### Theory of Structures

1. If a solid shaft (diameter 20 cm, length 400 cm, N = 0.8 × 105 N/mm2) when subjected to a twisting moment, produces maximum shear stress of 50 N/mm2, the angle of twist in radians, is

1. 0.001
2. 0.002
3. 0.0025
4. 0.003

0.0025

2. A simply supported beam which carries a uniformly distributed load has two equal overhangs. To have maximum B.M. produced in the beam least possible, the ratio of the length of the overhang to the total length of the beam, is

1. 0.207
2. 0.307
3. 0.407
4. 0.508

0.207

3. For a strongest rectangular beam cut from a circular log, the ratio of the width and depth, is

1. 0.303
2. 0.404
3. 0.505
4. 0.707

0.707

4. The ratio of crippling loads of a column having both the ends fixed to the column having both the ends hinged, is

1. 1
2. 2
3. 3
4. 4

4

5. The ratio of maximum and average shear stresses on a rectangular section, is

1. 1
2. 1.25
3. 1.5
4. 2.5

1.5

6. The ratio of moments of inertia of a triangular section about its base and about a centroidal axis parallel to its base, is

1. 1
2. 1.5
3. 2
4. 3

3

7. In plastic analysis, the shape factor for rectangular section, is

1. 1.4
2. 1.5
3. 1.6
4. 1.7

1.5

8. In plastic analysis, the shape factor for a triangular section, is

1. 1.5
2. 1.34
3. 2.34
4. 2.5

2.34

9. In plastic analysis, the shape factor for a circular section, is

1. 1.5
2. 1.6
3. 1.7
4. 1.75