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UNIT - I 1. What is meant by factor of safety? [A/M-15] It is the ratio between ultimate stress to the working stress. Factor of safety = Ultimate stress Permissible stress 2. Define Resilience. [A/M-15] The capability of a strained body to recover its size and shape after deformation caused especially by compressive stress 3. Define Hooke Law. [N/D-16] It states that when a material is loaded, within its elastic limit, the stress is directly proportional to the strain. Stress α Strain σαe σ = Ee E = σ /e N/mm2 where E is young’s modulus σ is stress ande is strain 4. Define Poisson’s ratio. [N/D14, 16] The ratio of lateral strain to the longitudinal strain is a constant for a given material, when the material is stressed within the elastic limit. This ratio is called Poisson’s ratio and it is generally denoted by 1/m (or) µ µ= 5.
What is meant by Poinsson’s ratio? Which material has the higher value of Poisson’s ratio? [N/ D15 ] When a body is stressed, within its elastic limit, the ratio of lateral strain to the longitudinal strain is constant for a given material, which is known as Poisson’s ratio. Poisson’ ratio (μ or 1/m) = Lateral strain / Longitudinal strain The shear stress is directly proportional to shear strain.
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N = Shear stress / Shear strain 6. Define – Strain Energy. [N/D-15] Whenever a body is strained, some amount of energy is absorbed in thebody. The energy which is absorbed in the body due to straining effect is known as strain energy. 7. Define – Modulus of Elasticity. [M/J-14] It is defined as the ratio between the stress to strain is a constant when a material is loaded within an elastic limit.
8. Define – Modulus of rigidity. [M/J14] It is defined as the ratio between the shear stress to shear strain is a constant when a material is loaded within an elastic limit. 9. Define – Bulk Modulus. [N/D-14] It is defined as the ratio between the direct stress to volumetric strain is a constant when a material is loaded within an elastic limit. 10. What are [M/J-13] 1. Tensile stress 2. Compressive stress 3. Shear stress
the
three
types
of
stresses?
11. Define – Lateral Strain and Longitudinal Strain [A/M10] When a body is subjected to axial load P, the length of the body is increased. The ratio of axial deformation to the original length of the body is known as longitudinal strain. The strain, at right angle to the direction of the applied load, is called lateral strain. 12. State the relationship between Young’s Modulus and Modulus of Rigidity. E = 2G (1 + 1/m) where E is Young’s modulus G is modulus of rigidity and 1/m is Poisson’s ratio
[M/J -10, 14]
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1. (a) when a square bar of certain material subjected to an axial pull of 160 kN, the measured extension on a gauge length of 200mm is 0.1mm and the decrease in each side of the square bar is 0.005mm. Calculate the modulus of Elasticity, shear modulus and bulk modulus for a material. [A/M-15] [N/D-14]
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2. (b) A solid cylinder brass bar of 25mm diameter is enclosed in a steel tube of 50mm external diameter and 25mm internal diameter. The bar and the tube are both initially 1.5mm long and are rigidly fastened at both ends. Find the stresses induced in the two materials when the assembly is subjected to an increase in temperature of 500C . Take coefficients of thermal expansion of steel as 12x10-6/oC and that of brass is 18x10-6/oC. Modulus of steel as 200 GPa and modulus of elasticity of brass as 100 GPa. [A/M-15] , [N/D-14]
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3. (a) A steel bar 300mm long, 40mm wide and 25mm thick is subjected to a pull of 180kN. Determine the change in volume of the bar. Take E= 2x 105 N/mm2 and l/m= 0.3(16) 13, 16]
[N/D-
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5.
4. (b) An cylindrical shell 1 m diameter and 3 in length is subjected to an internal pressure, of 2 MPa. Calculate the minimum thickness if the stress should not exceed 50 MPa. Find the change in diameter and volume of the shell. Poisson’s ratio = 0.3 and E= 200kN/mm2. (16) [N/D-14,16]
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(a) A composite bar is made with copper flat of size 50mmx 30mm and a steel flat of 50 mm x 40mm of length 500mm each placed one over the other. Find the stress induced in the material, then the composite bar is subjected to an increase in temperature of 90,C. Take coefficients of thermal expansion of steel as 12x10-6/oC and that of brass is 18x10-6/oC. Modulus of steel as 200 GPa and modulus of elasticity of brass as 100 GPa. [N/D-15], [A/M-12] 6.
