SPPU Strength of Materials - December 2016 Exam Question Paper

SPPU Mechanical Engineering (Semester 4)
Strength of Materials
December 2016

Total marks: --
Total time: --

INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1(a) A square bar of 20 mm side is held between two rigid plates and loaded by an axial force P equal to 450 kN as shown in Fig. 1. Find the reactions at the ends A and C and the extension of the portion AB Take E = 200 Gpa.
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Solve any one question fromQ.1(a,b) and Q.2(a,b)

1(a) Calculate the vertical diplacement of point C for the structure shown in Fig.1. Neglect the weight of the bar and beam.
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Solve any one question.Q1(a,b) Q2(a,b)

1(a) CalCulate the vertical diplacement of point C for the structure shown in Fig.1. Neglect the weight of the bar and beam.
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1(a) A square bar of 20 mm side is held between two rigid plates and loaded by an axial force P equal to 450 kN as shown in Fig.1. Find the reactions at the ebds A and C and the extension of the portion AB. Take E = 200 Gpa.
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1(b) Draw shear force and bending moment diagrams for a beam shown in Fig .2.
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1(b) Draw the SFD and BMD for the beam as shown in Fig.2. Also find th point of contra-flexure if any.
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1(b) Draw the SFD and BMD for the beam as shown in Fig.2. Also fin the point of contra-flexure if any.
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1(b) Draw shear force and bending moment diagrams for a beam shown inn Fig.2.
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2( b) Shear force diagram for a loded beam is shown in Fig.3 Determine loading on the beam hence draw bending moment diagram. Locate point of contraflecture if any. All values are in kN.
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2(a) A steel rod of 20 mm diameter passes centrally through a copper tube of 50 mm external diameter and 49 mm internal diameter. The tube is closed at each end by rigid plates of negligible thickness. The nuts are tightended lightly home on the projecting parts of the rod. If the tempreature of the assembly is raised by 50°C, calculate the stresses developed in copper and steel. Take Efor steel and copper as 200 GN/m² and 100 GN/m² and a for steel and copper as 12&timmes;ao^-6 per °C and 18×10^-6 per °C.

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2(a) The bulk modulus for a material is 50 GPa. A 12 mm diameter rod of the material was subjected to an axial pull of 14 kN and the change in diametr was observed to be 3.6×10^-3mm.Calculate the Poisson's ratio and modulus of eleasticity for the material.

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2(a) The bulk modulus for a material is 50 Gpa.A 12 mm diameter rod of the material was subjected to an axial pull of 14kN and the change in diameter was observed to be 3.6×10^-3mm. Calculate th Poisson's ration and modulus of elasticity for the material.

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2(a) A steel rod of 20 mm diameter passes centrally through copper tube of 50 mm external diameter and 40 mm internal diameter. The tube is closed at each end by rigid plates of negligible thickness. The nuts are tightened lightly home on the projecting parts of the rod. If the tempreature of the assembly is raised by 50°C, calculate the stresses developed in copper ad steel. Take E for steel and copper as 200 GN/m² and 100GN/m² and a for steel and copper as 12×10^-6 per °C and 18×10^-6 per °C.

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2(b) Shear force diagram for a loaded beam is shown in Fig.3. Determine loading on the beam hence draw bending moment diagram. Locate point contraflecture if any. All values are is kN.
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2(b) Draw the SFD and BMD for the beam as shown in fig. 3. Also find the point of contra-flexure if any.
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2(b) Draw the SFD and BMD for the beam as shown in fig.3. Also find the point of contra-flexure if any.
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3(a) A cast iron bracket subject to bending has the cross-section of I form with uneual flanges. The dimensions of the section are shown in Fig.4. Find the position of the neutral axis and moment of inertia of the section about the netural axis. Ifthe maximum bending moment on the section is 40 MN mm, determine the maximum bending stress. What is the nature of the stress?
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Solve any one question fromQ3(a,b) and Q.4(a,b)

3(a) A steel channel of C section is used as a simply supported beam on a span of 4 m. The channel is to be designed for a working bending stress of 100 MPa. It has to carry a udl for the whole span. Calculate the permissible load when: i) The channel stands upright 225 mm high.
ii) The channel lies flat with the 225 mm horiziontal.
Take: A =3053 mm², l_xx=2547.9×10⁴mm⁴, l_xy=209.5×10⁴mm⁴, Position of N.A. for horiziontal case is 24.6 mm from the web outermost fibre, overall depth of the channel 225 mm and flange width 90 mm.

