Ies 2013 Solution Obj I

Detailed Solutions of

Civil EngineeringObjective Paper-I

IES-2013

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IES (ESE)-2013 AnSwErSCivil Engineering : Paper-I

Q. No.

Booklet Series

A B C D

1. B B B B

2. B A A A

3. B C B C

4. A D D B

5. B D C C

6. B D A A

7. A A C C

8. D None C C

9. C C D D

10. B A D D

11. C B C C

12. B C A D

13. D B B C

14. A B B C

15. B B D None

16. B B A B

17. C A B D

18. D B D A

19. B B C B

20. C A C A

21. A D D B

22. B C B A

23. D B B B

24. D C A D

25. B B C C

26. A D D A

27. B A D C

28. A B D C

29. C B A D

30. D C None D

Q. No.

Booklet Series

A B C D

61. D B A B

62. A D C A

63. None C D D

64. C A B C

65. A C C B

66. B C A C

67. C D B B

68. B D D D

69. C C D A

70. B A B B

71. C B A B

72. A B B C

73. D D A D

74. A A C A

75. C B D A

76. B D D A

77. A C C C

78. C C B A

79. B D B A

80. A B D A

81. B B D A

82. D A A A

83. C C A A

84. A B A A

85. C C C B

86. C A A A

87. D C A D

88. D C A B

89. C D A D

90. A D A A

Q. No.

Booklet Series

A B C D

31. D C C C

32. C B A A

33. B C B B

34. B A C B

35. D D B D

36. B A B A

37. A C B B

38. C B B D

39. B A A C

40. C C B C

41. A D B D

42. C B A B

43. C C D B

44. D A C A

45. D B B C

46. C D C D

47. D D B D

48. C B D D

49. C A A A

50. None B B None

51. B A B C

52. D C C A

53. A D C B

54. B D B C

55. A C C B

56. B B A B

57. A B D B

58. C D A B

59. D B C A

60. D A B B

Q. No.

Booklet Series

A B C D

91. B C A A

92. B D A C

93. D C B D

94. A C A B

95. B None D C

96. D B B A

97. C D D B

98. C A A D

99. D B A D

100. B A C B

101. D D B A

102. A A A B

103. A A C A

104. A A B C

105. C C C D

106. A A A D

107. A A C C

108. A A C B

109. A A D B

110. A A D D

111. A A C C

112. A A D B

113. B B C C

114. A A C A

115. D D None D

116. B B B A

117. D D D C

118. A A A B

119. A A B A

120. C C A C

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IES-2013 | CE : Paper-I (Set-C) Questions with Explanations

Q.1 Which of the following factors would greatly affect the attainment of best possible strength of the concrete mix produced using the weighbatcher? 1. Moisture content in the sand and gravel 2. Inadequate or excess use of approved admixtures 3. Speed of rotation of the drum 4. Nonemptying of the drum as fully as possible (a) 1 and 4 (b) 1 and 2 (c) 2 and 3 (d) 3 and 4

Solution: (b) Water content in sand and gravel will have an influence on water cement ratio of concrete thereby affecting the strength of concrete. Admixtures are added in concrete to improve/modify one and more property (ies) of the concrete mix.

Q.2 The initial cost of equipment is Rs. 1100, salvage value is Rs. 100 and life of equipment is 5 years. The rate of interest for sinking fund is 8%. The yearly depreciation by straight line method is (a) Rs. 200 (b) Rs. 400 (c) Rs. 600 (d) Rs. 800

Solution: (a) Initial cost of equipment: Rs. 1100 Salvage value: Rs.100 [This value is recoverable at the end of service life of the equipments.] ∴ Actual depreciation incurred

= 1100 – 100 = Rs. 100

This loss incurred in 5 years. ∴ Yearly depreciation by straight line method

= = 100 Rs.200/year

5

Q.3 In construction project, the costslope of an activity is an indication of (a) extratime needed (b) extra cost needed (c) reduction of duration of critical activity (d) crashing of an activity

Solution: (b) Case of construction project

= Direct + Indirect cost Direct cost is a function of time and indirect cost may on may not be a function of time.

cost – slope = ∆

= ∆ C function of time t

= change in cost per unit change in time ≡ extra cost which will incur




Page 3 MADE EASY IES-2013 | CE : Paper-I (Set-C) Questions with Explanations

Q.4 Which of the following statements are correct? Tilting type concrete mixers are preferred in situ: 1. Because problem of clogging the opening is avoided. 2. For large constructions only. 3. Because they are suitable for dry mix. 4. Whenever the rated capacity is more than 200 litres. (a) 1 and 2 (b) 2 and 3 (c) 1 and 3 (d) 2 and 4

Solution: (d) In order to avoid variation in the concrete quantity within different batches, these type of concrete mixers are preferred particularly in large projects.

Q.5 An equipment for use in construction activity is purchased now for Rs. 15000, and is used continuously on the job. The annual OMR costs assignable as lump sum at the respective year beginning are Rs. 5000. The equipment will be used for 5 years after which its salvage value is estimated to then be Rs. 1000. The equipment annual cost as reckoned at the end of each year when MACR is 10% for which SFF for 5 years is 0.1638 is (a) Rs. 7800 (b) Rs. 8000 (c) Rs. 8793 (d) Rs. 8957

Answer: (c)

Q.6 Which of the following statements are correct? 1. Drag lines are superior to hoes in excavation jobs. 2. Hoes are more rigid than power shovels. 3. For deeper excavations power shovels give lesser output than hoes. 4. Hoes exert greater tooth power as compared to draglines. (a) 1 and 2 (b) 2 and 3 (c) 1 and 3 (d) 2 and 4

Answer: (a)

Q.7 If the free haul distance is 200 m, the cost of borrow (including excavation and hauling) is Rs. 4/m 3 at station. Cost of haulage beyond free haul is Rs. 0.75/m 3

per station meter. The limit of economical haul distance is (a) 160 m (b) 260 m (c) 360 m (d) 460 m

Answer: (c)

Q.8 A fourwheel tractor whose operating weight is 15,000 kg is pulled along a level haul road at a uniform speed by another tractor. The average tension in the toe cable is 675 kg. The rolling resistance of the haul road is (a) 25 kg/t (b) 35 kg/t (c) 45 kg/t (d) 55 kg/t

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Solution: (c)

15000 kg

675 kg

Tractor being pulled

≡ 675 kg

15000 kg

675 = µ(15000)

