Posted: May 8th, 2015

# Engineering

Engineering

A crane is required to lift 2.5 tonnes with a 12 m jib. Modelling the jib as a 2-D truss, determine the
minimum cross-sectional area so that all members are able to withstand their yield strength (the
critical normal stress = normal force divided by cross-sectional area) of 320 MPa.
which member(s) is/are the most critical to withstand the applied stress within an appropriate safety
factor.
Figure 1: Schematic of crane truss.
In Figure 1, L = 12 m, H = 1 m, W represents the maximum weight of the load, the bottom-left corner
is a pin joint (with reaction forces in both directions) and the top-left corner is a roller joint (with a
reaction force normal to the shaded wall that can act in either direction). All joints are considered pin
joints, so there are only normal forces along each member of the structure and the free-body diagram
can be split so that only the sum of the x- and y-forces at each joint (which equal zero) need to be
solved. For instance, to analyse the joint at the right end of the top horizontal member, the forces can
be represented as:
Figure 2: Free-body diagram for top joint in the middle of the truss.
Where the sum of the x-components of all forces must be zero and so must the sum of the ycomponents.
For consistency, the forces at opposite ends of a member must cancel, so the joint at the
bottom-right can be represented as:
Figure 3: Free-body diagram for bottom-right joint
Note that you should use a numbering system for the forces that is methodical (don’t use the numbers
shown in these examples). To solve this problem, you will need to calculate the unknown variables,
which are the axial forces in each member and the 3 reaction forces.
Requirements
MATLAB code which:
1. Solves the set of simultaneous equations for the sum of forces in the x- and y-direction at each
joint.
2. Calculates the axial force in each member.
3. Displays a message in the Command Window that reports the axial force in the two members
at the right end of the truss. You are to submit a separate pdf file with hand calculations to
determine these forces (as shown in Figure 3) and also compares the answer with the values
F1
F2
F3
F4
F3
W
ENG3104 Engineering Simulations and Computations Semester 2, 2014
Page 2 of 4
4. Calculates the critical cross-sectional area.
5. Determines which member(s) must match the critical cross-sectional area.
6. Displays a message in the Command Window stating the critical cross-sectional area and which member(s) match the critical cross-sectional area.
7. Displays a message in the Command Window with the value of the safety factor used and justification of the choice.
8. Produces a plot which visualises the minimum cross-sectional area of each member (colours each member so that there is an indication of what the minimum cross-sectional area is for each).
Assessment Criteria
Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method/code will receive full marks.
Quality of the code
5 marks
5 marks
Quality of the calculation of the forces
15 marks
Quality of the verification of the forces using hand calculations
5 marks
Quality of calculation of the cross-sectional areas
15 marks
Quality of safety factor selection and display
5 marks
Quality of visualisation
10 marks
Question 2 (35 marks)
Introduction
Measurements of the compressive strength of concrete after 1 day and 28 days of curing have been taken for a range of curing temperatures. Determine appropriate trend equations for each set of data (the 1-day and 28-day curing) as a function of temperature.
Curing Temperature (°C)
Compressive Strength (MPa)
1 day of curing
28 days of curing
12
4
41
22
9
39
32
12
37
41
14
33
49
16
29
Requirements
produce MATLAB code which:
1. Determines what type of curve-fit is appropriate for each set of data.
2. Demonstrates that the chosen curve-fit is the best both graphically and numerically.
3. Plots both sets of data and the chosen curve-fit on a single graph.
4. Displays a message in the Command Window stating which type of curve-fit was chosen, stating the parameters of the curve-fit and the result of the numerical test of the curve-fit.
Assessment Criteria
code  be assessed using the following scheme.
Quality of the code

Quality of determination of appropriate curve-fit

Quality of plots (e.g., axis labels, titles)

Quality of reporting of curve-fit

ENG3104 Engineering Simulations and Computations Semester 2, 2014
Page 3 of 4

Introduction
Accelerometer data is required at 100 Hz for a duration of up to 6.28 s for the signal
? ?
? ?
2 3 96sin cos 48sin
13cos 20cos 2 18cos3 16cos 4
x
y
a t t t t
a t t t t t
? ?
? ? ? ? ?
(1)
In practice, the accelerometer is unable to measure at such a high frequency. To compensate for this,
interpolation of the measured signal is used to reproduce the required frequency.
determine the minimum frequency (as a whole number) at which signals can be
sampled to a satisfactory accuracy for the following interpolation schemes:
a) linear
b) spline
c) cubic
sampling at frequencies lower than 100 Hz,  collect data up to the highestpossible
time that is less than or equal to 6.28 s, then interpolate from this data to reproduce a signal
that is at 100 Hz all the way to 6.28 s.
Accuracy is defined as the error in the y-location at the end of the sampling for the lowerfrequency
signal; the location is to be calculated using the same method as Assignment 1. Note that if
the acceleration is computed to 6.2832 s that the shape will be closed (the end-point will be the startpoint).
The minimum absolute error to be chosen is 10-3. Use the same level of accuracy for all three
interpolation schemes.
Requirements
produce MATLAB code which:
1. Calculates the acceleration and position for the 100 Hz signal.
2. Calculates the acceleration and position for different frequencies to find the lowest frequency
which is within the specified error tolerance.
3. Plots the results for the x-acceleration and y-acceleration versus time, including a plot zoomed
in on the first local maxima.
4. Displays a message in the Command Window with the value of the error tolerance and the
minimum sampling frequency for that interpolation method.
5. Repeats steps 2-4 for all 3 interpolation methods.
6. Displays a message in the Command Window with a brief description of why the different
interpolation methods have different errors. Comment on which method you think is best and
Assessment Criteria
Your code will be assessed using the following scheme. Note that you are marked based on how well
you perform for each category, so the correct answer determined in a basic way will receive half
marks and the correct answer determined using an excellent method/code will receive full marks.
Quality of the code
Quality of calculation of lowest frequencies 15 marks
Quality of plots (e.g., axis labels, titles) 10 marks
Quality of reporting 10 marks
Quality of discussion
ENG3104 Engineering Simulations and Computations Semester 2, 2014

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