**Introduction**

A typical pin-jointed plane framework formed from tie/strut members is used to hold the tension in a cable. Three tie/struts members (1), (2) and (3), are structurally used in the frame in resisting the cable tension, T. A simplified diagram of the framework is displayed in Figure 1 and a 2D solid model is shown in Figure 2.

Node 1, 3 and 4 are constrained in both directions

**Figure 1**: 2D plane truss model of three pin-jointed tie/strut elements forming a framework resisting a cable tension T.

To represent the framework under a static loading condition, it is assumed the tension, T, acts upwards at angle β on Node 2. The pin-joints at Nodes 1, 3 and 4 are constrained in both directions and Node 2 is free to move in any direction.

The strut members are specified to be structural steel and has a Young’s modulus, E, of 200 GPa and a Poisson’s ratio of 0.3. All the dimensions including the length and cross-sectional area of the three members, angles and the cable tension are given in the Coursework Allocation Table on Moodle. Any information not given can be assumed but must be stated.

A Coursework Forum has been set up on Moodle. Questions relating to this coursework will ONLY be answered via the Forum or in the scheduled ANSYS workshops. Individual emails will NOT be answered and directed to the Forum.

**Problem **

Referring to the Coursework Deliverables on the following page, you will analyse the framework in two dimensions (2D) in four ways, using:

1. Theoretical equilibrium analysis of a simple 2D plane truss model

2. Finite element analysis of a simple 2D plane truss model ‘by hand’

3. Finite element analysis of a simple 2D beam model using ANSYS Workbench with one element per line

4. A converged 2D solid finite element analysis model

For methods 1 – 3 you should be able to determine:

a. Displacements of Nodes 2

b. Axial forces in the members

c. Reaction forces at Nodes 1, 3 and 4

For method 4 you should be able to determine:

a. Displacement at the point of applied load

b. Sum of reaction forces

c. Stress distribution

The results from all analyses must be compared and the reasons for any differences critically discussed. Present your work as the Deliverables outlined on page 4, NOT as a report.

**Figure 2**: 2D solid model

**Coursework Deliverables **

An electronic copy of the deliverables outlined in the table below should be submitted to the coursework drop box on Moodle – in one document with the coursework front cover as the first page.

**Marking Criteria **

The marking scheme is as shown in the Deliverables section. NO introduction, contents page, appendices etc. should be included. Do NOT present your coursework as outlined on the first 2 pages.

Headings of Deliverable 1, Deliverable 2 etc. should be clearly given and should contain the items asked for. If an item asked for is in the wrong Deliverable section, marks will not be allocated to it. Start each Deliverable on a new page.

Include any relevant references (not course handouts) in the appropriate deliverable.

The maximum page numbers given are just that – a maximum. Do not go over the given number. You can use less than the maximum. Do not try to get round the limit by using a tiny font and figures! You should use a minimum font size of 10 points, sensible margins and figures, including legends, should be large enough to be legible.

The Deliverables will be marked on content in terms of the specific items asked for and also taking into account the criteria outlined below in terms of professionalism of presentation:

– All graphs and figures should be appropriately numbered, titled, referred to and described. By convention a Figure number and title are below the figure and Table number and title above the table (I don’t know why).

– You should NOT use what is known as “the 1st person” when writing. You should always use the “3rd person”. This means you should NOT use I, we, you, us etc or give personal opinions. Do not say “… the dimensions allocated to me …” or “… in my opinion …”.

– ALWAYS include units with quantities in your answers (and make sure they are the correct units). Answers are **completely meaningless **without units.

– Be consistent with the number of significant figures in the data presented in tables.

**DATA:**

**L1= L2 (m)：1.50**

**L3 (m)：1.60**

**α (degrees)：45**

**β (degrees)：35**

**B (mm)：0.10**

**W (m)：0.20**

**R1 (m)：0.10**

**R2 (m)：0.08**

**T (KN)：45**