SECTION A. 8 kn/m. C 3 m 3m
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1 SECTION Question m 40 kn 5 kn 8 kn/m C 3 m 3m D 50 ll dimensions in mm Figure Q1(a) Figure Q1(b) The horizontal beam CD shown in Figure Q1(a) has a uniform cross-section as shown in Figure Q1(b). It is simply supported at and D. (a) (b) Calculate the second moment of area, I, and the elastic section modulus, Z, for the beam section about its major axis. [3 marks] For the loading shown: (i) (ii) draw the shear force and bending moment diagrams, showing all principal values, [10 marks] calculate the maximum value of stress in the beam due to bending moment. [ marks] (c) Sketch the distribution of shear stress in the webs of the section. [ marks] (d) If the end of the beam were fixed at the support, describe the effect this would have on the deflection and bending moment distribution in the beam. [3 marks] Page of 9
2 Question 60 kn 0 kn C D 5m 3m Figure Q m The uniform beam, CD, shown in Figure Q is simply supported at its end, and propped at C. The beam carries concentrated loads of 60 kn at and 0 kn at D. The modulus of elasticity of the material of the beam is 05 x 10 3 N/mm and the second moment of area of the beam about the axis of bending is 10 x 10 6 mm 4. (a) Sketch the deflected form, indicating points where the deflection, slope or curvature are zero. [ marks] (b) Find the position and value of the maximum deflection of the beam. [18 marks] Page - - of 9
3 Question 3 40 kn 1.5 m 1.5 m 40 kn D 1.5 m E C Figure Q3 The pin-jointed truss shown in Figure Q3 lies in a vertical plane and is pinned to a vertical, rigid support at D and E. (a) Find the force in each member of the truss due to the loading shown. [14 marks] (b) Find the magnitudes and directions of the reactions at D and E. [6 marks] Page of 9
4 Question 4 (a) circular, hollow shaft has a cross-section with an external diameter of 100 mm and wall thickness 15 mm. It has a length of 1.5 m and transmits a torque of 15 knm when rotating at 300 revolutions per minute. The shear modulus, G, for the material of the shaft is 78 x 10 3 N/mm. Find: (i) the maximum shear stress in the shaft (ii) the angle of twist (iii) the power transmitted. [6 marks] [4 marks] [ marks] (b) solid circular shaft has the same length and mass. What torque would be transmitted if the maximum shear stress were the same as for the hollow shaft? [8 marks] Page of 9
5 SECTION Question 5 (a) Car is travelling along a straight motorway, while car is moving along a circular exit ramp of 100 m radius. The speed of is being increased at a rate of 1.6 m/s while car is moving with a constant velocity of 1 m/s. For the position shown, determine: (i) the velocity of relative to and its direction (to horizontal axis) from a velocity vector diagram or any other method. (ii) the acceleration of relative to and its direction [7 marks] V = m/s 30 o 100 m V = 1 m/s Figure Q5(a) (b) The bar O is supported at O and held in a vertical position by three cables C, D and E, figure Q5(b). If the tension in the cable E is T =453.5i -151.j 109.k, determine: (i) The magnitude of tension force. [1 marks] (ii) The moment of this vector T with respect to base of the pillar at O. [7 marks] z D T y C O 4.5 ll dimension in m O=1 m E 1.5 x Figure Q5 (b) Page of 9
6 Question 6 The van shown in Fig. Q6 has a mass 1800 kg with mass centre at G. The coefficient of friction between the tyres and the road surface is The brakes are applied when the van is travelling down a slop of 5 degrees and at this instant all the wheels are on the point of slipping. (a) Draw an appropriate free body diagram [4 marks] (b) Calculate: (i) the deceleration of the van [8 marks] (ii) the distance required that the van comes to rest from a speed of km/h [3 marks] (ii) the normal forces at the front and rear wheels km/h 0.6 m G 1.7 m 1.3 m θ = Figure Q6 Page of 9
7 Question7 The unbalanced 5 kg flywheel shown in Fig. Q7 has a radius of gyration of 0.18 m about an axis passing through its mass centre G. If it has a clockwise angular velocity of 8 rad/s at the instant shown, draw the free body diagram and mass acceleration diagram. lso determine: (a) the angular acceleration of the flywheel [10 marks] (b) the horizontal and vertical reaction forces at O ω = 8 rad/s 0.15 m 10 N.m O G Figure Q7 Page of 9
8 Question 8 In the forging device shown in Fig. Q8, The 40 kg hammer is lifted to position 1 and released from rest. It falls and strikes a 0 kg pile embedded in the wood when it is in position. The two identical springs have a constant of k=1500 N/m, and the tension in each spring is 150 N when the hammer is in position. Neglect friction between the hammer and slide bars and calculate: (a) the unstretched length of the springs. (b) the velocity of the hammer just before it strikes the pile by using the conservation of energy. [10 marks] (c) the velocity of pile immediately after the impact if the hammer velocity is reduced to 1.7 m/s. Hammer mm k k 400 mm Pile Figure Q8 DT SHEET Page of 9
9 PRT I MECHNICS OF SOLID One-dimensional motion ds ds d s v = a = = dt dt dt Constant velocity, a=0 s = s o +vt Constant cceleration v=v o +at s=s o +v o t+ 1 at dv = v ds Curvilinear motion Cartesian (rectangular) co-ordinates Position vector r =xi+yj+zk Velocity vector v = v i+ x v y j+ v z k = x& i+ y& j+ z& k cceleration a = a i+ x a y j+ a z k = & x& i+ & y& j+ & z& k Normal (n) and tangential (t) coordinates v = v o +as velocity v = v e t = rω e t = rθ & e t cceleration a = e n + v& e r t a n =v /r a t = v& =dv/dt a = a n + a t Radial-Transverse (Polar) coordinates Position vector r = r e r Velocity vector v = r& e r + rθ & e θ cceleration a = (& r& - rθ & )e r + ( r& & θ + rθ & ) e θ a r =( & r& - rθ & ) a θ =( r& & θ + rθ & ) a = a + r v a θ Rigid body plane motion M G =I G α M o =I G α+ma G d Energy equation U= KE + PE+ SE where KE=0.5mv, PE =mgh and Strain energy SE = V e = 1 k x Kinetic energy of rigid body in plane motion KE= T = 1 mvg + 1 ΙG ω Coefficient of Restitution e = v u v u = relative relative velocity velocity of of separation approach Moment of a Force M=r x F= (rfsinθ) e p Page of 9
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