代做UBGMW9-15-3、代写MATLAB、代做Civil Engineering、代写MATLAB程序语言

日期：2020-02-24 09:37

Coursework – Assessment Brief

UBGMW9-15-3 Computational Civil Engineering

Preamble

All assessments on this module are individual work. The work you submit must be your own

work. Submitting work that is copied in part or whole from another student with or without

their permission is an assessment offence.

You must fully attribute/reference all sources of information used during the completion of

your submission, failure to do so constitutes plagiarism, which is an assessment offence.

If you are not familiar with the definitions of plagiarism and collusion, more information can

be found here: http://www1.uwe.ac.uk/students/academicadvice/assessments/

assessmentoffences.aspx

Please ensure you are familiar with assessment procedures and policies, which can be

found here: http://www1.uwe.ac.uk/students/academicadvice/assessments/

assessmentsguide.aspx

Structure of assessments

This module is assessed by two components, A and B:

? Component A is a one hour written exam and is weighted as 25 % of the final mark.

? Component B is a coursework portfolio and is weighted as 75 % of the final mark.

The coursework portfolio described here asks you to consider three problems entitled:

1. Structural analysis under variable loads (worth 30 % of the final module mark)

2. Geotechnical slope stability (worth 30 % of the final module mark)

3. Cantilever beam with exponential cross sectional evolution (worth 15 % of the final module

mark)

1

The final report on your coursework portfolio must include code routines developed for each

of the three elements in a text selectable form (no images or screenshots will be accepted).

Online blackboard submission due on the 26 March 2020.

Marks and feedback for the assessment will be returned until the 28 April 2020.

The following three sections describe the problems you are to develop computer programs

to solve. In each section, specific details of the tasks and outputs to feed in to your report

are described. An overall summary of the assessment criteria is provided at the end of this

document.

Structural analysis under variable loads – 30 %

When dealing with variable loads the internal forces or reactions that a structure generates

will vary according to a probability distribution. Then, the design of a structure is based on an

output value of this distribution which has a small probability, on an absolute basis, of being

exceeded. A workflow of this process is shown in Fig. 1.

1 - Generate samples for

input variable UDL

2 - Compute output

reactions/internal forces

3 - Plot outputs histograms

and estimate the 5% threshold

output value

-40 -35 -30 -25 V [kN]

Figure 1: Diagram of computational analysis for a simply supported beam subjected to a

variable uniformly distributed load (UDL).

Consider the isostatic structures shown in Figs. 2, 3, 4, 5, and the output reactions/internal

forces presented in Table 1. You are asked to assess the variability of one these structures’

outputs when subjected to the shown loads. Each of the loads is assumed to follow a normal

distribution, e.g. for a uniform distributed load assume p ～ N (μp, σp) with mean μp and

standard deviation σp.

Using MATLAB or other programming language generate 10 000 data points for each load,

according to its distribution parameters, and compute the corresponding output reactions/

internal forces.

Dr Andre Jesus & Dr Richard Sandford 2 University of the West of England

P2

Figure 4: Structure 3

Your report should include

? A description of the equations and histograms for each output reaction/internal force.

? An estimate of the 5 % threshold output value, which is defined here as the value which

is exceeded, on an absolute basis, by only 5 % of the load combination realizations.

Dr Andre Jesus & Dr Richard Sandford 3 University of the West of England

Figure 5: Structure 4

Structure Outputs

1 Bending moment at section C, bending moment

at section 5 and axial force at section 2

2 Axial force at bar 1-2 and shear force along section

2-3

3 Horizontal reaction at 2 and bending moment

at 7 towards 5

4 Vertical reaction at 1 and bending moment at 4

towards 3

Table 1: Output reactions and internal forces

? A pseudocode or flowchart of the algorithm that underlies your analysis.

The structure and numerical values that each student has to consider are made available

on Blackboard Learning Materials > Coursework > Coursework values html

file, or by following the URL https://blackboard.uwe.ac.uk/bbcswebdav/

pid-7216458-dt-content-rid-16362959_2/courses/UBGMW9-15-3_19jan_

1/my_values.html

Geotechnical slope stability – 30 %

An important task in geotechnical engineering is to assess the propensity for a slope to collapse.

