code no: r22015 ii b. tech ii semester supplementary ... · ii b. tech ii semester supplementary...

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Code No: R22015

II B. Tech II Semester Supplementary Examinations, May - 2015

ENGINEERING GEOLOGY (Civil Engineering)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions

All Questions carry Equal Marks

1. a) What is the importance of geology in civil engineering?

b) What is weathering? What are the factors of weathering?

2. a) Define mineral? What are the physical properties of minerals?

b) Write the physical prophecies of the fallowing minerals.

i) Bauxite ii) Quartz iii)Calcite.

3. a)Define rock? Give brief classification about igneous rocks?

b) Write a short notes on

i) Limestone ii)Schist ii)Galena

4. Answer the fallowing

i) What is fold? What are the parts of folds?

ii) Angular unconformity.

iii) Synclinorium and anticlinorium.

iv) Dykes and sills.

v) Strike and dip


i. Water table

ii) Cone of depression

iii) Shield areas and seismic belts of earthquakes.

6. What is the importance of geophysical studies in civil engineering? Explain- Electrical

resistivity method.

7. What is Dam? What are the types of dams explain with neat sketches.

8. Explain about over break and lining in tunneling?

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1. a) What is meant by weathering? Briefly explain Granite weathering?

b) Explain i) Exogenous weathering?

ii )Endogenous weathering?

2. a) Give brief notes on Texture and structures of sedimentary rocks.

b) Write the physical properties of the fallowing minerals.

i) Galena. ii) Quartz iii) Hematite.


i) Dykes and sills.

ii) Parts of faults?

ii) Slip faults

iv) Heave and throw.

v )Recognition of unconformities.

4. Explain the Electrical resistivity method in detail .

5. Write short notes on fallowing.

a) Terminology of earthquake.

b) What are the precautionary measures in the constriction of buildings in earthquakes zones?

6. Write notes on the following:

a) Principles of gravity methods

b) Principles of magnetic methods

7. What are the causes of silting in reservoirs? Indicate the impact of silting on functioning

of a reservoir.

8.Explain about

a) Tunnels in faulted strata.

b) Effects of tunneling on the ground.

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1. Write a short notes on

i) Valley development.

ii) Geological work of Rivers.

2. a) Discuss in detail.

i) Moh’s hardness table.

ii) Cleavage and fracture.

iii) Mineral and rock.

b) Write the physical properties of fallowing minerals.

i) Bauxite ii Calcite.

3. Briefly explain the fallowing.

i) Polymorphism ii) Isomorphism

ii) Stlag mites and statutes iv Ptophyritic textures.

4. Discribe the deferent types of unconformities encountered in the structural geology? Draw

neat sketches.

5. What is meant by fold? Give classification of folds? Explain with neat sketches.

6. Explain the following.

i) Types of aquifers. ii) Cone of depression.

7. What is the importance of geophysical methods in civil engineering aspect? Briefly explain

the Seismic refraction method.

8. a) What are the causes and effects of landslides?

b) Describe the geological consideration for successful tunneling?

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1. What is geology? Explain the main and allied branches of geology?

2. a) Define rock? How the rocks are classified?

b) Give short notes on Marble and Limestone.

3. Define mineral? Write the Physical properties of the fallowing minerals?

i) Talc ii)Magnetite iii)Muscovite

4. What is fault? Give brief classification of fault? Explain with neat sketches.

5. Answer the fallowing.

i) Richter scale

ii) What are the precautions to be taken for building construction in earthquake zones?

iii) Describe the causes and effects of landslides

6. What is the importance of Geophysical studies? Explain Electrical Resistivity method?

7. What is Dam? Briefly Explain the Geological causes for the failures of ST’Francies dam, Hales

bar dam and Hafayetha dam?

8. a) What are the requirements for a successful reservoir?

b) Write the purposes of tunneling? What are the effects of tunneling on the ground?

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Code No: R22014

II B. Tech II Semester Supplementary Examinations, May/June - 2015

HYDRAULICS AND HYDRAULIC MACHINERY (Civil Engineering)




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1. a) Distinguish between

i) Steady and unsteady flow ii) Uniform and non uniform flow

iii) Gradually and rapidly varied flow iv) Critical and subcritical flows

b) Determine the most economical section of rectangular channel carrying water at 0.75 m3/s.

The bed slope of the channel is being 1/1500. Take chezy’s constant C = 60.

2. a) A sluice gate discharges water into horizontal rectangular channel with a velocity of 10 m/s

and depth of flow of 1 m. Determine the depth of flow of water after the jump and

consequent loss in total head.

b) What is the essential difference between gradually varied flow and rapidly varied flow?

Illustrate with neatly drawn sketches.

3. a) Explain the terms distorted models and undistorted models. What is the use of distorted

models.

b) Define the terms: model, prototype, model analysis, and hydraulic similitude.

4. a) Derive an expression for the force, work done, and efficiency of a moving curved vane.

b) Find the force exerted by a jet of water of diameter 75 mm on a stationary flat plate when

the jet strikes the plate normally with velocity of 20 m/s.

5. a) Differentiate between an impulse turbines and a reaction turbines.

b) Describe briefly the functions of various main components of Pelton turbine with neat

sketches

6. a) What is cavitation? How can it be avoided in reaction turbine?

b) What is specific speed? State its significance in the study of hydraulic machines.

7. a) Name the various types of pumps used in civil engineering practice indicating their uses

b) State the difference between closed, semi-closed, and open impellers

8. a) Compare and contrast between hydropower station and thermal power station.

b) Discuss various classifications of different types of hydropower plants

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Code No: R22014






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1. a) Derive standard Chezy’s equation for uniform flow in an open channel

b) Compute the hydraulic radius and hydraulic depth of the trapezoidal section of the bed

width 6m, depth of flow 2m and side slopes2H:1V.

2. a) Prove that the loss of energy head in a hydraulic jump is equal to (d2-d1)3/4d1d2, where

d1 and d2 are the conjugate depths.

b) Determine the length of the backwater curve caused by an afflux of 1.5 min rectangular

channel of width 50m and depth 2.0 m. The slope of the bed is given as 1 in 2000. Take

Manning’s N as 0.03.

