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2005 Punjab Technical University B.Tech Mechanical Engineering METROLOGY MEASUREMENT AND CONTROL ME 307 Question paper
Course: B.Tech Mechanical Engineering University: Punjab Technical University
METROLOGY MEASUREMENT AND CONTROL ME 307 5th Sem May 2k5
Max marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and any Two questions from Section C.
Section A Marks 2 each
1.
(a) What do you understand by exposed and ungrounded thermocouple junctions?
(b) Draw and label strain gauge bridge circuit.
(c) For a second order system, express and explain the peak overshoot due to step input.
(d) What is the significance of Nyquist plot for the stability and controls f a system?
(e) Draw a block diagram of dead weight pressure gauge tester.
(f) Differentiate between hydraulic and pneumatic load cells.
(g) Explain the working of electromagnetic flux meter.
(h) What do you understand by report writing?
(i) What are the uses and demerits of vernier height gauge?
Section B Marks 5 each
2. Explain construction and working of Bourdon tube.
3. Explain the response of Second order system to a step input.
4. Explain the precautions to be followed for contact and non-contact type temperature measurement.
5. How will you measure straightness and flatness through interferometer?
6. Describe linearity and calibration.
Section C Marks 10 each
7. Explain the theory and construction of Bimetallic Thermometers. What are the commonly used metals. What are their advantages, disadvantages, range and applications?
8. Discuss the construction and working of Pneumatic comparator. Derive the expression for measuring head sensitivity and pneumatic head sensitivity.
9.For the system shown in figure below (please see the attachment):
(i) Derive an expression for the closed loop transfer function and also for characteristic equation.
(ii) Calculate the damping ratio of the system form its characteristic equation.
(iii) If the transfer function of the feedback element is one, what would be the corresponding damping ratio?
Course: B.Tech Mechanical Engineering University: Punjab Technical University
METROLOGY MEASUREMENT AND CONTROL ME 307 5th Sem May 2k5
Max marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and any Two questions from Section C.
Section A Marks 2 each
1.
(a) What do you understand by exposed and ungrounded thermocouple junctions?
(b) Draw and label strain gauge bridge circuit.
(c) For a second order system, express and explain the peak overshoot due to step input.
(d) What is the significance of Nyquist plot for the stability and controls f a system?
(e) Draw a block diagram of dead weight pressure gauge tester.
(f) Differentiate between hydraulic and pneumatic load cells.
(g) Explain the working of electromagnetic flux meter.
(h) What do you understand by report writing?
(i) What are the uses and demerits of vernier height gauge?
Section B Marks 5 each
2. Explain construction and working of Bourdon tube.
3. Explain the response of Second order system to a step input.
4. Explain the precautions to be followed for contact and non-contact type temperature measurement.
5. How will you measure straightness and flatness through interferometer?
6. Describe linearity and calibration.
Section C Marks 10 each
7. Explain the theory and construction of Bimetallic Thermometers. What are the commonly used metals. What are their advantages, disadvantages, range and applications?
8. Discuss the construction and working of Pneumatic comparator. Derive the expression for measuring head sensitivity and pneumatic head sensitivity.
9.For the system shown in figure below (please see the attachment):
(i) Derive an expression for the closed loop transfer function and also for characteristic equation.
(ii) Calculate the damping ratio of the system form its characteristic equation.
(iii) If the transfer function of the feedback element is one, what would be the corresponding damping ratio?
2005 Punjab Technical University B.Tech Mechanical Engineering NUMERICAL ANALYSIS ME 406 Question paper
Course: B.Tech Mechanical Engineering University: Punjab Technical University
NUMERICAL ANALYSIS ME 406 4th Sem May 2k5
Max marks 60
Note: Section A is compulsory. Attempt any Four questions from section B and two from Section C.
Section A Marks 2 each
1.
(a) With a=0, b=1, the following function changes sign in (a, b), what point does the bisection method locate? Is this point a zero of f(x)?
(b) Find the function whose first difference is
9x2+11x+5.
(c) What are the major drawbacks of the Lagrange’s form of interpolation?
(d) Prove that (please see the attachment)
(e) Show that the matrix (please see the attachment)
is
Invertible, but that A cannot be written as the product of a lower triangular matrix with an upper triangular matrix,
(f) Calculate the number of additions and number of multiplications necessary to multiply an n x n matrix with an n-vector.
(g) If third differences are constant, prove that:
(h) Prove that:
(i) Why higher order Newton-Cole’s formula for numerical integration are not commonly used?
(j) Convert the following second order initial value problem into a system of first order initial value problem.
ty’’-y+4t3y=0.˜
Y(1) = 1, y’ (1) = 2.
Section B Marks 5 each
2. Show that bisection method always converges and its order of convergence is one.
3. Solve he equations:
x1+ x2+ x3=6
3x1+ (3+ e)x2+ 4x3=20
2x1+ x2+3 x3=13
using Gauss elimination method, where e is small such that 1+ e2 ˜ 1.
4 (a) Define the operators d and m and prove that
d(f(x)g(x)] = mf(x)dg(x) + mg(x)df(x).
where d = delta and m is mu
(b) Use Newton’s formula for interpolation to find the number of deaths at 40-50 and 50-55 if the following are the number of deaths on for successive ten year age groups:
Age group Deaths
25-35 13229
35-45 18139
45-55 24225
55-65 31496
5. Use stirling formula to find the first derivative of the function y 2ex x – 1 tabulated below at the point x = 0.6
X y
0.4 1.5836494
0.5 1.7974426
0.6 2.0442376
0.7 2.3275054
0.8 2.6510818
Compare with the true value which is 2.044238
6. Derive Simpson’s 1/3 formula for numerical integration and show that its local truncation error is of the order h3.
Section C Marks 10 each
7. (a) Use Picard’s method to approximate y where x 0.1, x = 0.2, given that y = 0 when x = 0, dy/dx =x+y. Compare the results with exact value.
