UBGMXQ-30-1 Engineering Principles for Civil Engineering
Resit Coursework Brief Important notes:
1- You MUST use the experimental results that are provided for the resit work and NOT the results of the first attempt.
2- For the demec strain gauge, use the calibration factor of 7.8x10-6 .
UWE Bristol
University of the West of England
Contents
Contents
Key information Health and safety
Technical information Laboratory methodology
Report structure
Self-assessment form
Feedback request form Drawings Guide to the analysis
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Key information
Module leader
Dr Ghassan Nounu
Module tutor
Dr Ghassan Nounu and Dr Ghada Karaki
Contribution to This report is assessment task 2 which has 25% of the module module assessment mark.
Hand in date
Hand in method Online submission via Blackboard.
Hand in format
Although the experimental work for this coursework is normally
carried out in groups; the data analysis, discussion and report must
be completed independently.
Each student must submit their own report following the formatting requirements below:
. Microsoft Word (.doc or .docx) format file.
· A4 page size.
. 12 point black Arial, Tahoma or Calibri font.
· Single line spacing.
. 2.54 cm margins.
· Line space after each paragraph.
· Left justified.
· Figures must have descriptive captions.
Word limit
The body of the report including titles and captions should not exceed 1000 words. This limit excludes the front cover, contents page, figures, tables, references list and appendices.
There is no additional allowance above the word limit. Text beyond the word limit will not be marked.
To present and discuss the required content you will need to use precise, concise descriptions and discussions. It is likely that you will need to critically edit your initial draft in order to achieve the word limit. This reflects requirements of technical writing by professional engineers.
Learning outcomes Identify the failure mechanisms associated with reinforced concrete (RC) elements in bending by:
· Testing two RC beams under specified loading conditions and recording all relevant results.
. Analysing the results obtained during testing and formulating conclusions.
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Pre-requisite knowledge
You are expected to:
a) Be able to draw bending moments and shear force diagrams
b) Have competence in the application of the theory of bending
Health and safety
During all laboratory activities in 1Z014 you are required to bring, and wear, your own safety boots with toe protection.
As protection against dust and debris that may be created during testing you will be required to wear safety glasses during the work. Safety glasses will be provided by the laboratory technician at the start of the session.
The beam press used to load the beams has protrusions that are easy to knock your head against, therefore you must also wear a hard hat during testing. Hard hats will be provided by the laboratory technician at the start of the session.
At all times during testing you must follow the instructions of the lab technicians and teaching staff.
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Introduction
The coursework submission comprises of an individual laboratory report that presents the data, calculations and discussion associated with the laboratory testing fo two reinforced concrete beams.
The two beams have different reinforcement arrangements. A reinforcement drawing of the two beams is provided later in this document.
The laboratory work will be carried in groups that are allocated ahead of the timetabled session.
The laboratory work will take place in 1Z014 for making and testing the beams
Technical beam information
Physical conditions
. Dimensions: 2600 x 250 x 135 mm.
· Span: 2400 mm (distance between centerline of supports)
· Cover: 20 mm
Materials
. The cement type, concrete grade, fine and coarse aggregate used for the beams will be confirmed during the laboratory session.
· Reinforcement grade: B500.
Cube and prism samples
The beams are cast from two batches of concrete. Each batch has the same mix design.
. The first batch is used to fill the bottom half of the formwork of the two beams.
. The second batch is used to the upper half of the formwork of the two beams.
Three cubes are made from each batch and a prism (100 x 100 x 300 mm) is cast from one batch.
Two cubes from each batch is water cured. One cube from each batch is air cured in the same conditions as the beams.
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Laboratory methodology
Step 1: Test the beam with shear reinforcement
. You will test the beam with shear reinforcement to failure in load increments of 10 kN.
. During testing of the beam you are required to record mid span deflection of the beam; strains at four positions through the depth of the beam; and the cracking pattern (including the position, length and orientation of the cracks).
· Cracks should be marked using chalk provided and a sketch made before leaving the laboratory.
. All of the measurements should be recorded for each load increment (of 10 kN) applied to the beam until failure.
. You must record when the first flexural crack occurs, and when the first shear crack occurs.
. Before starting you must measure the position of the Demec gauges from the top or bottom of the beam. This is important information for plotting your strain distributions later. The ideal position of the studs is shown in the figure below, in practice they may be in a slightly different location (which will be confirmed by your measurements).
. A proforma will be provided on the day of testing to record the results.
