School of Built Environment and Architecture
Division of Civil and Building Services Engineering
2021-2022
Course
Level
Module
Code
Credit Value
Title
Marks
Submission date
Staff contact
Learning outcomes
MSc Civil/Structural/Transport Engineering
7 (FT and PT)
Finite Elements and Stress Analysis
BEA-7-494
20
Finite Element Modelling
30% of the module marks
Wendsday 8 December 2021
Rabee Shamass; shamassr@lsbu.ac.uk Room T 608
•
•
A comprehensive knowledge and understanding of the principles
behind the structural analysis and stress calculations and
comparison with finite element technique outputs. (SM1m, EA1m,
EA2)
Appreciate the complexities and pitfalls of using commercial
engineering software for design and analysis and interpret results
in a meaningful way from the computer analysis output. (D4,P2m,
P3)
This coursework will be anonymously marked.
Please follow the LSBU Anonymous Marking submission procedure.
Submission is via Moodle Site:
Finite elements and stress analysis > Assessment and Feedback
1
MSc – Finite Elements and Stress Analysis
Coursework 2021-22
Submit a report on Moodle by Wednsday 8 December 2021.
Note that normal University regulations apply for late submission of coursework.
Problem description:
A cantilevered beam made from an aluminium alloy material is subjected to a transverse
point load P at its free end, as shown below. In the experiment, load the beam in P = 100 N
increments to P = 300 N. Measure the strain readings obtained from the ten strain gauges.
Additionally, the free end vertical deflection is measured using a linear variable differential
transformer (LVDT).
Figure 1: the cantilever beam with its cross-section
For Aluminium alloy: E = 70 kN/mm2
The report should contain the following:
1- Problem formulation and schematic diagram of the test set-up.
2- Experimental Results:
o Determine the exact positions of the ten strain gauges around the mid-span profile.
o For each of the five pairs of strain gauge positions, calculate the five mid-plane
strain values by taking the average of the surface strain values (Take P=300 N).
2
o Convert these five experimental mid-plane strain values to direct stresses (P=300
N).
o Determain the free end vertical deflection (at P=0, 100, 200 and 300 N).
3- Theoretical Results (hand calculations):
o Calculate the spanwise vertical deflections at the flange/web corner (P=300 N).
o Calculate the free end vertical deflections at the flange/web corner (P=0, 100, 200
and 300 N).
o Calculate the spanwise direct bending stress at the flange/web corner (P=300 N).
o Calculate the direct bending stress at the mid-span, round the section profile (i.e.
along the web and the flange) (P=300 N).
o Calculate the shear flow at the mid-span, round the section profile (i.e. along the
web and the flange) (P=300 N).
4- Finite element results
Mesh densitiy for modelling using ABAQUS is proposed, as shown in the Figure 2:
Flange
Web
Figure 2: proposed mesh density using eighty 8-node element
o Calculate the spanwise vertical deflections at the flange/web corner (P=300 N).
o Calculate the free end vertical deflections at the flange/web corner (P=0, 100, 200
and 300 N).
o Calculate the spanwise direct bending stress at the flange/web corner (P=300 N).
o Calculate the direct bending stress at the mid-span, round the section profile (i.e.
along the web and the flange) (P=300 N).
o Calculate the shear flow at the mid-span, round the section profile (i.e. along the
web and the flange) (P=300 N).
5- Discussion: a brief discussion on the correlation between the experimental, numerical
and theoretical values.
3
Report requirements:
You report should contain the following requirements:
MARKS
Graphical Results
Spanwise deflections:
8
Plot of finite element values of beam spanwise vertical deflections, at the flange/web corner,
superimposed on the theoretical results, when P=300 N.
Deflections at the beam’s free end
8
Plot of finite element vertical deflections values at the beam’s free end, superimposed on the
experimental and theoretical results when P=0, 100, 200 and 300 N (Note: Take the horizontal
axis as P and vertical axis as deflection values).
Spanwise bending stress:
8
Plot of finite element values of beam spanwise direct bending stress, at the flange/web corner (at
the middle surface), superimposed on the theoretical results when P=300 N.
Round the section bending stress:
8
Plot of finite element values of direct bending stress (at the middle surface), at mid-span, round
the section profile (i.e. along the web and along the flange), superimposed on the experimental
and theoretical results when P=300 N.
Round the section shear flow:
8
Plot of finite element values of shear flow (at the middle surface), at mid-span, round the section
profile (i.e. along the web and along the flange), superimposed on the theoretical results when
P=300 N.
Technical Content
Problem formulation:
15
- Schematic diagram of the test set-up with description.
- Derive the equations required to obtain the defelctions over the beam span, bending stresses
over the beams span and round the beam section and the shear flow round the beam section.
- A brief description about your finite element model (i.e. brief modelling steps).
- Scaled diagrams of the mesh density should be included.
Theoretical results: deflection
5
Theoretical results: bending stress
5
Theoretical results: shear flow
5
Experimental results: bending stress round the section
5
4
Discussion : A brief discussion on the correlation between the:
15
- Finite element, theoretical and experimental results for the vertical defletion
- Finite element, experimental and theoretical results for the bending stress.
- Finite element and theoretical results for the shear flow.
Overall Presentation (report writing skills, clarity of drawing, suitable headings etc)
10
100
5