3. a) What are the methods of dimensional analysis? Describe the Rayleigh’s method for

dimensional analysis.

b) What is meant by geometric, kinematic and dynamic similarities?

4. a) Derive the expression for force, work done and efficiency of a jet striking at the center of

the series of vanes connected to a rim , such that each time one vane is facing the jet.

b) A 4 cm diameter water jet with a velocity of 35 m/s impinges on a single vane moving in the

same direction at a velocity of 20 m/s. The jet enters the vane tangentially along the x

direction. The vane deflects the jet by 150°. Calculate the force exerted by the water on the

vane.

5. a) Write a brief note on the classification of hydraulic turbines

b) What is the basis of selection of a turbine at a particular place?

6. a) Define specific speed of a turbine and derive an expression for the same?

b) What is cavitation ? How can it be avoided in reaction turbine?

7. a) What is priming of a centrifugal pump? Explain clearly why priming is essential before

starting a centrifugal pump

b) Explain the term manometric efficiency, mechanical efficiency and overall efficiency s

applied to centrifugal pump

8. a) What are the main components of hydropower plants and explain each in detail

b) Define the terms: (i) load factor, (ii) utilization factor and (iii) capacity factor

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Code No: R22014






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1. a) What is meant by the most economical channel? Show that length of the sloping side is

equal to half of the top width for a most economical trapezoidal channel section.

b) Explain the difference between pipe flow and open channel flow. Derive the predominant

dimensionless numbers of pipe flow and open channel flow.

2. a) A 3.6 m wide rectangular channel conveys 9.0 cumecs of water with a velocity of 6 m/s. Is

there a condition for hydraulic jump to occur? If so, calculate the height, length, and

strength of the jump.

b) Obtain the relationship between the Froude Number of flow before and after the hydraulic

jump in a horizontal rectangular channel.

3. a) What do you mean by dimensionless number? Name any three dimensionless number

b) Explain the different types of hydraulic similarities that must exist between a prototype and

its model.

4. a) Derive the expression for force, work done and efficiency of a jet striking at one end of the

vane and leaves other end of the vane of a series of vanes connected to a rim , such that each

time one vane is facing the jet.

b) A jet of water of diameter 100 mm moving with a velocity of 30 m/s strikes a curved fixed

symmetrical plate at the center. Find the force exerted by the jet of water in the direction of

the jet, if the jet is deflected through an angle of 120° at the outlet of the curved plate.

5. a) Define the terms unit power, unit speed, and unit discharge with reference to a hydraulic

turbine.

b) Explain the difference between Kaplan turbine and Propeller turbine

6. Define the terms ‘unit power’, ‘unit speed’, and ‘unit discharge’ with reference to hydraulic

turbine. Also derive expression for these terms.

7. a) Derive the expression for specific speed of a centrifugal pump

b) Define the terms: suction head, delivery head, static head and manometric head

8. Write short notes on the following:

a) Firm Power b) Secondary power c) Diversity factor d) Load duration curve.

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Code No: R22014






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1. a) Develop the criterion for the most economical triangular section of a channel

b) Define specific energy. Draw a neat sketch of specific energy curve for a rectangular

channel showing all the details

2. a) Define the following

i) Critical depth ii) Conjugate depth iii) Normal depth iv) Alternative depth

b) Determine the depth of flow of a hydraulic jump in a horizontal rectangular channel and

consequent loss in total head when the sluice gate discharges water into a channel with

velocity 15m/s and a depth of 2m.

3. a) State Buckingham’s П-theorem. Why this theorem is considered superior over the

Rayleigh’s method for dimensional analysis.

b) What do you mean by repeating variables? How are the repeating variables selected for

dimensional analysis?

4. a) Derive an expression for the force of a jet on a fixed plate

b) A blade turns the jet of diameter 3 cm at a velocity of 20 m/s by 60°. Determine the

force exerted by the blade on the fluid.

5. a) What do you understand by the term turbine? Discuss briefly the uses of turbines

b) Draw a neat sketchs of Pelton turbine and Francis turbine.

6. What do you understand by the characteristics curves of turbine? Name the important

characteristics of a turbine.

7. a) How does a centrifugal pump impart pressure energy to the fluid? Indicate the mechanism

involved.

b) Explain the working principles of a centrifugal pump with sketches

8. a) List out twelve important hydropower plants in India.

b) How do you estimate hydropower potential?

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Code No: R22013

II B. Tech II Semester Supplementary Examinations May/June - 2015

MANAGERIAL ECONOMICS AND FINANCIAL ANALYSIS (Com. to CE, MM)




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1. a) Define Managerial Economics and explain its characteristics.

b) What is demand? And explain law of demand and its exceptions. (7M+8M)

2. a) Define Elasticity of demand and its types and significance.

b) Describe any four methods of demand forecasting. (7M+8M)

3. a) Explain the salient features of Cobb-Douglas Production Function.

b) Describe the importance and limitations of Break-even analysis. (7M+8M)

4. a) Explain salient the features of perfect competition and monopoly.

b) Describe the conditions of Oligopoly and Kinked demand curve. (7M+8M)

5. Explain Importance of pricing policies and describe any five methods of pricing. (15M)

6. a) Describe the salient features of private limited company.

b) Explain the phases and features of business cycles. (7M+8M)

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Code No: R22013

7. a) Explain the importance of ratio analysis and objectives of solvency ratio.

b) The following trial balance was drawn from the books of Zig-Zag Traders: (5M+10M)

Trail Balance

Debit Rs. Credit Rs.

Building

Machinery

Returns outward

Bad debts

Cash

Discount received

Bank Overdraft

Creditors

Purchases

60,000

17,000

2,600

2,800

400

3,000

10,000

50,000

1,00,000

Capital

Fixtures

Sales

Debtors

Interest received

73,600

5,600

1,04,000

60,000

2,600

2,45,800 2,45,800

Even through the debit and credit sides agree, the trial balance contains mistakes. Redraft the

Trial Balance.