Demec stud
26 mm
66 mm
66 mm
66 mm
26 mm
Figure 1: Nominal position of the Demec studs
Step 2: Test the prism
. The cubes will be tested by the laboratory technician on the same day as the testing of the beams and the failure loads will be provided to you.
. You are required to test the prism to failure in compression.
. During loading you will measure the strain on the surface of the prism, using the pairs of Demec studs mounted on two sides of the prism. This will allow you to construct the stress-strain curve for the concrete.
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. To obtain sufficient data points you will need to predict the failure load of the prism (approximately 70% of the cube failure load) and choose load increments to measure the strains at. It is recommended to aim for 10 load increments.
Step 3: Test beam without shear reinforcement
. You will test the beam without shear reinforcement to failure in load increments of 10 kN.
. You are required to measure deflections of the beam and record crack patterns at each load increment.
. Strain measurements do not need to be taken.
. For your personal safety, you must stop approaching the beam at the load increment below which shear cracks appeared in the first beam.
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Report structure
The report should be presented in the following order, using the headings indicated in bold.
1. Self assessment: the self assessment form provided in this brief must be completed and submitted as part of the report.
2. Feedback request: the feedback request form provided in this brief must be completed and submitted as part of the report.
3. Introduction: The introduction should clearly state the aims of the exercise and relevant information about the materias used in the beam.
4. Test set-up: The test setup should be clearly communicated, with the aid of annotated diagrams showing the physical conditions of the test including position of: supports, loading points, deflection gauge and Demec studs.
5. Results: Results should be processed and presented for the reader. They must include:
. Results for the cube tests.
· Results of the prism test including a stress-strain graph.
. Deflection and strain readings for both beams tested.
6. Crack pattern: An annotated sketch of the crack pattern for both beams showing the orientation, length and distribution of the cracks should be included.
7. Analysis and discussion
7.1. Strength: Compare the values of compressive strength measured by testing the cubes (water and air cured) with the target strength of the concrete. Discuss any deviation and relate the results to the testing of the beams. (Note that the target strength should be higher than the grade of concrete by a margin that depends on statistical data. In absence of such data, a margin of 13 N/mm2 may be used. The "Grade" of the concrete is the concrete characteristic compressive strength at an age of 28 days).
7.2. Mode of failure: Describe the mode of failure in both beams and explain the dominant structural actions, i.e. flexure, shear, brittle, ductile, warning signs, crack pattern, etc.
7.3. Load-deflection: Plot the load-deflection relationships for both beams. Identify the stages (i.e. uncracked, cracked-elastic and plastic) and discuss any difference between the two beams.
7.4. Strain distribution: For the beam with the shear links: Select two load increments (one early during the loading, and the load increment just before failure). Plot the strain distribution across the depth of the beam. Compare and comment on the position of the neutral axis at the two load increments.
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7.5. Stress distribution: Using the stress-strain graph from the prism tests, plot the stress distribution for the strain distribution determined in the previous step (i.e. for the beam with links) at the load increment before failure.
7.6. Compressive force: Calculate the compressive force from the stress distribution plotted in the previous step (i.e. for the beam with links).
7.7. Stress in steel: Assuming that the section is in axial equilibrium, i.e. the tension in the steel equals the compression in the concrete, calculate the stress in the steel flexural reinforcement. Compare the result to the stated steel yield strength and discuss.
7.8. Moment of resistance: Determine the position of the centroid of the compression force and the effective depth. This will allow calculation of the lever arm between the compression and tension forces. Use this to calculate the internal bending moment on the beam. Calculate and plot the applied bending moment distribution. Compare and discuss the values of the internal bending moment and the maximum applied bending moment.
7.9. Shear force resistance: Draw the shear force diagram at the onset of failure.
8. Conclusions and recommendations
9. Reference list
A DETAILED GUIDE TO THE ANALYSIS SECTION IS PROVIDED AT THE END OF THIS DOCUMENT
Marking criteria
The report will be marked using the same form as the self assessment form. The marker will not take notice of the self assessment form prior to marking. The following points will be observed when allocating the marks to different sections:
1. Accuracy of the test set-up diagram and clarity of the description of the test.
2. Accuracy of the calculation of the results.
3. Clarity of the presentation of the results.
4. Accuracy and clarity of result diagrams and graphs. Depth of understanding demonstrated in the discussion of the results.
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Self-assessment form
This form must be completed and included in the report submission.