(b) Find the three term Taylor series solution for the third order initial value problem
W”’ + WW” = 0.
W(0) = 0, W’ = (0), W”(0) =1.
Find the bound on the error for t ? [0, 0.2]
8. By considering the limit of the three-point Lagrange interpolating polynomial relative to (please see the attachment)
9 (a) Factorize the following matrix into LU decomposition using direct factorization
(Please see the attachment)
with uii =1 for all i:
(b) The equation ex – 4x2 = 0 has a root between x = 4 and x = 5. Show that we cannot find this root using fixed point interaction with natural iteration function x = ½ ex/2
Find root of this equation correct to three decimal places selecting an appropriate iteration function.
Course: B.Tech Mechanical Engineering University: Punjab Technical University
NUMERICAL ANALYSIS ME 406 4th Sem May 2k5
Max marks 60
Note: Section A is compulsory. Attempt any Four questions from section B and two from Section C.
Section A Marks 2 each
1.
(a) With a=0, b=1, the following function changes sign in (a, b), what point does the bisection method locate? Is this point a zero of f(x)?
(b) Find the function whose first difference is
9x2+11x+5.
(c) What are the major drawbacks of the Lagrange’s form of interpolation?
(d) Prove that (please see the attachment)
(e) Show that the matrix (please see the attachment)
is
Invertible, but that A cannot be written as the product of a lower triangular matrix with an upper triangular matrix,
(f) Calculate the number of additions and number of multiplications necessary to multiply an n x n matrix with an n-vector.
(g) If third differences are constant, prove that:
(h) Prove that:
(i) Why higher order Newton-Cole’s formula for numerical integration are not commonly used?
(j) Convert the following second order initial value problem into a system of first order initial value problem.
ty’’-y+4t3y=0.˜
Y(1) = 1, y’ (1) = 2.
Section B Marks 5 each
2. Show that bisection method always converges and its order of convergence is one.
3. Solve he equations:
x1+ x2+ x3=6
3x1+ (3+ e)x2+ 4x3=20
2x1+ x2+3 x3=13
using Gauss elimination method, where e is small such that 1+ e2 ˜ 1.
4 (a) Define the operators d and m and prove that
d(f(x)g(x)] = mf(x)dg(x) + mg(x)df(x).
where d = delta and m is mu
(b) Use Newton’s formula for interpolation to find the number of deaths at 40-50 and 50-55 if the following are the number of deaths on for successive ten year age groups:
Age group Deaths
25-35 13229
35-45 18139
45-55 24225
55-65 31496
5. Use stirling formula to find the first derivative of the function y 2ex x – 1 tabulated below at the point x = 0.6
X y
0.4 1.5836494
0.5 1.7974426
0.6 2.0442376
0.7 2.3275054
0.8 2.6510818
Compare with the true value which is 2.044238
6. Derive Simpson’s 1/3 formula for numerical integration and show that its local truncation error is of the order h3.
Section C Marks 10 each
7. (a) Use Picard’s method to approximate y where x 0.1, x = 0.2, given that y = 0 when x = 0, dy/dx =x+y. Compare the results with exact value.
(b) Find the three term Taylor series solution for the third order initial value problem
W”’ + WW” = 0.
W(0) = 0, W’ = (0), W”(0) =1.
Find the bound on the error for t ? [0, 0.2]
8. By considering the limit of the three-point Lagrange interpolating polynomial relative to (please see the attachment)
9 (a) Factorize the following matrix into LU decomposition using direct factorization
(Please see the attachment)
with uii =1 for all i:
(b) The equation ex – 4x2 = 0 has a root between x = 4 and x = 5. Show that we cannot find this root using fixed point interaction with natural iteration function x = ½ ex/2
Find root of this equation correct to three decimal places selecting an appropriate iteration function.
) Average gas velocity = 1000 m/s
(e) Gaseous conductivity = 10 Mho/m
Section C Marks 10 each
7. (a) The following data are given for a family biogas digester suitable for the output of ten cows:
(i) The retention time is 25 days
(ii) Temperature = 30 oC.
(iii) Dry matter consumed per day = 3 kg.
(iv) Biogas yield = 0.34 m3 per kg.
(v) Burner efficiency = 60%.
(vi) Methane proportion = 0.8.
(vii) Heat of combustion of methane = 28 MJ/m3.
Calculate the volume of biogas digester and power available for it.
(b) Give a brief outline on application of solar energy in water refrigeration and air conditioning.
8. (a) for a thermoelectric power generator the following parameters are given:
Temperature of hot reservoir of source = 700 K
Figure of merit for the material z = 2 x 10 -3 K.
What will be the efficiency of the thermoelectric generation? What will be its cannot efficiency?
(b) Give the classification of fuel cells. Write their advantages and limitations.
9. Write short notes on any two of the following:
(a) Design of a community biogas plant.
(b) Tidal power potential in India
(c) Wind energy storage
(e) Gaseous conductivity = 10 Mho/m
Section C Marks 10 each
7. (a) The following data are given for a family biogas digester suitable for the output of ten cows:
(i) The retention time is 25 days
(ii) Temperature = 30 oC.
(iii) Dry matter consumed per day = 3 kg.