8. a) Explain the meaning and need for capital budgeting.

b) Find out the IRR of the following investment proposal. (5M+10M)

Initial Investment Rs. 70,000

Expected annual cash inflow Rs. 24,000

Economic life of the project 4 years

Present value of annuity of Re. 1 for 4 years.

@ 10% 3.170, 12% 3.037, @ 14% 2.914, @ 16% 2.798.

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1. a) Explain the basic economic tools using in Managerial Economics.

b) What is demand? And explain law of demand and its limitation. (7M+8M)

2. a) Define Elasticity of demand and explain its types and measurement of Price

Elasticity of demand.

b) What is demand forecasting? And explain any three methods of demand

Forecasting. (7M+8M)

3. a) Explain the law of diminishing returns.

b) A factory manufacturing sewing machines has the capacity to produce 500 (5M+10M)

Machines per year. The marginal (variable) cost of each machine is Rs.200 and

Each machine is sold for Rs.250. Fixed overheads are Rs.12,000 per year.

Calculate the break-even points for output and sales and show what profit will

Result if output is 90% of capacity?

4. a) Explain the salient features Monopoly and monopolistic competition

b) Describe any four methods of Pricing. (7M+8M)

5. a) Explain the salient features of Partnership.

b) Describe the meaning and salient features of business cycles (7M+8M)

6. a) Explain the importance financial accounting and list out the differences

Between Journal and Ledger.

b) What is double-entry system? And explain the limitations of financial (7M+8M)

Statements.

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Code No: R22013

7. a) What is a ratio? And explain briefly different types of ratios.

b) From the following Balance Sheet of XYZ Co. Ltd., calculate (8M+7M)

liquidity ratios.

Balance Sheet of XYZ Co. Ltd.

as on 31.12.20XX

(Rs .in thousand)

Liabilities Rs. Assets Rs.

Preference share capital

Equity share capital

General reserve

Debentures

Creditors

Bills payable

Outstanding expenses

Profit and loss account

Bank Loan

(Long-term)

100

150

250

400

200

50

50

100

200

Land and Buildings

Plant and Machinery

Furniture and Fixtures

Stock

Debtors

Cash at Bank

Cash in hand

Prepaid expenses

Marketable securities

225

250

100

250

125

250

125

50

125

1500 1500

8. a) Explain the meaning and importance of capital building.

b) Two projects, costing Rs 20,000 each, have the following cash inflows. Both (7M+8M)

Have the same payback period. Which one do you choose and why?

Same total cash inflows with a difference in size and timing.

(Figures in Rupees)

Year Project A Project B

I

II

III

IV

V

8,000

12,000

10,000

9,000

7,000

12,000

8,000

12,000

7,000

7,000

Total 46,000 46,000

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1. a) Define Managerial Economics and its characteristics.

b) What is demand? And explain the law of demand and its limitations. (7M+8M)

2. a) Define elasticity of demand and explain any two methods of measurement of

Elasticity of demand.

b) Explain the significance demand forecasting and describe any three methods (7M+8M)

of demand forecasting.

3. a) Describe the law of returns to scale.

b) Explain the significance, usefulness and limitations of Break-even analysis. (7M+8M)

4. a) What is a market? And explain the salient features perfect competition.

b) What is monopoly? And explain the price and output determination monopoly. (7M+8M)

5. Describe any five methods of pricing. (15M)

6. a) Briefly explain the salient features of Private and Public limited companies.

b) What is business cycle? And explain the phase and features of business cycles. (7M+8M)

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Code No: R22013

7. a) Explain the limitations of financial statements.

b) From the following Trial Balance and adjustments of Swaraj Emporium, (5M+10M)

Prepare trading and profit and loss account for the year ended

December, 31, 2013 and a Balance Sheet as on that date.

Rs. Rs.

Sundry debtors

Stock (1.1.2013)

Cash in hand

Plant and machinery

Sundry creditors

Trade expenses

Sales

Salaries

Carriage outwards

Rent

Bills payable

purchases

Discounts

Business premises

Capital (1.1.2013)

Cash at bank

64,000

44,000

70

35,000

2,150

4,450

800

1800

2,37,740

2,200

69,000

3090

-------------

4,64,300

21,300

2,69,000

15,000

1,59,000

------------

4,64,300

Adjustments:

The stock as on December 31,2013 was Rs. 24,900.

Rent was unpaid to the extent of Rs. 170.

Outstanding trade expenses were Rs. 300.

Write off for bad debts Rs. 800.

Provide 5% for doubtful debts.

Depreciate plant and machinery @ 10% per annum.

Business premises are to be depreciated by 2% per annum.

8. a) What is ratio analysis? And briefly explain the salient features of different ratio analysis.

b) Explain the meaning of capital Budgeting and briefly describe the different methods of

Capitalbudgeting. (7M+8M)

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1. a) Describe the importance of managerial Economics and explain the basic economic tools

Used in Managerial Economics.

b) Describe the demand analysis? And the salient features and limitations of demand law.

(7M+8M)

2. a) Define elasticity of demand. And explain different methods of price elasticity of demand.

b) Explain the importance of demand forecasting. And describe different methods of demand

Forecasting. (7M+8M)

3. a) Explain the salient features of Cobb-Douglas production function.

b) Describe the significance, assumptions and limitations of Break- even analysis.

(7M+8M)

4. a) Explain the conditions of perfect competition and monopoly.

b) Explain the importance of pricing policy and describe any three methods of pricing.

(7M+8M)

5. a)What is business? And explain the salient features of partnership.

b) Define business cycle and explain phases and features of business cycle. (7M+8M)

6. a) Explain the salient features Journal and ledger and their differences.

b) Explain the significance of trial balance and limitations of financial statements. (7M+8M)

7. a)What is ratio analysis? And briefly explain the salient features of different ratio analysis.

b) Calculate the funds from operations from the following particulars. (7M+8M)

March31, 2013 March 31, 2014

Rs. Rs.

