# Module Analytical Methods for Engioneers Assignment PDF

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BTEC HND in Civil Engineering

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Unit / ModuleAnalytical Methods for Engioneers

AssessmentAssignment-Individual

LecturerMr. Vidura Sonnadara

Student NameL.Y sachth madushankaIDCE/M/02/15

Date Handed OverDate Due

Initial Submission DateRe-Submission Date

Assessment

Criteria /Grading

Opportunity

Offered

Met

Initially?

Yes/no

Met On

Re-

Submissi

on?

Yes/no

Assessor’s Feedback on submission

LO 1

Decision

LO 2

LO 3

LO 4

M1

M2

M3

D1

Assessor’s Feedback On Re-Submission( if required)

D2

D3

Assessed by :

Evaluation on

Submission :Achieves Assessment Criteria

Resubmit

Signature:Date Assessed :

Evaluation on Re-

Submission :Achieves Assessment Criteria

Resubmit

Signature:Date Assessed :

Important Information for Students

1 |P a g e

Unit / ModuleAnalytical Methods for Engioneers

AssessmentAssignment-Individual

LecturerMr. Vidura Sonnadara

Student NameL.Y sachth madushankaIDCE/M/02/15

Date Handed OverDate Due

Initial Submission DateRe-Submission Date

Assessment

Criteria /Grading

Opportunity

Offered

Met

Initially?

Yes/no

Met On

Re-

Submissi

on?

Yes/no

Assessor’s Feedback on submission

LO 1

Decision

LO 2

LO 3

LO 4

M1

M2

M3

D1

Assessor’s Feedback On Re-Submission( if required)

D2

D3

Assessed by :

Evaluation on

Submission :Achieves Assessment Criteria

Resubmit

Signature:Date Assessed :

Evaluation on Re-

Submission :Achieves Assessment Criteria

Resubmit

Signature:Date Assessed :

Important Information for Students

BTEC HND in Civil Engineering

2 |P a g e

The criteria each task relates to are shown against that task where possible.

Please note thatplagiarismis treated as a serious offence and therefore the work you produce

must be individual and originalalthough may work in groups in some instances (Please refer to

Student Handbook on Plagiarism & Cheating).

All sources of information must bereferenced using “Harvard referencing” where areference

list/Bibliographyshould be included at the end of the assignment.

Please note that the submission date given for this assignment is thefinal datethat you can hand

over the assignment. Aone week grace periodmaybe extended withprior approval from the

Program Manager–Undergraduate. However,note that submissions handed in one week

late will be graded lower(Please refer to the Student Handbook on Assessments - Late

Submissions & Penalties).

Assignments returned to students for re-working must bere-submitted within 10 days(Please

refer to Student Handbook on Assignments – Re-submission).

Failure to re-submitthe previously marked assignment with the re-submitted assignment will

mean thatresults cannot be released for the respective unit.

Please read, follow and reference both thecontents of the unit outlineand thegrading criteria

of the assignmentbefore completing this assignment.

Plagiarism:

While research and discussion are an essential part of an assignment, the deliberate copying of someone else’s

work or unacknowledged copying from printed or electronic sources is NOT permitted. You may be subject to

disciplinary procedure if you do this. You should sign this sheet to show that you comply with these regulations.

Student’s Signature: ................................. ..............................................Date: ......................

Student’s Comments:

Assessment has been internally verified for use.

Internal Verifier Name :

Signature :Date

Verified :

Task 01

a)Use matrix method to solve the following simultaneous equations

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The criteria each task relates to are shown against that task where possible.

Please note thatplagiarismis treated as a serious offence and therefore the work you produce

must be individual and originalalthough may work in groups in some instances (Please refer to

Student Handbook on Plagiarism & Cheating).

All sources of information must bereferenced using “Harvard referencing” where areference

list/Bibliographyshould be included at the end of the assignment.

Please note that the submission date given for this assignment is thefinal datethat you can hand

over the assignment. Aone week grace periodmaybe extended withprior approval from the

Program Manager–Undergraduate. However,note that submissions handed in one week

late will be graded lower(Please refer to the Student Handbook on Assessments - Late

Submissions & Penalties).

Assignments returned to students for re-working must bere-submitted within 10 days(Please

refer to Student Handbook on Assignments – Re-submission).

Failure to re-submitthe previously marked assignment with the re-submitted assignment will

mean thatresults cannot be released for the respective unit.

Please read, follow and reference both thecontents of the unit outlineand thegrading criteria

of the assignmentbefore completing this assignment.

Plagiarism:

While research and discussion are an essential part of an assignment, the deliberate copying of someone else’s

work or unacknowledged copying from printed or electronic sources is NOT permitted. You may be subject to

disciplinary procedure if you do this. You should sign this sheet to show that you comply with these regulations.