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7. (b) a thin cylinder sheel, 2m long has 800mm internal diameter and 10mm thickness. If the shell is
subjected to an internal pressure of 1.5 MPa, find (i) the hoop and longitudinal stresses developed, (ii) maximum shear stress induced and (iii) the changes in diameter, length and volume. Take modulus of elasticity of the wall material as 205 GPa and Poisson’s ratio as 0.3. [N/D-15], [M/J – 14]
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8. A flat steel plate of trapezoidal form of uniform thickness of 20 mm tapers uniformly from a width of
100 mm to 200 mm in a length of 800 mm. If an axial tensile force of 100 kN is applied at each end, Find the elongation of the plate. [N/D-14]
9. A metallic bar 250 mm x 100 mm x 150 mm is loaded as shown in figure. (i) Find the change in
volume. Take E= 200 kN/mm2 and Poisson’s ratio = 0.25. Also find change the should be made in the 4000 kN, in order that there should be no change in the volume of the bar. [M/J-14]
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UNIT – II 1. How do you relate shearing force and bending moment? [A/M-15] Shear force at any cross section is defined as the algebraic sum of all the forces acting on any one side of the section. Bending moment at any cross section is defined as the algebraic sum of the moments of all the forces, which are placed on any one side of that section. 2.
Write a short note on location of point of maximum bending moment in a simply supported beam. [A/M-15] The bending moment is maximum, when shear force is zero. Equating the shear force at that point to zero, one can find out the distance x from one end. Then find the maximum bending moment at that point by taking moments of all the forces on right or left hand side.
3. List out any two assumptions in simple bending. [N/D-16] 1. The material of the beam is homogeneous and isotropic. 2. The beam material is stressed within the elastic limit and thus obey hooke‟s law. 3. The transverse section which was plane before bending remains plains after bending also. 4. Each layer of the beam is free to expand or contract independently about the layer, above or below. 5. The value of E is the same in both compression and tension. 4. Define the term’ moment of resistance’. [N/D-15] Due to pure bending, the layers above the N.A are subjected to compressive stresses, whereas the layers below the N.A are subjected to tensile stresses. Due to these stresses, the forces will be acting on the layers. These forces will have moment about the N.A. The total moment of these forces about the N.A for a section is known as moment of resistance of the section. 5. Define point of contra flexure? In which beam it occurs? [N/D-16],[A/M-14] It is the point where the B.M is zero after changing its sign from positive to negative or vice versa. It occurs in overhanging beam. 6. Define shear force and bending moment? [N/D-14, 15],[M/J-13] SF at any cross section is defined as algebraic sum of the vertical forces acting either side of beam. BM at any cross section is defined as algebraic sum of the moments of all the forces which are placed either side from that point.
