TKIET, Warananagar

Department of Civil Engineering

T.E. Civil (Semester- VI)

THOERY OF STRUCTURES

Question Bank (MCQ) _______________________________________________________________

1. By applying the static equations i.e. ΣH = 0, ΣV = 0 and ΣM = 0 to a determinate

structure, we may determine (01)

A Supporting reactions only

B Shear force only

C Bending moments only

D Internal forces only

E All are above

2. While using three moment equation, a fixed end of a continuous beam is replaced

by an additional span of (01)

A. Zero length

B. Infinite length

C. Zero moment of inertia

D. None of the above

3. In moment distribution method, the sum of distribution factors of all the members

meeting at any joint is always (01)

A Zero

B Less than 1

C 1

D Greater than 1

4. The carry over factor in a prismatic member whose far end fixed is (01)

A 0

B 0.5

C 0.75

D 1

5. Consider the following statements: (02)

Sinking of an intermediate support of a continuous beam

1. Reduces the negative moment at support

2. Increases the negative moment at support

3. Reduces the positive moment at support

4. Increases the positive moment at the center of the span

Of these statements

A 1 and 4 are correct

B 1 and 3 are correct

C 2 and 3 are correct

D 2 and 4 are correct

6. The moment distribution method is best suited for (01)

A Indeterminate pin jointed truss

B Rigid frame

C Space frames

D Composite structure

7. The stiffness factor for a prismatic beam of length L and moment of inertia I (01)

A E/L

B 2E/L

C 3E/L

D 4E/L

8. The ratio of the stiffness of the beam at near end when far end is hinged to the stiffness

when far end is fixed is (01)

A 1/2

B 3/4

C 1

D 4/3

9. In a two span continuous beam loaded by UDL, point of contra-flexure exist (01)

A At mid support

B In both spans near middle support

C Near end support

D At the end support

10. Which of the following is not the displacement method (01)

A Equilibrium method

B Column analogy method

C Moment distribution method

D Kani's method

11. Which of the following methods of structural analysis is a displacement method? (01)

A Moment distribution method

B Column analogy method

C Three moment equation

D None of the above

12. The carryover factor in a prismatic member whose far end is fixed is (01)

A 0

B 0.5

C 0.75

D 1

13. In the displacement method of structural analysis, the basic unknowns are (01)

A Displacements

B Force

C Displacements and forces

D None of the above

14. For stable structures, one of the important properties of flexibility and stiffness

matrices is that the elements on the main diagonal (01)

(i) Of a stiffness matrix must be positive

(ii) Of a stiffness matrix must be negative

(iii) Of a flexibility matrix must be positive

(iv) Of a flexibility matrix must be negative

The correct answer is

A (i) and (iii)

B (ii) and (iii)

C (i) and (iv)

D (ii) and (iv)

15. Select the correct statement (01)

A Flexibility matrix is a square symmetrical matrix

B Stiffness matrix is a square symmetrical matrix

C Both (a) and (b)

D None of the above

16. While using three moments equation, a fixed end of a continuous beam is replaced by

an additional span of (01)

A Zero length

B Infinite length

C Zero moment of inertia

D None of the above

17. The number of independent equations to be satisfied for static equilibrium of a plane

structure is (01)

A 1

B 2

C 3

D 6

18. The three moments equation is applicable only when (01)

A The beam is prismatic

B There is no settlement of supports

C There is no discontinuity such as hinges within the span

D The spans are equal

19. The Castigliano's second theorem can be used to compute deflections (01)

A In statically determinate structures only

B For any type of structure

C At the point under the load only

D For beams and frames only

20. The number of independent equations to be satisfied for static equilibrium in a space

structure is (01)

A 2

B 3

C 4

D 6

21. Castigliano’s first theorem is applicable (01)

A For statically determinate structures only

B When the system behaves elastically

C Only when principle of superposition is valid

D None of the above

22. Which of the following methods of structural analysis is a force method? (01)

A Slope deflection method

B Column analogy method

C Moment distribution method

D None of the above

23. In moment distribution method, the sum of distribution factors of all the members

meeting at any joint is always (01)

A Zero

B Less than 1

C 1

D Greater than 1

24. Consider the following statements: (02)

Sinking of an intermediate support of a continuous beam

1. reduces the negative moment at support.

2. increases the negative moment at support.

3. reduces the positive moment at support.

4. increases the positive moment at the center of span.