(iv) Biogas yield = 0.34 m3 per kg.
(v) Burner efficiency = 60%.
(vi) Methane proportion = 0.8.
(vii) Heat of combustion of methane = 28 MJ/m3.
Calculate the volume of biogas digester and power available for it.
(b) Give a brief outline on application of solar energy in water refrigeration and air conditioning.
8. (a) for a thermoelectric power generator the following parameters are given:
Temperature of hot reservoir of source = 700 K
Figure of merit for the material z = 2 x 10 -3 K.
What will be the efficiency of the thermoelectric generation? What will be its cannot efficiency?
(b) Give the classification of fuel cells. Write their advantages and limitations.
9. Write short notes on any two of the following:
(a) Design of a community biogas plant.
(b) Tidal power potential in India
(c) Wind energy storage
2005 Punjab Technical University B.Tech Mechanical Engineering OPERATIONS MANAGEMENT DEME 2.3 Question paper
Course: B.Tech Mechanical Engineering University: Punjab Technical University
OPERATIONS MANAGEMENT DEME 2.3 6th Sem May 2k5
Max Marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and any Two questions from Section C.
Section A Marks 2 each
1.
(a) Define operations management and name the three approaches of management.
(b) What is meant by Product Design and Development?
(c) Draw and label a product life cycle.
(d) What do you understand by Capacity and man Power Requirement Planning?
(e) What is the effect f location changes on the cost of a product?
(f) Give the objectives and functions of materials management.
(g) What are the steps in designing a management information system?
(h) Differentiate between forecasting and prediction.
(i) Discuss in brief preventive maintenance.
(j) Differentiate between lead time and Reorder point.
Section B Marks 5 each
2. Discuss the role of a customer in improving the quality of a product.
3. Discuss the various production control functions.
4. A hospital has experienced irregular and usually increasing, demand for disposable kits throughout the hospital. The demand for a plastic disposable tubing in pediatrics for January was 300 units and for February 350 units. The old forecast procedure was to use last year’s average monthly demand of the forecast for each month this year. Last year’s average monthly demand was 200 units. Using 200 units as the January forecast and a smoothing coefficient of 0.7 to weight recent demand most heavily, calculate the forecast for the month of February and March.
5. Derive a relationship to calculate Economic Order Quantity where C = Total cost per year, Q = Lot size, H = annual holding cost, D = Annual demand and S = Ordering cost.
Plot a graph to show the same.
6. Discuss the application of concurrent Engineering in Product Design and Development.
Section C Marks 10 each
7. Discuss the salient features of three major philosophies and their impact on quality.
8. Name the process which eliminates 100^ inspection. Discuss the seven Basic Tools of Statistical Quality Control with examples.
9. (a) What s process capability? Show it graphically.
(b) Discuss the concept of Six sigma with example.
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2005 Punjab Technical University B.Tech Mechanical Engineering OPERATIONS MANAGEMENT ME 308 Question paper
Course: B.Tech Mechanical Engineering University: Punjab Technical University
OPERATIONS MANAGEMENT ME 308 6th/7th Sem May 2k5
Max Marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and any Two questions from Section C.
Section A Marks 2 each
1.
(a) Identify different types of productivity.
(b) What are ergonomic considerations in product design?
(c) Identify different techniques of forecasting.
(d) Distinguish between MRP-I and MRP-II
(e) Identify need for capacity planning.
(f) Define lead time and reorder point.
(g) Identify requirements of effective MIS.
(h) State the benefits of control charts.
(i) Identify benefits of planned maintenance.
(j) Identify elements of planned maintenance.
Section B Marks 5 each
2. Describe briefly the characteristics of various types of production systems.
3. Identify and briefly discuss the steps involved in product design and development.
4. Explain exponential smoothing technique. Discuss the choice of smoothing coefficient. A company uses exponential smoothing with ? = 0.1 to forecast demand. The forecast for the month of February was 500 units whereas actual demand turned out to be 450 units. Forecast the demand for the month of March.
5. Derive an expression for EOQ. The annual demand for an item is 3600 units. The cost of placing an order is Rs. 16 and cost of holding inventory is 25% of investment in inventories. The price per unit is Rs. 8. Determine EOQ.
6. Explain the forms AQL, LTPD producer risk and consumer risk for a sampling plan. Distinguish between control charts for variables and control charts for attributes.
Section c Marks 10 each
7. (a) Identify the reasons for increased use of computer based information systems. State the salient features f computer based MIS.
(b)Identify the operating elements of MIS. Describe briefly the processing fuctions of information systems.
8. (a) Describe briefly the basic model of a control system for planned maintenance with the help of a neat sketch.
(b) Identify and briefly discuss various techniques of condition monitoring.
9. Write notes on any two f the following:
(a) Concurrent Engineering
(b) Aggregate Planning
(c) Operations Scheduling
(d) Total Predictive Maintenance.
Course: B.Tech Mechanical Engineering University: Punjab Technical University
OPERATIONS MANAGEMENT DEME 2.3 6th Sem May 2k5
Max Marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and any Two questions from Section C.
Section A Marks 2 each
1.
(a) Define operations management and name the three approaches of management.
(b) What is meant by Product Design and Development?
(c) Draw and label a product life cycle.
(d) What do you understand by Capacity and man Power Requirement Planning?
(e) What is the effect f location changes on the cost of a product?
(f) Give the objectives and functions of materials management.
(g) What are the steps in designing a management information system?
(h) Differentiate between forecasting and prediction.
(i) Discuss in brief preventive maintenance.