⇒ µ = 675 kg/kg 1500

= 675 kg/ton 15

= 45 kg/ton

Q.9 A fourcycle gasoline engine when tested at temperature 35°C and pressure of 740 mm of Hg was found to develop 75 HP. Its horse power at standard condition is

(a) × × 308 740 75

288.5 760 (b) × × 288 760 75 308 740

(c) × × 308 740 75

288.5 760 (d) × × 760 308 75 740 288.5

Solution: (d)

o

P P

=

1/2

o o

P T P T

where p = pressure, P = power

⇒ o

P P

= o

o

T P P T

⇒ P = +

+ 760 35 273 (75 HP) 740 15.5 273

= 760 308 (75) 740 288.5

Q.10 Given that SPCAF, for 10%, for 1, 2 and 3 years are respectively, 1.1000, 1.2100 and 1.3310, what is C.R.F. for 10% for 3 years? (a) 0.7513 (b) 0.5187 (c) 0.3021 (d) 0.4021

Answer: (d)





Q.11 An equipment costs Rs. 25000 to purchase now. It will be used continuously for 8 years. At the end, its salvage value is estimated to be Rs. 1600. Its residual book value at the beginning for the 6th year its use, by the straight line method of depreciation is (a) Rs. 6250 (b) Rs. 9375 (c) Rs. 10375 (d) Rs. 7450

Solution: (c) Annual depreciation

= − cost price salvage value

Time (in years)

= −

= 25000 1600 2925

8 Book value is the original cost of equipment less cummulative depreciation upto the year under consideration.

= 25000 – 5 × 2925 Since beginning of 6 th year ⇒ 5 completed years

= Rs.10375

Q.12 Which of the following statements are correct in respect of a linkedbar chart? 1. Any activity can be shown split into several subparts if so desirable. 2. Interlinkages between WBS groups can be depicted. 3. Mandatory pauses between activities are also always demonstrated on the

chart. 4. Scheduling of material procurement can optionally enhance the utility. (a) 1 and 2 (b) 2 and 3 (c) 3 and 4 (d) 1 and 4

Answer: (a)

Q.13 Consider the following statements pertaining to CPM net work analysis: 1. It is eventoriented method. 2. It is activityoriented method. 3. Time and cost are controlling factors. 4. Time alone is controlling factor. Which of these statements are correct? (a) 1 and 2 (b) 2 and 3 (c) 3 and 4 (d) 1 and 4

Solution: (b) PERT → Event oriented → Time is the controlling factor. CPM → Activity oriented → Both time and cost are considered.

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Q.14 Which of the following do not characterize the critical path? 1. Falls on a single straight line between start and end nodes. 2. Has no dummies 3. Indicates the minimum feasible duration for the complete project. 4. Indicates the maximum sensible duration in which to complete the project. 5. Has no parallel subpaths between any two nodes on it. (a) 2, 4 and 5 (b) 1, 2 and 5 (c) 2, 3 and 4 (d) 1, 3 and 4

Solution: (b) Critical path need not be a straight time. Critical path can have dummies also. Critical path indicates the time duration earlier to which project can not be completed. Critical path can have parallel subpaths also between two nodes lying on it.

Q.15 In a critical path network, which of the following are involved? 1. A series of interconnected activities 2. Considerations for uncertainties in time estimate 3. A logical sequence of activities is provided 4. The node number at the arrow head is numerically smaller than that at tail

end (a) 1 and 2 (b) 2 and 3 (c) 3 and 4 (d) 1 and 3

Solution: (d) Here it is “critical path network” and NOT the “critical path method”.

Q.16 Which one of the following relates to determination of critical path in PERT? (a) Eventoriented slack (b) Activityoriented slack (c) Eventoriented float (d) Activityoriented float

Answer: (b)

Q.17 PERT calculations yield a project length of 70 weeks with a variance of 9 weeks. The number of weeks required to complete the project with a probability of 95% (probability factor for 95% = 1.647) is (a) 73.94 weeks (b) 74.94 weeks (c) 75.94 weeks (d) 76.94 weeks

Solution: (b)

Std. deviation = = = Variance 9 3

1.647 = − T 70 3

⇒ T = 74.941 weeks





Q.18 A linear project is split into six identical activities, each having a, m and b durations of 4, 8 and 10 days, which results in the standard deviation of the duration for the complete project being X 1 days. As an alternative attempt at project planning, the earliersplit six activities are clubbed as (1st and 2nd), (3rd and 4th) and (5th and 6th), thus needing to consider only three (nowmodified) activities; and the standard deviation of the duration for the complete project is

now reported as X 2 days. What will be the ratio 2

1

X ? X

(a) 2 3 (b) 7

6

(c) 5 6 (d) 1

Solution: (d)

Case I: 1 2 3 4 5 6

Case II: After clubbing the activities

1 2 3 4 5 6

Std. deviation of individual activities

= −

= 10 4 1 (before clubbing)

6 ∴ Std. deviation of whole project in caseI

= + + + + + = 2 2 2 2 2 2 1 1 1 1 1 1 6 Std. deviation of individual activities after clubbing

= + = 2 2 1 1 2 ∴ Std. deviation of whole project in caseII

(X 2 ) = + + = 2 2 2 ( 2) ( 2) ( 2) 6

∴ 2

1

x x

= = 6 1 6

Q.19 A father notes that his teenage son uses the telephone. He takes no less than 5 minutes for a call and sometimes as much as an hour. 20 minutes calls are more frequent that calls of any other duration. Considered as a PERT activity a phone call’s expected duration in minutes is

(a) 1 20 6 (b) 1 22

6

(c) 1 24 6 (d) 1 26

6

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Solution: (c)

t = + × + (5min) (4 20min) (60min)

6 = 24.16667 min

= 1 24 min 6

Q.20 A project is estimated to cost Rs. 100 million inclusive of 20% thereof as cost of direct labour. However, 60% of the labour hours budgeted for is nonproductive. If 15% of such wasted labour hours are intended to be curtailed by improved methods of control, then the resulting savings in labour cost would be (a) Rs. 1.2 m (b) Rs. 1.5 m (c) Rs. 1.8 m (d) Rs. 2.0 m

Solution: (c)

20% labour cost (20 million)

Project cost 100 million

80% other costs (80 million)

0.6x (nonproductive) 0.6 x 12 million ≡

0.4x (productive) x = labour hours

15% curtailed (savings) = 0.15 × 12

= 1.8 millions

85% not curtailed

Q.21 Consider the following statements regarding resource allocation/adjustment: 1. Economical utilization of resources. 2. Adjustment of resources to have leave variation in resource histogram. 3. Gradual increase in resources. 4. Activities are so rescheduled that maximum projected need for any resource

does not cross the limit of available resources. Which of these statements are correct? (a) 1 and 2 (b) 2 and 3 (c) 3 and 4 (d) 2 and 4

Solution: (d) In resource allocation, it is the efficient utilization of available of resources and not the economic utilization of resources. Thus the activities are so planned so as not have any requirement of resources beyond the available resources.