Profit and loss account

General reserve

Goodwill

Patents

Preliminary expenses

Provision for depreciation account

Funds flow statement

7,50,000

5,00,000

30,000

25,000

10,000

30,000

10,50,000

6,00,000

20,000

15,000

----

40,000

8. a)What is the meaning of capital budgeting? And explain its need for capital decisions.

b) Explain the various methods of capital budgeting and their advantages. (7M+8M)

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Code No: R22011


PROBABILITY AND STATISTICS (Com. to CE, CHEM, PE)




~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Define conditional probability and State general multiplication rule of probability.

b) If A and B be events with ( ) ( ) ( ) .2.03.0,6.0 =∩== BAPandBPAP

( ). ( ) ( )i P A B and P B A ( ). ( )ii P A B∪

( ). ( ) ( )c ciii P A and P B ( ). ( ) ( ) .c c c c

iv P A B and P B A c) State and prove Rule of total probability. (5M+5M+5M)

2. a) Define Distribution function for discrete and continuous random variables.

b) Find the value of k and the distribution function F(x) given the probability density function

of a random variable X as: 2

( ) ,1

kf x x

x= − ∞ < < ∞

+ (7M+8M)

3. a) If X is a Poisson variate such that ( 2) 9 ( 4) 90 ( 6),P X P X P X= = = + = find the standard

deviation.

b) Find Moment Generating Function for normal distribution and hence find its mean and

variance. (7M+8M)

4. a) If a 1-gallon can of paint covers on the average 513.3 square feet with a standard deviation

of 31.5 square feet, what is the probability that the sample mean area covered by a sample of

40 of these 1-gallon cans will be anywhere from 510.0 to 520.0 square feet?

b) Determine a 95% confidence interval for the mean of a normal distribution with variance 2σ = 0.25 , using a sample of 100n = values with mean 212.3.x =

c) Find the value of 0.95F for 1 212 15andν ν= = degrees of freedom. (5M+5M+5M)

5. a) Explain the test procedure for large sample test concerning one proportion.

b) A storekeeper wanted to buy a large quantity of bulbs from two brands A and B

respectively. He bought 100 bulbs from each brand A and B and found by testing brand A

had mean life time of 1120 hrs and the S.D of 75 hrs and brand B had mean life time 1062

hrs and S.D of 82 hrs. Examine whether the difference of means is significant. Use a 0.01

level of significance. (7M+8M)

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Code No: R22011

6. a) Explain the test procedure for test of equality of two variances.

b) In a shop study, a set of data was collected to determine whether or not the proportion of

defectives produced by workers are the same for the day, evening, or night shift was

worked. The data were collected and shown in Table.

Shift Day Evening Night

Defectives 45 55 70

Non defectives 905 890 870

Use a 0.05 level of significance to determine if the proportion of defectives is the same for

all three shifts. (7M+8M)

7. The following data shows the values of sample mean ( x ) and range (R) for 10 samples for size

6 each. Calculate the values for central line and the control limits for Mean – chart and Range –

chart. Draw the control charts and comment on the state of control.

Sample No. 1 2 3 4 5 6 7 8 9 10

Mean ( x ) 43 49 37 44 45 37 51 46 43 47

Range (R) 5 6 5 7 7 4 8 6 4 6

(15M)

8. The containers from railway goods wagons are unloaded at a single platform of a railway

goods yard. The arrival rate of wagons is 8 wagons per day and service rate is 14 wagons per

day. Assuming the arrival rate and service rate to follow Poisson distribution, determine the

following:

i) Utilization of railway goods yard

ii) Average number of waiting wagons in the queue

iii) Average number of waiting wagons in the system

iv) Average waiting time per wagon in the queue

v) Expected waiting time per wagon in the system (15M)

Note :- The following Statistical tables are required

i) Areas under the Standard Normal Curve from 0 to Z,

ii) Percentile Values tp for Student’s t- distribution with v degrees of freedom,

iii) Percentile Values χp2 for the Chi-Square distribution with v degrees of freedom,

iv) Percentile Values (0.05 levels), F0.05 for the F- Distribution and

v) Percentile Values (0.01 levels), F0.01 for the F Distribution

vi) Control Chart Constants

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1. a) State and prove Baye’s theorem

b) If A and B be independent events with ( ) 0.3 , ( ) 0.4 .P A P B= =

Find ( ). ( ) ( )i P A B and P A B∩ ∪ ( ). ( ) ( )ii P A B and P B A

( ). ( ) ( )c ciii P A and P B ( ). ( ) ( ) .c c c c

iv P A B and P B A (7M+8M)

2. a) A discrete random variable X has the following probability distribution

Value of X 0 1 2 3 4 5 6 7 8

( )P X x= k 3 k 5 k 7 k 9 k 11 k 13 k 15 k 17 k

(i) Find the value of ‘ k ’ (ii) Find ( 3), (0 3), ( 3)P X P X P X< < < ≥ [7 M]

b) Find the value of k and the distribution function F(x) given the probability density

function of a random variable X as:

(3 2 ) 0 2( )

0

k x if xf x

otherwise

+ < <=

(7M+8M)

3. a) Find the mean and variance of the Poisson distribution.

b) Find the probabilities that a random variable having the normal distribution with 16.2µ =

and 2 1.5625σ = will take on a value

i) between 13.6 and 18.8 ;

ii) between 16.5 and 16.7 ;

iii) greater than 16.8;

iv) Less than 14.9.

(7M+8M)

4. a) Find the value of 0.95F for 1 210 20andν ν= = degrees of freedom.

b) Determine a 99% confidence interval for the mean of a normal distribution with variance 2σ = 9, using a sample of 100n = values with mean 5.x =

c) Find the value of the finite population correction factor for 100 5000n and N= = .