Student’s Signature: ................................. ..............................................Date: ......................

Student’s Comments:

Assessment has been internally verified for use.

Internal Verifier Name :

Signature :Date

Verified :

Task 01

a)Use matrix method to solve the following simultaneous equations

BTEC HND in Civil Engineering

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3x – 5y = 204

4x + 5y = 412(LO1.4, D3)

b)Sketch the following functions of a single variable for the domain −3 ≤x≤ 3

I.f(x) = −x4

II.f(x) = 2 −x−x2

III.f(x) = 1/x

(LO1.2, M1)

c)Solve the following factorisation

i. 2x2–5x -3 = 0

ii. 7x2–20x -3 = 0

(LO1.1, M2)

d)Divide the following algebraic repression in to partial fractions

e)Write the remainder and quotient in the following algebraic division

(LO1.1, M3)

Task 02

a)A weight of 4 Tonnes is suspended on two ropes as shown. Calculate the length of the

ropes and the forces in them.

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3x – 5y = 204

4x + 5y = 412(LO1.4, D3)

b)Sketch the following functions of a single variable for the domain −3 ≤x≤ 3

I.f(x) = −x4

II.f(x) = 2 −x−x2

III.f(x) = 1/x

(LO1.2, M1)

c)Solve the following factorisation

i. 2x2–5x -3 = 0

ii. 7x2–20x -3 = 0

(LO1.1, M2)

d)Divide the following algebraic repression in to partial fractions

e)Write the remainder and quotient in the following algebraic division

(LO1.1, M3)

Task 02

a)A weight of 4 Tonnes is suspended on two ropes as shown. Calculate the length of the

ropes and the forces in them.

BTEC HND in Civil Engineering

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(LO2.3, D1)

b)A conical vessel of internal radius 14 cm and height 36 cm is full of water. If this water

is poured into a cylinder with internal radius 21 cm, find the height to which the water

rises in the cylinder.

(LO2.3, D1)

b)The length of a room is 1.5 times its breadth. The cost of carpeting it at Rs 150 per

square meter is Rs 14400 and the cost of white washing the four walls at Rs 5 per square

meter is Rs 625. Find the dimensions of the room.

(LO2.1, D3)

c)If the equation of a sinusoidal wave is given by

y = 4.5 sin (2ωt + 3Π/4) then find the displacement and the acceleration of the wave?

d)When a gas is compressed, it is found that the Pressure & Volume has a relationship as

PVn= C , where C and n are constants.

When P = 400 × 103& V = 0.0004 m3, the C = 45.7,

Then find the value of C, by using the knowledge of logarithms?

(LO2.2 , M1)

Task 03

a)Find the gradient of the curvey = (x3+1)(x2+2x+5)at the point x = 1.(LO4.2, M3)

b)A printer need to make a poster that will have a total area of 320 in2and will have 1 inch

margins on the sides, a 1.75 inch margin on the top and a 3.5 inch margin on the bottom.

What dimensions will give the largest printed area?(LO4.2, M3)

c)Show that if the coefficient of friction between the block and the plane is 0.25, the force

required to just start the block moving up the 40oincline is F= 1.38 W while the force

required to hold the block from sliding down the plane is F= 0.487 W

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(LO2.3, D1)

b)A conical vessel of internal radius 14 cm and height 36 cm is full of water. If this water

is poured into a cylinder with internal radius 21 cm, find the height to which the water

rises in the cylinder.

(LO2.3, D1)

b)The length of a room is 1.5 times its breadth. The cost of carpeting it at Rs 150 per

square meter is Rs 14400 and the cost of white washing the four walls at Rs 5 per square

meter is Rs 625. Find the dimensions of the room.

(LO2.1, D3)

c)If the equation of a sinusoidal wave is given by

y = 4.5 sin (2ωt + 3Π/4) then find the displacement and the acceleration of the wave?

d)When a gas is compressed, it is found that the Pressure & Volume has a relationship as

PVn= C , where C and n are constants.

When P = 400 × 103& V = 0.0004 m3, the C = 45.7,

Then find the value of C, by using the knowledge of logarithms?

(LO2.2 , M1)

Task 03

a)Find the gradient of the curvey = (x3+1)(x2+2x+5)at the point x = 1.(LO4.2, M3)

b)A printer need to make a poster that will have a total area of 320 in2and will have 1 inch

margins on the sides, a 1.75 inch margin on the top and a 3.5 inch margin on the bottom.

