overhang as shown below, assuming negligible axial deformation, the degree of static indeterminacy, d, and the degree of kinematic indeterminacy, k, are

(a)   d = 3 and k = 10  (b)  d = 3 and k = 13

(c) d = 9 and k = 10   (d)  d= 9 and k = 13

30. The unit load method used in structural analysis is(a) applicable only to statistically indeterminate structures (b) another name for stiffness method (c) an extension of Maxwell's reciprocal theorem (d) derived from Castigliano's theorem

31. A three-span continuous beam has a internal hinge at B Section B is at the mind-span of AC. Section R is at the mid-span of CG. The 20 kN load is applied at section B whereas 10 kN loads are applied at sections D and F as shown in the figure. Span GH is subjected to uniformly distributed load of magnitude 5 kN/m. For the loading shown, shear force immediate to the right of section E is 9.84 kN upwards and the sagging moment at section E is 10.31 kN-m.

A) The magnitude of the shear force immediate to the left and immediate to the right of section B are, respectively            (a)  0 and 20 kN   (b)  10 kN and 10 kN      (c) 20 kN and 0  (d) 9.84 kN and 10.16 kN

B)  The vertical reaction at support H is            (a) 15kN upward (b)9.84 kN upward   (c) 15 kN downward (d) 9.84 kN downward

32. Considering beam as axially rigid, the degree of freedom of a plane frame shown below is

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(a)   9  (b)   8   (c)    7     (d)        6

33. Vertical reaction developed at B in the frame be-low due to the applied load of 100 kN (with 150, 000mm2 cross-sectional area and 3.125 x 109 mm4 moment of inertia for both members) is

(a) 5.9 kN (b)302 kN (c) 66.3 kN  (d) 94.1 kN

34. Consider a propped cantilever beam ABC under two loads of magnitude P each as shown in the figure below. Flexural rigidity of the beam is EI.

  A)   The reaction at C is

(a)     9 P a16 L

    (upwards) 

(b)   9 P a16 L

      (downwards)

(c)  9 P a8 L

       (upwards)     

(d)   9 P a8 L

      (downwards)

B)   The rotation at B is

(a)      5 PL a16 EI

   (clockwise)      

 

(b)     5 PL a16 EI

     (anticlockwise)

(c)     59 PL a16 EI

     (clockwise)    

          

(d)   59 PL a16 EI

      (anticlockwise)

 35. The right triangular truss is made of

members having equal cross sectional area of 1550 mm2 and Young’s modulus of 2 × 105 MPa. The horizontal deflection of the joint Q is

(a) 2.47 mm (b) 10.25 mm (c) 14.31 mm (d) 15.68 mm

36. A two span continuous beam having equal spans each of length L is subjected to a uniformly distributed load w per unit length. The beam has constant flexural rigidly.a) The reaction at the middle support is

(A) wL (B) 5 wL

2 (C)

5 wL4

(D)

w L2

16b) The bending moment at the middle support is

(a) w L2

4 (b)

w L2

8 (c)

w L2

12 (d)

w L2

16

37. The degree of static indeterminacy of the rigid frame having two internal hinges as shown in the figure below, is

(A) 8 (B) 7 (C) 6 (D) 5

38. The members EJ and IJ of a steel truss shown in the figure below are subjected to

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a temperature rise of 30°C. The coefficient of thermal expansion of steel is 0.000012 per °C per unit length. The displacement (mm) of joint E relative to joint H along the direction HE of truss, is

            (A)        0.255            (B)        0.589            (C)        0.764            (D)        1.026

39. Beam GHI is supported by three pontoons as shown in the figure below. The horizontal cross-sectional area of each pontoon is 8 m2, the flexural rigidity of the beam is 10000 kN-m2 and the unit weight of water is 10 kN/m3

a) When the middle pontoon is removed, the deflection at H will be(A) 0.2m (B) 0.4m(C) 0.6m (D)  0.8mb) When the middle pontoon is brought back to its position as shown in the figure above, the reaction at H will be      (A) 8.6kN(B)15.7kN(C) 19.2kN (D)4.2kN

40. The degree of static indeterminacy of a rigidly jointed frame in a horizontal plane and subjected to vertical loads only, as shown in figure below is

 (A)    6    (B)    4     (C)    3       (D)  1

41. In the cantilever beam PQR shown in figure below, the segment PQ has flexural rigidity EI and the segment QR has infinite flexural rigidity.

 a) The deflection and slope of the beam at 'Q' are respectively

(A) 5 W L3

6 EI∧3W L2

2 EI

(B)

W L3

3 EI∧W L2

2 EI

(C)W L3

2EI∧W L2

EI

(D)

W L3

3 EI∧3 W L2

2 EI

b) The deflection of the beam at 'R' is

(A) 8 W L3

EI (B)

5W L3

6 EI (C)

7 W L3

EI(D)

8 W L3

6 EI

42. A simply supported beam is subjected to a uniformly distributed load of intensity w per unit length, on half of the span from one end. The length of the span and the flexural stiffness are denoted as l and EI, respectively. The deflection at mid-span of the beam is

(A)5

6144w l 4

EI (B)

5768

w l4

EI

(C)5

384w l 4

EI (D)

5192

w l4

EI

43. For a linear elastic structural system, minimization of potential energy yields (a) compatibility conditions (b) constitutive relations (c) equilibrium equations

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 (d) strain-displacement relations

44. For linear elastic systems, the type of displacement function for the strain energy is(a)  linear             (b)        quadratic           (c)  cubic            (d)        quartic

45. U1 and U2 are the strain energies stored in a prismatic bar due to axial tensile forces P1 and P2, respectively. The strain energy U stored in the same bar due to combined action of P1 and P2 will be.