(5M+5M+5M)

5. a) Explain the test procedure for test concerning difference between two proportions.

b) A manufacturer claims that the average tensile strength of thread A exceed the average

tensile strength of thread B by at least 12 kilograms. To test his claim, 50 pieces of each

type of thread are tested under similar conditions. Type A thread had an average tensile

strength of 86.7 kilograms with known standard deviation of 6.28Aσ = kilograms, while

type B thread had an average tensile strength of 77.8 kilograms with known standard

deviation of 5.61Bσ = kilograms. Test the manufacturers claim at 0.05 level of

significance. (7M+8M)

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Code No: R22011

6. a) Explain the test procedure of 2χ test for analysis of r c× table.

b) The following random samples are measurements of the heat-producing capacity (in

millions of calories per ton) of specimens of coal from two mines:

Mine 1: 8,260 8,130 8,350 8,070 8,340

Mine 2: 7,950 7,890 7,900 8,140 7,920 7,840

Use the 0.01 level of significance to test whether the differences between the mean of these

two samples is significance. (7M+8M)

7. Samples of 100 tubes are drawn randomly from the output of a process that produces several

thousand units daily. Sample items are inspected for quality and defective tubes are rejected.

The results of 15 samples are shown below :

Sample

No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

No. of

Defective

tubes

8 10 13 9 8 10 14 6 10 13 18 15 12 14 9

On the basis of information given above prepare a control chart for fraction defective

(p - chart). What conclusion do you draw from the control chart? (15M)

8. A self-service store employs one cashier at its counter. 9 customers arrive on an average every

5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson

distribution for arrival rate and exponential distribution for service rate, find

i) Average number of customers in the system.

ii) Average number of customers in queue or average queue length.

iii) Average time a customer spends in the system.

iv) Average time a customer waits before being served. (15M)








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Code No: R22011






~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Define probability and write the axioms of probability for a finite sample space.

b) Given ( ) 0.35 , ( ) 0.40 ( ) 0.20P A P B and P A B= = ∩ = , Find

(i) ( )P A B∪ (ii) ( )P A B∩ (iii) ( )P A B∩ (iv) ( )P A B∪ (v) Are A and B independent?

c) Two cards are drawn at random from an ordinary deck of 52 playing cards. What is the

probability of getting two aces if (i) the first card is replaced before the second card is

drawn; (ii) the first card is not replaced before the second card is drawn? (5M+5M+5M)

2. a) Define discrete random variable and discrete probability distribution.

b) Let X be a continuous random variable with distribution :

2 0 1( )

0

k x if xf x

elsewhere

≤ ≤=

(i) Evaluate k (ii) Find (1 / 4 3 / 4).p X≤ ≤ (iii) Find ( 2 / 3).p X > (7M+8M)

3. a) Find Moment Generating Function for Binomial distribution and hence find its mean and

variance.

b) Find the probabilities that a random variable having the standard normal distribution will

take on a value

i) between 0.87 and 1.28 ;

ii) between -0.34 and 0.62 ;


iv) greater than -0.65. (7M+8M)

4. a) Take 30 slips of paper and label five each and -4,four each and -3,three each -2 and 2, and

two each -1,0 and 1.If each slip of paper has the same probability of being drawn , find the

probability of getting and find the mean and the variance of this distribution.

b) Determine a 99% confidence interval for the mean of a normal distribution with variance 2σ = 9 , using a sample of 100n = values with mean 5.x = (8M+7M)

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Code No: R22011

5. a) Explain the test procedure for large sample test concerning mean when σ is known.

b) A study of TV viewers was conducted to find the opinion about the mega serial

‘Ramayana’. If 56% of a sample of 300 viewers from south and 48% of 200 viewers from

north preferred the serial, , test the claim at 0.05 level of significance that there is a

difference of opinion between south and north. (7M+8M)

6. a) Explain the test procedure for small sample test concerning difference between two means.

b) Explain procedure for one-way classification of analysis of variance (7M+8M)

7. The following table shows the outer diameter values, 16 samples each measured five times, of

cores used for winding of a transparent tape in millimetres. Develop a control chart scheme

using both Mean ( X ) and Range (R) charts. (15M)

Sample

no.

Sub-Sample

observations

(in milliliters)

Sample

no.

Sub-Sample

observations

(in milliliters)

1 2 3 4 5 1 2 3 4 5

1 37 37 35 41 39 9 39 37 42 40 38

2 29 28 31 33 31 10 35 35 35 36 40

3 33 30 35 42 31 11 38 33 32 35 32

4 35 37 33 34 36 12 28 30 28 32 31

5 35 35 33 34 33 13 31 35 35 35 34

6 33 34 35 33 34 14 29 32 34 35 37

7 30 31 32 34 31 15 38 35 34 34 34

8 35 40 38 39 39 16 31 37 39 44 38

8. a) Explain briefly the main characteristics of Queuing system?

b) Explain Traffic intensity?

c) Explain (M/ M/ 1): (∞ / FCFS) Queuing model. (5M+5M+5M)








