DET

Civil Engineering

Structural Mechanics and Design 1

(Higher)

7529

August 2000

DET

Civil Engineering

Structural Mechanics and Design 1

Higher

Support Materials

HIGHER STILL

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

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CONTENTS

Overview

Teacher’s/Lecturer’s guide

Student’s guide

Tutorials

1. Loads and support reactions for statically determinate beams

2. Construction of shear force and bending moment diagrams

3. Bending and shear stresses in simple beams

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: Civil Engineering: Structural Mechanics and Design 1 (Higher)

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: Civil Engineering: Structural Mechanics and Design 1 (Higher)

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OVERVIEW

These Support Materials are provided to assist teachers/lecturers in delivery of the

Higher Civil Engineering unit Structural Mechanics and Design 1.

The Teacher’s/Lecturer’s guide contains a suggested teaching programme and a

summary of the course content. Advice is offered on use of the additional 40 hours of

the course and on induction to the unit. Essential resources are highlighted, along

with additional resources which will enhance learning and teaching.

Guidance is provided on use of the National Assessment Bank Support Materials and

on the preparation of candidates for external assessment of the Higher course.

The Teacher’s/Lecturer’s guide should be read in conjunction with the Subject Guide

for DET Construction (published by SCCC/HSDU/SFEU 1997) and any subsequent

supplements to the Guide. Reference is also made to the Arrangements Documents

for Higher Civil Engineering.

A series of tutorials, with model solutions, are provided which will assist students in

their learning, and teachers/lecturers in formative assessment and in the preparation of

course estimates. The subjects covered by the tutorials are:

1.

loads and support reactions for statically determinate beams

2.

shear force and bending moment diagrams

3.

bending and shear stresses in simple beams.

The Student’s guide provides a brief introduction to the unit, along with details of

assessment and reassessment. Information is included on use of the additional 40

hours of the course to enhance learning and for consolidation.

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

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TEACHER’S/LECTURER’S GUIDE

Possible Teaching Programme

Notes

1.

each block in the table represents a nominal 2 hour period

2.

the Internal Assessment items and associated duration are those contained in the

National Assessment Bank Support Materials

3.

those items in the table which are associated with the additional 40 hours allocated

to the course, are indicated in

italics

4.

as it may be assumed that a centre will provide a general induction to all

candidates, only those induction aspects pertaining to the Higher Civil

Engineering have been timetabled here.

Table 1 – Possible Teaching Programme

BLOCK

NUMBER

CONTENT

1 Induction to Higher Civil Engineering

2 Basic Principles of Structural Analysis and Design outcome 1

3 do outcome 1

do (30 minutes) outcome 1

4

Estimation of Loads on Simple Structures outcome 2

Internal Assessment 1 – 30 minutes

5

Estimation of Loads on Simple Structures outcome 2

6 Evaluation of Support Reactions for Statically Determinate Beams outcome 2

7 do outcome 2

Internal Assessment 2 – 45 minutes

8

Construction of Shear Force and Bending Moment Diagrams outcome 3

9 Construction of Shear Force and Bending Moment Diagrams outcome 3

10 Review of Overall Progress in Course

11 Guest Lecture in Building Control

12 Construction of Shear Force and Bending Moment Diagrams outcome 3

13 do outcome 3

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: Civil Engineering: Structural Mechanics and Design 1 (Higher)

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Table 1 – Possible Teaching Programme - continued

BLOCK

NUMBER

CONTENT

14 do outcome 3

15 do outcome 3

Internal Assessment 3 – 45 minutes

16

Determination of Bending and Shear Stresses in Simple Members outcome 4

17 Determination of Bending and Shear Stresses in Simple Members outcome 4

18 do outcome 4

19 do outcome 4

20 do outcome 4

do (60 minutes) outcome 4

21

Computer Solutions to Shear Force and Bending Moment Diagrams and

determination of Bending and Shear Stresses

outcome 5

22 Computer Solutions to Shear Force and Bending Moment Diagrams and

determination of Bending and Shear Stresses

outcome 5

Computer Solutions to Shear Force and Bending Moment Diagrams and

determination of Bending and Shear Stresses (60 minutes)

outcome 5

23

Additional Computing (60 minutes)

24

Additional Computing

25 Internal Assessments 4 and 5 – 80 minutes

26

Final Assessment Preparation

27

Final Assessment Preparation

Total

40 hours plus additional 13 hours

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Teaching programme content

Induction

It is assumed that the centre will provide a general overall induction to candidates

outwith

the time allocated to this unit.

Such general induction might cover areas such as:

•

role of the construction industry in 20/21st centuries

•

reference to recent major Scottish construction projects

•

study facilities within centre.

Induction areas relating particularly to the Higher Civil Engineering course and which

may be covered within the time allocated to this unit are:

•

overview of course, key learning, (60 mins)

•

course expectations and milestones, (30 mins)

•

staff support, (30 mins)

•

learning activities, standards of achievement for course units and course

assessment methods of generating evidence of achievement (60 mins).

Reference should be made to the

Possible Teaching Programmes

for the other two

course units, where time is also allocated to cover the induction areas pertaining to the

Higher Civil Engineering course.

Outcome 1

Explain the basic principles of structural analysis and design (nominally 5 hours,

including assessment).

Performance criteria

PC (a) The purposes of structural analysis and design are explained clearly and

accurately.

Content

•

the purpose of structural analysis and the concept of breaking down complex

structures into simpler elements

•

the interaction between structural analysis and design.