(a) U = U1 + U2 (b) U = U1U2 (c) U < U1 + U2 (d) U > V1 + U2

46. A mild steel specimen is under uni-axial tensile stress. Young's modules and yield stress for mild steel are 2 105 MPa respectively. The maximum amount of strain energy per unit volume that can be stored in this specimen without permanent set is(A)  156 Nmm/mm3   (B)  15.6 Nmm/mm3

(C) 1.56 Nmm/mm3  (D) 0.156 Nmm/mm3

47. A uniform beam (EI = Constant) PQ in the form of a quarter-circle of radius R is fixed at end P and free at the end Q, where a load W is applied as shown. The vertical downward displacement,δQ at the loaded

point Q is given by: δQ=β (W R3

EI ). Find

the value of β (correct to 4-decimalplaces).

48. The frame below shows three beam elements OA, OB and OC, with identical length L and flexural rigidity EI, subject to an external moment M applied at the rigid joint O. The correct set of bending

moments[ M OA , MOB ,∧M OC ] that

develop at O in the three beam elements OA, OB and OC respectively is,

(A) [ 3 M8

,M8

,4 M8 ] (B)

[ 3 M11

,4 M11

,4 M11 ]

(C) [ M3

,M3

,M3 ] (D)

[ 3 M7

,0 ,4 M7 ]

49. The plane frame below is analyzed by neglecting axial deformations. Following statements are made with respect to the analysis

(I) Column AB carries axial force only            (II)  Vertical deflection at the center of beam BC is 1 mm            With reference to the above statements, which of the following applies ?            El = 81380 kN-m2            (a) Both the statements are true            (b) Statement I is true but II is false            (c) Statement II is true but I is false            (d) Both the statements are false

50. Match the following :Group I                               Group 2P. Slope deflection method    1. Force methodQ. Moment distribution method       2. Displacement methodR. Method of three momentsS. Castigliano's second theorem(a) P-1, Q-2, R-1, S-2                                  (b) P-1, Q-1, R-2, S-2(c) P-2, Q-2, R-1, S-1                                  (d) P-2, Q-1, R-2, S-1

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51. All members of the frame shown below have the same flexural rigidity EI and length L. If a moment M is applied at joint B, the rotation of the point is

   (a)   ML

12 EI         (b)    

ML11 EI

      

   (c)          ML8 EI

            (d)      ML7 EI

    

52. Carry-over factor CAB for the beam shown in the figure below is

(a) ¼ (b) ½ (c) ¾ (d) 1

53. All members in the rigid-jointed frame shown are prismatic and have the same flexural stiffness EI.Find the magnitude of the bending moment at Q (in KNm) due to the given loading. __________

54. Muller Breslau principle in structural analysis is used for      

(a) drawing influence line diagram for any force function       (b)        writing virtual work equation       (c)        super-position of load effects       (d)        none of these

55. A beam PQRS is 18m long and is simply supported at points Q and R 10m. Overhangs PQ and RS are 3m and 10m part. Overhangs PQ

and RS are 3m and 5m respectively. A train of two point loads of 150 kN and 100 kN, 5m apart, crosses this beam from left to right with 100 kM load leading. A) The maximum sagging moment under the 150 kN load anywhere is(a) 500 kNm     (b)        45 kNm             (c) 400 kNm     (d)        375 kNm B)  During the passage of the loads, the maximum and the minimum reactions at support R, in kN, are respectively(a)  300 and -30  (b)        300 and -25       (c)  225 and -30 (d)        225 and -25 C)  The maximum hogging moment in the beam anywhere is(a) 300 kNm (b)        450 kNm            (c) 500 kNm  (d)        750 kNm

56. Consider the beam ABCD and the influence line as shown below. The inflience the pertains to

(a)  reaction at A, RA            (b) shear force at B, VB       (c) shear force on the left of C, V c

−¿ ¿       

(d) shear force on the right of C, V c+¿ ¿

57. The influence line diagram (ILD) shown is for the member

(a) PS (b) RS (c) PQ (d) QS

58. The span(s) to be loaded uniformly for maximum positive (upward) reaction at support P, as shown in the figure below, is (are) 

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(A)        PQ only      (B)     PQ and QR(C)       QR and RS  (D)     PQ and RS

59. The stiffness K of a beam deflecting in a symmetric mode, as shown in the figure, is

            (a)  EIL

                  (b)  2 EI

L 

     

            (c)  4 EI

L               (d)   

6 EIL

 

    

60. For a linear elastic frame, if stiffness matrix is doubled, the existing stiffness matrix, the deflection of the resulting frame will be(a)  twice the existing value                           (b) half the existing value            (c) the same as existing value                      (d)  indeterminate value

61. The stiffness coefficient kij indicates            (a)   force at i due to a unit deformation at j            (b)   deformation at j due to a unit force at i            (c)   deformation at i due to a unit force j            (d)  force at j due to a unit deformation i

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