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7. Define – Cantilever Beam and Simply Supported Beam (N/D 14) a) A beam with one end free and the other end fixed is called cantilever beam. b) A beam which is simply supported at its both ends is termed as simply supported beam. 8. Define – Uniformly Distributed Load. (A/M -14, 15) If a load, which is spread over a beam in such a manner that the rate of loading w is uniform throughout the length then it is called uniformly distributed load. 9. What are the types of beams? (A/M10) The types of beams are: a) Cantilever beam b) Simply supported beam c) Fixed beam d) Continuous beam e) Over hanging beam 10. What are the types of loads? (N/D 09) Types of loads are: a) Concentrated load or point load b) Uniformly distributed load c) Uniformly varying load
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1.(a) A 10m long beam ABC is simply supported at B and C over a span of 8m with end A being free. It carries point loads of 8 kN and 4kN at distances 3m and 5m from C. The beam also has uniformly distributed loads of intensity 4 kN/m for a distance of 4m starting from C and of 6 kN/m on AB. Draw shearing force and bending moment diagram indicating all principal values. [A/M-14, 15]
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2. (b) A fletched beam is made up of two timber joists, each 60mm wide and 100mm deep with a10mm thick and 80mm deep steel plate placed symmetrically between them on vertical faces. Determine the total moment of resistance of the section if the permissible stress in the timber joist is 7N/mm2. Take the modular ratio between steel and timber as 20. [A/M-15]
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3. (a) A simply supported beam of span 10 carries a concentrated load of 10 kN at 2 m from the left support and a UDL of 4 kN/m over the entire length. Sketch the shearing force and bending moment diagrams for the beam. (16) [N/D-09, 14, 16], [M/J-10,13],
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4. (b) Find the dimensions of a timber joist span 5m to carry a brick wall 200mm thick and 3.2m high, if the weight of brickwork is 19kN/m3 and the maximum stress is limited to 8 N/mm2. The depth is to be twice the width. (16) [N/D-16],[M/J-13]
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5. (a) An overhanging beam ABC of length 8m is simply supported at B and C over a span of 6m and the portion AB overhangs by 2m. Draw the shearing force and bending moment diagrams and determine the point of contra-flexure if it is subjected to UDL of 3 kN/m over th e portion BC. (16) [N/D-15]
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6. (b) A channel section made with 120mm x 10mm horizontal flanges and 160mmx 10mm vertical web is subjected to a vertical shearing force of 120 kN. Draw the shear stress distribution diagram across the section. (16) [N/D-15]
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11. A cantilever beam 1.5 meter long, fixed at A is carrying paint load of 1000 kg at B, C and c each and at distances of 0.5 meter, 1.0 meter and 1.5 meter from the fixed end. Calculate the shear force and bending moments at salient points. (N/D-09, 14)
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UNIT - III 1. A beam 3 m long, simply supported at its ends, is carrying appoint load at its center. If the slope at the ends is 10, find the deflection at the mid span of the beam.
[A/M-
15] The deflection at the MID SPAN is given by: yB = WL3/ 3EI yB = (25000 x 30003) / (3 x 2.1 x 105 x 108) yB = 10.71 mm The deflection at the free end is given by: yB = WL3/ 3EI yB = (25000 x 30003) / (3 x 2.1 x 105 x 108) yB = 10.71 mm 2. Define: conjugate beam.
[A/M-
15] Conjugate beam is an imaginary beam of length equal to that of original beam but for which load diagram is M/EI diagram. 3. Write the maximum value of deflection for a simply supported beam of constant EI, span L carrying central concentration loud W.
[N/D-16]
The deflection at the centre of a simply supported beam carrying a point load at the centre is given by: yc = – (WL3/ 48EI) 4. Where the maximum deflection will occur in a simply supported beam loaded with UDL of w kN/m run? [N/D-16] The deflection at the centre of a simply supported beam carrying a point load at the centre is given by: yc = – (WL3/ 48EI) 5. What are the advantages of Macaulay’s method over double integration method for beam deflection analysis?
[N/D-
15] Macaulay’s method is used in finding slope and deflection at any point of a beam. The points used in this method are: a) Brackets are to be integrated as a whole b) Constants are written after the first term c) The section, for which BM is to be found, should be taken in the last part
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6. What is meant by propped cantilever?
[N/D-
15] A cantilever which has an additional support at the free end is termed as propped cantilever. 7. What are the methods for finding out the slope and deflection at a section? (N/D -14) The important methods used for finding out the slope and deflection at a section in a loaded beam are: a) Double integration method b) Moment area method c) Macaulay’s method The first two methods are suitable for a single load, whereas the last one is suitable for several loads. 8. What is a conjugate beam? (A/M-15) Conjugate beam is an imaginary beam of length equal to that of original beam but for which load diagram is M/EI diagram. 9. A cantilever of length 4 m carriesa uniformly varying load of zero at the free end and 50 kN at the fixed end. If I = 108 mm4 and E = 2.1 x 105 N/mm2, find the deflection at the free end. (A/M-13) The deflection at the free end is given by: yB= WL4/ 30EI yB = (50 x 40004) / (30 x 2 x 105 x 103) yB= 21.33 mm 10. Write an expression for deflection by moment area method. The shear stress at a fiber in a section of a beam is given by: y = Ax / EI where A is area of BM diagram between A and B and x is distance of CG of area from B
(A/M-10)
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PART B 1.
