code no: r22015 ii b. tech ii semester …...ii b. tech ii semester supplementary examinations...

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Code No: R22015

II B. Tech II Semester Supplementary Examinations Jan/Feb - 2015

ENGINEERING GEOLOGY (Civil Engineering)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions

All Questions carry Equal Marks

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1. Describe the role of geology in various civil engineering projects. Add some case histories

where lack of geological knowledge resulted failure of projects.

2. Write physical properties, chemical composition and characteristics features of following

minerals

a) Quartz b) Hematite c) Galena d) Talc

e) calcite f) Muscovite g) Pyrite h) Magnetite

3. Classify different rock types as per geological nomenclature and add a note on the origin of

different rock types. Give examples.

4. Write notes on the following:

a) Folds b) Faults c) Unconformities d) Joints

5. Write an essay on the causes behind the occurrence of Earth quakes. Add a notes on shield

areas and seismic belts.


a) Principles of gravity methods

b) Principles of magnetic methods

7. Discuss various geological considerations to be taken up in the selection of a dam site. Give

examples and present neat figures.

8. What is meant by tunneling? Give different types of affects due to tunneling and add a notes

on geological consideration in tunneling.

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Code No: R22015






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1. What is meant by “weathering of rocks” and discuss the affects of weathering with reference to

the construction of dams, reservoir, tunnels etc.

2. Write down the physical properties, chemical composition and origin of following minerals

a) Olivine b) Jasper c) Chlorite d) Biotite

e) Kyanite f) Garnet g) Hornblende h) Galena


a) Structures of igneous rocks

b) Conglomerate and Sandstone

c) Marble and Slate

4. Discuss in detail the origin, occurrence of different types of soils in India. Add a note on how

we can stabilize the soils.

5. Discuss in detail the origin and occurrence of groundwater. Add a note on techniques of

ground water exploration


a) Rock mechanics b) Environmental geology

7. Write an account on the dam failures with relevant examples


a) Role of geology in tunneling

b) Types and purpose of tunneling

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Code No: R22015






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1. What is the importance of the geological knowledge to be a successful civil Engineer? Give

examples while elaborating the above statement.

2. Define a “Mineral”. Discuss the importance and methods of study of minerals. Give some

examples of identifying minerals using their physical properties.


a) Basalts b) Dolerite c) Conglomerate d) Shale e) Schist f) gneiss

4. Write an account on the common geological structures associated with various types of rocks.

Describe their morphology with the help of neat figures.


a) Ground water exploration

b) Landslide causes and affects

c) Earth quakes causes and affects

6. Write notes on the principles and applications of radiometric methods and electrical resistivity

methods in exploration. Give examples.

7. What are various factors that contribute the success of a reservoir? Give some geological

factors which are important for the success of a reservoir.

8. Discuss role of lithology, structure and groundwater conditions of a given area in the successful

implementation of a tunneling project.

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Code No: R22015






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1. Discuss the importance of physical geology, petrology and structural geology in the Civil

engineering construction projects. Give examples.

2. Write notes on physical properties and chemical composition of the following economic

minerals

a) Graphite b) Bauxite c) Pyrolusite d) Pyrite e) Chlorite f) Calcite

3. What is the basis for rock classification. Give the origin, occurrence of igneous, sedimentary

and metamorphic rocks. Give examples.


a) Out crop b) Srike and Dip c) Folds and Faults


a) Ground water table b) Ground water exploration c) Earthquakes d) Landslides

6. Write an account on principles and importance of geophysical methods.

7. Discuss in detail different types of dams and geological considerations to be taken up for each

type of dam. Give suitable examples substantiated by neat figures.

8. What is the role of geology in the successful tunneling program? Give different factors to be

considered in different lithologoical terrains.

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Code No: R22014


HYDRAULICS AND HYDRAULIC MACHINERY (Civil Engineering)




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1. a) Define an open channel and compare open channel with pipe flow.

b) Determine the expressions for the most economical depths of flow of water in terms of the

diameter of a channel of circular cross-section for maximum velocity. (7M+8M)

2. a) Derive the equation for gradually varied flow.

b) In a rectangular channel 0.6 m wide, a hydraulic jump occurs where the Froude number is 3.

The depth after the jump is 0.6 m. Estimate the total loss of head and the power dissipated

due to jump. (7M+8M)

3. a) What are the limitations of hydraulic similitude?

b) Explain what is meant by dynamic similarity between a flow system and its model. If the

dynamic behavior of the flow system for an overflow spillway is governed by the Froude

law of similarity, what would be the discharge Qr, when the (model) scale ratio is Lr? Show

that the same result would be obtained if the weir formula is used instead and it is assumed

that the prototype and the model spillways have the same coefficient of discharge. (7M+8M)

4. a) Derive the expression for force of jet impinging on a moving curved vane.

b) A jet of water having a velocity of 45 m/s impinges without shock on a series of vanes

moving at 15 m/s. The direction of motion of the vanes is inclined at 200 to that of jet, the

relative velocity at outlet is 0.9 of that at inlet and absolute velocity of water at exit is to be

normal to the motion of vanes. Find i) vane angles at inlet and outlet and ii) Work done on

vanes per N (newton) of water supplied by jet. (7M+8M)

5. a) Classify hydraulic turbines based on head, flow type and specific speed.

b) Determine the maximum height of straight conical draft tube of 13240 KW Francis turbine

running at 150 r.p.m., under a net head of 27 m. The turbine is installed at station where the

effective atmospheric pressure is 10.6 m of water. The draft tube must sink at least 0.77 m

below the tail race. (7M+8M)

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Code No: R22014

6. a) Explain the performance characteristics of Kaplan turbine.

b) In a hydroelectric station, the water is available under a head of 15 m at the rate of 100 m3/s.

Calculate the number of turbines with a speed of 65 r.p.m and 82% efficiency. The specific

speed of the turbine is not to exceed 125 r.p.m. Also calculate the power produced by each

turbine. (5M+10M)

7. a) Classify centrifugal pumps and give advantages of centrifugal pumps over reciprocating

pumps.

b) A three stage centrifugal pump has impellers 400 mm in diameter and 20 mm wide at outlet.