(j) Differentiate between lead time and Reorder point.
Section B Marks 5 each
2. Discuss the role of a customer in improving the quality of a product.
3. Discuss the various production control functions.
4. A hospital has experienced irregular and usually increasing, demand for disposable kits throughout the hospital. The demand for a plastic disposable tubing in pediatrics for January was 300 units and for February 350 units. The old forecast procedure was to use last year’s average monthly demand of the forecast for each month this year. Last year’s average monthly demand was 200 units. Using 200 units as the January forecast and a smoothing coefficient of 0.7 to weight recent demand most heavily, calculate the forecast for the month of February and March.
5. Derive a relationship to calculate Economic Order Quantity where C = Total cost per year, Q = Lot size, H = annual holding cost, D = Annual demand and S = Ordering cost.
Plot a graph to show the same.
6. Discuss the application of concurrent Engineering in Product Design and Development.
Section C Marks 10 each
7. Discuss the salient features of three major philosophies and their impact on quality.
8. Name the process which eliminates 100^ inspection. Discuss the seven Basic Tools of Statistical Quality Control with examples.
9. (a) What s process capability? Show it graphically.
(b) Discuss the concept of Six sigma with example.
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2005 Punjab Technical University B.Tech Mechanical Engineering OPERATIONS MANAGEMENT ME 308 Question paper
Course: B.Tech Mechanical Engineering University: Punjab Technical University
OPERATIONS MANAGEMENT ME 308 6th/7th Sem May 2k5
Max Marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and any Two questions from Section C.
Section A Marks 2 each
1.
(a) Identify different types of productivity.
(b) What are ergonomic considerations in product design?
(c) Identify different techniques of forecasting.
(d) Distinguish between MRP-I and MRP-II
(e) Identify need for capacity planning.
(f) Define lead time and reorder point.
(g) Identify requirements of effective MIS.
(h) State the benefits of control charts.
(i) Identify benefits of planned maintenance.
(j) Identify elements of planned maintenance.
Section B Marks 5 each
2. Describe briefly the characteristics of various types of production systems.
3. Identify and briefly discuss the steps involved in product design and development.
4. Explain exponential smoothing technique. Discuss the choice of smoothing coefficient. A company uses exponential smoothing with ? = 0.1 to forecast demand. The forecast for the month of February was 500 units whereas actual demand turned out to be 450 units. Forecast the demand for the month of March.
5. Derive an expression for EOQ. The annual demand for an item is 3600 units. The cost of placing an order is Rs. 16 and cost of holding inventory is 25% of investment in inventories. The price per unit is Rs. 8. Determine EOQ.
6. Explain the forms AQL, LTPD producer risk and consumer risk for a sampling plan. Distinguish between control charts for variables and control charts for attributes.
Section c Marks 10 each
7. (a) Identify the reasons for increased use of computer based information systems. State the salient features f computer based MIS.
(b)Identify the operating elements of MIS. Describe briefly the processing fuctions of information systems.
8. (a) Describe briefly the basic model of a control system for planned maintenance with the help of a neat sketch.
(b) Identify and briefly discuss various techniques of condition monitoring.
9. Write notes on any two f the following:
(a) Concurrent Engineering
(b) Aggregate Planning
(c) Operations Scheduling
(d) Total Predictive Maintenance.
2005 Punjab Technical University B.Tech Mechanical Engineering STRENGTH OF MATERIALS II ME202 (2K3)/204 (2K2) Question paper
Course: B.Tech Mechanical Engineering University: Punjab Technical University
STRENGTH OF MATERIALS II ME202 (2K3)/204 (2K2) 4th Sem May 2k6
Max marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and 2 from Section c.
Section A Marks 2 each
1.
(a) Define proof resilience
(b) Define Rankine’s maximum principal stress theory.
(c) Determine the shear center of a semi-circular arc of radius ‘r’.
(d) The ratio of maximum horizontal shear stress to the mean shear stress in a circular beam is___
(e) Determine the ratio of the maximum bending stress in flat spiral spring of rectangular cross-section to the maximum bending stress in a beam of the same rectangular cross-section.
(f) To make a shrink fitted cylinder the outside diameter of the inner cylinder is made ( ).
(i) equal to the inside dia of the outer cylinder
(ii) smaller than the inside dia of the outer cylinder
(iii) larger than the inside dia of the outer cylinder
(g) Distribution of bending stress in curved beam is __________
(h) A cantilever beam of length L is loaded with a point load ‘W’ at its free end. Using strain energy method determine the deflection at the free end EI = constant.
(i) A leaf string of semi elliptic type consists of 8 plates, each of 40 mm width and 6 mm thickness. The length of the longest plate being 500 mm and young’s modulus is 2 x 10 5 MPa and central deflection is limited to 12 mm. Determine the load that can be applied.
(j) State the assumptions made in the problem of stress distribution in thick shells.
Section B Marks 5 each
2. Determine the strain energy of the prismatic beam AB for the loading shown in Fig. 1 (please see the attachment) taking into account only the effect of normal stresses due to bending.
3. A steel ring of 20 cm mean diameter has a rectangular cross-section 5 cm in the radial direction and 3 cm perpendicular to the radial direction. If the maximum tensile stress is limited to 120 MPa determine the tensile load that the ring can carry.
4. A solid circular shaft is subjected to a B.M. of 80 kNm. IN a uni axial tensile test the shaft material gave the following results:
E = 2 x 10 5 N/mm2; Stress at yield point = 300 N/mm2.