Q.22 There is a task involving 160 m 2 of fixing timber formwork for the roof slab of a singlestorey building. The time earmarked for completion is four days, working eight hours per day. If a workers’ team consisting of two skilled workers and a unskilled worker can install the formwork at the rate of 1.25 m 2 /hr, then the number of teams required is (a) 3 (b) 4 (c) 5 (d) 6

Solution: (b)

160 m [4 days × 8 hours/day = 32 hours]

2

Team works @ 1.25 m 2 /hr In 32 hours, 160 m 2 area is to be covered i.e. in one hour area to be covered is

160 32 = 5 m 2 /hr

∴ Number of terms required

= = 5 4 teams

1.25

Q.23 Which one of the following four shapes for a compound, column of the same effective height formed with two equal angles has the largest axial compressive load carrying capacity?

(a) (b)

(c) (d)

Solution: (b) I xx = I yy is available in (b) only thereby giving the maximum value of r min .

Q.24 Two angles of ISA 100 × 100 × 6 have been used as a tie member. The angles are welded on either side of a gusset and tag welded over its length. The maximum length of the member is: (For ISA 100 × 100 × 6, Area = 2334 mm 2 and Y xx = 30 mm) (a) 5.4 m (b) 6.0 m (c) 12.0 m (d) 24.0 m

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Solution: (a)

≥ λ l

min 180 for tension members where there is a possibility of stress reversal

due to forces other than wind or earthquake ⇒ l ≥ 180 × 30 mm ⇒ l ≥ 5.4 m

Q.25 A crane with two wheels per side has a capacity of 50 kN. Weight of the crane is 100 kN, weight of the trolley is 10 kN and the span is 12 m. The maximum static wheel load with hook clearance of 1.0 m from the wheel is (a) 50 kN (b) 52.5 kN (c) 55 kN (d) 60 kN

Answer: (c)

Q.26 Gantry girders are designed to resist: 1. Lateral loads 2. Longitudinal loads 3. Vertical loads (a) 1 and 2 only (b) 1 and 3 only (c) 2 and 3 only (d) 1, 2 and 3

Solution: (d)

Lateral load

Vertical load

longitudinal load

Q.27 The effective width of outstand in compound steel columns for design purposes is equal to (a) half the flange width (b) distance of the free edge from the rivet line (c) distance of the free edge from the stiffeners (d) distance of the free edge to the nearest row of rivets

Answer: (d)

Q.28 For a steel builtup column subjected to an axial force of 1200 kN, the lacing system is to be designed for resisting transverse shear of (a) 15 kN (b) 20 kN (c) 25 kN (d) 30 kN





Solution: (d) Lacing system in a column is designed to resist a transverse shear of 2.5% of axial load

= × = 2.5 1200 30 kN 100

Q.29 At a certain location of a plate girder of web size 1000 mm × 10 mm, a pair of bearing stiffeners 100 mm × 5 mm is welded. The effective area of bearing stiffeners is (a) 1000 mm 2 (b) 2000 mm 2

(c) 3000 mm 2 (d) 5000 mm 2

Solution: (a)

100

100

10

5

5

Bearing area = (100 × 5) + (100 × 5)mm 2

= 1000 mm 2

Q.30 ISMB 250 (Ze = 410 × 10 3 mm 3 ) has been chosen as a beam crosssection to resist a bending moment. Two plates 100 mm × 10 mm are welded to each flange to enhance the moment capacity. The enhanced moment capacity is (a) 71.5 kNm (b) 79.5 kNm (c) 99.0 kNm (d) 148.0 kNm

Solution: (*)

125

10

10

100

100

X X

Z e = 410 × 10 3 mm 3

I xx of plates only

= × + × × +

2 3 4 10 10 2 100 100 10 125 mm

12 2

= 33.8167 × 10 6 mm 4

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∴ Z xx of plates only

= ×

= × +

6 3 3 33.8167 10 250.494 10 mm

(125 10)

∴ Z xx of the whole section = (250.494 + 410)10 3 mm 3

= 660.494 × 10 3 mm 3

∴ Enhanced moment capacity = (0.66 × 250) 660.494 × 10 3 Nmm = 108.98 kNm

Q.31 A monorail crane runs on an Isection of span 6 m, which is simply supported. Estimate the deflection for crane capacity of 20 kN, crab weight of 4 kN, impact factor of 25% and EI = 10 × 10 12 Nmm 2 . Deflection due to selfweight is neglected (a) 6 mm (b) 9 mm (c) 12 mm (d) 18 mm

Answer: (c)

Q.32 An industrial building with 5 bays each 3 m wide has columns of height 4 m. The two end bays are braced by rods as shown in the below figure. Each column carries an axial load of 120 kN. The design force for each brace is

3 m 3 m 3 m 3 m 3 m

4 m

(a) 6 kN (b) 9 kN (c) 15 kN (d) 30 kN

Solution: (a) Bracings are designed for 2.5% for column load and each bracing is connected to two columns.

∴ × × 2.5 120 2 100

= 6kN

Q.33 Which of the following statements are correct? 1. In a steel compound column section, the width will be smaller when they are

placed face to face than when they are placed back to back. 2. In the design of steel compound columns the length of battens are normally

longer than the lacings. 3. Lacings in a steel compound column are designed as slender compression

members. (a) 1 and 3 only (b) 1 and 2 only (c) 2 and 3 only (d) 1, 2 and 3





Solution: (b)

Here to have I = I , width required is larger xx yy

Lacings are designed as short compressive members.

Q.34 Bearing stiffeners in plate girders are provided to (a) decrease the effective depth of web (b) transfer the load from the top flange to the bottom flange (c) prevent buckling of web (d) increase the bearing capacity of the flange

Solution: (c) Bearing stiffness provide additional bearing area thereby reducing the possibility of web buckling since web in plate girder behaves like a column.