The vanes are curved back at the outlet at 450 and reduce the circumferential area by 10 %.

The manometric efficiency is 90 % and overall efficiency is 80 %. The pump is running at

1000 r.p.m and delivering 0.05 m3/s. Determine:

i) Head generated by the pump and ii) Shaft power required to run the pump.

(7M+8M)

8. a) Compare hydropower stations with thermal power stations.

b) A hydro-electric power plant produces 20 MW under a head of 15m. If the overall efficiency

of the plant is 72%, determine: i) Type of turbine ii) Synchronous speed of the generator.

(7M+8M)

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Code No: R22014






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1. a) List out and explain the types of flow in channels.

b) A rectangular channel 3 m wide takes a discharge of 5 m3/s at a water depth of 1m. If it is

converted to a trapezoidal channel of side slopes 1:2, would there be an appreciable saving

in the power lost? Take C, the Chezy’s constant as 50 in SI units for each case. (7M+8M)

2. a) Define critical depth, critical velocity and critical flow.

b) A rectangular channel 6 m wide discharges 1440 liters/s of water into a 6 m wide apron with

no slope with a mean velocity of 6 m/s. What is the height of the jump? How much energy

is absorbed in the jump? (7M+8M)

3. a) Define and explain geometric, kinematic and dynamic similarities.

b) An air duct is to be modeled to a scale of 1:20 and tested with water which is 50 times

viscous and 800 times denser than air. When tested under dynamically similar conditions,

the pressure drop between two sections in the model is 235 kPa. What is the corresponding

pressure drop in the prototype? (7M+8M)

4. a) Derive the expression for work done and efficiency of jet striking centrally on a moving

curved vane. Also find the condition for maximum efficiency.

b) A 75 mm diameter jet having a velocity of 30 m/s strikes a flat plate, the normal of which is

inclined at 450 to the axis of the jet. Find the normal pressure on the plate,

i) When the plate is stationary

ii) When the plate is moving with a velocity of 15 m/s in the direction of the jet, away from

the jet. Also determine the power and efficiency of the jet when the plate is moving.

(7M+8M)

5. a) Compare impulse turbine with reaction turbine.

b) An inward flow reaction turbine is working under a head of 25 m and running at 300 r.p.m.

The velocity of periphery of the wheel is 30 m/s and velocity of flow is 4 m/s. If the

hydraulic losses are 20 % of the available head and the discharge is radial, find:

i) Guide blade at inlet, ii) Wheel angle at inlet and iii) Diameter of the wheel.

(5M+10M)

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Code No: R22014

6. a) Explain the governing of impulse turbines.

b) Find the type of turbine you would employ to develop 1700 kW under a head of 150 m at

350 r.p.m, while discharging 1.75 cubic meters of water per second. (7M+8M)

7. a) Derive the expression for work done by centrifugal pump on liquid.

b) It is required to deliver 0.048 m3/s of water to a height of 24 m through a 150 mm diameter

pipe and 120 m long by a centrifugal pump. If the overall efficiency of the pump is 75 %

and co-efficient of friction, f = 0.01 for the pipe line, find the power required to drive the

pump. (7M+8M)

8. a) A hydro-electric power plant produces 20 MW under a head of 15 m. If the overall efficiency

of the plant is 72%, determine:

i) Type of turbine ii) Synchronous speed of the generator.

b) Define and explain the following terms in detail:

i) Load factor ii) Utilization factor iii) Capacity factor

(7M+8M)

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1. a) Give a brief note on energy and momentum correction factors.

b) Design a concrete lined channel to carry a discharge of 500 m3/s at a slope of 1 in 4000. The

side slopes of channel may be taken as 1:1. The manning’s roughness co-efficient for the

lining is 0.014. Assume the permissible velocity in the section as 2.5 m/s. (7M+8M)

2. a) Derive the equation for Non-uniform flow.

b) Determine the depth flow after the jump in a horizontal rectangular channel and consequent

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

20 m/s and depth of 2 m. (6M+9M)

3. a) Explain Rayleigh’s method of dimensional analysis.

b) An overflow structure 30m long discharges water at the rate of 750 m3/s under a head of 8m.

A model test of this structure is to be carried out in a laboratory with a maximum supply

available at 50 lit/sec. Recommend a suitable scale ratio for the model. (7M+8M)

4. a) Derive the expression for work done and efficiency of jet striking at the tip of a moving

curved vane.

b) A jet of water moving with a velocity of 20 m/s strikes curved vanes moving with a velocity

of 10 m/s. The jet makes an angle of 200 with the direction of motion of vanes at inlet and

leaves at an angle of 1300 with the direction of motion of the vanes. Calculate the vane

angles at inlet and outlet, so that the water has shock less entry and exit. (7M+8M)

5. a) What is a draft tube. Derive the expression for efficiency of draft tube and explain the types

of draft tubes.

b) A Pelton wheel has a mean bucket speed of 12 m/s and is supplied with water at the rate of

0.7 m3/s under a head of 30 m. If the buckets deflect the jet through an angle of 160

0, find

the power and the efficiency of the turbine. (7M+8M)

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Code No: R22014

6. a) What is cavitation? How we can prevent cavitation in turbines.

b) A hydraulic turbine is to develop 1015 KW when running at 120 r.p.m under a net head of

12 m. Work out the maximum flow rate and specific speed for the turbine if the overall

efficiency at the best operating point is 92%. In order to predict its performance, a 1:10 scale

model is tested under a head of 7.2 m. What would be the speed, power output and water

consumption of the model if it runs under the conditions similar to the prototype?

(7M+8M)

7. a) Explain various head, losses and efficiencies of a pump.

b) A centrifugal pump is required to discharge 0.2 m3 of water per second against a head of

22 m when the impeller rotates at a speed of 1500 r.p.m. The manometric efficiency is 75%.