It is common to analyse the stability of cohesive soil slopes by considering limiting

plastic equilibrium. To carry out a limiting plastic equilibrium analysis, it is first necessary to

define the failure mechanism, which is specified by the geometry of the failure surface. The

mass of soil bounded by this failure surface is assumed to move over this surface as a free body

Dr Andre Jesus & Dr Richard Sandford 4 University of the West of England

in equilibrium. The forces and moments acting to induce failure are then compared with the

resistance to slip that is mobilised along the assumed failure surface.

A variety of different failure surfaces can be considered, but a common choice is a circular segment

in two-dimensions. An important analysis case is that relevant to short-term conditions,

immediately after a cutting is made or an embankment is built. In the short-term, there is insufficient

time for excess pore water pressures to dissipate; such conditions are referred to as

undrained. The shear strength, τ , along a failure surface in undrained conditions is constant

and denoted as cu. The difficulty in carrying out a limiting equilibrium analysis is the choice

of failure surface. The key task is therefore to find the critical failure surface, that is the failure

surface along which failure is most likely to occur and, hence, gives the lowest factor of safety.

Figure 6: Example of the slope stability problem

Figure 6 is an example of the class of problem that you are to address. The figure shows a

two-dimensional slope of constant inclination. The soil consists of a cohesive homogeneous

soil of undrained strength, cu, and unit weight, γ. The slope overlies a stiff strata. The geometry

and material parameters shown in Figure 6 are an example for illustration - you have

been assigned an individual problem, with a set of geometric and material properties that are

individual to you and can be downloaded from: Blackboard Learning Materials > Coursework

> Coursework values html file, or by following the URL https://blackboard.

uwe.ac.uk/bbcswebdav/pid-7216458-dt-content-rid-16362959_2/courses/

UBGMW9-15-3_19jan_1/my_values.html.

Your task is to determine the safety factor against collapse for the slope geometry and maDr

Andre Jesus & Dr Richard Sandford 5 University of the West of England

terials to which you have been assigned. The material properties (γ and cu) relevant to your

individual problem are given on the diagram together with your slope geometry (which can be

read-off from the scale). You are to consider only rotational failure along circular slip surfaces,

but are to vary the radius and centre coordinates of the failure surface in order to find the minimum

safety factor against collapse. A bounding box, termed the ’search area’, is provided to

limit the bounds on the search of your circle centre coordinates. The approach to minimising

the safety factor by varying the location of the slip circle centre and its radius is your choice,

although recommendations and possibilities will be discussed in the lectures and tutorials.

For a particular choice of circular slip surface, the safety factor, SF is calculated as:

SF =

resisting moment

disturbing moment (0.1)

where the disturbing moment is given as:

disturbing moment = W d (0.2)

and the resisting moment due to shear along the slip plane is given as:

resisting moment = cuR

2

θ (0.3)

In these equations, W is the weight of the soil bounded within the failure surface, d is the

horizontal distance from the slip circle centre to the centre of gravity of the soil mass bounded

within the failure surface, R is the slip-circle radius and θ is the angle subtended by the slip

surface (see Figure 7). Note that W and d are typically found by dividing the soil bounded with

the failure surface into slices or rectangular segments and then taking area-moments about a

convenient point. Substitution of Equations 0.2 and 0.3 into Equation 0.1 gives:

SF =resisting moment

disturbing moment =cuR2θW d (0.4)

To aid the validation of the computer program you will develop, a particular slope geometry

is shown in Figure 8. For the particular circular slip line shown (i.e. the given circle centre

position and radius), and for γ=18.5kN/m3 and cu=40kPa, the safety factor against collapse is

1.44 (correct to 2 decimal places). Demonstrating that your computer program can correctly

calculate this safety factor is a valuable task and one you should document in your report.

[You might find it valuable to note that for this problem: θ=84.06?

, R=17.43m and d=6.54m].

Note that to consider a variety of different combinations of the circle centre positions and

circle radii in a time-efficient manner, it is necessary to implement a test as to whether a particular

slip circle intersects the inclined or horizontal portions of the slope surface. To assist

with carrying out this test, you may find the following resource useful: http://mathworld.

wolfram.com/Circle-LineIntersection.html.