(a) A beam AB of span 7m ios simply supported at its ends A and B. it carries appoint load of 10kN at
a distance of 3m from the ends A and a UDL of 6 kN/m over rigid half span length. Determine (i) the maximum deflection in the beam and (ii) slopes at the ends. Take EI= 10000 kN-m2. [A/M-13,15],[N/D-
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14]
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2.
(b) a cantilever of length ‘L’ is carrying a load of W at the free end and another load of 2 W at its mid span. Determine the slope and deflection of the cantilever at tehe free end using conjucate beam method. Take the flexural rigidity for the half length from fixed end as twice that of the remaining length. [A/M-15], [N/D-15]
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3. (a) A SSB of span 6m carries UDL 5 kN/m over a length of 3m extending from left end. Calculate deflection at mid- span. E= 2x105 N/mm2, I= 6.2 x 106 mm4
[N/D-15, 16],
[M/J-14]
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4. (b) A cantilever beam 4m long carries a load of 500 kN at a distance of 2m from the free end, and a load of W at the free end. If the deflection at the free end is 25mm, calculate the magnitude of the load W, and the slope at the free end. E= 200kN/mm2. I= 5x 107 mm4. [N/D-14, 16]
5. A beam of length 6 m is simply supported at its ends and carries two point loads of 48 kN and 40 kN at a distance of 1 m and 3 m respectively from the left support. Find (i) Deflection under each load (ii) Maximum deflection (iii) The point at which the maximum deflection occurs. Take E = 2 10 N/mm , 5 2 I = 6 4 8510 mm. [M/J-10,12], [N/D-09]
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UNIT - IV 1. Define – Polar Modulus
[A/M-
15] Polar modulus is the ratio between polar moment of inertia and radius of the shaft. Polar Modulus = Polar moment of inertia (J) / Radius (R) 2. What is a composite shaft? [A/M-15] Sometimes a shaft is made up of composite section i.e. one type of shaft is sleeved over other types of shaft. At the time of sleeving, the two shafts are joined together in a way that the composite shaft behaves like a single shaft. 3. Why hollow circular shafts are preferred over solid circular shafts.
[N/D-16]
The torque transmitted by the hollow shaft is greater than the solid shaft. For the same material, length and given torque, the weight of the hollow shaft will be less compared to that of solid shaft. 4. Define Torsional rigidity. [N/D-16] When a pair of forces of equal magnitude but opposite directions act on a body, it tends to twist the body. The resistant to that magnitude is called torsional rigidity. 5. Write the expression for strain energy stores in a shaft of uniform section subjected to torsion.
[N/D-15] 6. Mention the various types of springs.
[N/D-
15],[M/J-10] Various types of springs are: a) Helical springs b) Spiral springs c) Leaf springs d) Disc spring or Belleville springs 7. Write the expression for power transmitted by a shaft. The expression for power transmitted by a shaft is: P = 2πNT/60 where N is speed in rpm and T is torque 8. Classify the helical springs. The helical springs are classified as:
(N/D -14)
(A/M-10)
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a) Close – coiled or tension helical spring b) Open – coiled or compression helical spring 9. Write the torsion equation. The torsion equation is given as: T/J = Cθ/L = q/R where T is torque J is polar moment of inertia C is modulus of rigidity L is length θ is angle of twist q is shear stress and R is radius
(M/J-13)
1. (a) The maximum torque may be 1.5 times of the mean torquie and the shear stress in the shaft not to exceed 50 N/mm2. Determine the diameter required if (i) the shaft is solid (ii) the shaft is hollow with external diameter twice the internal diameter. Take modulus of rigidity = 80kN/mm2.
