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’
代做UBGMW9-15-3作业、代写MATLAB实验作业、代做Civil Engineering作业
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
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