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Solve any one question.Q3(a,b) Q4(a,b)

3(a) A steel channel of C section is used as a simply supported beam on a span of 4m. The channel is to be designed for a working bending stress of 100MPa. It has to carry a udl for the whole span. Calculate the permissible load when:
i) The channel stands upright 225mm high.
ii) The channel lies flat with the 225 mm horizontal. Take:
A=3053 mm²,
l_xx=2547.9×10⁴mm⁴,
l_yy=209.5×10⁴mm⁴, Position of N.A. for horizontal case is 24.6 mm from the web outermost fibre, overall depth of the channel 225mm and flange width 90mm.

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3(a) A cast iron bracket subject to bending has the cross- section I-form with unequal flanges. The dimensions of the section are shon in Fig.4. Find the position of the neutral axis and moment of intertia of the section about the neutral axis. If the maximum bending moment on the section is 40 MN mm, determine the maximum bending stress. What is the nature of the stress?
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3(b) A cantilever 75 mm wide and 200 mm deep is loaded as shown in Fig.5 Find the slope and deflection at B. Take E = 200 Gpa.
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3(b) Find t the deflection at C for the beam loaded as shown in Fig. 4. Take EI = 40, 000 kNm²
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3(b) Find the deflection at C for the beam loaded as shown in Fig.4. Take EI=40,000 kNm².
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3(b) A contilever 75 mm wide and 200 mm deep is loaded as shown in Fig.5. Find the slope and deflection at B. Take E = 200GPa.
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4(a) A simply supported beam carries a UDL of 25 kN/m over the entire span of the beam is shown in Fig.6. If the maximum bending stress is 60 Mpa, find the span of the beam. Also find the maximum shear stress developed in the section. Draw the shear stress distribution diagram.
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4(a) Calculate the shear stress at the salient positions and also draw the shear stress distribution diagram for the beam section shown in Fig. 5.
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4(a) Calculate the shear stress at the salient positions and also draw the shear stress distribution diagram for the beam section shown in Fig.5.
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4(a) A simply supported beam carries a UDL of 25 kN/m over entire span of the beam is shown in Fig.6. If the maximum bending stress is 60 Mpa. Find the span of the beam. Also find the maximum shear stress developed in the section. Draw the shear stress distribution diagram.
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4(b) A wagon 35 weighing 35 kN is attached to wire rope and moving down an inclined at speed of 3.6 kmph, when the rope jams and wagon is suddenly brought to rest. If the length of rope is 60 m at the time of sudden stoppage, calculate the maximum instantaneous stress and maximum instantaneous elongation produced. Diameter of rope is 40 mm. E= 2.1×10⁵N/mm².

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4(b) A uniform rod AB has σ_y= 250 Mpa and E = 200 Gpa. Collar D moves along the rod and has a speed of 3 m/s. It strikes a small plate attached to the end B of the rod as shown in Fig.6. Using FOS =4, determine the largest allowable mass of the collar if the rod is not to be permanently deformed.

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4(b) A uniform rod AB has σ_y=250 Mpa and E=200GPa. Collar D moves along the rod and has a speed of 3 m/s. It strikes a small palte attached to the end B of the rod as shown in Fig.6. Using FOS=4, determine the largest allowable mass of the collar if the rod is not to be permanently deformed.

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4(b) A wagion weighing 35 kN is attached is a wire rope and moving down as inclined at speed of 3.6 kmph when the rope wagon is suddenly brought to rest. If the length of rope is 60 m at the time of sudden stoppage, calculate the maximum instantaneous strem and maximum instantaneous alongation produced Diameter of rope is 40 mm E = 21×10⁵ N/mm².

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5(a) Fig. 7 shows a horizointal shaft with keyed pulleys, rotating at 1800 rpm. The pulleys of the tight and slack sides of the belts over the pulleys are indicated in the figure. Neglecting the weight of the shaft and assuming smooth bearing close to the pulleys, find the diameter of the shaft if the shear stress in the shaft is not to be exceed 60 N/mm².
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Solve any one question fromQ5(a,b) and Q.6(a,b)

5(a) A hollow marin propeller shaft truning at 110 rpm is required to propel a vessel at 12 m/s for the expenditure of 6337.5 kW of shaft power, the efficiency of the propeller being 68%. The diameter ratio of the shaft is to be 2/3 and the direct stress due to the trust is not to exceed 8 MPa. Calculate:
i) the shaft diameter, ii) the maximum shearing stress due to the torque.