Poisson’s ratio = 0.3; Factor of safety = 3
Estimate the least diameter of shaft using
(i) maximum principal stress theory
(j) maximum principal strain theory
5. a laminated spring 1 m long is made up of plates each 50 mm wide and 10 mm thick. If the bending stress in plates is limited to 1 x 10 5 MPa how many plates would be required to enable the spring to carry a central point load of 2 kN. If E = 2 x 105 MPa, what is the deflection under the given load?
6. The maximum stress permitted in a thick cylinder of internal and external radii 200 mm and 300 mm respectively is 16 MPa. Find the internal pressure that can be applied. Plot the curves showing the variation of hoop and radial stresses through the material. What will be the change in thickness of the cylinder? E = 2 x 105 MPa. 1/m = 0.3
Section C Marks 10 each
7. A bar of square section is used as a beam so that the plane of bending is parallel to the diagonal. The side of the square is 2 cm. The S.F. at a section is 16 kN. Determine the formula for shear stress at a distance ‘h’ from the top/ Hence calculate the value of shear stress at neutral axis and magnitude and position of maximum shear stress.
8. An open coil helical spring is made of wire 10 mm diameter. It has 15 coils of mean diameter 6 cm. What is the greatest axial compressive load that can be applied to the ends of the spring if the principal stress is not to exceed 120 MPa and maximum shear stress is not to exceed 80 MPa. Calculate for this load the axial and angular deflection of the spring. E = 2 x 105 MPa; N = 0.8 x 105 MPa.
9. A vertical tie rod rigidly fixed at the top end consists of steel rod 2 m long and 20 mm diameter encased throughout in a brass tube 20 mm internal diameter and 30 mm external diameter. The rod and the casing are fixed together at the ends. The compound bar is suddenly loaded in tension by a mass of 1530 kg falling freely through 3 mm before being arrested by the tie. Compute the maximum stress in steel and brass.
Take Es= 2 x 105 MPa ; Eb= 1 x 105 MPa.
2005 Punjab Technical University B.Tech Mechanical Engineering STRENGTH OF MATERIAL I (New) ME 201 Question paper
Course: B.Tech Mechanical Engineering University: Punjab Technical University
STRENGTH OF MATERIAL I (New) ME 201 3rd Sem May 2k5
Max Marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and 2 from Section C.
Section A Marks 2 each
1.
(a) What is complementary shear stress?
(b) What is a compound bar?
(c) What is a principal stress?
(d) What is point of contraflexure?
(e) What do you understand by the term equivalent moment of inertia?
(f) Why do we prefer hollow shafts to solid shafts for power transmission?
(g) Why is the determination of deflection important?
(h) What is a thin cylinder?
(i) What do you understand by slenderness ratio?
(j) Differentiate between slope and deflection.
Section B Marks 5 each
2. Derive the following relation between elastic constants:
E = 2 C (1 + v)
3. Write a note on Mohr’s circle of stresses.
4. A rectangular beam 100 mm deep,50 mm wide and 1.5 m long is simply supported at its ends. Vertical loads of k kN each are applied at 0.5 m and 1 m from one end. Determine and plot the distribution of longitudinal stress across the section at mid-span.
5. Derive the torsion equation for a circular shaft from the first principle. State te assumptions made.
6. a steel column 50 mm diameter is pin jointed at both ends. If E = 200 GPa and yield stress sigmao = 3-- <{a for steel, calculate the length of the column for which the failure by yielding and buckling by Euler’s formula is equally likely, when the column is subjected to axial compression.
Section C Marks 10 each
7. Draw the S.F. and B.M. diagram for a cantilever of length L carrying a uniformly distributed load of W per m length over its entire length.
8. A cylindrical thin drum 80 cm in diameter and 3 m long has a shell thickness of 1 cm. If the drum is subjected to an internal pressure of 2.5 N/mm2, determine the change id diameter, length and volume.
Take E = 2 x 105 N/mm2, Poisson’s ratio = 0.25.
9. Explain how Rankine-Gordon’s formula is used to calculate the intensity of stress in short , intermediate and long columns.
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2005 Punjab Technical University B.Tech Mechanical Engineering STRENGTH OF MATERIAL (New) ME 204 Question paper
Course: B.Tech Mechanical Engineering University: Punjab Technical University
STRENGTH OF MATERIAL (New) ME 204 4th Sem 2k5
Max Marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and 2 from Section C.
Section A Marks 2 each
1.
(a) What are the assumptions for solving the problems on thick cylindrical shells?
(b) Define modulus of resilience.
(c) Write expression for link radius for rectangular section. Explain all the symbols used.
(d) Differentiate between bending and torsion springs.
(e) Define shear centre.
(f) What do you understand by rotating disc of uniform strength?
(g) Why cross-section of a crane hook is generally trapezoidal?
(h) Define Wahl factor for springs.
(i) Write expression for total strain energy per unit volume. Explain all the symbols.
(j) Give graphical representation of maximum principal stress theory.
2. Give graphical comparison of maximum shear and distortion energy theory.
Section B Marks 5 each
3. A simply supported beam of span L is carrying a concentrated load P at the centre and a uniformly distributed load of intensity w per unit length. Show that Maxwell’s reciprocal theorem holds good at the centre of the beam.
4. State and prove Castigliano’s theorem.
5. Determine the shear centre of the cross-section shown in Fig 1. (please see the attachment)
6. A carriage spring is 1.3 m long has leaves of 100 mm width and 12 mm thickness. The maximum bending stress is 150 MPa and the spring must absorb 120 N-m of energy when straightened. Calculate the number of leaves and their initial radius of curvature. Assume E = 200 GPa.