Bearing stiffener

Q.35 Which of the following statements is/are correct? 1. A steel structure designer can guarantee the safety of the structure. 2. Working stress method of design of steel structures offers a safer and economical

structure. 3. Strength and serviceability of a structure cannot be predicted on account of

several unforeseen factors (a) 1, 2 and 3 (b) 3 only (c) 2 only (d) 1 only

Solution: (b) No structural engineer can guarantee the safety of a structure. WSM results in uneconomical design. To account for uncertainity in strength and serviceability of a structure FOSs are introduced.

Q.36 Which of the following statements are correct? 1. Knots in a tree affect the continuity of fibres. 2. Nail knots do not influence the strength of timber. 3. Druxiness of wood is not a defect. 4. Tall trees with twisted fibres give good timber of poles. (a) 1, 2, 3 and 4 (b) 1, 2 and 4 only (c) 1, 2 and 3 only (d) 2, 3 and 4 only

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Solution: (b) Druxiness is a wood defect.

Q.37 Excrescences in wood are 1. Defects found in trees 2. Formed due to injuries inflicted on trees when they are growing 3. Defects which render wood suitable as firewood only (a) 1, 2 and 3 (b) 1 and 2 only (c) 1 and 3 only (d) 2 and 3 only

Answer: (b)

Q.38 What treatment is adopted for making timber fireresistant? (a) ASCU treatment (b) Abel’s process (c) Creosoting (d) Tarring

Solution: (b) Sir Abel’s process is used.

Q.39 Deterioration of structure of timber due to dry rot is 1. Caused by fungi 2. Due to dryspell after heavy rains 3. Due to attack to termites 4. Indicated by surface stripes on scantlings (a) 1 and 2 (b) 3 and 4 (c) 2 and 3 (d) 1 and 4

Solution: (a) Dry rot is a fungal defect and is caused due to wet and humid conditions.

Q.40 Alternate wetting and drying of timber: 1. Results in shrinkage and swelling 2. Brings about wet rot onset 3. Increases the durability 4. Causes transmission of spores from germination (a) 1, 2, 3 and 4 (b) 1, 2 and 4 only (c) 1, 2 and 3 only (d) 2, 3 and 4 only

Answer: (b)

Q.41 As per IS classification, the minimum compressive strength of a first class brick should be (a) 75 kg/cm 2 (b) 100 kg/cm 2

(c) 125 kg/cm 2 (d) 150 kg/cm 2

Answer: (b)





Q.42 When provided with alternating courses of (a) all headers and (b) all stretchers, the front elevation of such brick masonry is designated as (a) English bond (b) Single Flemish bond (c) Double Flemish bond (d) Rattrap bond

Solution: (a)

Stretcher

Header

Q.43 I.S. Code specifies that the compressive strength of brick shall be determined by keeping the brick: 1. On edge 2. On bed 3. After soaking in water for 2 hrs 4. After soaking in water for 24 hrs (a) 1 and 2 (b) 2 and 3 (c) 3 and 4 (d) 2 and 4

Answer: (d)

Q.44 Soundness test of cement is carried out of determine its (a) alumina content (b) iron oxide content (c) free lime content (d) durability under sea water 4

Solution: (c) Test for free lime in cement is carried out by soundness test.

Q.45 The objectives of producing cement include 1. Incorporating industrial wastes 2. Increasing free lime 3. Increasing fineness 4. Saving energy needed in the process (a) 1, 2 3 and 4 (b) 1, 3 and 4 only (c) 1, 2 and 4 only (d) 2, 3 and 4 only

Solution: (b) Fly ash, an industrial waste of thermal power plants is used in cement manufacturing. Free lime in cement is always tried to kept low. Fineness of cement aids in hydration of cement. Energy saving methods are invariably tried to keep cost of production as low as possible.

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Q.46 The principal stresses in N/mm 2 on a rectangular element are shown in the below figure. The intensity of normal stress σ n on the oblique plane BE is

100 N/mm 2

100 N/mm 2

400 N/mm 2 400 N/mm 2

D E A

B C

30°

σ n

(a) 125 N/mm 2 (b) 425 N/mm 2

(c) 375 N/mm 2 (d) 250 N/mm 2

Solution: (c) σ 1 = 400 N/mm 2

σ 2 = –100 N/mm 2 θ = 30°

σ n = σ + σ σ − σ + θ 1 2 1 2 cos2

2 2 =

− + + ° 400 100 400 100 cos60

2 2 = 150 + 125 = 275 N/mm 2

Option given as 375 N/mm 2

Q.47 The strength of concrete depends on 1. Type of mortar 2. Proportion between coarse and fine aggregates 3. Water cement ratio 4. Temperature at time of mixing (a) 1 and 2 (b) 2 and 3 (c) 2 and 4 (d) 3 only

Solution: (b) CA: FA and w/c ratio affects the strength of concrete.

Q.48 Consider the following statements: 1. Strength of structural concrete is absolutely dependent upon water cement

ratio. 2. Increase in temperature during curing period improves the strength, especially

for aluminous cements. 3. The concern for onset of fatigue in concrete can be overcome by increasing

design loads in limit state design. 4. Even though concrete gains strength after 28 days, such increase is not

considered at design stage. Which of these statements are correct? (a) 1, 2 and 3 (b) 2, 3 and 4 (c) 3 and 4 only (d) 2 and 4 only





Solution: (d) Though strength of concrete depends on w/c ratio but other factors are also there which affect the strength of concrete. Increasing the design load cannot solve the problem of fatigue.

Q.49 The workability of concrete is assessed through: 1. Slump test 2. Compaction factor test 3. Setting time of cement 4. LeChatelier’s apparatus (a) 1 and 2 (b) 2 and 3 (c) 3 and 4 (d) 4 and 1

Answer: (a)

Q.50 Consider the following statements as describing the Rheological behaviour of fresh concrete: 1. Newtonian 2. NonNewtonian 3. Ratio of shear stress to shear rate is constant 4. Ratio of shear stress to shear rate depends upon the shear rate Which of these statements are correct? (a) 1, 2, 3 and 4 (b) 2 and 4 only (c) 1, 2 and 4 only (d) 2, 3 and 4 only

Solution: (b)

Q.51 Which of the following tests compares the dynamic modulus of elasticity of samples of concrete? (a) Compression test (b) Ultrasonic pulse velocity test (c) Split test (d) Tension test

Solution: (b) Initial tangent modulus of stressstrain curve of concrete is also called as dynamic modulus of elasticity.