The head loss in pump in meters due to fluid resistance is 0.03V22 where V2 m/s is the

velocity of water leaving the impeller. The area of the impeller outlet surface is 1.2 D22 m

2,

where D is the impeller diameter in m. Determine: i) The impeller diameter and

ii) The outlet vane angle. (7M+8M)

8. a) Define and explain the following terms in detail:

i) Load factor ii) Utilization factor iii) Capacity factor

b) Classify hydro power plants and list out the advantages and applications of hydro power

plants. (7M+8M)

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1. a) Calculate the specific energy, critical depth and velocity for the flow of 10 m3/s in a cement

lined rectangular channel 2.5 m wide with 2 m depth of water. Is the given flow subcritical

or supercritical?

b) Determine the most economical section of rectangular channel carrying water at the rate of

0.5 m3/s, the bed slope of the channels being 1 in 2000. Take Chezy’s constant C = 50.

(7M+8M)

2. a) What is hydraulic jump, explain in detail.

b) Water flows at a velocity of 1 m/s and a depth of 2 m in an open channel of rectangular cross

section, 3 m wide. At a certain section the width is reduced to 1.8 m and the bed is raised by

0.65 m. Will the upstream depth be affected? If so, to what extent? (7M+8M)

3. a) Explain the relation between model and prototype.

b) The efficiency of a fan depends upon density, dynamic viscosity of the fluid, angular

velocity of rotor, diameter of rotor and discharge of fluid. Explain in terms of dimensionless

parameters. (7M+8M)

4. a) Derive the expression for work done and efficiency of jet impinging on a series of vanes.

b) A jet of water moving at 12 m/s impinges on a concave vane shaped to deflect the jet

through 1200 when stationary. If the vane is moving at 5 m/s, find the angle of jet so that

there is no shock at outlet. What is the absolute velocity of jet at exit and the work done per

KN of water? Assume that the vane is smooth. (7M+8M)

5. a) Derive the expression for work done and efficiency of Francis turbine.

b) Calculate the efficiency of a Kaplan turbine developing 2900 KW under a net head of 5 m. It

is provided with a draft tube with its inlet (diameter 3 m) set 1.6 m above the tail race level.

A vacuum gauge connected to the draft tube indicates a reading of 5 m of water. Assume

draft tube efficiency as 78%. (7M+8M)

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Code No: R22014

6. a) What is surge tank? Give a brief note on different types of surge tanks.

b) A Pelton wheel generates 8000 KW under a net head of 130 m at a speed of 200 r.p.m.

Assuming the co-efficient of velocity for the nozzle 0.98, hydraulic efficiency 87%,

mechanical efficiency 75%, speed ratio 0.46 and jet diameter to wheel diameter ratio is 1/9,

determine: i) Discharge required ii) Diameter of the wheel

iii) Diameter and number of jets required and iv) Specific speed (6M+9M)

7. a) Explain the characteristics of centrifugal pump.

b) Two geometrically similar pumps are running at the same speed of 1000 r.p.m. One pump

has an impeller diameter of 300 mm and lifts water at the rate of 0.02 m3/s against a head of

15 m. Determine the head and impeller diameter of the other pump to deliver half the

discharge. (6M+9M)

8. a) Classify hydro power plants and list out the advantages and applications of hydro power

plants.

b) Compare hydropower stations with thermal power stations. (7M+8M)

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Code No: R22013


MANAGERIAL ECONOMICS AND FINANCIAL ANALYSIS

(Com. to CE, MM)




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1. a) Explain the importance of managerial economics and describe its characteristics.

b) What is demand? And explain its functions, law of demand and its exceptions.

2. a) Define elasticity of demand and explain different types of elasticity of demand.

b) Explain the importance of demand forecasting and describe the factors governing demand

forecasting.

3. a) Explain production function and describe the Cobb-Douglas production function.

b) Describe the importance of costs in the production and explain any two cost concepts.

4. a) Explain the market structures and describe salient features of perfect competition.

b) Describe the importance of pricing policies and write down any three methods of pricing.

5. a) Explain the characteristics of industrial organization and describe the salient features of

Sole proprietorship.

b) Describe the salient features of private and public limited companies of Joint Stock

Companies.

6. What is financial accounting? And explain the concepts Journal, Ledger and Trial Balance.

7. Explain the importance of ratio analysis and describe the concepts of Liquidity, Profitability

and Solvency Ratios.

8. Describe the meaning and need of the capital budgeting and explain any two methods of capital

budgeting.

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Code No: R22013



(Com. to CE, MM)




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1. a) Explain the scope and meaning of Managerial Economics.

b) Describe the importance of demand analysis and explain its determinants.

2. a) Define elasticity of demand and write any two methods of price elasticity of demand.

b) Explain the importance of demand forecasting and write any two methods of demand

forecasting.

3. a) Describe Isoquant and Isocost curves and explain the least cost combination of inputs.

b) Explain the significance of Break-even point and its assumptions and limitations.

4. Describe the salient features of monopoly and its price -output determination in the short-run.

5. Describe the salient features of partnership, its types, advantages and disadvantages.

6. Describe the importance of financial accounting and explain the concepts of Double-entry

system, Journal, Trail Balance and Final accounts.

7. What is ratio analysis? And explain Liquidity, Profitability and Solvency ratios.

8. Describe the importance of capital in the production and explain the capital budgeting, its

meaning, need and decisions.

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Code No: R22013



(Com. to CE, MM)




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1. a) Explain the relation of Managerial Economics with other subjects and mention the basic

tools in Managerial Economics.

b) What is Demand? And explain the law of demand and its limitations.

2. a) What is price elasticity of demand? And explain the types of elasticity of demand.

b) Explain the forecasting demand for new products and describe the criteria for good

forecasting method.

3. a) Describe law of variable proportions and explain its different phases.

b) Explain the importance of costs in the production and describe the opportunity cost.

4. a) Explain the types of market structures and describe the salient features of perfect

competition.

b) Describe the importance of pricing policy and explain any two methods of pricing.

5. Explain the characteristic features of industrial organization and describe the different types of

public enterprises.