PC (b) The sources of loading upon structures are identified correctly.

Content

•

the meanings of dead, imposed, wind and snow loadings

•

the distinction between concentrated and uniformly distributed loads

•

sources of loading, dead (materials), imposed, snow and wind

•

partial factors of safety.

References

BS 6399 (appropriate parts), weights of common building materials.

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PC (c) The load paths and primary frames of simple structures are illustrated

correctly.

Content

•

concurrent and non-concurrent co-planar force systems

•

the understanding of the nature and effect of hinged, roller and fixed supports on

the analysis of structural members

•

the load carrying mechanisms for structural members such as: slabs, beams,

columns, foundations and simple plane frames, subject to compressive, tensile,

bending and shear effects as appropriate

•

the tracing of load transfer paths through skeletal structures consisting of slabs,

beams, columns, foundations and frames.

Laboratory equipment

•

demonstration of effects of different supports to beams and columns

•

demonstration of loading paths in a full-scale frame.

Assessment

Referring to National Assessment Bank Unit Assessment, Question 1, parts a, b and c

may be used and should be allocated 30 minutes.

Outcome 2

Estimate the loads acting upon simple structures and evaluate the support reactions for

statically determinate beams (nominally 7 hours, including assessment).

Performance criteria

PC (a) The conditions of determinacy for beams are stated correctly.

Content

•

the equations of equilibrium (

∑

V = 0,

∑

H =0,

∑

M =0)

•

the determinacy of beams, applied to simply supported beams, cantilever beams

and simply supported beams with overhangs.

PC (b) The loading on statically determinate beams is assessed correctly.

Content

•

calculation of loadings on statically determinate beams of the forms covered in

PC (a).

Tutorial

Tutorial 1 – Determination of loads and evaluation of support reactions for

statistically determinate beams. (Questions 1, 2, 3 and 4).

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PC (c) The support reactions for statically determinate beams are evaluated

correctly.

Content

•

evaluation of support reactions for statically determinate beams of the forms

covered in PC (a).

Tutorial

Tutorial 1 – Determination of loads and evaluation of support reactions for

statistically determinate beams. (Questions 5, 6, 7, 8 and 9).

Assessment

Referring to National Assessment Bank Unit Assessment, Question 1, part d, question

2, parts a and b and question 3, parts a and b may be used and should be allocated 45

minutes.

Outcome 3

Construct shear force and bending moment diagrams for statically determinate beams

(nominally 11 hours, including assessment).

Performance criteria

PC (a) Shear force and bending moment diagrams are drawn accurately.

PC (b) Significant values of shear force and bending moment are identified

correctly.

PC (c) Shear force and bending moment values for standard applied loading cases

are identified and used correctly.

PC (d) The location of points of contraflexure for simply supported beams with

overhangs are calculated correctly.

Content

•

sign conventions for shear force and bending moment calculations

•

relationships between shear force and bending moment e.g. maximum bending

moment occurring at point of zero shear

•

points of contraflexure on appropriate beams (using a quadratic equation for

solution)

•

the importance and uses of shear force and bending moment diagrams in the

design process

•

shear force and bending moment diagrams to be drawn for simply supported

beams, cantilever beams and simply supported beams with overhangs, considering

concentrated loads, uniformly distributed loads (partly or wholly covering a span),

or a combination of concentrated and uniformly distributed loads

•

development and use of shear force and bending moment values for standard cases

viz: uniformly distributed load on simply supported and on cantilever beams,

central concentrated load on simply supported beam, end concentrated load on

cantilever beam.

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: Civil Engineering: Structural Mechanics and Design 1 (Higher)

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Tutorial

Tutorial 2 – Construction of shear force and bending moment diagrams.

Laboratory equipment

Demonstration of changes of longitudinal beam profile under variation of load.

Assessment

Referring to National Assessment Bank Unit Assessment, question 1, part e, question

2, part c and question 3, part c may be used and should be allocated 40 minutes.

Outcome 4

Determine the bending and shear stresses in simple members (nominally 13 hours,

including assessment).

Performance criteria

PC (a) Second moments of area of symmetrical sections are calculated accurately.

Content

•

calculation of second moment of area of solid rectangular sections and of hollow

rectangular sections in steel and in timber

•

second moment of area of standard steelwork sections obtained from appropriate

section properties.

References

Tables of section properties of standard steel sections viz: universal beams and hollow

rectangular sections.

Tutorial

Tutorial 3 – Determination of bending and shear stresses in simple members.

PC (b) The equation of simple bending is applied correctly to determine bending

stresses.

PC (c) Shear stresses at significant positions are determined correctly.

PC (d) Comparisons between evaluated and permissible bending and shear

stresses are carried out correctly.

Content

•

development of expressions

σ

= M y/I (bending) and

τ

= V A y/I b (shear) for

beams of cross-section indicated in PC (a)

•

bending and shear stress distribution over the depth of section

•

permissible stresses in timber and steel.

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: Civil Engineering: Structural Mechanics and Design 1 (Higher)

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Tutorial

Tutorial 3 – Determination of bending and shear stresses in simple members.

Assessment

Referring to National Assessment Bank Unit Assessment, question 1, part f, question

2, parts d, e and f and question 3, part d may be used and should be allocated 50

minutes.

Outcome 5

Solve structural problems using computerised techniques (nominally 4 hours,

including assessment).

Performance Criteria

PC (a) Statically determinate beams are analysed correctly to determine the shear

force and bending values using computer techniques.