Section C Marks 10 each
7. (a) The pressure within the cylinder of a hydraulic press is 9 MPa. The inside diameter of the cylinder is 25 mm. Determine the thickness of the cylinder wall if permissible stress is 18 MPa.
(b) A flat spring of rectangular section is 25 mm broad and 0.5 m thick and 6 m long. What twisting moment may it exert on a central spindle if bending stress is not to exceed 700 MPa. How many complete turns may be given to the spring when it is run down and how much work is then stored in it? Take E = 210 GPa.
8. (a) A steel rod is to be bent in form of a hook to lift a load of 8 kN such that the maximum stress does not exceed 140 MPa. The ratio of the radius of curvature of centroidal plane to the radius of the rod is to be 4 and load acts through the centre of curvature. Determine the diameter of the rod.
(b) an I-section with rectangular end has the following dimensions:
Flanges = 150 mm x 20 mm. Wed = 300 mm x 10 mm. Total depth = 340 mm.
Find the maximum shearing stress developed in the beam for a shearing force of 50 kN.
9. A uniform thickness flat steel disc of 800 mm in diameter is shrunk fit on a solid steel shaft of 160 mm diameter. The shrink fit pressure is 100 MPa. Calculate:
(a) Interference allowance.
(b) RPM at which disc will loosen on the shaft, and
(c) The stress at inner radius at half the speed at (b)
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2005 Punjab Technical University B.Tech Mechanical Engineering STRENGTH OF MATERIAL ME 202 Question paper
Course: B.Tech Mechanical Engineering University: Punjab Technical University
STRENGTH OF MATERIAL ME 202 4th Sem May 2k5
Max Marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and 2 from Section C.
Section A Marks 2 each
1.
(a) State Maxwell’s theorem of reciprocal deflection.
(b) Name the theories of failures suitable for brittle materials.
(c) Determine the ratio of maximum horizontal shear stress to mean shear stress in a circular beam.
(d) What is spring index and shear stress for close coiled Helical spring?
(e) What is resilience of a closed coil helical spring under axial twist?
(f) What is Shrink fit Assembly?
(g) While fabricating a chain link, comment on location of joint.
(h) Write the expression for bending stress under unsymmetrical bending.
(i) What is shear center? Write expression for the shear center of a semicircular arc of radius ‘R’.
(j) What is the ratio of maximum hoop stress in a circular rotating disc having small hole at the centre to max hoop stress in a solid circular rotating disc?
Section B Marks 5 each
2. Using Castigliano’s theorem calculate vertical deflection at the middle of simply supported beam carrying a uniformly distributed load of ‘w’ N/m over full span.
3. List various theories of failure. Explain Maximum Shear Stress Theory.
4. For the section shown in Fig. 1 (please refer to the attachment) determine average shear stress at A, B, C, D for a shear force of 20 kN and find the ratio of max to mean shear stress.
5. A closed coiled helical spring of whose free length when not compressed is 15 cm is required to absorb strain energy 500 kg-cm when fully compressed with coils in contact. The maximum shear stress is 1400 kg/cm2. Assume mean coil diameter of 10 cm. Find diameter of steel wire required and number of coils. Take G = 8.5 x 105 kg/cm2.
6. Prove that strain energy of a curved beam with a small initial curvature can be given by (please see the attachment)
Section C Marks 10 each
7. A chain link made of circular section has dimensions as shown in Gig. 2 (please see the attachment). Prove that maximum bending moment at the point of application of load is
PR(l+2R)/[2(l+ pi R)
8. (a) The stress component at a point are given by sx= 25 MPa, sy=15 MPa, sz=10 MPa. Txt=10 MPa, txz=15 MPa, tyz= 5 MPa, E= 200 GPa, Poisson’s ratio = 0.25.
Find the strain components.
(b) Prove that the deflection at themed-point in case of Flat Sprigs (Leaf) is given by
Delta = 3WL3 / 8 n E b d3
9. (a) The rotor of a steam turbine is a solid disc of uniform strength and is 20 cm in diameter at the blade ring and 2.5 cm thick at the center. It is running at a constant speed of 30,000 rpm. Calculate thickness of rotor at the radius of 5 cm. Take density rho = 7470 kg/ m3. The maximum allowable stress in rotor is 145 MPa.
(b) For the section shown in fig. 3 prove that shear centre is to the left side of web and given by the following expression:
e = 3 (b2- b12) / [wh/l + b(b + b1)]
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Course: B.Tech Mechanical Engineering University: Punjab Technical University
STRENGTH OF MATERIALS II ME202 (2K3)/204 (2K2) 4th Sem May 2k6
Max marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and 2 from Section c.
Section A Marks 2 each
1.
(a) Define proof resilience
(b) Define Rankine’s maximum principal stress theory.
(c) Determine the shear center of a semi-circular arc of radius ‘r’.
(d) The ratio of maximum horizontal shear stress to the mean shear stress in a circular beam is___
(e) Determine the ratio of the maximum bending stress in flat spiral spring of rectangular cross-section to the maximum bending stress in a beam of the same rectangular cross-section.
(f) To make a shrink fitted cylinder the outside diameter of the inner cylinder is made ( ).
(i) equal to the inside dia of the outer cylinder
(ii) smaller than the inside dia of the outer cylinder
(iii) larger than the inside dia of the outer cylinder
(g) Distribution of bending stress in curved beam is __________
(h) A cantilever beam of length L is loaded with a point load ‘W’ at its free end. Using strain energy method determine the deflection at the free end EI = constant.