6. a) Describe the significance of financial accounting and explain the concepts of Trail balance

and Ledger.

b) Explain the limitations of financial statements.

7. Explain the importance of financial statement and describe the Liquidity, Profitability, and

Solvency ratios.

8. What is capital budgeting? Explain any three methods of capital budgeting.

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Code No: R22013



(Com. to CE, MM)




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1. a) Explain the scope and meaning of Managerial Economics and list out basic economic tools

in Managerial Economics.

b) What is Demand? Explain its determinants.

2. a) Define Elasticity of demand and explain its types with diagrams.

b) Explain the importance demand forecasting and describe any two methods of it.

3. a) Describe Production Function and explain the Cobb- Douglas production function.

b) Explain the importance of Break-even Point and mention its significance and limitations.

4. a) Explain the different types of competition and describe the salient features of Monopolistic

Competition.

b) Describe the importance of Pricing Policy and explain briefly any two methods of pricing.

5. Explain the meaning, phases and salient features of Business Cycles.

6. What is financial accounting? And explain the concepts of Double-entry system, Trail balance

and limitations of Financial Statements.

7. Explain the importance of ratio analysis and describe the Liquidity, Profitability and Solvency

ratios.

8. Describe the importance of Capital and Capital Budgeting and explain the any three methods of

Capital Budgeting.

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Code No: R22011


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




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1. a) Show that for any two events A&B, ( ) ( ) ( ) ( ) .BPAPBAPAPBAP +≤∪≤≤∩

b) A given lot of IC chips contain 2% defective chips. Each chip is tested before delivery. The

tester itself is not totally reliable. Probability of tester says the chip is good when it is really

good is 0.95 and the chip is defective when it actually defective is 0.94. If a tested device is

indicated to be defective, what is the probability that it is actually defective? (8M+7M)

2. Let X be a random variable such that

P(X = -2) = P(X = -1) = P(X = 1) = P(X = 2)

and

P(X < 0) = P(X = 0) = P(X > 0)

Determine the probability mass function and the distribution of X. (15M)

3. a) A coin is tossed until a head appears. What is the expected number of tosses?

b) A distribution is known to be normal. The quartiles are 8.64 and 14.32. Calculate the mean

and the standard deviation of the distribution. (7M+8M)

4. a) The guaranteed average life of a certain type of electric light bulbs is 1000 hours with a

standard deviation of 125 hours. It is proposed to sample the output so as to ensure that 90%

of the bulbs do not fall short of the guaranteed average by more than 2.5 percent. What

should be the minimum size of the sample?

b) Determine the mean and standard deviation of the sampling distribution of means of 300

random samples each of size 36 drawn from a population of size 1500 which is normally

distributed with mean 22.4 and standard deviation 0.048, if sampling is done i) with

replacement and ii) without replacement. (7M+8M)

5. a) Explain how a statistical hypothesis is tested.

b) A briefcase manufacturing company claims that 80% of executives carried briefcases

produced by them. Verify its claim if in a random sample of 900 executives, 675 used the

company’s briefcases. Use 5% level of significance. (7M+8M)

6. a) In 1950 in India the mean life expectancy was 50 years. If the life expectancies from a

random sample of 11 persons are 58.2, 56.6, 54.2, 50.4, 44.2, 61.9, 57.5, 53.4, 49.7, 55.4,

57.0, does it confirm the expected view?

b) Explain steps involved in computation of two-way Analysis of Variance? (8M+7M)

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Code No: R22011

7. a) Explain the various techniques used for statistical quality control.

b) For 20 army personal, the regression of weight of kidneys (y) on weight of heart (x) both

measured in Australia is y = 0.399x + 6.394 and the regression of weight of heart on weight

of kidneys is x = 1.212y - 2.461. Find the correlation coefficient between the two variables

and also their means. (7M+8M)

8. a) In a color T.V. manufacturing plant, a loading unit takes exactly 10 minutes to load 2 T.V.

sets into a wagon and again comes back to the position to another set of T.V. If the arrival

rate is 2 T.V. sets per 20 minutes. Calculate the average time of T.V. sets in a stationary

state.

b) Discuss about classification of queuing models. (8M+7M)

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Code No: R22011






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1. a) Show that for any two events A and B, P(A ∩ B) ≤ P(A) ≤ P(A ∪ B) ≤ P(A) + P(B).

b) There are three identical coins, one of which is ideal and the other two are biased with

probabilities4

1 and

4

3, respectively for getting a head. One coin is taken at random and

tossed twice. If a head appears both the times, show that the probability that the ideal coin

was chosen is equal to7

2. (7M+8M)

2. a) A continuous random variable X has probability density function ƒ(x) = 3x2; 0 ≤ x ≤ 1. Find

a such that P(X ≤ a) = P(X > a).

b) If 3 fair coins are tossed and if X is the total number of heads in the outcome. Show that X is

a random variable. (8M+7M)

3. a) A man draws 3 balls from an urn containing 5 white and 7 black balls. He gets Rs.10 for

each white ball and Rs.5 for each black ball. Find his expectation.

b) A coin is biased so that a head is twice as likely to appear as a tail. If the coin is tossed 6

times, find the probability of getting at least 3 heads. (7M+8M)

4. a) The mean of certain normal population is equal to the standard error of the mean of the

samples of 64 from that distribution. Find the probability that the mean of the sample size

36 will be negative.

b) A sample of 11 rats from a central population had an average blood viscosity of 3.92 with a

standard deviation of 0.61. Estimate the 95% confidence limits for the mean blood viscosity

of the population. (8M+7M)

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Code No: R22011

5. a) What is meant by a statistical hypothesis? What are the two types of errors of decision that

arise in testing a hypothesis?

b) A random sample of boots worn by 40 combat soldiers in a desert region showed an average

life of 1.08 years with a standard deviation of 0.05 years. Under standard conditions the

boots are known to have an average life of 1.28 years. Is there reason to assert at a level of

significance of 0.05 that use in the desert causes the mean life of such boots to decrease?