PC (b) Bending and shear stresses for standard sections are determined accurately

using computer techniques.

PC (c) The results from computer programmes are correctly checked by manual

means.

Content

•

use of appropriate commercial software and/or in-house packages and/or

spreadsheets to solve problems covered in Outcomes 3 and 4

•

information on range of commercial software available

•

importance of manual checks on computer output.

Assessment

Referring to National Assessment Bank Unit Assessment, an assignment may be used

and should be allocated 30 minutes.

Notes on Outcome 5

•

The Assessment for this outcome is shown in the Possible Teaching Programme

as being combined with that for Outcome 4.

•

Time for candidates to gain more experience in the use of computer software is

shown in the Possible Teaching Programme. This time is part of the additional 40

hours available in the Higher Civil Engineering Course.

General resources

It is expected that centre staff will use references to relevant text book(s) during the

delivery of the unit. Candidates may also be recommended to refer to such texts.

As there are many textbooks covering the material of the unit, it was felt that it was

not therefore necessary to indicate a specific text here.

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: Civil Engineering: Structural Mechanics and Design 1 (Higher)

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Assessment

Internal assessment

As indicated in the Possible Teaching Programme, time is allocated for Internal

Assessments.

The National Assessment Bank contains examples of suitable Internal Assessments

which will assess all the Performance Criteria within each Outcome of the unit.

Maximum times for the completion of each assessment is also indicated in the

National Assessment Bank.

All Internal Assessment should be undertaken under supervision to ensure that it is the

candidate’s own work.

Reassessment

Where a candidate has not attained the standard necessary to pass a particular

Outcome or Outcomes, there should be the opportunity for that candidate to be

reassessed. As a general rule, reassessment in a particular instrument should be

offered on a maximum of two occasions. While the actual timing of reassessment is

at the discretion of the individual centre, it may be beneficial to the candidate

concerned if the first opportunity for reassessment was made available, as soon as

practicable after the original assessment had been undertaken.

The second reassessment might have to be delayed until near the end of the unit, for

practical reasons.

Evidence from the original unit assessment should assist staff in identifying why an

individual candidate has failed to achieve a particular outcome and hence to plan

suitable support for learning.

The actual reassessment instrument will depend upon the extent to which the

candidate has failed to achieve the outcome concerned. It might, for example require

the candidate to repeat all or part of the original instrument, or, in other cases,

undertake a new instrument. In all cases, the original conditions under which the

instrument was undertaken should be repeated but the time allowed would be

allocated on a pro-rata basis.

While any overall discussion/analysis of the original assessment instrument should be

delayed until the first opportunity for reassessment has been undertaken, those

candidates requiring the reassessment should be advised of their weaknesses and

guidance should be given to them on how they can find information which would help

them in their reassessment. It may be beneficial to hold a more formal revision lesson

if there are a substantial number of candidates requiring reassessment.

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Recording and retention of evidence

It is important that records of unit assessment and evidence of assessment be retained

for external moderation and appeals purposes, in accordance with the requirements of

the Scottish Qualifications Authority.

While centres will normally have their own standardised recording systems, examples

of possible attainment and marks records and an assessment summary record are

given in the National Assessment Bank pack for this unit. Particular attention should

be made to those Instruments of Assessment for which cut-off scores are applicable.

(See later notes on course estimates).

Uses of internal assessments as teaching aids

In addition to the most obvious use of the Internal Assessments i.e. to judge the

competence of the candidate in each outcome, they can also be used in the following

ways:

•

Once the assessment and the initial reassessment have been completed, then an

overall discussion/analysis of the instrument can take place. This will provide an

opportunity for candidate feedback, consolidation of learning and any integration

with other outcomes within this unit and with other units in the course.

•

Together with the attainment and marks records of the other units of the course, a

periodic review of the course can be undertaken. (See Possible Teaching

Programme for all three units). It is suggested that such reviews should take place

twice during the year, at such times when sufficient evidence is available to allow

meaningful decisions to be made on individual candidate’s future targets,

modification to teaching programmes and techniques, etc.

External assessment

The external assessment for the course consists of a 3 hour examination paper,

externally devised and assessed.

The Paper will be in two sections viz:

Section A - five short answer and restricted response questions, of which all must be

attempted, worth 40 marks.

Section B - five extended response and/or structured questions, of which candidates

will be required to attempt three, worth 60 marks.

The questions in both sections of the examination paper will sample across the content

of the three units of the course and the spread of marks, in both sections will be

roughly in proportion to the time allocated to the teaching of each outcome.

A specimen question paper will be available to indicate the format in which the

examination paper will be set.

On the basis of this examination paper, successful candidates will be graded A, B or

C, for the course. The relative grade descriptions are given in the Arrangements

Document.

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Preparation of candidates for external assessment

As the nature and purpose of the Instruments of Internal Assessment may differ from

the those of the questions in the External Assessment examination paper, it will be

necessary to give candidates some practice in answering the relative types of question

and guidance in examination techniques.

From the Possible Teaching Programme, it can be seen that time is scheduled for this

towards the end of the unit. (See also the programmes for the other two units of the

course).

Candidate estimates

Centres will be required to furnish estimates of candidates likely performance in the

course and of their likely grading. This information will be used in the case of

appeals by the centre and to eventually establish the degree of concordance of a

centre. The estimates must be submitted by April, at the latest.