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Code No: R22011






~~~~~~~~~~~~~~~~~~~~~~~~

1. a) If A and B are any events in then prove that

( ) ( ) ( ) ( )P A B P A P B P A B∪ = + − ∩

b) If A and B be events with 1 1 1

( ) , ( ) ( ) .3 4 2

P A P B and P A B= = ∪ = Find

i) ( )BAP / ii) ( )ABP / iii) ( )cBAP ∩ iv) ( )c

BAP /

c) If ( ) 0.65 , ( ) 0.40 ( ) 0.24 ,P A P B and P A B= = ∩ = are the events A and B is independent?

(5M+5M+5M)

2. a) Define continuous random variable and continuous probability distribution.

b) Let X be a continuous random variable with distribution :

0 1

( ) 2 1 2

0

x for x

f x x for x

elsewhere

< <

= − ≤ <

Find (i) (0.2 0.8)p X≤ ≤ (ii) (0.6 1.2)p X≤ ≤ (7M+8M)

3. a) Find Moment Generating Function for Poisson distribution and hence find its mean and

variance.

b) Find the probabilities that a random variable having the standard normal distribution will

take on a value

i) less than 1.75 ;

ii) less than -1.25 ;


iv) greater than -1.82. (7M+8M)

4. a) Find the value of the finite population correction factor for 10 1000n and N= = .

b) Find the value of 0.99F for 1 26 20andν ν= = degrees of freedom.

c) Determine a 95% confidence interval for the mean of a normal distribution with variance 2σ = 4 , using a sample of 200n = values with mean 120.x = (5M+5M+5M)

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Code No: R22011

5. a) Explain the test procedure for large sample test concerning difference between two means.

b) In a survey of A.C. machines produced by company A it was found that 19 machines were

defective in a random sample of 200 while for company B 5 were defective out of 100. At

0.05 level of significance is there reason to believe that there is significance difference in

performance of A.C. machines between the two companies A and B. (7M+8M)

6. a) Explain the test procedure for small sample test concerning mean.

b) Explain procedure for two-way classification of analysis of variance. (7M+8M)

7. During an inspection, 20 of successively selected samples of polished metal sheet, the number

of defects observed per sheet is recorded, as shown in the following table. Construct a C-chart

for the number of defects. (15M)

Sample no. No. of defects Sample no. No. of defects

1 3 11 5

2 0 12 2

3 5 13 1

4 1 14 1

5 2 15 2

6 3 16 3

7 2 17 4

8 4 18 0

9 0 19 1

10 2 20 2

8. a) Derive the average number of customers in the Queue. In (M/M/1) ( ∞ /FCFS) model.

b) At a public telephone booth the arrivals are on the average 15 per hour. A call on the

average takes 3 minutes. If there is just one phone.

i) What is expected number of callers in the booth at any time?

ii) For what proportion of time in the booth expected to be idle. (7M+8M)








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Code No: R22012


STRENGTH OF MATERIALS

(Civil Engineering)




~~~~~~~~~~~~~~~~~~~~~~~~~

1. For the beam shown in Figure. Find the deflection at D and the maximum deflection between

A and B.

2. A cylindrical shell 900 mm long, 150 mm internal diameter, having a thickness of metal 8mm,

is filled with a fluid at atmospheric pressure. If an additional 20,000 mm3 of fluid is pumped

into the cylinder find. (i) the pressure exerted by the fluid on the cylinder, and (ii) the hoop

stress induced.

Take. E = 2x105 N/mm

2 and

�

� = 0.3

3. A beam 3 metres long, of I section is freely supported at its ends with the web vertical. It

carries concentrated loads of 100 kN at 0.6 metre from each end. The flanges are each 150

mm wide and 25 mm thick, the overall depth being 400 mm. The thickness of the web is 12.5

mm. Calculate the principal stresses and the maximum shearing stress in a section of the beam

where the bending moment and shearing forces, both have maximum values.

4. The stepped shaft is as shown in Figure is rigidly attached to a wall at E. Determine the angle

of twist of the end A when the two torques at B and at D are applied. Assume the shear

modulus G to be 80 GPa for steels.

5. a) What are the limitations of Euler’s formula.

b) A cast iron column with a 10 cm external diameter and 8 cm internal diameter is 3 m long.

Calculate the safe load using Rankine’s formula if (i) both ends are hinged, (ii) both ends are

fixed. �c = 600 N/mm2 and a = 1/1600. Adopt a factor of safety of 3.

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Code No: R22012

6. A masonry pier of 3 m x 4 m supports a vertical load of 80kN as shown in figure.

i) Find the stresses developed at each corner of the pier.

ii) What additional load should be placed at the centre of the pier, so that there is no tension

anywhere in the pier section?

iii) What are the stresses at the corners with the additional load in the centre?

7. A cantilever beam of I-section is used to support the loads inclined to the V-axis as shown in

Figure. Calculate the stresses at the corners A,B,C and D. Also locate the neutral axis.

8. Determine the forces in the members AB, AC, DF and CE of the scissors truss shown in

figure.

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Code No: R22012



(Civil Engineering)




~~~~~~~~~~~~~~~~~~~~~~~~~

1. A beam simply supported at the ends has a span l carries three point’s load W each

symmetrically placed on the span at interval of �

� . Find the central deflection and slope at the

ends.

2. A cylinder 250 mm in diameter has a wall thickness of 5 mm and is full of a fluid at

atmospheric pressure. Its ends are closed by rigid plates and an axial compressive force of

80kN is applied to the cylinder so that the pressure of the fluid rises by 90 kPa. Calculate the

bulk modulus of the fluid. Take for the cylinder material E = 200kN/mm2

and �

� = 0.25.

3. Figure shows the normal and tangential stresses on two planes. Determine the principal

stresses.

4. A solid shaft is required to transmit 330 kW at 120 r.p.m. The shear stress of the material must

not exceed 80 MN/m2. (a) Find the diameter required. (b) If the shaft is replaced by a hollow

one with a diameter ratio of 3:5 and the maximum shear stress remaining unchanged, calculate

the percentage saving in weight that could be obtained.

5. Derive the Rankine Gordon empirical formula established for the design of columns.

6. a) What conditions are implemented to ensure the stability of the dam.

b) A concrete dam of rectangular section 15 m high and 6 m wide contains water up to a

height of 13 m. Find

total pressure per metre length of the dam,

Point, where the resultant cuts the base and

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Code No: R22012

Maximum and minimum intensities of stress at the base.

Assume weight of water and concrete as 10 and 25 kN/m3 respectively.

7. For the beam loaded as shown in Figure. Determine the stress at A and locate the neutral axis.

A Force of 30 kN at 300 is applied at O. The Flange thickness is 5 mm and height of the

flange(vertically) is 15 cm.

8.Find the forces in all the members of a truss as shown in figure.

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Code No: R22012



(Civil Engineering)




~~~~~~~~~~~~~~~~~~~~~~~~~

1. Describe the procedure to find out the deflection of a beam using Macaulay’s method with

various conditions about the slope and deflection.