(7M+8M)

6. a) Explain steps involved in computation of one-way analysis of variance?

b) The heights of six randomly chosen sailors are in inches: 63, 65, 68, 69, 71 and 72. Those of

10 randomly chosen soldiers are 61, 62, 65, 66, 69, 69, 70, 71, 72 and 73. Discuss, the light

that these data throw on the suggestion that sailors are on the average taller than soldiers?

(7M+8M)

7. a) Explain are the major parts of a Control Chart.

b) Ten samples each of size 5 are drawn at regular intervals from a manufacturing process. The

sample means and their ranges are given below :

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

Mean (��) 49 45 48 53 39 47 47 39 51 45

Range (R) 7 5 7 9 5 8 8 6 7 6

Calculate the control limits in respect of X - Chart and R – Chart. (Use A2=0.58, D3=0, D4=2.115)

(7M+8M)

8. The arrival rates of telephone calls at telephone booth are according to Poisson distribution

with an average time of 12 minutes between arrivals of two consecutive calls. The length of

telephonic call is assumed to be exponentially distributed with mean 4 minutes.

i) Determine the probability that the person arriving at the booth will have to wait.

ii) Find the average queue length that is formed from time to time.

iii) The telephone company will install the second booth when convinced that an arrival would

expect to wait at least 5 minutes for the phone. Find the increase in flows of arrivals which

will justify the second booth.

iv) What is the probability that an arrival will have to wait for more than 15 minutes before the

phone is free? (15M)

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Code No: R22011






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

1. a) In a city, three English dailies A, B and C are published, and a recent survey of readers

indicated the following : 30% read A, 20% read B, 15% read C, 10% read both A and B, 8%

read both B and C, 4% read both A and C and 2% read A, B and C. Compute the probability

that at least one paper among A, B and C is read by a randomly chosen person in the city.

b) There are three unbiased coins and one biased coin with head on both sides. A coin is chosen

at random and tossed 4 times. If head occurs all the 4 times, what is the probability that the

biased coin has been chosen? (7M+8M)

2. A continuous random variable X has the probability density function

≤≤

=otherwise

xifxxf

0

102)(

Find the cumulative distribution function for X. Also find P (4

1< X ≤

4

3) and P(X <

2

1).

(15M)

3. a) For a binomial distribution, the mean is 6 and standard deviation is 2 . Find the first two

terms of the distribution.

b) The moment generating function of a Poisson random variable X is given by

)1(3)(

−=

te

etM X . Find P(X = 1). (6M+9M)

4. a) Calculate the probability that a random sample of 16 computers will have an average life of

less than 775 hours assuming that length of life of computers is approximately normally

distributed with mean 800 hours and standard deviation 40 hours.

b) Discuss the properties of a good estimator. (9M+6M)

5. a) Discuss various types of alternative hypothesis with suitable example.

b) The average hourly wage of a sample of 150 workers in a plant ‘A’ was Rs.2.56 with a

standard deviation of Rs.1.08. The average wage of a sample of 200 workers in plant ‘B’

was Rs.2.87 with a standard deviation of Rs.1.28. Can an applicant safely assume that the

hourly wages paid by plant ‘B’ are higher than those paid by plant ‘A’? (7M+8M)

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Code No: R22011

6. a) Discuss test of independence of attributes with a suitable example.

b) To test the effect of fertilizer on rice production 24 plots of land were chosen. Half of them

were treated with fertilizer and half without it. Mean yield on untreated plots was 4.8

quintals with standard deviation of 0.4 quintals, while on treated plots it was 5.1 quintals

with standard deviations of 0.36 quintals. Can we conclude that fertilizers provide

significant improvement in production? (7M+8M)

7. a) What are the advantages of statistical quality control?

b) In the production of certain rods, a process is said to be in control if the outside diameters

have a mean = 2.5 and a standard deviation of 0.002. i) Construct a control chart for the

mean of random samples of size 4 ii) Means of 10 such random samples taken at regular

intervals were 2.5014, 2.5022, 2.4995, 2.5076, 2.5040, 2.5001, 2.4993, 2.4993, 2.4962,

2.4966 and 2.4971. Was the process ever out of control? (6M+9M)

8. a) Define the terms

i) Waiting line

ii) Queue length

iii) ideal period

iv) Traffic Intensity

b) A PC repairman finds that the time spend on jobs has an exponential distribution with mean

30 minutes. If the sets are repaired in the order, in which they come in, and if the arrival of

sets is approximately Poisson with an average of 10 per 8 hour day, what is the repairman’s

expected idle time each day? How many jobs are ahead of the average set just brought in?

(7M+8M)

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Code No: R22011






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

1. a) Let P(A∪B) = 6

5, P(A∩B) =

2

1 and P( B ) =

2

1. Are the events A and B independent?

b) For a certain binary communication channel, the probability that a transmitted ‘0’ is received

as a ‘0’ is 0.95 and the probability that a transmitted ‘1’ is received as ‘1’ is 0.90. If the

probability that a ‘0’ is transmitted is 0.4, find the probability that a ‘1’ is received.

(7M+8M)

2. If

<

≥−=

.00

.02/2

)(

xif

xifx

xexp show that p(x) is a probability density function of a continuous

random variable X. Also, find its mean. (15M)

3. a) Obtain the moment generating function of the normal distribution.

b) If X is a binomially distributed random variable with E(X) = 2 and Var(X) = 3

4. Find

P(X = 5). (8M+7M)

4. Construct sampling distribution of means for the population 3, 7, 11, 15 by drawing samples of

size two with replacement. Determine i) µ ii) σ iii) Sampling distribution of means

iv)X

µ v) X

σ Verify the results. (15M)

5. a) Construct 95% confidence interval for the true proportion of computer literates if 47 out of

150 persons from rural areas are computer literates.

b) The owner of a machine shop must decide which of two snack vending machines to install in

his shop. If each is tested 250 times, the first machine fails to work 13 times and the second

machine fails to work 7 times. Test at the 0.05 level of significance whether the difference

between the corresponding sample proportions is significant. (7M+8M)

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Code No: R22011

6. a) Write the conditions of validity of χ2-test.