[A/M-
12, 15]
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2. (b) A bumper is to be designed to arrest a wagon weighing 500 kN moving at 80 km/hour. Details of buffer available are diameter= 30mm, mean radius =100mm, number of truss= 18, modulus of rigidity= 80kN/mm2, and maximum compression permitted= 200mm. determine the number of springs required for the buffer. [A/M-15]
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3. (a) A hollow shaft is to transmit 200kW at 80 rpm. The shear stress in the shaft should not to exceed 70 N/mm2 and internal diameter is 0.5 of the external diameter. Find the external and internal diameters assuming that maximum torque is 1.6 times the mean. (16)
[N/D-16]
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4. (b) A closed coil helical spring is to deflect 1mm under the axial load of 100N at shearing stress of 980 N/mm2. The spring is to be made of round wire having rigidity modulus of 80x10 4 N/mm2. The mean diameter of the spring is to be 10 times the diameter of the wire. Find the diameter and length of the wire necessary to form the spring?
(16) [N/D-14, 16]
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5. (a) A shaft is required to transmit a power of 210 kW at 200 rpm. The maximum torque may be 1.5 times the mean torque. The shear stress in the shaft should not to exceed 45 N/mm 2 and the twist 1o per meter (i) the shaft is solid (ii) the shaft is hollow with external diameter twice the internal diameter. Take modulus of rigidity= 80 kN/mm2. 15],
(16)
[N/D[M/J-13]
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6. (b) A bumper is to be designed to arrest a wagon weighing 500 kN moving at 18 km/hour. Details of buffer available are diameter= 30mm, mean radius =100mm, number of truss= 18, modulus of rigidity= 80kN/m2, and maximum compression permitted= 200mm. Find the number of springs required for the buffer.(16) [N/D-14, 15]
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7. An open coil helical spring made of 10 mm diameter wire and of mean diameter 10 cm has 12 coils, angle of helix 15 degrees. Determine the axial deflection and the intensities of bending and shear stress
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under a load of 500 N. Take C as 80 kN/mm2and E = 200 kN/m2. 12, 14)
(N/D-
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UNIT - V 1.
What is tension coefficient? The force per unit length of a member is known as tension coefficient. T = F/ L where T is tension coefficient F is force and L is length of the member
[A/M-15]
2. What are the assumptions made in analysis of a pin-joined plane truss?[A/M-15] The assumptions are a. The frame is a perfect frame. b. The frame carries a load at the joints. c. All the members are pin-jointed. 3. What is the use of Mohr’s circle?
[N/D-14, 16],[M/J-13]
Mohr’s circle is used to find normal, tangential and resultant stresses on an oblique plane 4. What are Deficient and Redundant frames?
[N/D-16]
If the number of members are more than (2j – 3), then the frame is known as redundant frame. 5. What are principal planes?
[N/D-15]
The planes, which have no shear stress, are known as principal planes. These planes carry only normal stresses. 6. What are the assumptions made in finding out the forces in a frame? The assumptions made in finding out the forces in a frame are: a) The frame is perfect b) The frame carries load at the joints c) All the members are pin-jointed 7. What are the methods available for the analysis of a frame? The following are the methods available for the analysis of a frame: a) Methods of joints b) Methods of sections c) Graphical method
[N/D-15]
(N/D -14), [M/J-13]
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1. (a) At a point in the web of a girder the bending stress is 60 N/mm2 tensile and the shearing stress at the same point is 30 N/mm2. Determine, (i) principal stresses and principal planes, (ii) maximum shear stress and its orientations.
[A/M-12,15],[N/D-10]
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2. Analyze the simply supported truss as shown in Fig. Q.15(b) by method of joints.
[A/M-12,15]
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3. (a) An element has a tensile stress of 600 N/mm2 acting on two mutually perpendicular planes and shear stress of 100 N/mm2 on these planes. Find the principal stress and maximum shear stress. (16)
[N/D-16],[M/J-09]
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4. (b) Determine the forces in all members of a cantilever truss as shown in Fig.
(16) [N/D-16],[A/M-13]
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5. (a) The stress on two mutually perpendicular planes through a point on a body are 30 MPa ansd 20 MPa both tensile, along with a shear stress of 15 MPa, find (i) The position of principal p[lanes and stress across them. (ii) The planes of maximum shear stress (iii) The normal and tangential stress son the plane of maximum shear stress. (16)
[N/D-13,15]
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6. (b) Analyze the cantilever truss as shown in Fig. Q.15(b) by method of sections.
(16) [N/D-15,13]
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