Max
mark
Mark
Remarks
Self assessment form
Included and complete
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Feedback request form
Included and complete
3
Introduction
4
Test set-up
Diagram and description
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Results
Processing and presentation
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Crack pattern
Diagram and discussion
5
Analysis and discussion
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Strength
Results and discussion
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Mode of failure
Calculation and discussion
5
Load-deflection
Calculation, plot and
discussion
5
Strain distribution
Diagram and calculation
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Stress distribution
Diagram and calculation
10
Compressive force
Calculation
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Stress in steel
Calculation and discussion
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Moment of resistance
Calculation, diagram and
discussion
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Shear force
Calculation and diagram
4
Conclusion and
recommendations
3
Clarity and presentation
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Excellent
Good [ ] [ ]
Total
100
Poor Units [ ]
Discussion [ ]
[ ]
[ ]
Presentation [ ] [] []
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Feedback request form
This form must be completed and included in the report submission.
Identify the three components of the submitted report you consider the strongest and state what you think the strengths are.
1.
2.
3.
Identify the three components of the submitted report you consider the weakest and state what you think the weaknesses are.
1.
2.
3.
List up to three specific areas you would like detailed feedback on:
1.
2.
3.
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Drawings
Beam's total Dimensions are 2600 x 250 x 135
A
2 - H8 - 02
A
BEAM Mk A
16- H8 -03 - 150
2 - H16 - 01
B
D
B
BEAM Mk B
1 - H16- 04
2 - H16 - 01
02
02
Number Mk A
Number
Mark
&
MkB
01
H16
2
2
02
H8
2
03
H8
16
04
H16
1
04
01
01
01
01
A - A
B - B
Cover to outer bars = 20mm Lifting handles to be provided 150mm from each end
Bar
Type
Size
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Guide to the analysis
Authors: Dr. Ghassan Nounu and Mr. Nick Simpson
This section provides guidance on the key calculations required in the report. It does not provide guidance on the discussion elements of the report - but you may find the modules notes and reading list for the module as useful resources (remember that sources must be correctly citred and referenced to the UWE Bristol Harvard standard).
Take care to read the brief thoroughly and complete all required parts - don't simply attempt the sections that are covered in this guide!
Plotting the load-deflection relationship
The load-deflection diagram for a beam should look similar to the example below:
Load, kN
Plastic
Cracked-elastic
Uncracked
Deflection, mm
Figure 2: Example of an annotated load deflection plot.
Note: If the beam is very stiff in bending (i.e. over-reinforced) it may fail in shear prior to the onset of the plastic stage.
Plotting the strain distribution across the depth of the beam
The figure below shows the position of the Demec studs at zero load.
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Zero strain position of
b
>A
Demec studs
*
*
ℎ
-*
.-*
*-*
-
-
A
Elevation
Section A-A
Figure 3: Demec stud location at zero load / strain.
During the testing you should have taken readings at each load increment. These should show that the strain gauges move from the zero load position.
The strain at zero load should be zero. Since the Demec gauge gives a higher initial reading you will need to convert your data to obtain the true strain. To do so, set the initial strain reading as zero, and reduce all other readings by the initial reading. Multiply the results by the calibration factor (the calibration factor is specific to the Demec gauge, the Demec gauges typically used in 2Q13 have a calibration factor of 0.81 x 10-5 or 0.78 x 10-5).
An example of this procedure is shown below:
Load, kN
Original data 860
Converted data
0
(860 - 860 =) 0
20
890
(890 - 860 =) 30 x calibration factor
Note: you may find it easier to work in micro-strains (us). Using a calibration factor of 0.78 x 10-5, the strain shown in the example above will be:
30 x0.78×10-5=0.000243=234x10-6=243us
You are asked to calculate and plot the strain distribution at two load increments, one should be the increment before failure. For the other, the 20 kN load increment is recommended.
To draw the strain distribution you should use graph paper and a suitable horizontal and vertical scale to produce a diagram large enough to be read, but still fits on the page with space for annotation around it. The diagram below shows what your strain diagrams should look like:
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Reference line
Strain
distribution
line
x
*
E2
Neutral
axis
ℎ
84 *
Figure 4: Example of a basic strain distribution diagram.
The reference line is a line of zero strain through the depth of the beam, with negative (compressive) strains plotted to the right and positive (tensile) strains plotted to the left.