Dr Andre Jesus & Dr Richard Sandford 6 University of the West of England

Figure 7: Parameters involved in the calculation of the safety factor

Figure 8: Validation problem geometry

Your report should include:

1. A description of the mathematical equations needed to find the safety factor against collapse.

2. The results of a validation case to demonstrate that your code can calculate the safety

factor correctly for a particular choice of circle centre coordinates, slip circle radius and

parameters that specify the geometry and strength of the slope.

3. Justification of your approach to find the critical slip circle radius and centre coordinates.

Dr Andre Jesus & Dr Richard Sandford 7 University of the West of England

4. Pseudocode or a flow chart showing your approach to (i) find the safety factor for a given

combination of slip-circle centre coordinates and slip-circle radius, and (ii) optimise the

slip circle centre coordinates and slip-circle radius to find the critical safety factor.

5. A graphical presentation of the dependence of the safety factor on the slip circle centre

coordinates.

6. Your calculation of the critical safety factor (as well as the circle centre coordinates and

slip-circle radius that generated the critical safety factor).

Cantilever beam with exponential cross sectional evolution – 15 %

You have been given the task of assessing the serviceability of a super-light carbon fibre reinforced

polymer (FRP) cantilever beam, shown in Fig. 9, with width b, length L subjected to a

point load P. The height of the beam h(x) varies along its length x according to the equation

h(x) = Ae?x + B, (0.5)

where A and B are two constants to be determined by substitution of the height and length of

the beam at its support/end.

You can assume a constant Young’s modulus E = 200 GPa and neglect the beam’s self-weight.

The geometry and load of your individual beam are made available on Blackboard Learning

Materials > Coursework > Coursework values html file, or by following the URL https://

blackboard.uwe.ac.uk/bbcswebdav/pid-7216458-dt-content-rid-16362959_

2/courses/UBGMW9-15-3_19jan_1/my_values.html.

Figure 9: Cantilever beam with exponential cross sectional evolution

It is recalled that the bending moment of a beam is related to its curvature (second derivative

of the deflection) by the elastica bending equation from Euler-Bernoulli beam theory

M(x) = EIy00(x), (0.6)

Dr Andre Jesus & Dr Richard Sandford 8 University of the West of England

where M(x), E, I and y

00(x) stand for the bending moment, Young’s modulus, second moment

of area and curvature of the beam, respectively.

Using MATLAB or other programming language estimate the deflection curve of the cantilever

beam and its maximum displacement.

Your report should include the following points

1. Calculation of the constants A and B from Eq. (0.5).

2. Pseudocode or flowchart of the algorithm which computes the deflection curve and maximum

displacement.

3. A plot of the deflection curve of the beam.

4. An estimate of the beam’s maximum vertical displacement.

5. Appropriate referencing and justification of the approach used for integration of the

Euler-Bernoulli equation.

You are free to use any existent subroutine to carry out the above analysis, as long as you

provide appropriate reference and justification for its use within your algorithm. Additional

marks will be awarded if the error associated with the computation of the displacement is

properly quantified, e.g. by providing a confidence interval or maximum error bound of the

estimate.

Assessment criteria

Your report should contain the following and you will be assessed according to the criteria

described in Table 2.

? Problem description: A summary of the problem you are attempting to solve, to include

the assumptions needed to obtain a solution and any mathematical elaboration of the

equations that are used within your computer program. (15%)

? Program development: The pseudocode or flowchart used to solve the problem, together

with an explanation and justification for your chosen numerical approach to solve

the problem. Note that you are also required to submit, as part of your report, the code

used to generate your results. (25%)

? Presentation of the results: To include plots showing the outputs from your work and

accompanying text to describe their meaning. This section should include the outcomes

of any validation exercises you undertake to demonstrate the correct functioning of the

programs you develop. (50%)

? Concluding comments: To explain how your computer program could be extended or

generalised for increased functionality. (10%)

Dr Andre Jesus & Dr Richard Sandford 9 University of the West of England

% Descriptor Problem

Dr Andre Jesus & Dr Richard Sandford 10 University of the West of England

50-59 Competent: 55-59

Adequate: 50-54

Dr Andre Jesus & Dr Richard Sandford 11 University of the West of England

<30 Very poor (FAIL) Problem

descriptions

very unclear,

Table 2: Assessment Criteria

Dr Andre Jesus & Dr Richard Sandford 12 University of the West of England