Matlab CW Basic and Programming

Q1. Use your favourite manual method to solve the simultaneous equations

Now use Matlab to solve the equations and compare your results (4 marks).

Q2. Find out what function polyfit does. A proximity probe is a sensor which measures the gap between its tip and a metallic surface. The sensitivity of the probe is defined as the increase in its output voltage per unit increase in gap and is measured in volts per mm. One such probe was calibrated by measuring the output voltage over a range of gaps, as shown in the following table.

Write a program to perform the following tasks: 

(a) Plot a labelled graph of voltage versus gap: the points on your graph should be  indicated by a cross (‘×’) and not joined by straight line segments. (3 marks) (b) Use function polyfit to fit a straight line through the data in (a). This straight line  should then be plotted onto the plot in (a). (4 marks) 

(c) Use the listed output Voltage as an input vector, outputs further a vector of the  consecutive voltage variations.  

Hint: e.g. for the input V=[0.15 1.00 2.49 3.80 ……], will output delV=[0.85 1.49 1.31 ……]. Recall what end does; or you could use the function length instead (3 marks). 

Q3. Use Matlab to develop a simple program analysing a right triangle truss shown below.  (16 marks)

CIVL12201 Tools for Civil Engineers 1 Jack Wu/ October 2023 

A right triangular truss has been pin-joined on a wall at joints 1 and 2. The vertex 3 of the truss is hinged. A vertical upwards load P, as shown in Fig Q3, is applied at the vertex. 

You are required to edit a program accommodating all required input parameters, and output axial forces F13 and F23 in members of 13 and 23, respectively, after the analysis is carried out. Here Fij means internal axial force in the member joining joints i and j, with its sign  convention: tension (+) and compression (-). 

Since axial forces in the truss members can be calculated by using any standard method, you  can consult "Structures 1" lecture notes or any Structural and Stress analysis textbooks for  further details.  

After being received the appropriate inputs, the Matlab program which should include the  given parameters (l, h, and P as shown in Fig Q3) will generate a graph showing the internal  axial force F13. 

• The program should have a facility to input the data interactively i.e. prompt the user to input the member lengths, the applied load (i.e. handle any lengths of the truss members, any concentrated loading at joint 3) 
• Matlab figures for the internal force F13 generated by your program should be titled and  labelled appropriately.

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