b) Weekly sales (in Rs.) in small shops in 3 towns A, B, C are as follows

A = 620, 600, 740, 800

B = 410, 380, 350

C = 920, 870, 1040, 1030, 1010

Can we conclude that the shops in the 3 towns have the same average sales? (6M+9M)

7. a) What are the steps involved in control chart for Mean or X Chart.

b) The difference between the ranks are 0.5, -6, -4.5, -3, -5, -1, 3, 0, 5, 5.5, 0 and -0.5 for

refracted ranks x and y .5.312

)1( 2

=−

∑mm

The rank correlation coefficient is 0.44. Find the

number of terms. (7M+8M)

8. a) Discuss different states of the queuing system

b) Workers come to a tool store room to enquiry about the special tools for a particular job. The

average time between the arrivals is 60 seconds and the arrivals are assumed to be in

Poisson distribution. The average service time is 40 seconds. Find: i) average queue length

ii) average length of non-empty queue (7M+8M)

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Code No: R22012


STRENGTH OF MATERIALS (Civil Engineering)




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

1. a) State and prove the moment area theorems? What are the limitations of the moment area

method?

b) Determine the minimum flexural rigidity of the cantilever beam so that the span to

maximum deflection ratio is not less than 250 and slope does not exceed 0.003 radians,

when supporting 10 KN/m over a span of 7.4 m?

2. Calculate the safe working pressure for a spherical vessel, 1 m diameter and 1 cm wall

thickness, if the tensile stress is limited to 40 N/mm2.

3. At a point in a bracket the shear stresses on two mutually perpendicular planes are 400 N/mm2

tensile and 300 N/mm2 tensile. The shear stress across these planes is 200 N/mm

2. Find the

principal stresses and maximum shear stress at that point.

4. Determine the maximum shearing stress and elongation in a helical steel spring composed of

20 turns of 20-mm-diameter wire on a mean radius of 90 mm when the spring is supporting a

load of 1.5 kN and G = 83 GPa.

5. a) Explain the difference between buckling and crushing failure of a column

b) A column of 7.2 m length with both ends hinged, compresses two ISMC 250. Determine the

maximum load permissible on the column when the sections are i) placed back to back and

ii) placed with the flanges facing each other. (A = 3867.0 mm2, Ix = 38.17 x 10

6 mm

4, Iy =

2.19 x 106 mm

4, σy = 250 N/mm

2 and E = 210 GPa, ex = 23.0 mm, flange width 80.0 mm).

6. a) What do you mean by eccentricity of loading? What are its effects on a column section?

b) A hollow rectangular column is 120cm deep, 80cm wide and 15cm thick. An eccentric load

of 200kN acts on the centroidal axis bisecting 120cm long side, the eccentricity being 10cm.

Determine the maximum and minimum stress in the column.

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R10 SET - 1

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Code No: R22012

7. a) Define unsymmetrical bending? State any two reasons of unsymmetrical Bending?

b) An angle section 9 cm × 6 cm × 1.2 cm is used as a cantilever of one meter length with 6 cm

leg horizontal as shown in Figure 1. A vertical load of 1000 N is applied at the free end.

Determine the position of the neutral axis and the maximum stress set up. Iuu = 147.5 cm4,

Ivv = 26.8 cm4, tanα = 0.42.

8. Determine the forces in all the members of the truss shown in Figure 2 using method of joints

and indicate the magnitude and nature of forces on the diagram of the truss. All inclined

members are at 60° to horizontal and length of each member is 3 m.

2 of 2

R10 SET - 1

X

Figure 1

9 cm

6 cm

3.12 cm

1.63 cm Y V

U

α = 220 47

1

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Code No: R22012






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

1. a) Develop the governing differential equations of deflection of a beam and discuss its

limitations.

b) Compute the mid span value of EIδ for the beam loaded as shown in Figure 1.

2. Calculate the increase in volume enclosed by a boiler shell, 2.5 m long and 1 m in diameter,

when it is subjected to an internal pressure of 1.5 N/mm2. The wall thickness is such that the

maximum tensile stress in the shell is 25 N/mm2 under pressure. Take µ = 0.3.

3. a) Discuss briefly about maximum principal stress theory

b) The Bending moment, M applied to a solid shaft carries a maximum direct stress of σy at

elastic failure. Determine the numerical relationship between M and Twisting moment, T

which acting alone on the shaft, will produce elastic failure according to i) Maximum

principal stress theory ii) maximum shear stress theory iii) maximum strain energy theory

iv) maximum distortion energy theory. Take µ = 0.3.

4. Determine the maximum torque that can be applied to a hollow circular steel shaft of 100-mm

outside diameter and an 80-mm inside diameter without exceeding a shearing stress of 60 MPa

or a twist of 0.5 deg/m. Use G = 83 GPa.

5. a) Explain why the failure load of a slender column is independent of the yield strength of its

material.

b) A hallow cast iron column, hinged at both ends is 4 m long. Its external diameter is 200 mm

and internal diameter is 150 mm. Find the maximum load it can carry if factor of safety is 4.

Use Rankine’s Formula. For cast iron, σy = 550 N/mm2 and α = 1/1600.

1 of 2

R10 SET - 2

1.5 m 0.5 m

300 N/m

Figure 1

4 m

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Code No: R22012

6. a) What do you mean by eccentricity of loading? What are its effects on a column section?

b) A hollow rectangular column is 120cm deep, 80cm wide and 15cm thick. An eccentric load

of 200kN acts on the centroidal axis bisecting 120cm long side, the eccentricity being 10cm.

Determine the maximum and minimum stress in the column.

7. a) Write down the detailed procedure to compute the maximum stresses of beam in

unsymmetrical bending.

b) A beam of rectangular section, 80 mm wide and 120 mm deep as shown in Figure 2, is

subjected to a bending moment of 10 kNm. The trace of the plane of the loading is at 450 to

the axis of the section. Locate the neutral axis of the section, and calculate the maximum

bending stress induced in section.

8. Determine the forces in the members of a pin jointed steel structure in the given Figure 3 by

method of slices.

