B.Tech. Civil (Construction Management) / B.Tech. Civil (Water Resources Engineering)

Transcription

1 I B.Tech. Civil (Construction Management) / B.Tech. Civil (Water Resources Engineering) Term-End Examination 00 December, 2009 Co : ENGINEERING MECHANICS CD Time : 3 hours Maximum Marks : 70 Note : Attempt any five questions. All questions carry equal marks. Use of calculator is allowed. 1. (a) A weight of 2 kn is supported by two strings as shown in Fig. 1. Determine tension in the strings. 6+8=14 P 2 IN Fig. 1 (b) Determine the reactions at the supports for the beam loaded as shown in Fig N 40 N/m,60N 20 N/m C44QI.M24" m-) m-* E-1 m m-* Fig. 2 1 P.T.O.

2 2. (a) Find the value of 0 in Fig. 3 that will make the motion of 1000 N block down the plane to impend. All the surfaces have coefficient of friction as =14 10 N Fig. 3 (b) A uniform ladder rests with one end against a smooth vertical wall and the other one on a rough floor whose coefficient of friction is 0.75 and inclination to the ground is 45. Show that a man whose weight is equal to that of the ladder can just climb to the top of the ladder without its slipping?. (a) Determine the nature and magnitude of forces in members BD, CD and CE of the truss shown in Fig =14 20N 40N 14-2 m--0-12m12m14-2 m-*i Fig. 4

3 brass B steel ' F2M5 r ifam=c" A 20 kn m m 0.5 m-01 Fig. 7 Three marks A, B and C are made on a straight road at a distance of 100 m each. A car starting from rest moves with uniform acceleration. In its way, it covers distance AB in 10 seconds and BC is covered in 8 seconds. Calculate (i) the magnitude of acceleration, (ii) the velocities of car at A and B and (iii) the distance of A from starting point of car. 14 (a) Find the moment of inertia of an I section about an axis passing through the centroid and parallel to the horizontal flanges. The thickness of both flanges is 20 mm. Upper horizontal flange is 100 mm wide whereas lower flange is 200 mm wide. The total height of the section is 140 mm. 7+7=14 (b) A block of 500 N is supported by two springs with the block free to move up and down in the guides. The spring constants of the springs are 4 kn/m and 6 kn/m. Determine period of vibration, maximum velocity and acceleration when the block is 4 P.T.O.

4 pulled by 40 mm and released when springs support the block in series, springs support the block in parallel (a) A wheel is rotating about its axis with a constant angular acceleration of 1 rad/s2. If the initial and final angular velocities are 5.25 rad/s and 10.5 rad/s, determine the total angle turned through during the time interval this change of angular velocity took place. 7+7=14 (b) A motor cyclist wants to jump over a ditch shown in Fig. 8. Find the minimum velocity of motor cycle at A in km/hr. Also find the magnitude of velocity and the direction by which the motor cycle comes at B after clearing the ditch. en, Fig. 8 (a) A bullet of mass 81 gm and moving with a velocity of 300 m/s is fired into a wooden block and it penetrates in the block by 10 cm. If the bullet moving with same velocity is fired into a similar wooden block of 5 cm thick, with what velocity the bullet will come out of the block? 6+8=14 5 P.T.O.

5 (b) Draw shear force diagram and bending moment diagram of the given beam loaded as shown in Fig N. 10 N/m N 20 N/m C D E m-d<- 2.5 m 0.5m I*-1.5m_*.I Fig (a) A conical bar of length '1' and base diameter 'D' is shown in Fig. 6. The weight density of bar material is '2'. Determine elongation of the bar under its own weight. 6+8=14 Fig. 6 (b) A stepped composite bar made of brass and steel is shown in Fig. 7. Outer diameter of brass and steel portions are 25 mm and 10 mm respectively. The inner diameter of brass tube in CD portion is 15 mm. Determine (i) the segment in which the maximum stress is induced and the value of this stress, and (ii) the displacement of free end A.

6 (b) Two bodies of weight 1500 N and 1000 N are connected to two ends of a string which passes over a smooth pulley. The weight of 1500 N is placed on a rough horizontal surface while the weight 1000 N is hanging freely in the air. If the kinetic friction is 0.2 at all contact surfaces, find : the acceleration of the system and tension in the string - o 0 o - 6