Course estimates will require to be made by considering the performance of

candidates over all three units. In the case of this particular unit, guidance is given in

the National Assessment Bank, where, in each of the Instruments, candidates can

exceed the cut-off scores which signify competence in an outcome. Thus the actual

scores can be used to provide part of a candidate’s estimate. As an alternative to this,

a prelim examination could be held.

Such a prelim will be more meaningful if held towards the end of a unit but in order to

produce the estimate by April, it will need to be undertaken by March.

Additional 40 hours

For convenience, this time is shown as being spread over the three units,

approximately 13 hours per unit (see Possible Teaching Programme). Some of the

time shown is clearly dedicated to this unit viz:

•

additional computing, which is intended to give sufficient practice to all

candidates, whatever their background and computer experience

•

external assessment practice.

The remaining time scheduled for induction, review of overall progress and guest

lecture on building control can be considered as being general and should be read in

conjunction with the general aspects shown in the Possible Teaching Programmes of

the other two units.

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: Civil Engineering: Structural Mechanics and Design 1 (Higher)

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STUDENT’S GUIDE

Outcomes covered in unit

1.

Explain the basic principles of structural analysis and design:

i)

The purposes of structural analysis and design.

ii)

The sources of loading upon structures.

iii)

The load paths and primary frames of simple structures.

2.

Estimate the loads acting upon simple structures and evaluate the support

reactions for statically determinate beams:

i)

The conditions of determinacy for beams.

ii)

The loading on statically determinate beams.

iii)

The support reactions for statically determinate beams.

3.

Construct shear force and bending moment diagrams for statically determinate

beams:

i)

The drawing of shear force and bending moment diagrams.

ii)

Significant values of shear force and bending moments.

iii)

Shear force and bending moment values for standard loading cases.

iv)

Location of points of contraflexure for simply supported beams with

overhangs.

4.

Determine bending and shear stresses in simple members:

i)

Second moments of area of symmetrical sections.

ii)

The equation of simple bending.

iii)

Shear stresses at significant positions.

iv)

Comparison between evaluated and permissible bending and shear stresses.

5.

Solve structural problems using computerised techniques:

i)

Shear force and bending values in statically determinate beams by computer

techniques.

ii)

Bending and shear stresses for standard sections by computer techniques.

iii)

Computer program results checked manually.

Internal assessment

The unit shall be assessed internally by means of a series of Instruments of

Assessment.

These Instruments will cover all of the Outcomes and all of the Performance Criteria

within each Outcome.

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: Civil Engineering: Structural Mechanics and Design 1 (Higher)

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Structural Mechanics and Design will be assessed by two Instruments, as follows:

•

Instrument of Assessment 1

–

will consist of three structured questions, each

question being based upon a particular beam. The three beams will cover a range

of loading criteria, support conditions and constituent materials. In the context of

the three beams, all of the Performance Criteria of Outcomes 1,2,3 and 4. This

will involve explaining the basic principles of structural analysis and design,

estimating the loads acting on beams, evaluating the support reactions,

constructing relevant shear force and bending moment diagrams and checking if

the beam sections allocated are satisfactory, under the given loading.

The questions undertaken will be ‘closed book’, although any relevant section

property tables will be provided. A total time allowance of 2 hours 45 minutes

will be allowed, however it is anticipated that this will be split up to allow the

relevant part(s) of each question to be undertaken at the end of the appropriate

outcome.

•

Instrument of Assessment 2

– will consist of an assignment, using a relevant

computer package or packages to cover Outcome 5. The shear force and bending

moment diagrams will be created and hence the maximum bending and shear

stresses found for one of the beams in Instrument of Assessment 1. The results

obtained will be compared with those deuced by manual calculation.

Access to the appropriate instruction manual or explanatory notes on the

program(s) will be available and a time allowance of 30 minutes will be given.

Required achievement standard in instruments of assessment

The criteria for determining whether an Outcome/Performance Criteria has been

satisfactorily completed will be clearly indicated, prior to the undertaking of the

relevant Instrument. For example, the minimum mark required to constitute a pass,

the cut-off score, will be indicated prior to that part being undertaken.

Reassessment

In the event of a part-pass or non-pass being recorded, there will be an early

opportunity for reassessment in that particular Outcome. There will be some guidance

given by the teacher/lecturer on the shortcomings of the original response before the

reassessment s attempted. Depending upon the original response, the reassessment

may consist of:

•

a repeat of the original instrument

•

a new instrument requiring responses to all sections covered in the outcome

•

a repeat of the section(s) of the original instrument in which the responses had

been unsatisfactory

•

a new instrument requiring responses only in the section(s) in which the original

responses had been unsatisfactory.

If c or d above is used, then the time allocation will be on a pro-rata basis to the

original.

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: Civil Engineering: Structural Mechanics and Design 1 (Higher)

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If after this reassessment, a pass is still not attained, then a second reassessment will

be arranged, towards the end of the unit. This reassessment will follow the format a,

b, c and d above and at this stage, a reassessment will be available for any of the unit

outcomes yet to be passed.

No further opportunities for reassessment are likely to be available during that present

running of the unit.

External assessment

The external assessment for the course consists of a 3 hour examination paper,

externally devised and assessed.

The Paper will be in two sections viz:

Section A –five short answer and restricted response questions, of which all must be

attempted, worth 40 marks.

Section B –five extended response and/or structured questions, of which candidates

will be required to attempt three, worth 60 marks.

The questions in both sections of the examination paper will sample across the content

of the three units of the course and the spread of marks, in both sections will be

roughly in proportion to the time allocated to the teaching of each outcome.