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Solve any one question.Q5(a,b) Q6(a,b)

5(a) A hollow propeller shaft turning at 110 rpm is required to propel a vessel at 12m/s for the expenditure of 6337.5 kW of shaft power, the efficiency of the propeller being 68%. The diameter ratio of the shaft is to be 2/3 and the direct stress due to the thrust is not to exceed 8 Mpa. Calculate:
i) the shaft diameter,
ii) the maximum shearing stress due to the torque.

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5(a) Fig.7 shows a horiziontal shaft with keyed pulleys, rotating at 1800 rpm. The pulleys of the light and slack sides of the belts over the puleys are indicated in the figure. Neglecting the weight of the shaft and assuming smooth bearings close to the pulleys, find the diameter of the shaft if the shear stress in the shaft is not to exceed 60 N/mm²
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5(b) A hollow tube 4 long with external and internal diameter of 40 mm and 25 mm resp. is found to extend 4.8 mm under tensile load of 60kN. Find the buckling load if both ends are pinned. Also find safe load on the tube taking factor of safety as 5.

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5(b) Find the Euler's critical load for a hollow cylindrical cast iron column with 200 mm O.D. and 25 mm thickness. If it is 6 m long and hinged at both ends.
Take E = 8×10⁴ Mpa. Compare Euler's critical load with Rankine's critical load taking σ_c= 550 MPa and a = 1/1600.

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5(b) Find the Euler's critical load for a hollow cylindrical cast iron column with 200 mm O.D. and 25 mm thickness, if it is 6 m long and hinged at both ends. Take E =8×10⁴MPa. Compare Euler's critical load with Rankine's critical load taking σ_c=550 Mpa and a=1/1600.

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5(b) A hollow alloy tube 4 m long with external and internal diameter of 40 mm and 25 mm resp. Is found to extend 4.8 mm under tensile load of 60 kN. Find the buckling load if both enda are pinned. Also find safe load on the tube, taking factor of safety as 5.

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6(a) The stepped steel shaft shown in Fig. 8 is 800 mm long and fixed at both ends subjected to a torque T at C. If allowable shear stress is 70 Mpa, find the safe value of torque T at C.
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6(a) Fig. 6. shows a horiziontal shaft ABCD fixed to a rigid base at D and subjected to torques. A hole 60 mm in diameter has been drilled into the part CD of the shaft. Determine the angle of twist at the end A. Take G = 7.7 × 10⁴ Mpa.
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6(a) Fig.6 shows a horizontal shaft ABCD fixed to a rigid base at D and subjected to torques. A hole 60 mm in diameter has been drilled into the part CD of the shaft. Determine the angle of twist at the end A. Take G=7.7×10⁴ Mpa.
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6(a) The stepped steel shaft shown Fig. 8 is 800 mm long and fixed at both endes subjected to a torque T at C. If allowable shear stress is 70MPa, find the safe value of torque T at C.
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6(b) Fig.9 T shows a T-section column of mild steal 3.50m long, with both ends fixed. Find the safe axial load on the column. Take f_c=385N/mm² and α=1/7500 and a factor of safey of 3.
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6(b) Fig. 9 T shows a T-section column of mild steel 3.50 m long, with both ends fixed. Find the safe axial load on the column. Take f^c=385N/mm² and α=1/7500 and a factor of safety of 3
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6(b) The following particulars refer to an engine cylinder.
Diameter of the cylinder = 400 mm.
Steam pressure in cylinder = 0.6 MPa. Distcance between the piston and cross head = 1.25 m.Find the diameter of the piston rod allowing of F.O.S of 4. Assume that the piston rod is firmly fixed to the piston and the cross head. Take σ_c=330 Mpa and a = 1/7500.Use Rankine's method.

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6(b) The following particulars refers to an engine cylinder, Diameter of the cylinder=400mm. Steam pressure in cylinder=0.6MPa. Distance between the piston and cross head =1.25 m. Find the diameter of the piston rod allowing a F.O.S of 4. Assume that the piston rod is firmly fixed to the piston and the cross head. Take σ_c=330 Mpa and a = 1/7500. Use Rankine's method.

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7(a) A point is a strained material is subjected to the stresses as shown in Fig.10. Locate the principal planes,and evaluate the principal stresses.
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7(a) A point in a strained material is subjected to the streesses as shown in Fig. 10. Locate the principal palnes, and evaluate the principal stresses.
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Solve any one question fromQ.7(a,b) and Q.8(a,b)

7(a) At a certain point on a strained material the principal stresses are 100 MPa and 40 MPa, both tensile. Find the normal, tangential and resultant stresses across a plane through the point at 48 degrees to the major principal plane, using Mohr's circle.

