## 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/s^{2}. 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)