Q.52 UPV method in nondestructive testing for concrete is used to determine 1. Compressive strength 2. Existence of voids 3. Tensile strength 4. Static modulus of concrete 5. Dynamic modulus of concrete (a) 1, 2, 3 and 4 (b) 1 and 3 only (c) 2 and 5 only (d) 3 and 5 only

Answer: (c)

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Q.53 Which one of the following states falls under the ‘Limit state of Serviceability’ as per IS456? (a) Stability under load (b) Loss for equilibrium of a structure (c) Floor vibration (d) Formation of mechanism

Solution: (c) Excessive floor vibration can render a structure to be of little or no use.

Q.54 Splicing of rebars in RCC beams can be done at a section where (a) bending moment is zero (b) bending moment is less than half of the maximum bending moment in beam (c) bending moment is maximum (d) shear force is zero

Solution: (b) Splicing is never done at the location of maximum BM or where BM = 0 i.e. at maximum S.F.

Q.55 Which of the following statements are correct? 1. The conventional rigid frame system of columns and beans works well for

carrying both vertical and lateral loads for buildings up to 28 storeys height. 2. A shear wall does not provide stability against lateral loads. 3. Drying shrinkage is caused by the evaporation of water from concrete stored

in unsaturated air. (a) 1, 2 and 3 (b) 1 and 2 only (c) 1 and 3 only (d) 2 and 3 only

Solution: (c) Shear wall is infact a lateral load resisting element.

Q.56 As per IS456 : 2000, side face reinforcement in a beam is provided where depth of the web exceeds (a) 750 mm (b) 250 mm (c) 500 mm (d) 1000 mm

Answer: (a)

Q.57 Factor of safety is the ratio of (a) tensile stress to working stress (b) compressive stress to working stress (c) bending stress to working stress (d) yield stress to working stress

Answer: (d)





Q.58 Consider the following statements for prediction of yield lines in a reinforced concrete slab: 1. They represent the axis of rotation. 2. They will propagate outward from a point load. 3. They are straight lines between two intersecting planes. 4. They end at the boundary of the slab or at another yield line. Which of these statements are correct? (a) 1, 2, 3 and 4 (b) 1, 2, and 3 only (c) 1, 2 and 4 only (d) 2, 3 and 4 only

Answer: (a)

Q.59 The below figure represents a section of a prestressed beam. For a notension design where σ c is the permissible stress in concrete, the total moment carrying capacity is

b

d/2

d/2

(a) σ 2 c bd

3 (b) σ 2 c bd

4

(c) σ 2 c bd

6 (d) σ 2 c bd

12

Solution: (c) For no tension

P A = M

Z

⇒ M = σ

= σ = 2

c c

bd P Z Z A 6

Q.60 Spalling stresses are produced in posttensioned prestressed concrete members because of (a) bursting force (b) highly concentrated tendon force (c) inadequate anchor block (d) maximum shear zone

Answer: (b)

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Q.61 Which of the following statements are correct? 1. Splices in flexural members should not be at sections where the BM is more

than 50% of the moment of resistance. 2. Normal lap splines can be used for all types of bars irrespective of the sizes. 3. Where bars of two different diameters are to be spliced, the lap length shall

be calculated on the basis of the diameter of the smaller bar. (a) 1 and 2 only (b) 1 and 3 only (c) 2 and 3 only (d) 1, 2 and 3

Answer: (c)

Q.62 A concordant cable profile in prestressed concrete is (a) parallel to the beam axis (b) one which coincides with the centroidal axis of beam (c) one which does not cause secondary stresses (d) one which eliminates primary stresses

Answer: (c)

Q.63 A mild steel rod tapers uniformly from 24 mm dia. to 12 mm dia. over its length of 400 mm. The rod when held vertical is subjected to an axial tensile load of 12 kN. E = 2 × 10 5 N/mm 2 . The extension of the rod in mm would be

(a) π 3 2 (b)

π 2

3

(c) π 3 (d)

π 1 3

Solution: (d)

P d = 12 mm 2

d = 24 mm 1

400 mm

P

∆ = π 1 2

4PL Ed d

= = π π × 5

4(12000)400 1 3 (2 10 )24(12)

Q.64 A mild steel bar of square crosssection has a sectional area 200 mm 2 . It is subjected to an axial force of 20 kN as shown in the below figure. The intensity of the normal tensile stress is N/mm 2 on the oblique plane 11 at 45° with the YYaxis which is normal to the longitudinal axis will be





20 kN 20 kN

1 Y

Y 1

Θ =45°

(a) 25 (b) 50 (c) 75 (d) 100

Solution: (b) A = 200 mm 2

σ 1 = ×

= 2 P 20 1000 N A 200 mm

= 100 N/mm 2

θ = 45°

δ A = σ + σ − + θ

1 1 0 0 cos2 2 2

= + ° 100 100 cos90

2 2 = 50 N/mm 2

Q.65 Poisson’s ratio of a material is 0.3. Then the ratio of Young’s modulus to bulk modulus is (a) 0.6 (b) 0.8 (c) 1.2 (d) 1.4

Solution: (c)

K = −

mE 3(m 2)

Where Poisson’s ratio = = = 1 µ 0.3 m

⇒ E K =

− = − 3(m 1) 2 3 1

m m

= 3(1 – 2 × 0.3) = 1.2

Q.66 The relationship between Young’s Modulus E, Modulus of Rigidity C and Bulk Modulus K in an elastic material is given by the relation

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(a) = +

9KC E 3K C

(b) = +

3KC E 3K C

(c) = +

9KC E 9K C (d) =

+ 3KC E

9K C

Solution: (a)

Q.67 Which of the following statements are correct? 1. In a ductile material elastic deformation is more predominant than plastic

one. 2. Brittleness is not an absolute property of a metal. 3. Rate of loading has no influence in changing the behaviour of a metal

from ‘ductile’ to ‘brittle’ at low temperatures. 4. Under hydrostatic compression, a brittle metal may change into a ductile

one. (a) 1 and 2 (b) 2 and 3 (c) 3 and 4 (d) 2 and 4

Solution: (b) Ductile material can have substantial plastic deformation also.

Q.68 The total deflection of a structure when subjected simultaneously to different sets of loading is equal to the sum of the deflections under each such set of loads as if acting separately on the structure. Which one of the following justifies this statement? (a) Elastic limits is not exceeded (b) Elastic limit including buckling is not exceeded (c) Limit state is not exceeded (d) Proportional limit without buckling is not exceeded

Solution: (d) Hook’s law is applicable within the limit of proportionality and superposition principle is applicable only for small deformations.