Of these statements

A 1 and 4 are correct

B 1 and 3 are correct

C 2 and 3 are correct

D 2 and 4 are correct

25. Which of the following is method for solving indeterminate structures (01)

A` 1 moment equation

B 2 moment equation

C 3 moment equation

D 4 moment equation

26. The flexibility matrix method is also known as (01)

A Displacement method

B Force method

C Stress function method

D Displacement field method

27. Sway Analysis of a portal frame becomes essentials when (01)

A Loading is non-symmetric

B Section of members is unequal

C Different types of joints at support occurs

D All of the above

28. In stiffness matrix method of structure analysis, the quantity taken as redundant is

(01)

A Deflection

B Rotation

C Both of the above

D None of the above

29. A propped cantilever is indeterminate externally of (01)

A First degree

B Second degree

C Third degree

D Fourth degree

30. The cases of support sinking are encountered when (01)

A Soil conditions change at nearby distances

B Load geography is undulated

C Both of the above

D None of the above

31. The point of contra-flexure is the point where (01)

A B.M. changes sign

B B.M. is maximum

C B.M. is minimum

D S.F. is zero

32. Determination of B.M. of structures by slope deflection method falls in the category of

(01)

A Determinate analysis

B Matrix analysis

C Indeterminate analysis

D Fictitious analysis

33. Clapeyron's theorem is also known as the theory of (01)

A 3 - moments

B 2 - moments

C Single moment

D None of above

34. Finding the internal stresses in component of structure is known as (01)

A Component design

B Frame design

C Structural design

D None of above

35. The flexibility method is also known as the (01)

A Energy method

B Equilibrium method

C Displacement method

D Force method

36. Distribution factor for members at joint in a frame depend up on (01)

A Moment of inertia for that moment

B Both moment of inertia and length of that member

C Length of that member

D None of above

37. In moment distribution method, the carry over moment is equal to (01)

A Double of its corresponding distributed moment and has same sign

B One-half of its corresponding distributed moment and has same sign

C One-half of its corresponding distributed moment and has opposite sign

D None of the above

38. The distribution factor is (01)

A Ratio of stiffness of member and member

B Ratio of stiffness of near joint and far joint

C Ratio of stiffness of member and joint (sum of member stiffness)

D Ratio of stiffness of joint and member

39. When one of the supports of a beam is at a lower level as compared to the other, it will

cause a moment at both ends. The magnitude of this moment introduced in slope deflection

equation is (01)

A -3EIδ/L2

B -4EIδ/L2

C -6EIδ/L2

D -2EIδ/L2

40. A beam AB of length ‘L’ is hinged at its ends and carries a transverse external loading

such that the end ‘B’ is sunk by an amount ‘δ’. The fundamental slope deflection equation

is (02)

A MAB = 2EI/L (θA + 2θB - 3δ/L) + MFAB

B MAB = 3EI/L (2θA + θB - 3δ/L) - MFAB

C MAB = 3EI/L (2θA + θB + 3δ/L) - MFAB

D MAB = 2EI/L (2θA + θB - 3δ/L) + MFAB

41. The moments at the ends A and B of a beam AB where end A is fixed and B is hinged ,

when the end B sinks by an amount δ, are given as (02)

A 6EI δ/L2 , 6EI δ/L

2

B 6EI δ/L2, 0

C 3EI δ/L2, 3EI δ/L

2

D 3EI δ/L2, 0

42. The fixed end moment of uniform beam of span ‘L’ and fixed at the ends to a central

point load ‘P’ on fixed beam AB is (01)

A PL/2

B PL/8

C PL/12

D PL/16

43. A single bay portal frame of height ‘h’ fixed at the base is subjected to horizontal

displacement ‘δ’ at the top. The base moments developed is proportional to (02)

A 1/h

B 1/h2

C 1/h3

D None of these

44. The number of simultaneous equations to the solved in the slope deflection method is

equal to (01)

A The degree of static indeterminacy

B The degree of kinematic indeterminacy

C The number of joints in the structure

D None of the above

45. A single bay single storey portal frame has hinged left support and a fixed right

support. It is loaded with uniformly distributed load on the beam. Which one of the

following statements is true with regard to the deformation of the frame? (01)

A It would sway to the left side

B It would sway to the right

C It would not sway at all

D None of the above

46. The order of the flexibility matrix for a structure is (01)

A Equal to the number of redundant forces

B More than the number of redundant forces

C Less than the number of redundant forces

D Equal to the number of redundant forces plus three

47. 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 rigidity.

The reaction at the middle support is (02)

A wL

B 5WL/2

C 5WL/4

D 5WL/8

48. 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 rigidity.

