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