Q.69 A rectangular bar of crosssectional area A is subjected to an axial tensile load P. The maximum shear stress will occur on a plane at X° to any normal crosssection where X° is (a) 90° (b) 270° (c) 180° (d) 45°

Answer: (d)

Q.70 A solid circular shaft has been subjected to a pure torsion moment. The ratio of maximum shear stress to maximum normal stress at any point would be (a) 1 : 2 (b) 1 : 1 (c) 2 : 3 (d) 2 : 1

Answer: (b)





Q.71 Which of the following statements are correct? 1. All load carrying members transmit load through basic modes of tension,

compression, torsion and shear only. 2. Beams carry transverse loads. 3. Combined loading is a complicated loading. 4. Nature of internal forces decided the aspect of combined loading. (a) 1 and 2 (b) 2 and 3 (c) 3 and 4 (d) 2 and 4

Solution: (a) Combined loading is not a complicated loading.

Q.72 A rectangular beam of dimensions b × d is to be cut from a circular log of wood of diameter D. For the beam to be strongest in bending, the dimensions will be

(a) D 2 and D 3 2

(b) D 2 and D

3 3

(c) D 2D and

3 2 (d) D 2D and

3 3

Solution: (b)

θ

D/2

d/2

d/2

b/2 b/2

D/2

y

y

x x

d 2 = D sin

2 θ

⇒ d = Dsinθ

b 2 = D cos

2 θ

⇒ b = Dcosθ

Z = 2 3 2 bd D cos sin

6 6 θ θ

= = 3

3 D (cos cos ) 6

θ − θ

For strongest flexural beam, dz 0 d

= θ

⇒ –sinθ + 3cos 2 θ sinθ = 0

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⇒ sinθ(3cos 2 θ – 1) = 0

⇒ cosθ = 1 3

∴ sinθ = 2 3

∴ b = D 3

& d = 2 D 3

Q.73 Which of the following statements are correct? 1. Experimental results on thinwalled tubes show that maximum normal stress

theory is valid. 2. Normal stress theory is valid in case of brittle materials. 3. In case of pure shear, St. Venant’s theory is more valid than other theories. 4. Tresca’s theory is very closely substantiated by experimental results. 5. In maximum stress theory, the yield locus is a hexagon. (a) 1, 2 and 3 (b) 2, 4 and 5 (c) 1, 2 and 4 (d) 2, 3 and 4

Answer: (a)

Q.74 A thin cylindrical shell made of mild steel plate is 1000 mm in diameter. It is to be subjected to an internal pressure of 2 N/mm 2 . If the material yields at 200 N/mm 2 , the thickness of the plate in mm on the basis of Rankine’s theory of failure with assuming a factor of safety of 3 would be (a) 10 (b) 12 (c) 15 (d) 18

Solution: (c)

Q.75 Consider the following statements with reference to a continuous beam supported at A, C and E for which shear force diagram is shown in the below figure.

+

–

+

– A B C D E

There is 1. A concentrated load acting at point B. 2. A concentrated load acting at point D. 3. A uniformly distributed load acting on the portion CE. Which of these statements are correct? (a) 1, 2 and 3 (b) 1 and 2 only (c) 2 and 3 only (d) 1 and 3 only





Solution: (d) At B, S.F. is changing sign ⇒ point load at B. Portion CE is carrying a udl ⇒ SF varies with x.

Q.76 Which of the following loads should be applied on a simply supported beam, so that the shear force is constant throughout its span? (a) UDL over the entire span (b) Two concentrated loads equally spaced in the span (c) A central concentrated load and a UDL over the entire span (d) A couple anywhere in the span

Solution: (d)

M

L M/L M/L

∴ SF = M L

throughout the beam

Q.77 A simply supported rolled steel joist of Isection has flange width 250 mm and overall depth 600 mm. Its moment of inertia I xx = 12 × 10 8 mm 4 . The steel joist is used as a beam over a simply supported span of 6 m. It carries a load of 40 kN/m including its self weight throughout the span. The maximum stress induced in the beam in N/mm 2 due to bending would be (a) 30 (b) 90 (c) 45 (d) 60

Solution: (c)

f y

= M I

⇒ f = M Z

Where Z = I/y = 8

3 12 10 mm 300 ×

= 4 × 10 6 mm 3

M = 2 2 w 6 40 180 kNm

8 8 = × = l

= 6

2 6

180 10 45 N/mm 4 10

× =

×

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Q.78 Which of the following terms represents the torque that produces a twist of one radian in a shaft of unit length? (a) Torsional stress (b) Torsional rigidity (c) Flexural rigidity (d) Moment of resistance

Solution: (b)

T = CJL

θ

CJ → Torsional rigidity

CJL

→ Torsional stiffness

Q.79 A 60 mm dia. shaft is subjected to a torque of 6 kNm. C = 8 × 10 4 N/mm 2 . The maximum shear stress induced in the shaft in N/mm 2 will be

(a) 8000 9 π (b)

4000 9 π

(c) 12000

9 π (d) 16000

9 π

Solution: (b)

T = 6 kNm

d = 60 mm C = 8 × 10 N/mm 4 2

C = 8 × 10 4 N/mm 2

f s = T R J

= 6

4

6 10 30 (60)

32

× ×

π =

6

4 4 32 30 10

(36) (36)10 × × ×

π

= 2 4000 N/mm 9π

Q.80 A water main 160 cm dia. contains water at a pressure head of 200 m. Take weight of water to be 1000 kg/m 3 . The thickness of the metal shell required for the water main, given that the maximum permissible stress in the metal is 400 kg/cm 2 , will be (a) 1 cm (b) 2 cm (c) 3 cm (d) 4 cm

Solution: (d) pd2t

≤ 400 kg/cm 2





Directions: Each of the next Twenty (20) items consists of two statements, one labelled as the ‘Statement (I)’ and the other ‘Statement (II)’. You are to examine these two statements carefully and select the answers to these items using the codes given below: Codes:

(a) Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I).

(b) Both Statement (I) and Statement (II) are individually true but Statement (II) is NOT the correct explanation of Statement (I).

(c) Statement (I) is true but Statement (II) is false (d) Statement (I) is false but Statement (II) is true.

Q.81 Statement (I): Weight batching method does not produce concrete of required strength. Statement (II): Bulking of aggregates does not influence the weight batching method.

Solution: (d) Weigh batching produce concrete of desired strength.

Q.82 Statement (I): Shutter vibrators are preferred over needle vibrators for pre stressed precast beams for bridges. Statement (II): Needle vibrators may get choked by the leaking in of cement paste.

