Reference no: EM132474036

MG6039 - Applied Computational Modelling - Manukau Institute of Technology

Problem One: Statics

Determine the force in Each Member of the truss structure shown in (Figure 1) as a function of (x) using MATLAB program and then plot the force in each member (F_AB, F_BC and F_AC) for 30 mm ≤ x ≤ 100 mm.

Part 1. Illustrate the equation to be use in your code based on your mechanical engineering knowledge

Part 2. In your plot show the following:
a) The Title and Labelling for axis with units
b) Set the Line Width to 3 for your lines

Problem Two: Dynamics

Figure 2 shows the motion of a particle which is fired with initial velocity 50 m/s and the angle 45º. Write a MATLAB code using the function (input/output) to determine the Maximum Height and Distance and plot the trajectory as a function of distance (x) using: y = v_oyt - 0.5gt² and x = v_oxt

Problem Three: Strengths of Materials

A client wants a computer program that will calculate the Stress and Deflection of a cantilever beam (as shown in Figure 3) subject to a Point Load Anywhere along its length. The weight of the beam is also to be accounted for.

Figure 3: (a) Cantilever beam with point load; (b) Axes definition

The client has an Excel spreadsheet (universal_beam_data.xlsx), which contains the universal beam designations she works with. The spreadsheet lists the mass per unit length (kg/m), the second moment of area about the X-axis Ixx (x10⁶ mm⁴), and the section modulus about the X-axis Zx (mm³) for each beam.

The maximum allowable stress is 170 MPa and the deflection cannot exceed 1/360 of the beam length. The Young's modulus is 200 GPa.
The user is to specify the mass per unit length of the beam, the beam length, the point load, and the location it acts.

Create a script that

1. Reads the universal_beam_data.xlsx and extracts the appropriate data. If the specified mass per unit length is not in the spreadsheet, an appropriate message should be output to the command window.

2. Calculates the bending stress and deflection along the length of the beam.

3. Plots the bending stress and beam deflection on one graph.

4. Indicates whether the maximum allowable bending stress or deflection has been exceeded given the user specifications.

5. Generates appropriate error messages. For example, an error message should be displayed if the user specifies a point load location that is greater than the beam length.

Appropriate user-defined functions should be created that are called from the script.