On the basis of this examination paper, successful candidates will be graded A, B or

C, for the course.

Preparation of candidates for external assessment

As the nature and purpose of the Instruments of Internal Assessment may differ from

the those of the questions in the External Assessment examination paper, it will be

necessary for candidates to have some practice in answering the relative types of

question and guidance in examination techniques. It is expected that this will be

carried out for all three units towards the end of the course. (See below).

Presentation of unit

The centre will prepare a structured teaching programme for the unit. This

programme will detail the coverage of the unit material in a logical order and will

timetable the Instruments of Assessment as they are required. Structured tutorial

sheets will be issued and tutorial time will be allocated in the teaching programme.

Laboratory demonstrations/experiments will also be carried out within the

programme.

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Use of additional 40 hours

In addition to the three units of the course, which are allocated 40 hours each, an

additional 40 hours is included in the course. This additional 40 hours is intended to

be used to provide:

•

Induction – see below.

•

Contacts with industry which will enable candidates to see the relevance of what

they are learning. This is accomplished by site visits, supplemented with pre-visit

and post-visit discussions, guest visiting lecturers and the use of videos.

•

Periodic review of the overall course. This will probably take place at two suitable

points during the course and will give candidates the opportunity to evaluate their

progress to date and discuss any changes which they will need to make in the

remainder of the course to achieve success.

•

Additional time to gain more expertise in areas of the course with which they may

be having difficulty e.g. in this unit, there will be additional time available for

practice with the computing programs used in analysis.

•

Preparation for the external assessment.

For timetabling convenience, it is likely that the 40 hours will be split amongst the

three units, except for those areas which are directly applicable to a particular unit.

Induction

A well planned induction is intended and will provide candidates with a confident

start and will also break down the barriers to learning. The Induction should be seen

as being in two parts:

1.

General

: This is not specific to the Higher Civil Engineering Course and should

be a general induction to the centre. It should cover Study facilities available in

the centre, the concepts of Internal and External Assessment, Scottish Group

Awards, etc.

2.

Specific

: For the Higher Civil Engineering Course the following should be

covered, in all three units:

•

overview of the course, key learning points

•

course expectations and milestones

•

teaching programmes, incorporating aspects of the additional 40 hours

•

learning activities

•

standards of achievement for units and course

•

assessment and methods of generating evidence of achievement

•

reference material, mandatory and non-mandatory.

Portfolios of internally assessed work

All work submitted by candidates for Internal Assessment will be marked and kept in

individual portfolios. Although candidates will see the marked assessments for

information on progress, advice for reassessment etc., the portfolios will be retained

by the centre, during the currency of the unit. This is done for the purpose of

inspection by External Verifiers and the possible mounting of appeals in relation to

the course result.

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Candidate estimates

Centres will be required to furnish estimates of candidate’s likely performance in the

course and of their likely grading. This information will be used in the case of

appeals by the centre, and require to be submitted by April, at the latest.

Course estimates will require to be made by considering the performance of

candidates over all three units. In the case of this particular unit, candidates can

exceed the cut-off scores which signify competence in an outcome. Thus the actual

scores can be used to provide part of a candidate’s estimate. As an alternative to this,

a prelim examination could be held. Such a prelim will be more meaningful if held

towards the end of a unit but in order to produce the estimate by April, it will need to

be undertaken by March.

Guidance on this will be provided during the induction period.

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TUTORIAL 1

Loads and support reactions for statically determinate beams

(Loading on beams should be illustrated on line diagrams, where this will be clearer)

1.

For the part floor plan of the steel-framed structure, shown in figure Q1, together

with the relevant design data, evaluate:

i)

The loading on Beam A, which is simply supported over a span of 4 m.

ii)

The loading on Beam B, which is simply supported over a span of 6 m.

2.

For the part floor plan of the steel-framed structure, shown in figure Q2, together

with the relevant design data, evaluate the loading on Beams B1, B2 and B3.

3.

A timber – floored structure, together with the relevant design data is shown in

plan in Fig.Q3. Evaluate the loading on Beams A, B, C and D.

4.

Fig.Q4 shows, in plan, part of a steel-framed structure, together with the relevant

design data. Considering Beam C, evaluate the loading on the complete length of

the beam.

5.

Considering the beam loadings found in Q1, above, evaluate:

i)

The end reaction from Beam A on Beam B.

ii)

The end reaction from Beam B on the column X.

6.

Considering the beam loadings found in Q2, above, evaluate the end reactions

from Beam B3 on columns X and Y.

7.

Considering the beam loadings found in Q3, above, evaluate:

i)

The end reactions of the five beams on Beam E.

ii)

The end reactions of Beam E on the supporting walls.

8.

Considering the loading on Beam C, found in question 4 above, evaluate the end

reactions from the beam on the supporting columns.

9.

For the beams shown in figure Q9, evaluate the end reactions.