Answer: (a)

Q.83 Statement (I): In concreting for large roof slabs, internal vibrators are preferred. Statement (II): External vibrators consume more energy and disturb the formwork.

Answer: (a)

Q.84 Statement (I): In the erection of tall buildings, tower crane is preferred. Statement (II): Tower crane is a combination crane and it is suitable when the area is small and congested.

Answer: (a)

Q.85 Statement (I): For short distance hauls, dumpers are well suited. Statement (II): Dumpers have the advantages of larger capacity of 5 cu m or more, and they are hauled by power units.

Answer: (c)

Q.86 Statement (I): Power shovels mounted on trawlers are universally used for excavating earth. Statement (II): They have a dipper with hard teeth to break even hard rocks.

Answer: (a)

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Q.87 Statement (I): Drawbar pull exerted in crawlertractors overlaps between different speed ranges, which latter are achieved by operating in different gears. Statement (II): Variations in rolling resistance of ground surfaces and the grade of the surfaces rolled on, influence the magnitude of the needed draw bar pull.

Answer: (a)

Q.88 Statement (I): A wheel type tractor with a scraper is employed to move earth for short hauls. Statement (II): Wheel type tractor moves faster than crawler type tractor.

Answer: (a)

Q.89 Statement (I): Diaphragm pump is very popular in constructions requiring dewatering of trenches. Statement (II): Diaphragm pump is more adaptable in performance than other types of pumps.

Answer: (a)

Q.90 Statement (I): An air vessel on the suction side of a reciprocating pump contributes much to increase in efficiency. Statement (II): Water gets sucked into the pump cylinder faster.

Answer: (a)

Q.91 Statement (I): Negative slip is a possibility in reciprocating pumps. Statement (II): Noncavitations in a long suction pipe with simultaneously a short delivery pipe may cause the delivery valve to open before the discharge stroke starts.

Answer: (a)

Q.92 Statement (I): Reciprocating pumps may have more severe restrictions on their suction piping system than centrifugal pumps. Statement (II): Centrifugal pumps can have the advantage of axial balancing to alleviate possible axial thrust at the eye of the pump.

Answer: (a)

Q.93 Statement (I): A bar chart may look awkward when demonstrating the works to be executed for external finishes in multistorey constructions. Statement (II): External scaffolding can be dismantled in a toptodown sequence only

Answer: (b)

Q.94 Statement (I): When LSS is drawn as a squared diagram, the respective total float for each subpath will be shown in full at the headend of that subpath.





Statement (II): By considering LS for scheduling , the sparable time is pushed to the headend.

Answer: (a)

Q.95 Statement (I): Interdependence between various events is shown on a milestone chart. Statement (II): Milestones are key events in time which occur as the project progresses.

Answer: (d) Interdependence is shown by bar charts.

Q.96 Statement (I): Probabilistic activity durations may yet be relevantly assigned even when work outputs have been standardized for labour gangs for the specified project. Statement (II): Results of workstudy are dependent on rest allowances and work ratings.

Answer: (b)

Q.97 Statement (I): PERT network is eventoriented and it does not reflect on time or resources. Statement (II): Planners can decide about the uncertainties involved in time duration while planning itself.

Solution: (d) PERT reflects on time.

Q.98 Statement (I): When developing the timecost study of a project as a whole, the timecost relationships of every activity therein may have necessarily to be inputted. Statement (II): Any project is constituted by all the activities therein.

Answer: (a)

Q.99 Statement (I): Inherent weakness of finished plain concrete is the presence of microcracks at the aggregate interface. It is minimized by placing fibres in the concrete mix. Statement (II): The fibres help to transfer all incidental loads at the internal microcracks.

Answer: (a)

Q.100 Statement (I): When an equipment is used at a reduced post of service, the ROR cannot be uniquely determined even when the log book of the equipment has been maintained regularly. Statement (II): OMR expenditure may be very much reduced when used in reduced post of service.

Answer: (c)

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Q.101 Which of the following statements is/are correct? 1. For statically determinate structures, magnitudes for maximum effects

due to a series of concentrated loads can be established with the aid of influence lines.

2. Cables in suspension bridges will not take the parabolic shape if uniformly loaded along the horizontal span.

3. In a threehinged arch structure, the normal force, shear and moment at any section are not influenced by the horizontal reaction at the support.

(a) 1, 2 and 3 (b) 1 only (c) 2 only (d) 3 only

Answer: (b)

Q.102 A threehinged arch of span L and rise R is subjected to a concentrated load P at the crownpoint. The horizontal thrust at the support is

(a) PL 4R (b) PL

R

(c) PRL (d)

PL 3R

Solution: (a) P

H H

R

R 1 R 2 L

R 1 + R 2 = P ...(i)

1 L R 2 = HR ...(ii)

R 1 L = PL2

⇒ R 1 = P 2 ...(iii)

∴ P L. HR 2 2

= ⇒ H = PL 4R

Q.103 A simply supported beam of span L shown in the below figure is subjected to a concentrated load W at its midspan and also to a uniformly distributed load equivalent to W. It has a flexural rigidity of EI. What is the total deflection at its midpoint?





L/2

L

W B A

(a) 3 5 WL

384 EI (b) 3 9 WL

384 EI

(c) 3 13 WL

384 EI (d) 3 18 WL

384 EI

Solution: (c) 3 3 5 (w ) W

384 EI 48EI + l l l =

3 13 W 384 EI

l

Q.104 The force in member BC is P A

60° 60° C B

(a) P

2 2 (b) Zero

(c) 2P 3

(d) P 3 2

Solution: (b) Ends B and C do not move relative to each other i.e. member BC has no change in length ⇒ No strain ⇒ Zero force.

Q.105 The degree of static indeterminacy for the rigid frame as shown below is

(a) 3 (b) 4 (c) 5 (d) 6

Answer: (c)

Q.106 Clockwise moments are applied to both the ends of a uniform simply supported beam. If the ratio of the rotation of two ends is 2, then the ratio of the applied moments will be

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(a) 5 4 (b) 7

5

(c) 5 3 (d) 3

2

Answer: (a)

Q.107 Which of the following statements are correct? 1. It is common practice to discount the influence of axial thrust on bending

stiffness of members of frames. 2. In a portal frame of single bay, the columns have different thermal coefficients

of expansion. If the whole frame is subjected to a same temperature, there will be a component of deformation in the vertical directions.