For this beam, due to a span to depth ratio greater than 5, the assumption plane sections remain plane can be made. Therefore the strain distribution can be described as a straight line. If three points lie close to a straight line and the fourth point lies far from the line, this may indicate the fourth data point is spurious. On your plot, you should include the actual strain values at each point.
The neutral axis is the position of zero strain in the cross section. The depth of the neutral axis from the top of the section is assigned the letter 'x'. This position may change with load. That change, or lack of, could be a point of discussion in your report.
Once drawn you will need to digitise your sketches. Make sure the quality of the digitisation is sufficient for the diagrams to be legible. This requires consideration of the resolution, brightness and evenness of light of the digitisation. Scanners are available in the R block and the Library and there are a range of smartphone applications that will correct perspective and light unevenness automatically, available for free.
Construction a stress distribution diagram
In this step we are only concerned with the load increment just before failure, as this will tell us something about the overall resistance of the beam.
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At this load increment we will have observed the beam to have cracked. The concrete is no longer carrying tension because the cracks have formed. As a result when plotting stresses in the concrete, we are only interested in plotting the compressive stress distribution. There is no significant tensile stress in the cracked concrete!
To convert the strain distribution in to a stress distribution you will need to divide the strain distribution in the compression zone in to approximately 5 equal divisions, labelled here as a, b, c, d and e. For each division read off the strain value from the strain distribution line of best fit you plotted.
The stress-strain relationship of the specific concrete mix used was investigated using the 300 mm prism sample. We can use this data to convert the strains in the concrete beam in to stresses, by reading off from the stress-strain curve, as illustrated below.
Stress
0d
Ốc
0a
Ed
Ee
Strain
Figure 5: Example of reading off stress values from the prism stress-strain curve.
The stress values should be multiplied by the acc correction factor in Eurocode 2, which is 0.85.
Now the stress values have been found, the stress distribution can be plotted. At low loads (relative to the bending resistance of the beam) the stress distribution will tend to be linear. As the stress levels increase the concrete at the extreme fibre in compression will act in a more plastic manner, resulting in rectangular-parabolic stress block, as shown below:
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Linear stress block
Rectangular-parabolic stress block
Ód
Ód
Ốc
x
x
Figure 6: Examples of linear and rectangular-parabolic stress blocks.
Calculating the compressive force
To calculate the compressive force, and the position of the resultant compressive force, you must sum (integrate) the stress distribution. This can be done using numerical integration, e.g. the trapezium rule. The area enclosed by the compressive stress block can be subdivided (using the divisions used for strain distribution) and approximated as trapeziums.
A5
0d
A4
x
A3
A2
A1
0a
Figure 7: Example of application of the trapezium rule for numerical integration.
Total area = Atotal = A1 + A2 + A3 + A4 + A5
Compressive force = C = Atotal X breadth of beam
Once the compressive force is found, the position of the resultant compressive force can be determined by taking first moments of area about the top of the section, as shown below:
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Óe
y5
A5
y4
y3
1
A4
C
y2
y
A3
Ốc
A1
Figure 8: Example of how first moments of area can be calculated using the areas already determine and lever arms from the top of the stress block.
Position of C = y
Atotal X y = (A1 × y1) + (A2 ×y2) +(A3×y3)+(A4Xy4)+(A5×y5)
The above expression can then be solved for y.
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Calculating the stress in the steel
The beam has no external axial load applied to it, therefore we expect the internal axial forces of tension and compression to be in equilibrium. This means the compression force, C, calculated in the concrete is equal and opposite to the tension force, T, in the steel flexural reinforcement.
Total compressive force in concrete, C = Total tensile force in steel, T = As X Os
Once the stress in the steel, 05, is found, it can be compared to the yield strength of the reinforcement. The comparison of the two values should be discussed.
Internal bending moment resistance
Once the position of the resultant compressive force, y, is found the internal moment of the beam can be calculated by recognizing that the resultant compression in the concrete, and the tension in the reinforcement, form a couple:
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C
x
ℎ
d
Z
M = C · z
=
T
Reinforcement bar
Figure 9: Diagram showing the couple formed between the resultant compressive force and the tension in the reinforcement.
Calculating the maximum applied bending moment
Calculating the maximum applied bending moment will require application of bending theory. You should draw the bending moment diagram at the failure load and annotate the maximum value.
You should compare and discuss the internal and external bending moments calculated.
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Calculating the maximum applied shear force
Calculating the maximum applied shear force will require the calculations of reactions at the failure load of the beam that failed in shear. You should draw the shear force diagram at the failure load and annotate the maximum value.
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