2. The internal and external radii of a thick cylinder are 200 mm and 300 mm respectively. The

external pressure on the cylinder is 4 N/mm2. Find the internal pressure that can be applied if

the maximum hoop stress is limited to 15N/mm2. Sketch also the distribution of radial

pressure and hoop stress across the wall section.

3. A bending moment M applied to a solid round shaft causes a maximum direct stress at elastic

failure. Determine the numerical relation between M and a twisting moment T which acting

alone on the shaft will produce elastic failure, according to each of the following theories of

failure.

Maximum principal stress theory,

Maximum principal strain theory,

Maximum strain energy theory,

Maximum shear stress theory,

Take Poisson’s ratio = 0.30.

4. Prove that a hollow shaft is stronger and stiffer than a solid shaft of same material, length and

weight.

5. A steel strut, 3 m long and hinged at both ends, has a circular cross-section. Find the necessary

diameter in order that a thrust of 200 kN acting at an eccentricity of 1/10th

diameter will not

produce a compressive stress greater than 100 N/mm2. If the yield stress is 330 N/mm

2, find

the crippling load of the strut for the same eccentricity. E = 205 kN/mm2.

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Code No: R22012

6. Find the stability of the retaining wall shown in Figure. Also find the extreme stresses at the

base of the wall as 16 kN/m3 respectively. Assume angle of internal friction of the soil as 30°.

7. The cross-section of a beam is shown in Figure. It carries a load of 10kN/m over its whole

simply supported span of 1 m. Determine central deflection. Take E = 70 GN/m2. The plane of

loading is 50° to the plane of the web.

8.A truss 15 m long is subjected to a point load of 10 kN as shown in Figure. Find the forces in the

members 1, 2 and 3 of the truss.

