Unit – I

Q1.

Radius of ball 1=100mm and ball 2=50mm ; Weight of ball 1=2000N and ball 2 =800N Determine reactions at A, B, C, D

Q2.

Three uniform, homogeneous and smooth spheres A, B & C weighing 300N, 600N & 300N respectively and having diameters 800mm, 1200mm & 800mm respectively are placed in a trench as shown in Fig. above. Determine the reactions at the contact points P, Q, R and S

Q3.A rigid circular roller of weight 5000N rest on a smooth inclined plane and is held in position by a chord AC as shown in Fig below. Find the tension in the chord if there is a horizontal force of magnitude 1000N acting at C.

Q4.

A Cylinder 1m diameter and 10kg mass is lodged between cross pieces thatmakes an angle of 600 with each other As shown in Fig. above. Determine theTension in the horizontal rope DE.

Q5.Find support reactions at A,E,C& D.

Q6.

Q7.

Find x to keep the bar AB in equilibrium.

Q8.Determine the magnitude and direction of the resultant of the following set of forces acting on a body.(i) 200N inclined 30 degree with east towards north(ii) 250N towards the north(iii) 300N towards North West(iv) 350N inclined at 40 degree with west towards south.What will be the equilibrant of the force system?Q9.Find the resultant of forces 2, 3, 4, 5, 6 N that act at an angular point of a regular hexagon towards the other angular points taken in order.Q10.A uniform wheel of 50cm diameter and 1kN weight rest against a rigid rectangular block of thickness 20 cm as shown in Fig.. Considering all surfaces smooth, determine(a) Least Pull to be applied through the centre of wheel to just turn it over the corner of the block.(b) Reaction of the block

Q11.

Fig below shows a sphere resting in a smooth V shaped groove and subjected to a spring force. The spring is compressed to a length of 100mm from its free Length of 150mm. If the stiffness of spring is 2KN/mm. Determine the contact reactions at A and B.

Q12.Determine the resultant of the forces acting tangential to the circle of radius 3m as shown in Fig given below. What will be its location with respect to the centre of the circle?

Q13.

A rigid bar is subjected to a system of parallel forces as shown in Fig given below.Reduce this system to(i) A single force (ii) a single force –moment system at A(iii) A single force-moment system at BQ14.Forces equal to P, 2P, 3P and 4P act along the sides AB,BC,CD and DA of a square ABCD. Find the magnitude, direction and line of action of the resultant.

Q15.

The frictional less pulley A shown in Fig is supported by two bars AB and AC which are hinged at B and C to a vertical wall. The flexible cable DG hinged at D goes over the pulley and supports a load of 20KN at G. The angles between various members are shown in Fig. Determine the forces in AB and AC. Neglect the size of pulley.

Q16.

One end of a split horizontal beam ACB is fixed into wall and the other end B rests on a roller support. A hinge is at point A.A crane of weight 50KN is mounted on the beam and is lifting a load of 10KN at the end L. The C.G of the crane acts along the vertical line CD and KL=4m.Neglect the weight of the beam, find the reaction / moments at A &B.

Q17.

. The cross-section of a block is an equilateral triangle. It is hinged at A and rests on a roller at B. It is pulled by means of a string attached at C. If the weight of the block is Mg and the string is horizontal, determine the force P which should be applied through string to just lift the block off the roller.Q18.A 12m boom AB weighs 1KN, the distance of the centre of gravity G being 6m from A. For the position shown, determine the tension T in the cable and the reaction at B.

FRICTION

Q19.A body of weight 100N rest on a rough horizontal surface (µ=03) and is acted upon by a forceapplied at an angle of 30 degree to the horizontal.(a)What force is required to just cause the body to slide over the surface?

