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1.Objective 2.Theory 3.Experimental Set-up 4.Data Analysis 5.Sources of error 6.Discussion questions 7.Conclusion

Summer 2013
CIVE 302
T. Johnson
Dr. Dowell
Lab 0. Introduction to Laboratory Concepts and Presentation
While engineers rely heavily on equations and mathematics to perform design and analysis, it is
important to remember that the basis for these techniques comes from physics and applied
science. Thus, to properly use an equation and trust its results as accurate, an understanding of
the physical basis for each input is essential. This lab will explore many concepts relevant to this
process, including measurement, data processing, data/calculation presentation, comparison of
theory versus measured, and error analysis.
To start, let us cover some basic definitions that will be encountered throughout this lab. Data
refers to any quantity physically measured by equipment (the diameter of a circular bar); a
calculation, however, is any number that is derived from data (the area of a circular bar).
Distinguishing and labeling these two items not only good practice for double checking your
own work, but a clear way to present concepts and results to others not immediately familiar
with the project or experiment. In either case, any number presented should always be clearly
labeled with appropriate units, such as a diameter with units of inches or an area with units of
inches squared. Numbers by themselves have no meaning Ã¢â‚¬â€œ only by giving them units and
labels do they have any value or usefulness. Table 1-1 provides a list of common units and
dimensions.
Table 1-1: Common Parameters with Associated Units
Dimension
Unit
Length
Inches (in)
Feet (ft)
Meter (m)
Millimeter (mm)
Strain
Force
Stress
Moment
Angle
Time
in/in
mm/mm
Pound (lb)
Kip (k)
Newton (N)
psi
ksi
Pa
MPa
GPa
Lb-ft
Lb-in
Kip-in
Kip-ft
N-m
Degree
Second
(sec)
In practice, data can come in many different forms. Some measurements are discrete, single
values Ã¢â‚¬â€œ such as the length of beam Ã¢â‚¬â€œ but others may have hundreds of thousands of
measurements. An example of this is shown below Figure 1-1, which shows 3000 measured
acceleration values taken over 30 seconds during the Northridge earthquake in 1994. While the
actual data comes in a text file, note that it is presented in graphical format. Remember,
whenever presenting numerical values in calculations, reports, or other mediums, the goal is to
convey information and not to simply list numbers. In this case, we can quickly identify the
approximate maximum accelerations, the distribution of acceleration over time, and the
duration of the earthquake all at a glance; this is certainly more useful than listing several pages
of raw spreadsheet data as presented results.
0.50
0.40
Ground Acceleration (g)
0.30
0.20
0.10
0.00
-0.10
-0.20
-0.30
-0.40
-0.50
0
5
10
15
20
25
Time (sec)
Figure 1-1: Example of Continuous Data. Northridge Earthquake, Beverly Hills Station
Additionally, let us look carefully at the formatting of the plot and identify several key features:

The plot has a clear title and unit-labeled x- and y- axes.
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The numerical values on the axes are listed at easy-to-read, yet still useful, intervals with an
appropriate number of significant figures.

The plot is enclosed with a clearly defined border and does not have gridlines. This is prevent
visual clutter; unless you have a specific need or purpose to use items like gridlines, they are
discouraged.

The line representing the data is thin and clean. For multiple lines on the same plot varying,
easily-readable colors and line types should be chosen.
An important concept to keep in mind when working with measured numbers, too, is the concept of
significant figures. Using the appropriate number of significant figures is not only beneficial in making
presented values and calculations easily interpreted, but it also represents the level of confidence or
accuracy in the values being presented. For example, many engineering values of relevance are taken
from visual inspection off graphs; if asked to find the maximum acceleration and its associated time
from Figure 1-1, how would this be approached? One could print the graph, take a ruler, and estimate
about 0.4g at 8 seconds. If asked to find this directly from the data, however, the actual values are
0.4158g at 8.05 seconds. While carrying appropriate numbers of decimal places is good practice for
minimizing error, be mindful of not confusing decimal place accuracy with the actual accuracy of your
data or calculations.
Another important concept is measurement. When reading outputs from laboratory equipment,
understanding both the physics and tolerance behind how the values are being generated is vital to their
proper application. Most common are either mechanical or electrical measuring devices. Mechanical
devices operate using precisely-engineered intervals, such as the length intervals on a tape measure or
highly sensitive springs to measurement displacements. Electrical devices, the theory behind which will
be discussed later in this lab, use changes in an objectÃ¢â‚¬â„¢s resistance or input voltage to measure values.
Using physical relationships, these electrical changes can be correlated to other quantities such as
displacements, forces, or accelerations. Figure 1-2 shows a mechanical and electrical potentiometer Ã¢â‚¬â€œ a
displacement measuring device Ã¢â‚¬â€œ placed side by side.
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Figure 1-2: Electrical potentiometer (left). Mechanical potentiometer (right).
Images and tables are often valuable tools for presentation as well. Whenever including images, be
professional Ã¢â‚¬â€œ posting no image is sometimes preferable to posting low resolution or blurry photos. If
using images from an outside source, always cite that source. On that same note, posting random
images from a search engine is in very poor taste. Also, whenever including tables or figures always
provide a title/caption and discuss them in the text; if the figure is not being discussed, it should not be
included in the report.
When writing a laboratory report, keep in mind that it is intended to provide a technical description and
presentation of an experiment or procedure. Aim to be concise and to the point, but do not sacrifice
detail to so. Examples of a sentence in the experimental setup section, for example, may be:
Poor Statement: Ã¢â‚¬Å“The professor set up everything in the lab.Ã¢â‚¬Â
Good Statement: Ã¢â‚¬Å“A steel coupon with threaded ends was loaded into the grips of a tension testing
machine.Ã¢â‚¬Â
Note the difference in these statements beyond the obvious absurdity. The second statement notes
specifics about the setup that would be required to reciprocate it in another setting: the coupon has
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fixed into a machine capable of applying tensile forces to the coupon. A detailed explanation of exactly
what laboratory reports for this course should contain is provided in the syllabus, but do not simply
write to the template: think about the exact details of what happened in the experiment and what is
needed to verbally, graphically, and logically explain this information.
Lastly, think rationally about results obtained in the laboratory experiment when analyzing results. Error
analysis should be far more specific than Ã¢â‚¬Å“the equipment was oldÃ¢â‚¬Â or Ã¢â‚¬Å“humans operating the equipment
make mistakes.Ã¢â‚¬Â The purpose for doing error analysis is not to simply state that numbers may or may
differ from what was expected, but to examine why they differed and determine, using proper
judgment, whether they are acceptable or not. Examples of questions to consider while doing error
analysis are:

How were numerical values measured in the experiment? Were they approximated visually or

What is the significant figure accuracy of the measuring equipment being used? Furthermore,
what is the sensitivity of the equipment being used?

Were the calculations performed correctly?
The last question is not one that should only be asked at the end of performing calculations, but one
that should be asked throughout. Calculation mistakes are common and normal, but can often be
caught by critically examining results. For instance, if the expected yield stress for a material is 50 ksi
and you calculate 6500 ksi, this is a clear indication of a user-end mistake. Try to thoroughly analyze
your own work for significant errors before attributing faulty results to other sources.
EXPERIMENTS:
Tour the structural engineering laboratory and examine several different pieces of measurement and
testing equipment. Carefully record the order in which the tour was performed and use this as an
experimental procedure. This lab will have no experimental setup or theory sections.
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REQUIRED CALCULATIONS:
Using the earthquake data provided on Blackboard, develop a scatter plot representing this information.
Follow the general rules stated above to generate a properly formatted graph, complete with labeled
axes, units, and distinctly labeled lines. Present this in a clearly labeled Ã¢â‚¬Å“dataÃ¢â‚¬Â section of your lab report.
You will have no calculations for this lab report.
REQUIRED DISCUSSION:
Provide a brief description of at least three pieces of equipment and at least three measuring devices
discussed in the lab. Include its proper name and how it measures or performs its function. An example
of each would be:
Electrical Potentiometer. A displacement-measuring device which tracks the elongation or contraction
of a rod. Correlates changes in length to an electrical current that can be read by a computer.
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CIVE 302 Ã¢â‚¬â€œ Lab #1
Tensile Behavior of Steel
T. Johnson
Spring 2013
How do forces influence objects?
Say we have a block of material sitting on the ground and apply a load P to it:
P
P
P
P
Just by intuition, we expect that the force required to crush the small block will not
crush the large block. This is because objects do not feel forces, they feel stresses.
Forces are important to system-level performance, but stresses are important to
material performance.
So what is a stress?
A stress is a forced normalized by the area over which it is applied. There are two
definitions of stress which are commonly used: true stress and engineering stress. True
stress considers the area at any given point in time after loading begins, while
engineering stress only considers the initial area. For axial loads:
Ã¯ÂÂ³ true (t ) Ã¯â‚¬Â½
P (t )
A(t )
Ã¯ÂÂ³ engineerin g (t ) Ã¯â‚¬Â½
P(t )
Ai
where : P(t) = axial force at a given time t
A(t) = cross-sectional area at a given time t
Ai = original cross-sectional area
While similar, these two definitions state an important difference: true stress takes into
the consideration the cross-section at a given time during loading, while engineering
stress only considers the original cross-section. The latter is by far the most common in
engineering practice and will be the only type discussed in this course.
True vs. Engineering Stress
ÃÆ’
True Stress
Engineering Stress
ÃŽÂµ
Comparing the two, it is important to note the deception that engineering stress
indicates that the material is getting weaker as is it more heavily. In actuality, the
opposite is true: materials gain strength as they are heavily deformed up until failure.
Normalizing Displacement
While stresses provide us with a normalized way in which to evaluate how an object
will react to a load, it is important to recognize that they only take into consideration an
objectÃ¢â‚¬â„¢s geometry. Realistically speaking, however, we know that material plays an
important role as well.
To examine this relationship, letÃ¢â‚¬â„¢s introduce the concept of strain. We define
engineering strain as the change in length normalized by the original length:
Ã¯ÂÂ¥ engineerin g (t ) Ã¯â‚¬Â½
where :
Ã¯Ââ€žL(t )
Li
ÃŽâ€L(t) = net change in length at a given time t
Li = original length of the member
Defining Gage Lengths
This definition of strain seems very straightforward, but applying it to real situations is
tricky. By taking cuts in coupon we can use statics to calculate stresses, but what about
strains? LetÃ¢â‚¬â„¢s look at the threaded-end steel coupon we will be testing today:
Ends
P
Gage
Length
P
P
(a) Coupon
(b) Stress:
Take cut and use internal
force & cross section of
cut.
(c) Strain:
Define using different
criteria (discussed
later). Select specific
region.
Stress vs. Strain Behavior
90000
Important Locations:
80000
ÃÆ’u
ÃÆ’y = Yield Stress
ÃÆ’u = Ultimate Stress
ÃÆ’r = Rupture Stress
ÃŽÂµy = Yield Strain
ÃŽÂµh = Hardening Strain
ÃŽÂµu = Ultimate Strain
ÃŽÂµr = Rupture Strain
70000
60000
ÃÆ’y
Stress (psi)
ÃÆ’r
50000
40000
Linear-Elastic Region:
30000