2 of 2

R10 SET - 2

4 × 5 m

5 m

100 kN 100 kN 100 kN

Figure 3

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Code No: R22012


STRENGTH OF MATERIALS

(Civil Engineering)




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

1. a) State the advantages of Macaulay’s method over other methods? Discuss how the

Macaulay’s conditions applied to the slope deflection analysis of beam?

b) A cantilever beam of length L carries UDL of magnitude mmqN / throughout the length and

a point load W at its free end. Calculate slope and deflection at the free end of the bear using

principle of superposition?

2. Calculate the increase in volume of a spherical vessel, 1 m diameter and 1 cm thick, when it is

subjected to increase in pressure of 3.5 N/mm2, E = 2.1 x 10

5 N/mm

2 and µ = 0.3?

3. a) Define Principal Stresses, Principal planes and Principal strains?

b) If an element is subjected to the state of stress as shown in Figure 1, find the principal

stresses. Also compute the stress components on a plane at 30° counter clockwise from the

x-face?

Figure 1

4. A solid steel shaft 5 m long is stressed at 80 MPa when twisted through 4°. Using G = 83 GPa,

compute the shaft diameter. What power can be transmitted by the shaft at 20 Hz?

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R10 SET - 3

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Code No: R22012

5. a) Define the slenderness ratio of a column, and discuss its significance?

b) A 50 mm by 100 mm timber is used as a column with fixed ends. Determine the minimum

length Euler’s formula can be used if E = 10 GPa and the proportional limit is 30 MPa.

What central load can be carried with a factor of safety of 2, if the length is 2.5 m?

6. A compressive load of P = 100 kN is applied through Z-axis with an eccentricities of 70 mm

and 30 mm along the X-and Y-axis respectively from the centriod of a column. The column

dimensions are along x-axis 300 mm and along Y-axis 150 mm. Compute the stress at each

corner and the location of neutral axis. Illustrate your answers with a sketch. What additional

load applied at the centriod is necessary so that no tensile stress exists anywhere on the cross

section?

7. A rectangular beam 50 mm x 80 mm is arranged as a cantilever beam 1.3 m long and loaded at

its free end with a load of 5 kN inclined at an angle of 300 to the vertical axis and passing

through the centriod of the section. Determine the position and magnitude of the greatest

tensile stress in the section. E = 2.1 x 105 N/mm

2?

8. Find the forces in members of truss shown in Figure 2 and tabulate the values?

2 of 2

R10 SET - 3

10 m

4 × 10 m

40 kN 40 kN 40 kN

Figure 2

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Code No: R22012






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

1. A simple supported beam of span 8 m is loaded with three concentrated loads of 20 kN, 30 kN

and 40 kN at distance of 2 m, 4 m and 5 m respectively from right hand end. Find the position

and magnitude of maximum deflection?

2. Calculate the increase in volume enclosed by a boiler shell, 3.0 m long and 1 m in diameter,

when it is subjected to an internal pressure of 2.5 N/mm2. The wall thickness is such that the

maximum tensile stress in the shell is 35 N/mm2 under pressure. Take µ = 0.3?

3. a) Discuss briefly about maximum strain energy theory?

b) A bolt is subjected to an axial pull of 12 kN together with a transverse shear of 6 kN.

Determine the diameter of the bolt by according to i) Maximum principal stress theory

ii) maximum shear stress theory iii) maximum strain energy theory iv) maximum distortion

energy theory. Take E = 2 × 105 N/mm

2, failure stress in tension test to be 300 N/mm

2,

factor of safety 3 and µ = 0.3?

4. a) Derive an expression for the polar moment of inertia of the cross sectional area of hallow

circular shaft. What does this expression become for the special case of a solid circular

shaft?

b) If a twisting moment of 10 kN-m is impressed upon a 50 mm diameter shaft. What is the

maximum shearing stress developed? Also what is the angle of twist in a 1.50 m length of

the shaft? The material of steel for which G = 79.3 GPa?

5. a) Discuss the limitations of Euler’s buckling theory, and suggest possible improvements.

b) A square aluminum bar is to support 40 kN on a length of 3 m. Assume pinned support ends.

Determine the length of each side. Use E = 70 GPa?

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Code No: R22012

6. A compressive load of P = 80 kN is applied through Z-axis with an eccentricities of 40 mm and

60 mm along the X-and Y-axis respectively from the centriod of a column. The column

dimensions are along x-axis 200 mm and along Y-axis 400 mm. Compute the stress at each

corner and the location of neutral axis. Illustrate your answers with a sketch. What additional

load applied at the centriod is necessary so that no tensile stress exists anywhere on the cross

section?

7. a) Define Unsymmetrical bending? State any two reasons of unsymmetrical Bending?

b) An angle section 9 cm x 6 cm x 1.2 cm (Fig. 1) is used as a cantilever of one meter length

with 6 cm leg. Horizontal a vertical load of 1000 N is applied at the free end. Determine the

position of the neutral axis and the maximum stress set up. Iuu = 147.5 cm4, Ivv = 26.8 cm4,

tanα = 0.42?

8. Calculate the magnitude and nature of the forces in the member of the truss as shown in

Figure 2 by method of joints?

2 of 2

R10 SET - 4

X

Figure 1

9 cm

6 cm

3.12 cm

1.63 cm Y V

U

α = 220 47

1

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Code No: R22016


STRUCTURAL ANALYSIS – I (Civil Engineering)


Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~

1. Draw SFD and BMD for the propped cantilever carrying a uniformly distributed load of

90kN/m over entire span of length of 9m, propped at 4m from left end.

2. Draw S.F.D and B.M.D for a fixed beam carrying a symmetrical triangular load. Also find the

point of contra flexure.

3. A continuous beam ABC 8 metres long consists of two spans AB= 3m and BC=5m.The span

AB carries a load of 50kN/m while the span BC carries a load of 30kN/m. Find the support

moment at B and the reactions at supports and draw S.F and B.M diagrams.