(b) Proceed to determine the inclination and magnitude of minimum force required to set the block in to impending motionQ20.wooden block of weight 50N rest on a horizontal plane. Determine the force required to just (a) pull it and (b) push it. Take µ=04 between the mating surface. Comment on the result.Q21.A body resting on a rough horizontal plane required a pull of 24N inclined at 30 degree to the plane just to move it. It was also found that a push of 30N at 30 degree to the plane just enough to cause motion to impend. Make calculation for the weight of the body and the co-efficient of friction.Q22.Two blocks A & B of weight 4kN and 2 kN Respectively are in equilibrium as shown in Fig.. Presuming that co-efficient of friction between the blocks as well as between block and floor is 0.25, make calculation for the force P required to move the block A.

Q23.

Calculate the force P required to move the lower block B and tension in the cable. Take coefficient of friction at all the contact surfaces to be 0.3.Q24.State whether B is stationary with respect to ground and A or B is stationary with respect to A. Determine the minimum value of weight W in the pan so that motion starts .coefficient of friction between ground and block is 0.1 and between block A and B is 0.28.

Q25.

What should be the value of è in Fig given below which will make the motion of 900N block down the plane to impend? Coefficient of friction all contact surfaces is 1/3.Q26.What is the value of P in the system as shown in Fig to cause the motion to impend? Assume the pulley is smooth and coefficient of friction between the other contact surfaces is 0.2.

Q27.

Find whether block A is moving up or down the plane in Fig. for the data given below. Weight of block A and B are 300N and 600N respectively. Coefficient of friction between plane AB and block A is 0.2.Coefficient of friction between plane BC and block AB is 0.25.Assume the pulley is smooth.

Q28.Two identical blocks A and B are connected by a rod and they rest against vertical and horizontal planes respectively as shown in Fig. If sliding impends when θ=45 degree, determine the coefficient of friction, assuming it to be the same for both floor and wall.

Q29.

What is the least value of P to cause motion to impend? Assume the coefficient of friction to be 0.20.Q30.Block A of mass 12kg and block B of mass 6kg are connected by a string passing over a smooth pulley. If µ =0.12 at all surfaces of contact find smallest value of P force to maintain equilibrium.

Q31.

Two block having weights W1 and W2 are connected by A string and rest on horizontal plane as shown in Fig.If the angle of friction for each block is φ, find magnitude and direction of least force P.

Q32.Find whether a cylinder of 800N will slip or not under the action of a tangential force of 200N as shown in Fig. Take µ=0.5 at all contact surfaces.

Q33.

Two blocks connected by a horizontal link AB are supported on two rough planes as shown in Fig. The coefficient of friction for the block on the horizontal plane is 0.4. the limiting angle of friction for block B on the inclined plane is 20 degree. What is the smallest weight W of the block A for which equilibrium of the system can exist if weight of block B is 5kN.Q34.Two blocks A and B each weighing 1500N are connected by a uniform horizontal bar which weighs 1000N.If the angle of limiting friction under each block is 15 degree, find the force P directed parallel to the 60 degree plane that will cause motion impending to the right.

Q35.

The mass of A is 23 kg and the mass of B is 36kg.The coefficient of friction are 0.6 between A & B,0.2 between B and the plane and 0.3 between the rope and fixed drum. Determine the maximum mass of M before motion impends.Q36.Determine the force P to cause motion to impend.µ=0.25 at all contact contact surfaces. The pulley is frictionless.

Q37.

Determine the coefficient of friction between the rope and pulley if the coefficient of friction between the block A and the plane is 0.28.Q38.A uniform ladder, 5 m long weighs 180 N. it is placed against a wall making an angle of 600 with floor. The co-efficient of friction between the wall and the ladder is 0.25 and between the floor and ladder is 0.35. The ladder has to support a man 900N at its top. Calculate(i) The horizontal force P to be applied to the ladder at the floor level to prevent slipping. (ii) If the force P is not applied, what should be the minimum inclination of the ladder with the horizontal so that there is no slipping of it with the man at its top?