The bending moment at the middle support is (02)

A WL2/4

B WL2/8

C WL2/12

D WL2/16

49. The fixed end moment at both the sides of the beam for an eccentric clockwise couple

is (02)

A FEM AB = + [M a (3b-L)/L2] and FEM BA = + [M b (3a-L)/L

2]

B FEM AB = + [M a (3b-L)/L2] and FEM BA = - [M b (3a-L)/L

2]

C FEM AB = - [M b (3a-L)/L2] and FEM BA = + [M a (3b-L)/L

2]

D FEM AB = - [M b (3a-L)/L2] and FEM BA = - [M a (3b-L)/L

2]

50. A continuous beam ABC is fixed at A, simply supported at B and C. Span AB = 6m

and BC = 4m. An UDL of 30 kN/m throughout on span AB and a central point load of 80

kN on span BC. EI is constant throughout the beam. The distribution factor at joint B is

(02)

A BA = 0.33 and BC = 0.67

B BA = 0.40 and BC = 0.60

C BA = 0.53 and BC = 0.47

D BA = 0.47 and BC = 0.53

51. A two span continuous beam ABC has span AB of 6m and BC of 4m. End A is fixed

while end C is simply supported. Span AB carries through UDL 20 kN/m and BC carries a

central point load of 40 kN. Span AB has its inertia double that of span BC. Using slope-

deflection method, calculate EIθB. (02)

A -14.40

B -14.04

C 41.40

D 40.14

52. A continuous beam ABC is fixed at A and simply supported at C. Span AB = BC =

10m. An UDL of 10.5 kN/m throughout on span AB and a central point load of 20 kN on

span BC. The moment of inertia of the beam is IAB : IBC = 1:3. Find out the matrix K values

in a series of K11, K12, K21 and K22. (02)

A 1.6 EI, 0.6 EI, 0.6 EI and 1.2 EI

B 1.6 EI, 0.6 EI, 0.6 EI and 1.2 EI

C 1.6 EI, 0.2 EI, 0.2 EI and 0.4 EI

D 0.8 EI, 0.6 EI, 0.6 EI and 1.2 EI

53. A continuous beam ABC is fixed at A and simply supported at C. Span AB = 5m with

an UDL of 20 kN/m throughout. Also BC = 10m with a central point load of 80 kN. The

final support moments are MA = 36.45 kN.m, MB = 52.10 kN.m and Mc = 67.70 kN.m (All

are Hogging). Calculate the support reactions of the beam. (02)

A RA = 46.87 kN (↑), RB = 100.01 kN (↑), RC = 53.12 kN (↑)

B RA = 100.01 kN (↓), RB = 46.87 kN (↓), RC = 53.12 kN(↓)

C RA = 46.87 kN(↓), RB = 100.01 kN(↑), RC = 53.12 kN(↓)

D RA = 100.01 kN (↑), RB = 53.12 kN (↑), RC = 46.87 kN (↑)

54. A two span continuous beam ABC in which AB = BC = 4m. The beam is pin supported

at A, B and C. An UDL 20 kN/m is placed throughout. During loading support A settles by

6 mm, find out support moment at B. Take EI = 104. Use Clapeyron’s theorem of three

moment method. (02)

A 45.625 kN-m (Sagging)

B 45.625 kN-m (Hogging)

C 34.375 kN-m (Hogging)

D 40 kN-m (Sagging)

55. If a continuous beam ABC is fixed at A, simply supported at B and C, then the size of

matrix in stiffness matrix method is (01)

A 3 x 2

B 2 x 2

C 2 x 3

D 3 x 3

56. If a continuous beam ABC is simply supported at A, B and C, then the size of matrix

in stiffness matrix method is (01)

A 3 x 2

B 2 x 2

C 2 x 3

D 3 x 3

57. If value of EI in right frame member was twice that of the left one then this frame will

be a sway one. State whether this statement is true or false (02)

A True

B False

58. The fixed end moment of uniform beam of span ‘L’ and fixed at the ends to uniformly

distribution load ‘P’ is (02)

A PL2/2

B P L2/8

C P L2/12

D P L2/16

59. The fixed end moment of uniform beam of span ‘L’ and fixed at the ends to a anti-

clockwise couple ‘M’ at center of the beam is (01)

A + M/2

B - M/4

C + M/4

D - M/8

60. The fixed end moment at support ‘A’ of uniform beam of span ‘L’ when an eccentric

point load ‘W’ on the fixed beam AB is (01)

A - Wba2/L

2

B + Wab2/L

2

C - Wa2b/L

2

D - Wab2/L

2

61. The fixed end moment at support ‘B’ of uniform beam of span ‘L’ when an eccentric

point load ‘W’ on the fixed beam AB is (01)

A - Wba2/L

2

B + Wab2/L

2

C + Wa2b/L

2

D - Wa2b/L

2

62. If a continuous beam ABCD is simply supported at A and D, the final moment at

support A is (01)

A Sagging moment

B Zero

C Hogging moment

D None of above

63. If a continuous beam ABCD is simply supported at A and D, the final moment at

support D is (01)