4. A continuous beam ABC fixed at A simply supported at B and C, the spans AB and BC being

each 4m long. The span AB carries a uniformly distributed load of 9kN/m. The span BC carries

a point load of 40kN at its middle point. If Iab =1/2 Ibc find the moments and reactions at the

supports by slope deflection method.

5. a) Derive total strain energy stored due to bending.

b) Find the deflection of a simply supported carrying a point load eccentrically.

6. Two wheel loads 240kN and 100kN spaced 1.0m apart crosses a simply supported girder of

span 12m from left to right. Sketch the maximum bending moment and maximum shear force

diagrams showing the salient values.

7. A UDL of intensity 90KN/m and 8m long crosses a simply supported girder of 16m span.

Sketch the Influence line diagrams for Shear force and Bending moment at 1/3 span. Hence,

also find the absolute maximum SF and BM.

8. Calculate the forces in the members of the following truss

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R10 SET - 1

40 kN 50 kN

60 kN

2m 2m

D A

B C

60˚ 60˚ 60˚ 60˚

E

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Code No: R22016





1. The propped cantilever of span 10m is propped at a distance of 4m from free end and carrying a point load of 60 kN at a distance of 2m from the left support. Draw the SFD and BMD.

2. A fixed beam of span 6m carries two point loads 150kN and 240kN at distances 2m and 4m from left end. Find the end moments. Also find the maximum sagging bending moment. Draw SFD and BMD.

3. A continuous beam ABC 8 metres long is fixed at A and simply supported at B with an

overhang BC 2m long. The beam carries a uniformly distributed load of 12kN/m on AB and a point load of 12kN at C. Find the support moments and the reactions at supports and draw S.F and B.M diagrams.

4. A beam ABC 8m long consists of spans AB and BC of lengths 5m and 3m respectively. It is

fixed at both ends and simply supported at B. The span AB carries a uniformly distributed load of 70 kN/m while the span BC carries a point load of 80kN at a distance of 1m from B. Determine the reactions and moments at the supports by slope deflection method and draw B.M.D.

5. a) Derive Maxwell’s reciprocal deflection theorem. b) Derive the strain energy stored due to bending. 6. Two wheel loads 40kN and 80kN spaced 0.5m apart roll on a girder of span 30m with either

load leading the other. Sketch the maximum bending moment and maximum shear force diagrams showing the salient values

7. Draw the influence line diagram for the top chord member, bottom chord member and vertical member of the Deck type girder shown below Figure 1.

8. a) Differentiate between statically determinate and indeterminate structures. b) Explain with example the degree of external redundancy and degree of internal redundancy.

1 of 1

R10 SET - 2

4m V1

6 Panels @ 3m each = 18m

U1 U2 U3 U4 U5 U6 U7

L2 L3 L4 L5 L6

V2

Ө

Figure 1

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Code No: R22016





1. The propped cantilever of span 15m is propped at a distance of 5m from free end and carrying

a point load of 60 kN at a distance of 3m from the left support and a point of 40kN at a distance

of7m from left support. Draw the SFD and BMD.

2. A fixed beam of span 6m carries concentrated loads 120kN and 90 kN at distances 2m and 4m

from left end. Calculate the reactions and the fixing moments at supports. Draw SFD and

BMD.


AB carries a load of 60 kN/m while the span BC carries a point load of 30kN at a distance of

2m from B. Find the support moment at B and the reactions at supports and draw S.F and B.M

diagrams.

4. A continuous beam ABC fixed at A simply supported at B and C, the spans AB and BC being

each 5m long. The span AB carries a uniformly distributed load of 10kN/m. The span BC

carries a point load of 50kN at its middle point. If Iab =1/2 Ibc find the moments and reactions at

the supports by slope deflection method.

5. Derive the first theorem of Castigliano’s.

6. A uniformly distributed load of 12kN/m, 6m moves on a simply supported girder of span

10m.Find the greatest reaction at the supports and the absolute maximum bending moment for

the girder.

7. a) Define the influence line diagram. Draw I.L.D for simply supported beam for the reactions

at supports. When the live load shorter it an span moving

b) A live load of 20kN/m 6m long moves on a simply supported girder of span 20m, from left

to right. Find the maximum negative and positive shear forces that can occur at a section 8m

from the left end by drawing I.L.D.

8. a) What is the difference between statically determinate structures and indeterminate structures.

b) What is the degree of external redundancy and degree of internal redundancy explain with

example.

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R10 SET - 3

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Code No: R22016





1. Draw SFD and BMD for the propped cantilever carrying a uniformly distributed load of

80kN/m over entire span of length of 12m, propped at 5m from left end. Calculate the

deflection also.

2. A fixed beam of span 10m carries two point loads 250kN and 340kN at distances 3m and 5m

from left end. Find the end moments. Also find the maximum sagging bending moment. Draw

SFD and BMD.


AB carries a load of 60kN/m while the span BC carries a load of 40kN/m. Find the support

moment at B and the reactions at supports and draw S.F and B.M diagrams.

4. A beam ABC 10m long consists of spans AB and BC of lengths 5m and 5m respectively. It is

fixed at both ends and simply supported at B. The span AB carries a uniformly distributed load

of 50kN/m while the span BC carries a point load of 60kN at a distance of 3m from B.

Determine the reactions and moments at the supports by slope deflection method and draw

B.M.D.

5. a) Derive total strain energy stored due to axial loading

b) What is Betti’s law? Derive its governing differential equation.

6. Two wheel loads 340kN and 120kN spaced 1.2m apart crosses a simply supported girder of

span 14m from left to right. Sketch the maximum bending moment and maximum shear force

diagrams showing the salient values.

7. a) What is influence line diagram? Draw I.L.D for bending moment at supports for a simply

supported beam.

b) A live load of 30kN/m 8m long moves on a simply supported girder of span 24m, from left

to right. Find the maximum negative and positive shear forces that can occur at a section

10m from the left end by drawing I.L.D.

8. State and prove the second theorem of Castigliano’s

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R10 SET - 4

code no: r22015 ii b. tech ii semester …...ii b. tech ii semester supplementary examinations...

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