(i) A leaf string of semi elliptic type consists of 8 plates, each of 40 mm width and 6 mm thickness. The length of the longest plate being 500 mm and young’s modulus is 2 x 10 5 MPa and central deflection is limited to 12 mm. Determine the load that can be applied.
(j) State the assumptions made in the problem of stress distribution in thick shells.
Section B Marks 5 each
2. Determine the strain energy of the prismatic beam AB for the loading shown in Fig. 1 (please see the attachment) taking into account only the effect of normal stresses due to bending.
3. A steel ring of 20 cm mean diameter has a rectangular cross-section 5 cm in the radial direction and 3 cm perpendicular to the radial direction. If the maximum tensile stress is limited to 120 MPa determine the tensile load that the ring can carry.
4. A solid circular shaft is subjected to a B.M. of 80 kNm. IN a uni axial tensile test the shaft material gave the following results:
E = 2 x 10 5 N/mm2; Stress at yield point = 300 N/mm2.
Poisson’s ratio = 0.3; Factor of safety = 3
Estimate the least diameter of shaft using
(i) maximum principal stress theory
(j) maximum principal strain theory
5. a laminated spring 1 m long is made up of plates each 50 mm wide and 10 mm thick. If the bending stress in plates is limited to 1 x 10 5 MPa how many plates would be required to enable the spring to carry a central point load of 2 kN. If E = 2 x 105 MPa, what is the deflection under the given load?
6. The maximum stress permitted in a thick cylinder of internal and external radii 200 mm and 300 mm respectively is 16 MPa. Find the internal pressure that can be applied. Plot the curves showing the variation of hoop and radial stresses through the material. What will be the change in thickness of the cylinder? E = 2 x 105 MPa. 1/m = 0.3
Section C Marks 10 each
7. A bar of square section is used as a beam so that the plane of bending is parallel to the diagonal. The side of the square is 2 cm. The S.F. at a section is 16 kN. Determine the formula for shear stress at a distance ‘h’ from the top/ Hence calculate the value of shear stress at neutral axis and magnitude and position of maximum shear stress.
8. An open coil helical spring is made of wire 10 mm diameter. It has 15 coils of mean diameter 6 cm. What is the greatest axial compressive load that can be applied to the ends of the spring if the principal stress is not to exceed 120 MPa and maximum shear stress is not to exceed 80 MPa. Calculate for this load the axial and angular deflection of the spring. E = 2 x 105 MPa; N = 0.8 x 105 MPa.
9. A vertical tie rod rigidly fixed at the top end consists of steel rod 2 m long and 20 mm diameter encased throughout in a brass tube 20 mm internal diameter and 30 mm external diameter. The rod and the casing are fixed together at the ends. The compound bar is suddenly loaded in tension by a mass of 1530 kg falling freely through 3 mm before being arrested by the tie. Compute the maximum stress in steel and brass.
Take Es= 2 x 105 MPa ; Eb= 1 x 105 MPa.
2005 Punjab Technical University B.Tech Mechanical Engineering STRENGTH OF MATERIAL I (New) ME 201 Question paper
Course: B.Tech Mechanical Engineering University: Punjab Technical University
STRENGTH OF MATERIAL I (New) ME 201 3rd Sem May 2k5
Max Marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and 2 from Section C.
Section A Marks 2 each
1.
(a) What is complementary shear stress?
(b) What is a compound bar?
(c) What is a principal stress?
(d) What is point of contraflexure?
(e) What do you understand by the term equivalent moment of inertia?
(f) Why do we prefer hollow shafts to solid shafts for power transmission?
(g) Why is the determination of deflection important?
(h) What is a thin cylinder?
(i) What do you understand by slenderness ratio?
(j) Differentiate between slope and deflection.
Section B Marks 5 each
2. Derive the following relation between elastic constants:
E = 2 C (1 + v)
3. Write a note on Mohr’s circle of stresses.
4. A rectangular beam 100 mm deep,50 mm wide and 1.5 m long is simply supported at its ends. Vertical loads of k kN each are applied at 0.5 m and 1 m from one end. Determine and plot the distribution of longitudinal stress across the section at mid-span.
5. Derive the torsion equation for a circular shaft from the first principle. State te assumptions made.
6. a steel column 50 mm diameter is pin jointed at both ends. If E = 200 GPa and yield stress sigmao = 3-- <{a for steel, calculate the length of the column for which the failure by yielding and buckling by Euler’s formula is equally likely, when the column is subjected to axial compression.
Section C Marks 10 each
7. Draw the S.F. and B.M. diagram for a cantilever of length L carrying a uniformly distributed load of W per m length over its entire length.
8. A cylindrical thin drum 80 cm in diameter and 3 m long has a shell thickness of 1 cm. If the drum is subjected to an internal pressure of 2.5 N/mm2, determine the change id diameter, length and volume.
Take E = 2 x 105 N/mm2, Poisson’s ratio = 0.25.
9. Explain how Rankine-Gordon’s formula is used to calculate the intensity of stress in short , intermediate and long columns.
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2005 Punjab Technical University B.Tech Mechanical Engineering STRENGTH OF MATERIAL (New) ME 204 Question paper
Course: B.Tech Mechanical Engineering University: Punjab Technical University
STRENGTH OF MATERIAL (New) ME 204 4th Sem 2k5
Max Marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and 2 from Section C.
Section A Marks 2 each
1.
(a) What are the assumptions for solving the problems on thick cylindrical shells?
(b) Define modulus of resilience.
(c) Write expression for link radius for rectangular section. Explain all the symbols used.