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TUTORIAL 1: FIGURES

4

m

4

m

BEAM A

FLOOR

SPAN

X

FLOOR

SPAN

BEAM B

3 m

3 m

6 m

Figure Q1

Concrete floor slab = 250 mm thick Imposed load on slab = 5 kN/m

2

Self weight of all beams = 1.5 kN/m Brickwork on Beam B = 9kN/m

4m

4m 4m2m2m

10m

FLOOR

SPAN

FLOOR

SPAN

FLOOR

SPAN

FLOOR

SPAN

BEAM B3

BEAM B2

BRICKWORK

BEAM B1

S

T

A

I

R

W

E

L

L

S

T

A

I

R

W

E

L

L

Z

Y

X

Figure Q2

Brickwork as indicated = 9 kN/m Self weight of all beams = 1 kN/m

Concrete slab thickness = 200 mm Imposed load on floor = 4 kN/m

2

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

21

TUTORIAL 1 – FIGURES

500

500 500

5

00 500

5

00

5

00

3m

BEAM E

X

Y

S

UPPORTING

W

ALLS

HEAVY EQUIPMENT

NO IMPOSED ;LOAD

BENEATH - BUT 4

POINT LOADS - EACH 2kN

400400

400

1.5m

BEAM A

BEAM A

BEAM B

BEAM C

BEAM D

Figure Q3

Dead load of flooring, ceiling and Beams A, B, C and D equivalent to 1.5 kN/m

2

.

Self weight of Beam E = 0.6 kN/m. Imposed loading on floor = 2 kN/m

2

6m

3

m

1.5 m

COLUMN A

ABOVE & BELOW

FLOOR

C

OLUMN B

BELOW FLOOR

BEAM C

C

OLUMNS ABOVE

F

LOOR EACH

2

0kN LOADING

BRICKWORK

2 m

1.5 m

5 m

Figure Q4

Slab self weight = 5 kN/m

2

Brickwork = 8 kN/m

Self weight of all beams = 2 kN/m Imposed load on slab = 3 kN/m

2

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

22

TUTORIAL 1 – FIGURES

4kN/m

1

6kN/m

3

6kN

L

R

1

.5m3m

6

m

(

a)

1m3m

5

m

2kN

8

kN

1kN/m

L

(b)

L

R

(

c)

6m

1m

1

m

2

m

2

m

5kN

3

0kN

8

kN/m

Figure Q9

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

23

SOLUTIONS TO TUTORIAL 1

1.Beam A: Width of floor carried per m run = 3/2 + 3/2 = 3 m

Weight of slab per square metre = 1 x 1 x 0.25 x 24 = 6 kN

Load per m run = 1.5 + 3 x 1 x 6 + 3 x 1 x 5 = 34.5 kN

Beam B: Uniformly distributed load = 1.5 + 9 = 10.5 kN/m

Central concentrated load = 34.5 x 4/2 = 69 kN

2 Beam 1: Uniformly distributed load = 1 + 9 = 10 kN/m

Beam 2: Uniformly distributed load = 1 + 9 = 10 kN/m

Central concentrated load = 10 x 4/2 = 20 kN

Beam 3: Concentrated load at Z = 20/2 + 10 x 4/2 = 30 kN

Uniformly distributed load (XZ) = 1 + 4/2 x (1 x 1 x 0.2 x 24) + 4/2 x 4

= 18.6 kN/m

Uniformly distributed load (ZY) = 1 + 4 x(1 x 1 x 0.2 x 24) + 4 x 4

= 36.2 kN/m

3.Beam A: Uniformly distributed load = (0.5/2 + 0.5/2) x (1.5 + 2) = 1.75 kN/m

Beam B: Uniformly distributed load (not under equipment) = 1.75 kN/m

Uniformly distributed load (beneath equipment) = 0.5/2 x (1.5 + 2) + 0.5/2 x

1.5 = 1.25 kN/m

Concentrated loads at corners of equipment = 2 kN

Beams C and D:Similar to Beam B, in magnitudes but with different

combinations (best illustrated with diagrams).

4.Beam C: (6 m Span) Uniformly distributed load = 5/2 x (5 + 3) + 2 = 22 kN/m

(cantilever) Uniformly distributed load = 2 kN/m

End concentrated load = 1.5 x 8 + 5/2 x 2 + 20 + 3/2 x (5 + 3) x 2.5 = 67 kN

5.End reaction from Beam A on Beam B = 34.5 x 4/2 =69 kN

End reaction from Beam B on Column X = 69/2 + 10.5 x 6/2 = 66 kN

6.Taking moments about Y: RX x 10 = 30 x 6 + 18.6 x 4 x 8 + 36.2 x 6 x3

RX = 142.68 kN

RY = -30 - 18.6 x 4 - 36.2 x 6 + 142.68 = 178.92 kN

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

24

SOLUTIONS TO TUTORIAL 1

7.Reactions on Beam E:

From Beam A (2 beams) = 3/2 x 1.75 = 2.625 kN

From Beam B = (1.75 x 2.2 x 1.9 + 1.75 x 0.4 x 0.2 + 1.25 x 0.4 x 0.6 + 2 (0.8

+ 0.4))/3 = 3.385 kN

From Beam C = (1.75 x 1.5 x 2.25 + 1.75 x 0.3 x 0.95 + 1.75 x 0.4 x 0.2 +

1.25 x 0.4 x 1.3 + 1.25 x 0.4 x 0.6 + 2(0.4 + 0.8 + 1.1 +

1.5))/3 = 5.032 kN

From Beam D = (1.75 x 1.5 x 2.25 + 1.75 x 1.1 x 0.55 + 1.25 x 0.4 x 1.3 +

2(1.1 + 1.5))/3 = 4.272 kN

Taking moments about Y:

RX x 3 = 2.625 x 2.5 + 2.625 x 2 + 3.385 x 1.5 + 5.032 x 1 + 4.272 x 0.5 +

0.6 x 3 x 1.5

RX = 8.919kN

RY = 2.625 x 2 + 3.385 + 5.032 + 4.272 + 0.6 x 3 - 8.919 = 10.82 kN

8.Beam C:Taking moments about left hand supporting column A:

