Part I

A beam with dimensions L=4 m, W=0.4 m and t=0.4 m is fixed at both ends to a fixed wall, as illustrated in Figure 1. A load q=8500 kN/m2 is applied on the top surface of the beam. The beam is made of steel grade S275 with Young’s modulus E=205 GPa and Poisson’s ratio v= 0.3.

Figure 1: Steel beam with fixed ends

For the solution of this problem, three numerical models are suggested:

• The first model, depicted in Figure 2, uses structural elements to simplify the problem. 2-node linear beam elements are implemented to simulate the response.

Figure 2: Simplified model using 2-node beam elements

Property Description Value Units

E Young’s Modulus 205 GPa

v Poisson’s Ratio 0.3

sy Yield Stress 275 MPa

su Ultimate Stress 410 MPa

eu Ultimate Strain 0.2

• In the second model (Figure 3), the assumption of plain strain conditions is made. A longitudinal section is modeled using 3-node linear triangular elements.

Figure 3: Beam model with plain strain assumptions

• For the third model, the beam is to be modelled as a full 3D beam, as illustrated in Figure 3, using 8-node brick elements.

Part II

Consider the same beam geometry as in Part A (Figure 1) and loading equal to q=8500 kN/m2 applied on the top surface of the beam. For this case the linear elastic analysis is dropped and the material exhibits isotropic hardening with the following material properties shown in Table 1.

Design Requirements

You are required to provide a report comprising the following components:

Part I

Use Ansys to:

• Determine the maximum deflection of the structure using each of the suggested models. Investigate two different meshes, one very fine and one coarse. [15/100]

• Calculate the maximum stress developed in each case (1D, 2D, 3D) and present the distribution of the von Mises stress (2D, 3D). [15/100]

• Compare the three models which were investigated in terms of the deflection and maximum developed stress. [20/100]

Part II

Use Ansys to:

• Determine the maximum deflection of the structure using each of the suggested models. [15/100]

• Compare the deflection results of the elastic analysis in PART A to those of the plastic analysis in PART B. [15/100]

• Which are the possible locations of plastic hinges that might appear for each model? What is the location of the first plastification for each model? Are the results compatible with the indications of the linear theory of PART A? [20/100]

Hints

Part I

• Ensure you use consistent units

• For the definition of the first model, the applied pressure q needs to be appropriately converted to a line load q1.

• In the 2D case (second model), the distributed load acts again as a pressure but this time it is applied on a line.

• For question Part I-ii, to find the maximum stress predicted by the EulerBernoulli beam theory, first find the bending moment at the clamped end ?? and then use the formula ??=????/I, where I is the second moment of area and ?? represents the maximum distance from the neutral line.

Part II

• Geometric nonlinearities should be considered

• Include a sufficient number of steps, so that the plastification does not occur at different locations simultaneously (for example, more than 30 steps).

Submission Details

You must adhere to the following guidelines for the report submission:

• Submission Title: FirstName_LastName_StudentNumber_EC4ASE

• Preferred Format: Submit one report in electronic format (PDF or word)

• Word Count/ Page Limit: Maximum 15-20 pages & 2000 words (excluding references, appendices, Table of Contents etc.) using at least font size 11.

Keep the answers brief and concise.

• The report should include a cover page, Table of Contents, a brief introduction, mentioning what the objective of the report is and what methodology will be used. The report should also include a brief conclusions section summarising the key findings.

• The report should include a reference list at the end using Harvard style referencing if necessary.

• NOTE: although the front page and reference list carry no marks, they are very important and any assignment that does not include them will not be marked.

Recommended reading/online sources

• EC4ASE Lecture notes and blackboard resources

• EC4ASE Ansys lab notes

Key Dates

10/07/2023 Assignment briefing issued to students

Wednesday 10/08/2023 by16:00 Submission date and time

Wednesday 25/08/2022 Written feedback to be provided to whole cohort via Blackboard.

Submission Checklist

Before submission, make sure that you have completed the following:

• Have you used the correct title for your report?

• Have you referenced where needed using Harvard Referencing?

• Is your report a maximum of 15-20 pages?

• Are your appendices labelled correctly?

• Is the file in the correct format? Pdf or Word.

Marking Rubric

Marking Criteria Range A Range B, C, D Range E, F

Correct Procedure

60% of the total mark Solution procedure steps are correct and

applied appropriately.

Typically 40 – 60 Solution procedure is partly correct. The percentage here

depends on the exact

parts of the procedure that are applied correctly.

Typically 20 – 39

Solution procedure is not correct or the most critical

procedure steps are wrong

Typically 0 – 19

Correct Final Result

20% of the total mark Final Result is correct, only minor round off errors.

Typically 15 – 20 Result is not correct but is reasonable, e.g. correct order of

magnitude, contains

some round off errors, units are not

compatible, etc. For

unreasonable results comments are included.

Typically 10 – 14 Result is not correct and unreasonable,

e.g. different order of magnitude than

expected, negative values for positive quantities, etc. No

further comments are included or the

comments are partly relevant.

Typically 0 – 9

Presentation

Quality

20% of the total mark Solution procedure, comments and result is well presented:

Consistently, to the point and in a

comprehensive manner.

Typically 15 – 20 The procedure is presented in a way that one of the key

aspects (Consistently,

to the point and in a comprehensive

manner) is missing, or the some of them are not fully present.

Typically 10 – 14

Presentation quality is poor and/or the

procedure is difficult to follow, not well written, etc.

Typically 0 – 9

Total Mark 70 – 100 40 – 69 0 – 39

# Consider the same beam geometry as in Part A (Figure 1) and loading equal to q=8500 kN/m2 applied on the top surface of the beam. For this case the linear elastic analysis is dropped and the material exhibits isotropic hardening

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