(d) Differentiate between bending and torsion springs.
(e) Define shear centre.
(f) What do you understand by rotating disc of uniform strength?
(g) Why cross-section of a crane hook is generally trapezoidal?
(h) Define Wahl factor for springs.
(i) Write expression for total strain energy per unit volume. Explain all the symbols.
(j) Give graphical representation of maximum principal stress theory.
2. Give graphical comparison of maximum shear and distortion energy theory.
Section B Marks 5 each
3. A simply supported beam of span L is carrying a concentrated load P at the centre and a uniformly distributed load of intensity w per unit length. Show that Maxwell’s reciprocal theorem holds good at the centre of the beam.
4. State and prove Castigliano’s theorem.
5. Determine the shear centre of the cross-section shown in Fig 1. (please see the attachment)
6. A carriage spring is 1.3 m long has leaves of 100 mm width and 12 mm thickness. The maximum bending stress is 150 MPa and the spring must absorb 120 N-m of energy when straightened. Calculate the number of leaves and their initial radius of curvature. Assume E = 200 GPa.
Section C Marks 10 each
7. (a) The pressure within the cylinder of a hydraulic press is 9 MPa. The inside diameter of the cylinder is 25 mm. Determine the thickness of the cylinder wall if permissible stress is 18 MPa.
(b) A flat spring of rectangular section is 25 mm broad and 0.5 m thick and 6 m long. What twisting moment may it exert on a central spindle if bending stress is not to exceed 700 MPa. How many complete turns may be given to the spring when it is run down and how much work is then stored in it? Take E = 210 GPa.
8. (a) A steel rod is to be bent in form of a hook to lift a load of 8 kN such that the maximum stress does not exceed 140 MPa. The ratio of the radius of curvature of centroidal plane to the radius of the rod is to be 4 and load acts through the centre of curvature. Determine the diameter of the rod.
(b) an I-section with rectangular end has the following dimensions:
Flanges = 150 mm x 20 mm. Wed = 300 mm x 10 mm. Total depth = 340 mm.
Find the maximum shearing stress developed in the beam for a shearing force of 50 kN.
9. A uniform thickness flat steel disc of 800 mm in diameter is shrunk fit on a solid steel shaft of 160 mm diameter. The shrink fit pressure is 100 MPa. Calculate:
(a) Interference allowance.
(b) RPM at which disc will loosen on the shaft, and
(c) The stress at inner radius at half the speed at (b)
******************************************************************************
2005 Punjab Technical University B.Tech Mechanical Engineering STRENGTH OF MATERIAL ME 202 Question paper
Course: B.Tech Mechanical Engineering University: Punjab Technical University
STRENGTH OF MATERIAL ME 202 4th Sem May 2k5
Max Marks 60
Note: Section A is compulsory. Attempt any Four questions from Section B and 2 from Section C.
Section A Marks 2 each
1.
(a) State Maxwell’s theorem of reciprocal deflection.
(b) Name the theories of failures suitable for brittle materials.
(c) Determine the ratio of maximum horizontal shear stress to mean shear stress in a circular beam.
(d) What is spring index and shear stress for close coiled Helical spring?
(e) What is resilience of a closed coil helical spring under axial twist?
(f) What is Shrink fit Assembly?
(g) While fabricating a chain link, comment on location of joint.
(h) Write the expression for bending stress under unsymmetrical bending.
(i) What is shear center? Write expression for the shear center of a semicircular arc of radius ‘R’.
(j) What is the ratio of maximum hoop stress in a circular rotating disc having small hole at the centre to max hoop stress in a solid circular rotating disc?
Section B Marks 5 each
2. Using Castigliano’s theorem calculate vertical deflection at the middle of simply supported beam carrying a uniformly distributed load of ‘w’ N/m over full span.
3. List various theories of failure. Explain Maximum Shear Stress Theory.
4. For the section shown in Fig. 1 (please refer to the attachment) determine average shear stress at A, B, C, D for a shear force of 20 kN and find the ratio of max to mean shear stress.
5. A closed coiled helical spring of whose free length when not compressed is 15 cm is required to absorb strain energy 500 kg-cm when fully compressed with coils in contact. The maximum shear stress is 1400 kg/cm2. Assume mean coil diameter of 10 cm. Find diameter of steel wire required and number of coils. Take G = 8.5 x 105 kg/cm2.
6. Prove that strain energy of a curved beam with a small initial curvature can be given by (please see the attachment)
Section C Marks 10 each
7. A chain link made of circular section has dimensions as shown in Gig. 2 (please see the attachment). Prove that maximum bending moment at the point of application of load is
PR(l+2R)/[2(l+ pi R)
8. (a) The stress component at a point are given by sx= 25 MPa, sy=15 MPa, sz=10 MPa. Txt=10 MPa, txz=15 MPa, tyz= 5 MPa, E= 200 GPa, Poisson’s ratio = 0.25.
Find the strain components.
(b) Prove that the deflection at themed-point in case of Flat Sprigs (Leaf) is given by
Delta = 3WL3 / 8 n E b d3
9. (a) The rotor of a steam turbine is a solid disc of uniform strength and is 20 cm in diameter at the blade ring and 2.5 cm thick at the center. It is running at a constant speed of 30,000 rpm. Calculate thickness of rotor at the radius of 5 cm. Take density rho = 7470 kg/ m3. The maximum allowable stress in rotor is 145 MPa.
(b) For the section shown in fig. 3 prove that shear centre is to the left side of web and given by the following expression:
e = 3 (b2- b12) / [wh/l + b(b + b1)]
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