RB x 6 = 22 x 6 x 3 + 2 x 3 x 7.5 + 67 x 9

RB = 174 kN

RA = 22 x 6 + 2 x 3 + 67 - 174 = 31 kN

9. a) Taking moments about R:

RL x 6 = 16 x 6 x 3 + 4 x 3 x 4.5 + 36 x 1.5 thus RL = 66 kN

RR = 16 x 6 + 4 x 3 + 36 - 66 = 78 kN

b) RL = 3 x 1 + 8 + 2 = 13 kN

ML = 3 x 1 x 1.5 + 8 x 4 + 2 x 5 = 46.5 kNm

c) Taking moments about L:

RR x 6 = 30 x 1 + 5 x 8 + 8 x 3 x 5.5 thus RR = 33.67 kN

RL = 30 + 5 + 8 x 3 - 33.67 = 25.33 kN

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

25

TUTORIAL 2

Construction of shear force and bending moment diagrams

(The examples in this tutorial are those for which the support reactions were evaluated

in Tutorial 1).

Construct, to suitable scales, the shear force diagram and hence the bending moment

diagram, indicating salient values in all diagrams.

1.

6

9kN

3m

6

m

66kN

6

6kN

1

0.5kN/m

2.

3

0kN

1

0m

4m

1

8.6kN/m

3

6.2kN/m

178.92kN

142.68kN

3.

0.5m 0.5m

0

.5m

0

.5m

0

.5m 0.5m

3

m

2.625kN 2.625kN

3

.385kN

5

.032kN

4

.272kN

10.82kN8.919kN

0.6kN/m

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

26

TUTORIAL 2

4.

3

m

6m

31kN

1

47kN

67kN

22kN/m

2

kN/m

In addition, evaluate the position of the point of contraflexure.

5.

1

.5m3m

6

m

66kN 78kN

3

6kN

1

6kN/m

4

kN/m

6.

1m3m

5

m

13kN

2kN

8

kN

1kN/m

46.5kNm

7.

2m

2

m1m

1

m

6

m

25.33kN

5kN

3

0kN

8

kN/m

In addition, evaluate the position of the point of contraflexure.

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

27

SOLUTIONS TO TUTORIAL 2

SFD

66k N

66k N

34.5kN

34.5kN

BMD

150.75kNm

SFD

142.68kN

6

8.28kN

3

8.28kN

1

78.92kN

1.O57m

B

MD

4

21.92kNm

442.15kNm

SFD

8.919

8.619

5.994

5.694

3.069

2

.769

0

.616

0.916

5.948

6.248

10.52

1

0.82

B

MD

4

.385

k

Nm

7

.307

k

Nm

8

.767

k

Nm

8.384

kNm

5.34

kNm

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

28

SOLUTIONS TO TUTORIAL 2

SFD

BMD

31kN

101kN

73kN

6

7kN

1.409m

2

.818m

2

1.86kN

210kNm

P

OINT OF CONTRAFLEXURE:

3

1x = 22x

2

2

x = 2.818 m

SFD

3.375m

66kN

6

kN

18kN

54kN

7

8kN

B

MD

1

08

k

Nm

109.125

kNm

99

kNm

SFD

13kN

10kN10kN

2kN

BMD

46.5kNm

12kNm

2kNm

SFD

25.33kN

25.33kN

4.67kN

4.67kN

20.67kN

13k N

5kN5kN

BMD

5.197m

25.33kNm

11.33k Nm

14k Nm

5kNm

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

29

TUTORIAL 3

Bending and shear stresses in simple beams

1.

The analysis of a loaded steel beam gives the maximum shear force and the

maximum bending moment as 66 kN and 150.75 kNm, respectively. It is proposed

that a 533 x 210 x 82 Universal Beam be used for the beam.

a)

Calculate:

i)

The actual maximum shear stress on the section, using the beam dimensions from

the appropriate Section Property Tables.

ii)

The actual maximum bending stress on the section using the appropriate section

properties from tables.

b)

If the maximum permissible bending stress on the steel is 165 N/mm

2

, evaluate

the minimum second moment of area required for a suitable beam section and

hence choose the most economic Universal Beam section, from appropriate tables.

2.

The analysis of a loaded rectangular, hollow steel beam gives the maximum shear

force and the maximum bending moment as 178.92 kN and 442.15 kNm,

respectively.

The section proposed for the beam is to be 500 mm deep, 300 mm wide with webs

and flanges all 12.5 mm thick.

a)

Evaluating all the required section properties from the given section dimensions,

calculate the actual maximum shear stress and bending stress on the section and

compare the values obtained with the permissible shear and bending stresses of

115 N/mm

2

and 165 N/mm

2

, respectively.

b)

If at a later stage, it is found that the beam provided is of a higher grade material,

with a permissible bending stress of 230 N/mm

2

, calculate the maximum uniformly

distributed load which the beam could carry over a simply supported span of 10m.

3.

The analysis of a loaded rectangular timber beam gives the maximum shear force

and the maximum bending moment as 10.82 kN and 8.77 kNm respectively. The

beam is to be 50 mm wide.

a)

If the maximum permissible shear stress and bending stress for the timber is 0.66

N/mm

2

and 4.1 N/mm

2

, respectively, calculate a suitable depth for the rectangular

section.

b)

At a point in the span of the beam, where the bending moment is reduced to 4.4

kNm, the depth found in a) is reduced by 50 mm to allow for services. Check that

the reduced can carry the appropriate bending moment.