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Solve any one question.Q7(a,b) Q8(a,b)

7(a) At a certain point on a strained material the principal stresses are 100 Mpa and 40 Mpa, both tensile. Find the normal, tangential and resultant stresses across a plane through the point at a 48 degrees to the major principal plane, using Mohr's circle.

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7(b) A point is subjected to a tensile stress of 250 Mpa in the horizontal direction and another tensile stress of 100 Mpa in the vertical direction. The point s also subjected to a simple shear stress of 25MPa, such that when it is associated with the major tensile stressm,it tends to rotate the element int the clockwise direction. What is the magnitude of the normal and shear stresses inclined on a section at an angle of 20° with the major tensile stress? ( Use Mohr's circle method)

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7(b) A point is subjected to tensile stres of 250 Mpa in the horizontal direction and another tensile stress of 100 Mpa in the vertical direction. The point is also subjected to a simple shear stress of 25 Mpa, such that when it is tende to rotate the element in the clocwise direction. What is the magnitude of the normal and shear stresses inclined on a section at an angle of 20° with the major tensile stress? (Use Mohr's circle method)

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7(b) The stresses induced at a critical point in a machine component made of steel are σ_x = 100 Mpa, σ = 40 MPa, T_xy =80 Mpa. Calculate the F.O.S by maximum shear stress theory and maximum distortion energy theory. Assume S_yt = 380 Mpa.

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7(b) The stresses induced at a critical point in a machine component made of steel are σ_x=100MPa,
σ= 40MPa,
T_xy=80 Mpa. Calculate the F.O.S by maximum shear stress theory and maximum distortion energy theory. Assume S_yt=380MPa.

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8(a) A bolt is under an axial pull of 24 kN together with a transverse shear force of 5 kN. Calculate its diameter according to :
i) Maximum principal stress theory
ii) Maximum shear stress theory, and
iii) Strain energy theory. Take the elastic limit in steel = 250 N/mm². Possion's ratio = 0.3 Adopt factor of safety = 2.5.

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8(a) A bolt under an axial pull of 24kN together with a transverse shear force of 5kN. Calculate its diameter according to :
i) Maximum principal stress theory
ii) Maximum shear stress theory, and
iii) Strain energy theory. Take the elastic limit in steel = 250N/mm². Poisson's ratio = 0.3. Adopt factor of safety = 2.5.

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8(a) The principal tensile stresses at a point across two mutual perpendicular planes are 80 MPa and 40 MPa. Find the normal, tangential, resultant stresses and its obliquity on a plane at 20 degrees to the major principal plane. Find also the intensity of the stress which acting alone can produce the same maximum strain. Take Poission's ratio as 0.25. Use analytical metod only.

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8(a) The principle tensile stresses at a point across two mutual perpendicular planes are 80 Mpa and 40MPa. Find the normal, tangential, resultant stresses and its obliquity on a plane at 20 degrees to the major principal plane. Find also the intensity of the stress which acting alone can produce the same maximum strain.Take Poisson's ratio as 0.25. Use analytical method only

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8(b) An elemental cube is subjected to tensile stresses of 30 N/mm² and 10 N/mm_{2 on two mutually prependicular planes and a shear stress of 10N/mm² on these planes. Draw the Mohr's circle of stresses and hence or otherwise determine the magnitudes and directions of principal stresses and also the greatest shear stress.}

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8(b) An elemental cube is subjected to tensile stresses of 30N/mm² and 10 N/mm² acting on two mutually prependicular planes and a shear stress of 10N/mm² on these planes. Draw the Mohr's circle of stresses and hence or otherwise determine the magnitudes and directions of principal stresses and also the greatest shear stress.

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8(b) A solid circular shaft is subjected to a bending moment of 40 kN-m and a torque of 10 kN-m. Design the diameter of the shaft according to:
i) Max. Principal stress theory,
ii) Max. Shear stress theory.
Take μ = 0.25 Stress at elastic limit = 200 Mpa, F.O.S =2.

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9(a) A solid circular shaft is subjected to a bending moment of 40kN-m and a torque of 10kN-m. Design the diameter of the shaft according to:
i) Max. Principal stress theory,
ii) Max. shear stress theory. Take μ=0.25,
Stress at elastic limit =200MPa,
F.O.S=2

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