3. The flexibility method of analysis cannot be used to solve any kind of indeterminate structural problem.

(a) 1, 2 and 3 (b) 1 and 3 only (c) 1 and 2 only (d) 2 and 3 only

Answer: (c)

Q.108 Stiffness method of structural analysis starts with (a) forcedeformation relations (b) equilibrium condition (c) compatible deformation (d) equilibrium state of internal stress components

Answer: (c)

Q.109 A stepped circular shaft is fixed at A and C as shown in the below figure. The diameter of the shaft along BC is twice that of as along AB. The torsional rigidity of AB is GJ. The torque required for unit twist at B is

A B C

l l

(a) 2GJ l (b) 5GJ

l

(c) 9GJ l (d) 17GJ

l

Solution: (d)

l l

T T A T B





θ AC = 0 ⇒ θ AB + θ BC = 0

⇒ A A T (T T) GJ GJ

− +

′ l l = 0 ...(i)

J′ = 4 4 (2d) d 16 16J

32 32 π π

= ⋅ =

From equation (i)

⇒ A A T (T T) GJ 16GJ

− + l l = 0

⇒ 16 T A + T A – T = 0

⇒ 17 T A = T ⇒ T A = T17

θ AB = θ B – θ A = A T T GJ 17GJ

= l l

⇒ θ B = T 17GJ

l (As θ A = 0)

⇒ B

T 17GJ =

θ l

∴ Torque required for unit twist at B

= 17GJ l

Q.110 The force required to produce a unit displacement (translation without rotation) at either onethird point of a fixed beam of span l and of uniform flexural rigidity EI is

(a) 3 729EI l

(b) 3 724 EI l

(c) 3 724 EI

3l (d) 3 729EI

2l

Solution: (d)

A B 2 /3 l l/3

∆ = 1 A B

2 /3 l l/3

∆ = 1 ≡

12EI ( /3)

∆ l 3

12EI ( /3) 2l 3

∆

+

12EI ( /3) l 3

∆ 12EI ( /3) 2l 3

∆

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P = 3 3 12EI 12EI ( / 3) (2 /3)

+ l l

l = unity

= 3 729EI

2l

Q.111 The stiffness coefficient k 11 for the beam as shown below is

a b

C

1 Hinge

(a) 3 3 1 1 EI a b

+ (b) 3 3

1 1 2EI a b

+

(c) 3 3 1 1 3EI a b

+ (d) 3 3 1 1 4 EI a b

+

Solution: (c)

A B b a

∆

c P 2

≡ + P 2 P 1

1 1

∴ P 1 + P 2 = 3 3

1 1 3EI a b

+

Q.112 For which one of the following cases is the MullerBreslau principle applicable to get influence line? (a) Reaction at the ends of a simple beam (b) Bending moment at a section (c) Shear force at a section (d) Forces and moments at any section

Answer: (d)

Q.113 The area of influence diagram for the reaction at the hinged end of a uniform propped cantilever beam of span l is

(a) 3 8 l (b) 2

l

(c) 4 l (d) 8

l





Solution: (c)

h

b

n degree curve where n = (cubic parabola)

A = bh (1) n 1 3+1 4

= = +

l l

Q.114 Consider the following statements: 1. The virtual work method is preferred to the equilibrium method for the

determination of collapse load in a structure. 2. The number of plastic hinges required for the total collapse of a statically

indeterminate structure is one less than the degree of indeterminacy of the structure.

3. In a large system the uniformly distributed load can be replaced by a number of concentrated loads to simplify the plastic analysis.

Which of these statements are correct? (a) 1, 2 and 3 (b) 1 and 2 only (c) 1 and 3 only (d) 2 and 3 only

Solution: (c) A structure with indetermancy ‘r’ will become determinate by introduction of ‘r’ hinges. Any additional hinge will lead to collapse of structure i.e. (r + 1) hinges required.

Q.115 For the frame shown below, what is the horizontal thrust at A?

6 m 4 m

20 kN

2 m 2 m

(a) 5 kN (b) 8 kN (c) 10 kN (d) 12 kN

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Solution: (*)

6 m 4 m

20 kN

2 m 2 m

H

R 2

R 1

A H

B

H(2) + R 1 (4) = 20(2) ⇒ H + 2R 1 = 20 ...(i)

H(4) = R 1 (2) ⇒ R 1 = 2H ...(ii) ∴ H = 4 kN

Q.116 Midspan deflection for the beam load system shown below can be obtained by

P

B A C

EI = Constant

l/2 l/2 1. Area moment method 2. Energy method 3. Generalized three moment equation 4. Conjugate beam method (a) 1, 2 and 3 only (b) 1, 2 and 4 only (c) 2, 3 and 4 only (d) 1, 2, 3 and 4

Solution: (b) Three moment equation is used to determine moments.

Q.117 A frame ABCD is supported by a roller at A and is on a hinge at C as shown in the below figure. The reaction at the roller end A is given by

L/2 L/2 L/2 P P

∆ C B

L

A





(a) P (b) 2P (c) P/2 (d) Zero

Solution: (d)

R = 2P

L/2 L/2 L/2 P P

∆ C B

L

A H

R

L P 2

= L P HL 2

+

⇒ H = 0

Q.118 Dead load of the beams is ω/2 per unit run. Live load on the beams is ω/2 per unit run. The two segments are hoisted on simple supports; and then continuity is established at the midsupport before live load is applied. The design midspan moment is

l l EI = Constant

(a) 2

8 ωl (b)

2

16 ωl

(c) 2

32 ωl (d)

2 3 32 ωl

Solution: (a) For design purposes, total load will be ω and hence design moment

2

8 ωl

Q.119 The static indeterminacy of the frame shown below is Hinge

(a) 4 (b) 6 (c) 8 (d) 10

Solution: (b) 1

3 3

3

Total reactions = 10 Total equation = 4

∴ Static indetermancy = 10 – 4 = 6

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Q.120 The equivalent spring constant for the set up shown in the below figure, where EI = unity throughout, is

A B

C D

1 unit 1 unit

0.5 0.5

K = 48 units

(a) 30 units (b) 36 units (c) 40 units (d) 48 units

Solution: (b)

A B

∆3

P

R

R

R

R

∆2

∆1

∆3 = ∆1 – ∆2

3 R(1) 484) =

3 (P R)2 4 484) K −

−

⇒ ZR = 4P(P – R) ⇒ R = 4P – 4R

⇒ R = 4 P 5

∴ ∆ 1 = 3 (P R)2 P R

484) 6 − −

=

= 4 P P P 5

6 30

− =

P 1 ∆

= 30 = K eq .

nnnn

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