What dimensions will give the largest printed area?(LO4.2, M3)

c)Show that if the coefficient of friction between the block and the plane is 0.25, the force

required to just start the block moving up the 40oincline is F= 1.38 W while the force

required to hold the block from sliding down the plane is F= 0.487 W

BTEC HND in Civil Engineering

5 |P a g e

(LO4.1, D2)

Task 04

a)The breaking strength of 150 spot welds was measured in Newton and grouped into

bands of 20 N as shown.

Calculate the mean and the standard deviation

Rangef

160 - 1802

180 - 2006

200 – 22010

220 – 24028

240 – 26050

260 – 28031

280 – 30015

300 – 3208

(LO3.1,LO3.2, M1)

b)3 boxescontain balls as follow,

(Box A: 6 red, 4 black), (Box B: 4 red, 6 black), (Box C: 5 red, 6 black) respectively.

One box is selected randomly and a ball is taken from the selected box randomly, if the

ball isRed, find the probability that it’s drawn from theBox A?

C)Student takes his exam in four subjects, A,B,C and D. He estimates of passing each

subject as P(A) = 4/5 , P(B) = 3/4, P(C) = 5/6, P(D) = 2/3.

To qualify for the next semester he should passsubject Aand2 other subjectsat least.

Find the probability of qualifying him? (Clearly show the solving steps)

(LO 3.3, D3)

Grading Information

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(LO4.1, D2)

Task 04

a)The breaking strength of 150 spot welds was measured in Newton and grouped into

bands of 20 N as shown.

Calculate the mean and the standard deviation

Rangef

160 - 1802

180 - 2006

200 – 22010

220 – 24028

240 – 26050

260 – 28031

280 – 30015

300 – 3208

(LO3.1,LO3.2, M1)

b)3 boxescontain balls as follow,

(Box A: 6 red, 4 black), (Box B: 4 red, 6 black), (Box C: 5 red, 6 black) respectively.

One box is selected randomly and a ball is taken from the selected box randomly, if the

ball isRed, find the probability that it’s drawn from theBox A?

C)Student takes his exam in four subjects, A,B,C and D. He estimates of passing each

subject as P(A) = 4/5 , P(B) = 3/4, P(C) = 5/6, P(D) = 2/3.

To qualify for the next semester he should passsubject Aand2 other subjectsat least.

Find the probability of qualifying him? (Clearly show the solving steps)

(LO 3.3, D3)

Grading Information

BTEC HND in Civil Engineering

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LO 1

Algebra: linear, simultaneous and quadratic equations, laws of indices and

logarithms, common and Naperian logarithms, indicial equations, direct and

inverse proportion, inequalities, functional notation and manipulation of algebraic

problems

Graphical representation: functions, points of intersection between two graphs,

graph sketching (straight line, polynomial, exponential and logarithmic), fit lines to

experimental data using least squares method

Space, time and motion: plot space/time and velocity/time diagrams, determine

displacement, velocity and acceleration. Laws of motion, momentum, impulse

and projectiles

Matrices: multiplication, transposition and inversion, applications

LO 2

Trigonometry: basic trigonometric ratios and their inverses, trigonometric ratios for

the four quadrants, solution of triangles, calculation of areas and volumes of solids

Determine co-ordinates: in 2-D and 3-D geometry

Other functions: trapezoidal and Simpson’s rule

LO 4

Trigonometric methods: to solve problems such as static forces, relative motion,

frameworks, metrology, friction torque, electrical and mechanical energy problems

Calculus: to differentiate and integrate simple equations and demonstrate

applications of calculus (refer to Delivery guidance on delivering calculus to

construction disciplines)

M1Identify and apply strategies to find appropriate solutions

Effective judgments have been made

M2

Select/design and apply appropriate methods/ techniques

Relevant theories and techniques have been applied

A range of methods and techniques have been applied

M3

Present and communicate appropriate findings

The appropriate structure and approach has been used.

A range of methods of presentation have been used and technical language has

been accurately used.

D1

Use critical reflection to evaluate own work and justify valid conclusions

Conclusions have been arrived at through synthesis of ideas and have been

justified

D2

Take responsibility for managing and organizing activities

Autonomy/ independence have been demonstrated.

Substantial activities or investigations have been planned, managed and

organized.

The importance of interdependence has been recognized and achieved

D3

Demonstrate convergent / creative thinking

Ideas have been generated with self evaluation and decisions taken.

Problems have been solved with innovative and creative thoughts.