Q39.A uniform ladder of length 10m and weighing 20N is placed against a smooth vertical wall with its lower end 8m from the wall. In this position the ladder is just to slip. Determine(a) The co-efficient of friction between the ladder and floor.(b) Frictional force acting on the ladder at the point of contact between ladder and floor.Q40.A ladder of length “L” rests against a wall, the angle of inclination being 45 0. If the co-efficient of friction between the ladder and the ground and that between the ladder and the wall be 0.5 each. What will be the maximum distance along the ladder to which a man whose weight is 2 times the weight of ladder may ascend before the ladder begins to slip?

UNIT –II

DRAW SHEAR FORCE AND BENDING MOMENT DIAGRAM OF THE FOLLOWING LOAD DIAGRAM.

CANTILEVER

Q1

Q2.

Q3.

Q4.

OVER HANGING BEAM Q5.

Q6.

SIMPLY SUPPORTED BEAMQ7.

Q8.

Q9.

Q10.

Q11.

Q12.

UNIT:V

SIMPLE STRESS & STRAINQ.1 A steel bar 2.4m long and 30mm square is elongated by a load of 500N.If Poisson ratio is 0.25, find the increase in volume .Given E=0.2×106 N/mm2

Q.2. The piston of a steam engine is 300mm in diameter and the piston rod is of 50mm diameter. The steam pressure is 1N/mm2. Find the stress in the piston rod and elongation in a length of 800mm. Take E=200GPa.

Q.3. Three bars of equal length and having cross-sectional areas in the ratio 1:2:4 are all subjected to equal load. Compare their strain energy.

Q.4. A metallic rectangular rod 1.5m long and 40mm wide and 25mm thick is subjected to an axial tensile load of 120KN. The elongation of the rod is 0.9mm. Calculate the stress, strain and modulus of elasticity.

Q.5. One meter long steel rod of rectangular section 80mm x 40mm is subjected to an axial tensile load of 200 KN. Find the strain energy and maximum stress produced in it when the load is applied gradually. Take E=2x105 N/mm2.

Q.6. A circular rod of 100mm diameter and 500mm long is subjected to a tensile force of 1000KN. Determine the modulus of rigidity, bulk modulus and change in volume if poison’s ratio is 0.3 and E=2x105 N/mm2.

Q.7.The piston of a steam engine is 300mm in diameter and the piston rod is of 50mm diameter. The steam pressure is 1 N/mm2.Find the stress in the piston rod and elongation in a length of 800mm.Take:E=200GPa.

Q.8.A bar of 25mm diameter is subjected to a pull of 60kN.The measured extension over a gauge length of 250mm is 0.15mm and change in diameter is 0.004mm. Calculate the modulus of elasticity, modulus of rigidity and Poisson’s ratio.

Q.9.A steel rod of diameter 50mm and 2.5m long is subjected to a pull of 100kN. To what length the rod should be bored centrally so that the total extension will increase by 15% under the same pull, the bore being 25mm diameter? Take E=200GN/m2

Q.10.The bar shown in Fig is subjected to a tensile load of 50kN. Find the diameter of the middle portion if the stress is limited to 130MN/ m2. Find also the length of the middle portion if the total elongation of the bar is 0.15mm .Take E=200GN/m2 .

Q11. Find stresses in all three parts of the bar if cross-sectional area of bar is 1000mm2

BENDING STRESS:1.A wooden beam of rectangular section is subjected to a bending moment of 5kNm.If the depth of the section is to be twice the breadth and stress in the wood is not to exceed 60N/m2, find the dimension of the cross-section of the beam

2.A rectangular beam with depth 150mm and width 100mm is subjected to a maximum bending moment of 300 kNm, find the maximum stress in the beam. 3.A rectangular beam of 200mm in width and 400mm in depth is simply supported over a span of 4m and carried a udl of 10K=kN/m. determine the maximum bending stress in the beam.

4.A rectangular beam of cross-section(300x200) mm2 is simply supported over a span of 5m.What uniformly distributed load the beam may carry (i)when the height is 300mm (ii) when the height is 200mm.The bending stress is not to exceed 130N/ mm2

5.A beam made of C.I. having a circular section of 50mm external diameter and 25mm internal diameter is supported at two points 4m apart. The beam carries a concentrated load of 100N at the centre. Find the maximum bending stress in the beam?