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

30

TUTORIAL 3

4.

a)

A timber floor is carried by 222 x 40 mm rectangular timber joists, at 500

mm spacing, spanning 3.5 m, simply supported. If the floor loading is 2.0 kN/m

2

,

inclusive of all self weights,

check the suitability of the given joist section, in both

shear and bending, assuming the permissible shear and bending stresses to be 0.67

N/mm

2

and 5.3 N/mm

2

, respectively.

b)

Considering bending only, calculate a suitable spacing of the joists if they were

increased to 250 x 50 mm in section, under the same magnitude of loading, but

now using timber with a permissible bending stress reduced to 4.1 N/mm

2

.

5.

A small floor 5 m x 4.5 m is to be supported by one main steel beam and 200 x 50

mm timber joists, spanning between the wall and the steel beam, as shown in

Fig.Q5.

a)

Calculate the safe floor load in kN/m

2

, inclusive of all self weights and

considering only bending in the timber joists. The permissible bending stress of the

timber is 4.1 N/mm

2

.

b)

Considering bending only, calculate a suitable section modulus (I/y) for the steel

beam, assuming the permissible bending stress to be 165 N/mm

2

, and hence

choose, from Section Property Tables a suitable Universal Beam section.

(To simplify analysis, the loading on the UB may be assumed as uniformly

distributed).

Check the chosen Universal Beam section for shear, assuming the permissible stress

to be 115 N/mm

2

.

2.5m

2

.5m

TIMBER JOISTS

AT 500 CENTRES

S

UPPORTING WALLS

Figure Q5

4.5 m

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

31

SOLUTIONS TO TUTORIAL 3

1.

a) i)

Maximum shear stress = V A y/I b where V = 66000 N, I = 47540 x 10

4

mm

4

A y = (208.8 x 13.2 x 257.55 + 250.95 x 9.6 x 250.95/2) = 1.012 x 10

6

mm

3

b = 9.6 mm

Thus maximum shear stress = 14.64 N/mm

2

ii)

Maximum bending stress = (150.75 x 10

6

x 528.3 /2)/47540 x 10

4

= 83.76 N/mm

2

b)

If the maximum permissible stress is 165 N/mm

2

, then the minimum I/y required

to carry a bending moment of 150.75 kNm is found from:

150.75 x 10

6

/I = 165/y thus I/y = 0.9136 x 10

6

mm

3

= 913.6 cm

3

I/y is the elastic Modulus about XXaxis.

Thus from Tables select a 406 x 178 x 64 UB or a 457 x 152 x 52 UB

2.

a)

I = (300 x 500

3

- 275 x 475

3

)/12 = 0.66897 x 10

9

mm

4

Shear stress = 178.92 x 1000 (300 x 12.5 x 243.75 + 25 x 237.5 x 237.5/2)

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

0.66897x10

9

x 25

= 17.32 N/mm

2

< 115 N/mm

2

Bending stress =

442.15 x 10

6

x 250/0.66897 x 10

9

= 165.24 N/mm

2

> 165 N/mm

2

b)

Maximum Bending Moment = 230 x 0.66897 x 10

9

/250 Nmm = 615.45 kNm

= w x 10 x 10/8 thus w = 49.24 kN/m

3.

a)

Shear Force = 10.82 x 1000 = 0.667 x 0.66 x 50 x D thus D = 491.6 mm

Bending Moment = 8.77 x 10

6

= 4.1 x 50 x D

2

/6 thus D = 506.6 mm

Provide a beam 525 x 50 mm

Beam is now 475 x 50 thus bending stress is now = 4.4 x 10

6

x 6

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

50 x 475

2

= 2.34 N/mm

2

< 4.1 N/mm

2

DET

: Civil Engineering: Structural Mechanics and Design 1 (Higher)

32

SOLUTIONS TO TUTORIAL 3

4.

a) Loading per joist/m = 0.5 x 1 x 2 = 1 kN/m thus M = 1 x 3.5

2

/8 = 1.53 kNm

and V = 1 x 3.5/2 = 1.75 kN

Shear stress = 1.5 x 1.75 x 1000/40 x 225 = 0.292 N/mm

2

< 0.67 N/mm

2

Bending stress = 1.53 x 10

6

x 6/40 x 225

2

= 4.53 N/mm

2

< 5.3 N/mm

2

b) Moment Capacity of larger joists = 4.1 x 50 x 250

2

/6 x 10

6

kNm

= 2.135 kNm = w x 3.5 x 3.5/8

thus w = 1.394 kN/m thus joist spacing = 1.394/2 = 0.697 m say 700mm

5.

a) Moment capacity of joists = 4.1 x 50 x 200

2

/6 x 10

6

kNm = 1.37 kNm

1.37 = 0.5 x w x 2.5

2

/8 thus w = 3.5 kN/m

2

b) I/y required for UB = (2.5 x 3.5 x 4.5

2

/8) x 10

6

/ 165 = 134233 mm

3

= 134.233 cm

3

thus use 178 x 102 x 19 UB

c) Shear stress =

(2.5 x 3.5 x 4.5/2 x 1000) x (101.2 x 7.9 x 84.95 + 4.8 x 81 x 81/2)

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

1356 x 10

4

x 4.8

= 25.31 N/mm

2

< 115 N/mm

2

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