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Code No: R22012



(Civil Engineering)




~~~~~~~~~~~~~~~~~~~~~~~~~

1. A horizontal beam of symmetrical section simply supported at the ends, carries a load whose

intensity varies uniformly from 18kN/m at one end to 72 kN/m at the other. Find the central

deflection in the span is 6 m, the section is 450 mm deep and the maximum bending stress is

90 N/mm2. Take E = 200 kN/mm

2.

2. A thick spherical shell of 160 mm internal diameter is subjected to an internal fluid pressure

40 N/mm2. If the permissible tensile stress is 80N/mm

2, find the thickness of the shell.

3. A hollow shaft is subjected to a torque of 36000 Nm and a bending moment of 27000 Nm.

The internal diameter of the shaft is one half of the external diameter. If the maximum shear

stress shall not exceed 80 N/mm2, find the diameter of the shaft.

4. a) Derive the deflection of open coiled, helical spring under axial pull.

b) A close coiled helical compression spring of 12 acting coils has a spring stiffness of K. It is

cut into two springs having 5 & 7 turns. Determine spring stiffness of resulting spring.

5. a) Derive the maximum stress for a laterally loaded struts subjected to uniformly distributed

load.

b) Compare the effective length as a long column with different end conditions.

6. a) Classify and explain the earth pressure of the soil.

b) A chimney shaft 30 m high, tapers from 3 m external diameter at the base to 1.5 m external

diameter at the top. The inside diameter at the base 2 m. if the horizontal wind pressure

acting on a flat surface is 1500 N/m2, find the distribution of stress on the base. Weight of

chimney is 2 MN. Reduction factor for wind resistance for a circular section is 0.6.

7. A wooden beam of cross-section 80 mm x 240 mm rests on an earth foundation. The modulus

of elasticity of wood is 10 GN/m2 and modulus of foundation is 5 MN/m

2. A uniformly

distributed load of 2 kN/m acts on the middle portion of this very long beam over a span of

2m. Compute the maximum deflection and the maximum bending stress in the beam.

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Code No: R22012

8. A framed structure of 6 m span is carrying a central point load of 10 kN as shown in Figure.

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Code No: R22016


STRUCTURAL ANALYSIS – I (Civil Engineering)




~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) How is the propped reaction determined? Explain

b) Draw S.F.D and B.M.D for a propped cantilever shown in the Figure 1.

2. a) A fixed beam of span 6m is subjected to u.d.l of 30kN/m. Locate the point of contra flexure.

b) Determine the end moments of a fixed beam of span ABC with AC = 4cm, CB = 8cm fixed

at A and B. It carries a uniformly distributed load of 60kN/m for the span AC and a

concentrated load 60kN at C.

3. A continuous beam consists of three successive spans 8m,9m and 7m and carries loads of

60kN/m,40kN/m and 80kN/m respectively on the spans. Determine the B.M and the reactions

at the supports.

4. A continuous beam of uniform section consists of spans AB and BC of lengths 5m and 4m

respectively. The end A is fixed and span AB is subjected to clockwise couple of 90kNm at its

middle point .Find the moments and reactions at the support. Draw B.M.D.Use slope deflection

method

5. a) State and prove Castigliano’s first theorem.

b) Derive the energy stored due to axial loading.

6. a) What is the condition for absolute bending moment due to moving UDL longer than span.

b) Two point loads of 140 kN and 200kN spaced 4m apart, cross a girder of 22 metres span

from left to right with 140kN leading. Construct the maximum shear force and maximum

bending moment diagrams stating the absolute maximum values.

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C A

B 2 m

Figure 1

D

5 kN/m 20 kN

2 m

1 m

||''''|||''|'''||''|

Code No: R22016

7. a) Define Influence line.

b) Find the shear force at the section X shown in Figure 2 for the loaded beam by method of

influence lines.

8. Find the horizontal deflections of the joint C of the truss shown in Figure 3. The sectional areas

of the members are as follows

Horizontal members = 1200 mm2

Vertical members = 1600 mm2

Inclined members = 2500 mm2 .Take E = 200 kN/mm

2

2 of 2

R10 SET - 1

80 kN

A B

2 m 2m

Figure 2

3 m 1 m 4m

50 kN 45 kN

A

B C

E

D

5 kN

7 kN 5 m

1.5 m

1m 1m 2 m 2 m

Figure 3

||''''|||''|'''||''|

Code No: R22016






~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Classify different types of props. Explain with figures.

b) A propped cantilever beam of 5m is subjected to uniformly distributed load 50kN/m

throughout the span. Draw SFD and BMD.

2. a) A fixed beam of span 5m is subjected to u.d.l of 30kN/m. Find the fixing moment at the

either support and the bending moment at the support.

b) Determine the end moments of a fixed beam of span ABC with AC = 6cm, CB = 9cm fixed

at A and B. It carries a uniformly distributed load of 80kN/m for the span AC and a

concentrated load 80kN at C.

3. A continuous beam consists of three successive spans 6m,7m and 8m and carries loads of

50kN/m,40kN/m respectively on the two spans and 60kN at the mid span of third span.

Determine the B.M and the reactions at the supports.

4. A continuous beam of uniform section consists of spans AB and BC of lengths 6m and 4m

respectively. The end A is fixed and span AB is subjected to clockwise couple of 70kNm at its

middle point. Find the moments and reactions at the support. Draw B.M.D. Use slope

deflection method.

5. a) State and prove Maxwell’s Reciprocal theorem.

b) Derive the energy stored due to bending.

6. a) What is the condition for absolute bending moment due to moving UDL longer than span.




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Code No: R22016

7. a) Define Influence line. What is the shape of the influence line diagram for maximum bending

moment in a simply supported beam?

b) Draw the influence line diagram for a shear force at any section of a simply supported beam.

8. Find the horizontal deflection of the joint C of the truss shown in Figure 1.The sectional areas




Inclined members = 2500 mm2 Take E = 200 kN/mm

2

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R10 SET - 2

A

B C

E

D

5 kN

7 kN 5 m

1.5 m

1m 1m 2 m 2 m

Figure 1

||''''|||''|'''||''|

Code No: R22016






~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Classify different types of props. Explain with figures.

b) A propped cantilever of span of l is subjected to a moment M at the prop. Draw the shear

force and bending moment diagram indicating all the salient features..

2. a) What are the end moments induced at the end of fixed beam A and B due to rotation өA

b) A fixed beam AB of length 6m carries point loads of 160kN and 120kN at a distance of 2m

and 4m from left end A. Find the fixed end moments and reactions at the supports. Draw

SFD and BMD.

3. A continuous beam ABC consists of spans 4m and 5m respectively, the ends A and C being

simply supported .If spans carries loads of 50kN/m and 40kN/m respectively.. Draw the S.F.D

and B.M.D. Determine the supports moments at A,B and C. The moments of inertia for the

spans AB and BC are I and 2I respectively.

4. a) Derive the Claperyon’s theorem.

b) Analyse the continuous beam shown in Figure 1.by three moment theorems. Draw SFD and

BMD.

5. a) State and prove Maxwell’s Reciprocal theorem.

b) A cantilever beam of span 2m and is subjected to a concentrated load of 20kN at the free

end .The cross section of the beam is 100 x 200 mm,E = 30 kN/mm2.Calculate the slope and

deflection of the beam at the mid span. Use unit load method

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R10 SET - 3

16 kN/m

D

25 kN

Figure 1 A B C

4 m 6 m

5 m E

||''''|||''|'''||''|

Code No: R22016

6. a) What is the absolute bending moment when a single concentrated load rolls across the span..




7. a) A simply supported beam has a span of 25m.Draw the influence line diagram for a shearing

force at a section 10m from one end and by using this diagram determine the maximum

shear force due to the passage of 5kN load followed immediately by a uniformly distributed

load of 2.4kN/m extending over a length of 5m.

b) Draw the influence line diagram for a shear force at any section of a simply supported

beam.

8. Find the horizontal deflection of the joint C of the truss shown in Figure 3.The sectional areas





2

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R10 SET - 3

A

B C

E

D

5 kN

7 kN 5 m

1.5 m

1m 1m 2 m 2 m

Figure 2

||''''|||''|'''||''|

Code No: R22016






~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) List the support restraints and the unknown reactions in case of propped cantilevers..

b) A propped cantilever of span of l is subjected to a moment M at the prop. Draw the shear

force and bending moment diagram indicating all the salient features.

2. a) What are the end moments induced at the end of fixed beam A and B due to rotation өA

b) A fixed beam AB of length 8m carries point loads of 100kN and 120kN at a distance of 3m

and 5m from left end A. Find the fixed end moments and reactions at the supports. Draw

SFD and BMD.

3. A continuous beam ABC consists of spans 3m and 4m respectively, the ends A and C being

simply supported .If spans carries loads of 40kN/m and 30kN/m respectively . Draw the S.F.D

and B.M.D. Determine the supports moments at A,B and C. The moments of inertia for the

spans AB and BC are I and 2I respectively

4. Derive the Claperyon’s theorem.

b) Analyse the continuous beam shown in Figure 1.by three moment theorems. Draw SFD and

BMD.

5. a) State and prove Bette’s law

b) A cantilever beam is of span 3m and is subjected to a concentrated load of 30kN at the free

end .The cross section of the beam is 100 x 200 mm,E = 30 kN/mm2.Calculate the slope and

deflection of the beam at the mid span. Use unit load method

6. a)What is the absolute bending moment when a single concentrated load rolls across the span..




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R10 SET - 4

D

10 kN

Figure 1

A B C

4m 2m 3 m 3 m

6 m

10 kN

6 mE

||''''|||''|'''||''|

Code No: R22016

7. a) A uniformly distributed load 50kN/m of 6m length crosses a grider of span 40m left to right

with the help of influence lines ,determine the value of shear force and bending moment at

12m from the left support when the head of the load is 6m from the left support.

b) Draw the influence line diagram for a bending moment at any section of a simply supported

beam.

8. Find the horizontal deflection of the joint C of the truss shown in figure3.The sectional areas of

the members are as follows




2

2 of 2

R10 SET - 4

A

B C

E

D

5 kN

7 kN 5 m

1.5 m

1m 1m 2 m 2 m

Figure 3

code no: r22015 ii b. tech ii semester supplementary ... · ii b. tech ii semester supplementary...

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