Elements of Civil Engg. & Engg. Mechanics - Dec 2014

First Year Engineering (P Cycle) (Semester 2)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks. 1 (a) Briefly explain the role of civil engineers in the infrastructural development.(10 marks) 1 (b) In the traigle ABC, a force at 'A' produces a clockwise moment of 90 KN-m at B and an anticlockwise moment of 45 kN-m at C. Find the magnitude and direction of the force. (6 marks) 1 (c) Define force and its characteristics.(4 marks) 10 (a) What is projectile? Define the following terms briefly: i) Angle of projection
ii) Horizontal range
iii) Vertical height
iv) Time of flight(10 marks) 10 (b) A burglar's car starts at an acceleration of 2 m/s². A police vigilant party came after 5 s and continued to chase the burglar's car with a uniform velocity of 20 m/s. Find the time taken in which the police van will overtake the car.(10 marks) 2 (a) Explain the following with neat sketches:
i) Principle of superposition of forces
ii) Principle of transmissibility of forces.
iii) Couple and its characteristics.(10 marks) 2 (b) Draw typical cross section of a road and explain the parts.(10 marks) 3 (a) Four co-planar forces acting at a point are shown in Fig. Q3(a). One of the forces is unknown and its magnitude is shown by 'p'. The resultant has a magnitude of 500 N and is acting along the x-axis. Determine the unknown force 'P' and its inclination with x-axis.
  (8 marks) 3 (b) State and prove Varignon's theorem of moments.(6 marks) 3 (c) State and prove parallelgram law of forces.(6 marks) 4 (a) Determine the magnitude, direction of the resultant force for the force system as shown in Fig. Q4(a). Locate the resultant force with respect to point D.
  (8 marks) 4 (b) 26 kN force is the resultant of the two forces, one of which is as shown in Fig, Q4 (b). Determine the other force.
  (8 marks) 4 (c) Explain the principle of resolved parts.(4 marks) 5 (a) Determine the reactions at constant points for spheres A, B and C as shown in Fig. Q5 (a). it is given that W_A-W_B=4 kN, W_C-6kN, d_A=d_D=500mm, d_c=800mm
  (12 marks) 5 (b) For the beam with loading shown in Fig. Q5(b). determine the reactions at the supports.
  (8 marks) 6 (a) State and prove Lami's theorem.(8 marks) 6 (b) The ladder shown in Fig. Q6 (b) is 4 m long and is supported by a horizontal floor and vertical wall. The co-efficient of friction at the wall is 0.25 and at the floor is 0.50. The weight of the ladder is 200 N, considered concentrated at 'G'. The ladder supports a vertical load of 1000 N at 'C'. Determine the ractions 'A' and 'B' and compute the least value of '?' at which the ladder may be placed without slipping.
  (8 marks) 6 (c) State laws of friction.(4 marks) 7 (a) Determine the centroid of a semi-circular lamina of radius 'R' by method of integration.(8 marks) 7 (b) Determine the moment of inertia of the section shown in Fig. Q7(b) about its centroidal axes. Calculated the least radius of gyration for the section as well.
  (12 marks) 8 (a) State and prove parallel axis theorem.(6 marks) 8 (b) Locate the centroid of the shaded area as shown in Fig. Q8 (b)
  > (8 marks) 8 (c) Derive an expression for moment of inertia of a triangle with respect to horizontal centroidal axis.(6 marks) 9 (a) What is centrifugal force? What is super elevation?(4 marks) 9 (b) Determine the position at which the ball it thrown up the plane will strike the inclined plane as shown in Fig. Q9(b). The initial velocity is 30 m/s and angle of projection is $$ \tan^{-1} \left( \dfrac {4}{3} \right)$$ with horizontal.

(8 marks) 9 (c) A stone is dropped from the top of the tower 50 m high. At the same time another stone is thrown up from the tower with a velocity of 25 m/s, At what distance from the top and after how much time the two stones cross each other?(8 marks)