A Zero

B Sagging moment

C Hogging moment

D None of above

64. If a continuous beam ABCD is fixed supported at A and D, the beam is uniformly

distributed throughout the beam is W kN/m. The final moment at support A is (01)

A Zero

B Sagging moment

C Hogging moment

D None of above

65. If a continuous beam ABCD is fixed supported at A and D, the beam is uniformly

distributed throughout the beam is W kN/m. The final moment at support D is (01)

A Zero

B Hogging moment

C Sagging moment

D None of above

66. If a continuous beam ABCD is fixed supported at A and D, the beam is uniformly

distributed throughout the beam is W kN/m. The final moment at center of span AB is (01)

A Zero

B Hogging moment

C Sagging moment

D None of above

67. If a beam is uniformly distributed throughout the span, the bending moment diagram

of the beam is (01)

A Cubic

B Parabolic

C Straight

D Linear

68. If a beam is loaded with two point loads on the span, the bending moment diagram of

the beam is (01)

A Cubic

B Parabolic

C Straight

D Linear

69. If a beam is uniformly distributed throughout the span, the shear force diagram of the

beam is (01)

A Cubic

B Parabolic

C Straight

D Linear

70. If a beam is loaded with two point loads on the span, the shear force diagram of the

beam is (01)

A Cubic

B Parabolic

C Straight

D Linear

71. If a beam is uniformly varying load throughout the span, the shear force diagram of

the beam is (01)

A Cubic

B Parabolic

C Straight

D Linear

72. If a beam is uniformly varying load throughout the span, the bending moment

diagram of the beam is (01)

A Cubic

B Parabolic

C Straight

D Linear

73. In moment distribution method, the distribution factor is equal to (01)

A Total moment of inertia / length of the beam

B Total relative stiffness / relative stiffness

C Relative stiffness / total relative stiffness

D None of above

74. In moment distribution method, the relative stiffness factor to the fixed support is

equal to (01)

A 0

B 0.5

C 1

D 0.75

75. In moment distribution method, the relative stiffness factor to the simple support is

equal to (01)

A 0

B 0.5

C 1

D 0.75

76. In moment distribution method, the relative stiffness factor to the continuous support

is equal to (01)

A 0

B 0.5

C 1

D 0.75

77. A single bay single storey portal frame has fixed at left support and a hinged at right

support. It is loaded with uniformly distributed load on the beam. Which one of the

following statements is true with regard to the deformation of the frame? (01)

A It would sway to the left side

B It would sway to the right

C It would not sway at all

D None of the above

78. A single bay single storey portal frame has fixed at left and right supports. It is loaded

with uniformly distributed load on the beam. Which one of the following statements is true

with regard to the deformation of the frame? (01)

A It would sway to the left side

B It would sway to the right

C It would not sway at all

D None of the above

79. A single bay single storey portal frame has hinged at left and right supports. It is

loaded with uniformly distributed load on the beam. Which one of the following statements

is true with regard to the deformation of the frame? (01)

A It would sway to the left side

B It would not sway at all

C It would sway to the right

D None of the above

80. A continuous beam ABC consists of spans AB = 3m and BC = 4m, the ends A and C

being fixed carry UDL of intensity 4 kN/m and 5 kN/m respectively. Find the fixed end

moments of the span BA and BC (02)

A + 3 kN-m and + 6.67 kN-m

B - 3 kN-m and - 6.67 kN-m

C - 3 kN-m and + 6.67 kN-m

D + 3 kN-m and - 6.67 kN-m

81. A continuous beam ABC fixed at A and C and simply supported at B consists of

span AB and BC of lengths 4 m and 6 m respectively. The span AB carries a load of 20

kN/m while the span BC carries UDL of 12 kN/m. The fixed end moments of span AB and

CB as (02)

A + 26.67 kN-m and +36 kN-m

B - 26.67 kN-m and +36 kN-m

C - 26.67 kN-m and -36 kN-m

D - 36 kN-m and +26.67 kN-m

82. A beam ABC 7m long consists of spans AB and BC of lengths 4m and 3 m

respectively. It is fixed at end A and simply supported at B and C. the span AB carries a

point load of 48 kN a distance of 1m from A while the span BC carries a point load of 36

kN at a distance of 1m from C. the fixed end moments of span BA and CB as (02)

A + 9 KN-m and + 16 kN-m

B + 16 KN-m and + 9 kN-m

C - 9 KN-m and + 16 kN-m

D + 9 KN-m and + 16 kN-m

83. A propped cantilever of span L is loaded with UDL of intensity W kN/m throughout

the span then bending moment at the fixed support is (02)

A WL2/8

B WL2/2

C WL2/12

D WL2/24

84. To find out final moments at supports in stiffness matrix method, following method is

used (01)

A Three moment theorem

B Moment distribution method

C Slope-deflection method

D Consistent deformation method