Theory of Structures

61. A close coil helical spring of mean diameter D consists of n coils of diameter d. If it carries an axial load W, the energy stored in the spring, is

1. 4WD²n/d⁴N
2. 4W²Dn/d⁴N
3. 4W²D3n/d⁴N
4. 4W²D3n²/d⁴N

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62. The horizontal deflection of a parabolic curved beam of span 10 m and rise 3 m when loaded with a uniformly distributed load l t per horizontal length is (where I_c is the M.I. at the crown, which varies as the slope of the arch).

1. 50/EI_c
2. 100/EI_c
3. 150/EI_c
4. 200/EI_c

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63. A masonry dam (density = 20,000 N/m³) 6 m high, one metre wide at the top and 4 m wide at the base, has vertical water face. The minimum stress at the base of the dam when the reservoir is full, will be

1. 75 N/m²
2. 750 N/m²
3. 7500 N/m²
4. 75000 N/m²

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64. A steel rod of sectional area 250 sq. mm connects two parallel walls 5 m apart. The nuts at the ends were tightened when the rod was heated to 100°C. If α _steel= 0.000012/C°, αE_steel = 0.2 MN/mm², the tensile force developed at a temperature of 50°C, is

1. 80 N/mm²
2. 100 N/mm²
3. 120 N/mm²
4. 150 N/mm²

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65. The general expression for the B.M. of a beam of length l is the beam carries M = (wl/2) x - (wx²/2)

1. A uniformly distributed load w/unit length
2. A load varying linearly from zero at one end to w at the other end
3. An isolated load at mid span
4. None of these

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66. A simply supported beam carries a varying load from zero at one end and w at the other end. If the length of the beam is a, the shear force will be zero at a distance x from least loaded point where x is

1. a/2
2. a/3
3. a/√3
4. a √3/2

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67. The radius of gyration of a section of area A and least moment of inertia I about the centroidal axis, is

1. A/I
2. I/A
3. /A)
4. /I)

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68. Slenderness ratio of a long column, is

1. Area of cross-section divided by radius of gyration
2. Area of cross-section divided by least radius of gyration
3. Radius of gyration divided by area of cross-section
4. Length of column divided by least radius of gyration

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69. A three hinged arch is generally hinged at its supports and

1. At one quarter span
2. At the crown
3. Anywhere in the rib
4. None of these

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70. The maximum height of a masonry dam of a triangular section whose base width is b and specific gravity s, is

1. b√s
2. b.s
3. √(bs)
4. s √b

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