Effective thinking has taken place in unfamiliar contexts

6 |P a g e

LO 1

Algebra: linear, simultaneous and quadratic equations, laws of indices and

logarithms, common and Naperian logarithms, indicial equations, direct and

inverse proportion, inequalities, functional notation and manipulation of algebraic

problems

Graphical representation: functions, points of intersection between two graphs,

graph sketching (straight line, polynomial, exponential and logarithmic), fit lines to

experimental data using least squares method

Space, time and motion: plot space/time and velocity/time diagrams, determine

displacement, velocity and acceleration. Laws of motion, momentum, impulse

and projectiles

Matrices: multiplication, transposition and inversion, applications

LO 2

Trigonometry: basic trigonometric ratios and their inverses, trigonometric ratios for

the four quadrants, solution of triangles, calculation of areas and volumes of solids

Determine co-ordinates: in 2-D and 3-D geometry

Other functions: trapezoidal and Simpson’s rule

LO 4

Trigonometric methods: to solve problems such as static forces, relative motion,

frameworks, metrology, friction torque, electrical and mechanical energy problems

Calculus: to differentiate and integrate simple equations and demonstrate

applications of calculus (refer to Delivery guidance on delivering calculus to

construction disciplines)

M1Identify and apply strategies to find appropriate solutions

Effective judgments have been made

M2

Select/design and apply appropriate methods/ techniques

Relevant theories and techniques have been applied

A range of methods and techniques have been applied

M3

Present and communicate appropriate findings

The appropriate structure and approach has been used.

A range of methods of presentation have been used and technical language has

been accurately used.

D1

Use critical reflection to evaluate own work and justify valid conclusions

Conclusions have been arrived at through synthesis of ideas and have been

justified

D2

Take responsibility for managing and organizing activities

Autonomy/ independence have been demonstrated.

Substantial activities or investigations have been planned, managed and

organized.

The importance of interdependence has been recognized and achieved

D3

Demonstrate convergent / creative thinking

Ideas have been generated with self evaluation and decisions taken.

Problems have been solved with innovative and creative thoughts.

Effective thinking has taken place in unfamiliar contexts

BTEC HND in Civil Engineering

7 |P a g e

Acknowledgement

Iwould like to express my deepest gratitude to all those who helped me to complete this assignment.

A special gratitude I give to my lecturerMr. Vidura Sonnadarawho gave me this valuable

opportunity to do this on the topic ofAnalytical Methods for Engineersand encouraged me to learn.

after I would like to thanksMISHIMASHA GAMAGEadvise to how to create a

assement

furthermore I would like to thankmy parentswith much appreciation for give their fullest cooperation to

me.

besides I would like to take this opportunity to mention aboutICBT SOUTHERN CAMPUSwhich

provides me to good learning conditions for learning well.

also I would like to deliver my whole hearted thanks to all myfriendswho helped me to complete these

severe tasks within limited days.

finally I would like to thanks again all who helped me in various ways towards me to finish this

assignment with successfully.

Executive summary

Construction industry is very complex industry in the world .thatAssignmentis analytical

method of civil engineers .this lesson is very important lesson in the construction area. we got a

knowledge to how to use deflection , integration ,matrix’s part and probability in construction

site. ThisAssignmentpart uses to easy our work. That Assignment is very important to our

work site

7 |P a g e

Acknowledgement

Iwould like to express my deepest gratitude to all those who helped me to complete this assignment.

A special gratitude I give to my lecturerMr. Vidura Sonnadarawho gave me this valuable

opportunity to do this on the topic ofAnalytical Methods for Engineersand encouraged me to learn.

after I would like to thanksMISHIMASHA GAMAGEadvise to how to create a

assement

furthermore I would like to thankmy parentswith much appreciation for give their fullest cooperation to

me.

besides I would like to take this opportunity to mention aboutICBT SOUTHERN CAMPUSwhich

provides me to good learning conditions for learning well.

also I would like to deliver my whole hearted thanks to all myfriendswho helped me to complete these

severe tasks within limited days.

finally I would like to thanks again all who helped me in various ways towards me to finish this

assignment with successfully.

Executive summary

Construction industry is very complex industry in the world .thatAssignmentis analytical

method of civil engineers .this lesson is very important lesson in the construction area. we got a

knowledge to how to use deflection , integration ,matrix’s part and probability in construction

site. ThisAssignmentpart uses to easy our work. That Assignment is very important to our

work site

BTEC HND in Civil Engineering

8 |P a g e

Table of Contents

Acknowledgement..................................................... 07

Executive Summary..................................................07

List of Figures.........................................................09

Introduction............................................................10

Task 1....................................................................11

Task 2....................................................................21

Task 3....................................................................30

Task 4....................................................................36

Conclusion..............................................................41

Reference list...........................................................41

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Table of Contents

Acknowledgement..................................................... 07

Executive Summary..................................................07

List of Figures.........................................................09

Introduction............................................................10

Task 1....................................................................11

Task 2....................................................................21

Task 3....................................................................30

Task 4....................................................................36

Conclusion..............................................................41

Reference list...........................................................41

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