6.A hollow circular bar having outside diameter twice the inside diameter is used as a beam subjected to a bending moment of 50kNm.Determine the inside diameter of the bar if allowable bending stress is limited to 100MN/ m2 7. Find the dimension of the strongest rectangular beam that can be cut from a log of 250mm diameter.

8. Three beams have the same length, same stress and same bending moment. The cross-sections of the beams are a square, a rectangle with depth twice the width and a circle. Determine the ratios of weight of circular and rectangular beams with respect to that of square beam.9.For a given stress compare the moment of resistance of a beam of square section when placed (i) with two sides horizontal and(ii) with its diagonal horizontal.

10.A water mains 500mm external diameter and 25mm thick is full of water and is freely supported for 20mspan. Determine the maximum bending stress induced in the pipe metal if the weight of water and that of pipe is taken in to account. The specific weight of water and steel as 10kN/ m3and 75kN/m3 .

11.A cantilever with a constant breadth of 100mm has a span of 2.5m.It carries a uniformly distributed load of 20kN/m. Determine the depth of the section at the middle of the length of the cantilever and also at the fixed end if the stress remains the same throughout and is equal to 120 MN/ m2

12.A simply supported beam 1m long and (20mmx20mm) in cross-section fails when a central load of 600N is applied to it. What intensity of UDL would cause failure of a cantilever beam 2m long and 400mmwide x 80mm deep made of same material.

13.Deterrmine the longest span of a simply supported beam carry a UDL of 6kN/m without exceeding a bending stress of 120MN/ m2 .The depth and moment of inertia of the symmetrical I-section are 20cm and 2640cm4 respectively.

14.. A simply supported beam 200mm wide and 250mm deep carries a UDL of intensity 800N/mm over its entire span of 4m find maximum stress developed in the beam.

15. For I section given flange = 250mm wide and 25mm thick, web = 15mm thick, over all depth = 600mm. The beam has span of 10m and carries a UDL of intensity 50KN/m for the entire span. Find the stress produced due to bending.

TORSIONQ.1. Compare the strength between hollow and a solid circular shaft for same material, same length and same weight.

Q.2. The diameter of a shaft is 20cm. Find the safe maximum torque which can be transmitted by the shaft, if the permissible shear stress in the shaft material is 4000N/cm2

and permissible angle of twist is 0.2º per meter length. Take G= 8x106 N/cm2. if the shaft rotates at 320rpm what maximum power can be transmitted by the shaft .

Q.3.If the maximum torque transmitted by a solid shaft exceeds the mean by 30% in each revolution, find a suitable shaft diameter to transmit 75 kW power at 200rpm.Take allowable shear stress as 70 N/ mm2 .

Q.4.What external and internal diameter is required for a hollow shaft to transmit 50kW of power at 300rpm if the shear stress is limited to 100MN/ m2.Take outside diameter to be twice of inside diameter.

Q.5.Calculate the diameter of a circular shaft to transmit 75 kW at 200rpm.Allowable shear stress is restricted to 50MN/ m2 and twist 1o in 2 m shaft length .Take G=400GPa

Q.6.Compare the weight of a solid and hollow shaft of same material, same length, same torque and same stress. The internal diameter of hollow shaft is 2/3 of its outer diameter.

Q.7.A hollow shaft of 3m length is subjected to a torque such that the maximum shear stress produced is 75MPa.The external and internal diameters of the shaft are 150mm and 100mm respectively. Find the shear stress at the inside surface.Take:G=75MPa

Q.8.A solid circular shaft is required to transmit 200kW power at 100rpm.Determine the diameter of the shaft if permissible shear stress is 60 N/mm2.calculate the energy stored per meter length of the shaft.Take:G=100kN/mm2

Q.9.A solid circular shaft is to transmit power 160kW at 180rpm.What will be the suitable diameter of this shaft if the permissible stress in the shaft material should not exceed 2MPa and twist per meter length should not exceed 2o.Take:G=200GPa