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SECTION 1 0 INTRODUCTION
Figure Typical Experimental Layout
This guide describes how to set up and perform several experiments using the Pin Jointed Frame equipment.
rt
clearly
demonstrates the principles involved and gives practical support to your studies.
escription
The Pin Jointed frame experiment enables you to build up several frameworks based on 30° 45° and 60° angles. Each
one
of
the framework members has a force sensor bonded to the surface. To join the members use the special joint pieces
and nuts and bolts .
Use the electronic load cell to apply loads to the experiment. This load cell allows loading of a framework at any angle
45° each side
of
its vertical position. The Digital Force Display
STRIa)
electronically measures and displays this force
during the experiment.
The sensors used to measure the forces in the members are called strain gauges. The technique of strain gauging s
important to any structural engineer and this equipment gives you the opportunity to understand their use
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TecQulpment Pin Jointed Frameworks: Student Guide
Strain gauges are sensors that experience a change in electrical resistance when they stretch or compress. This change
in
resistance can be shown in terms of displacement (strain). Strain gauges are made from metal foil formed in a zigzag
pattern. They are only a few microns thick so they are mounted on a backing sheet. The backing sheet electrically
insulates the zigzag element and supports it so it does not collapse when handled.
The framework members have strain gauges bonded to them. Thus when a member stretches or compresses, the strain
gauge stretches or compresses the same amount.
Changes in temperature and other factors can affect the accuracy of strain gauges. To compensate for this, each member
has four gauges arranged in
a particular way.
The Digital Strain Display shows all member strains.
t
reads
in
microstrain . Using the strain, the cross-sectional area
and the Young s modulus of the members you can convert the strains into member forces.
The frameworks are mounted into two supports. One support allows pivoting only (pinned), the other support allows
pivoting and linear translation ( free or roller) thus representing the idealised supports.
How to et p the quipment
The frameworks fit into a Test Frame. Figure l shows a framework assembled
in
the test Frame.
Before setting up and using the equipment, always:
Visually inspect all parts, including electrical leads, for damage or wear.
Check electrical connections are correct and secure.
Check all components are secured correctly and fastenings are sufficiently tight.
Position the Test Frame safely. Make sure it is on a solid, level surface, is steady, and easily accessible.
Never apply excessive loads to any part of the equipment.
This guide shows three experiments, each using a different framework. However, there are many other frameworks you
can build.
The setting up procedure is basically the same for each experiment. However, the objectives of the experiments vary so
you need to refer to the instructions for each one. Steps l to 5
of
the following instructions may already have been
completed for you:
l Place an assembled Test Frame (refer to the separate instructions supplied with the Test Frame
if
necessary) on a
workbench. Make sure the window
of
the Test Frame is easily accessible.
2
Leaving the screws loose for fine adjustment later, fix the supports and load cell into position as shown in the
Figures in the experiments section.
3
Taking care, build the frame using the members and joint bosses. Make sure you match the joint halves correctly.
Using your hands, tighten the nut and bolt each side as tight as possible (never use tools to tighten the special nuts or
bolts).
You
m y use
ny
combination of the labelled members in the experiment but
they must be the correct length. For example in experiment 1 you may use ny
2 of the members labelled 1 to 7
nd
one of the members labelled 14 and 15.
You
must connect their strain gauge wires to the matching sockets on the Digital
Strain Display.
For
example member 1 must connect to socket
1.
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Figure 2 Strut and Joint Assembly
TecQuipment Pin Jointed Frameworks: Student Guide
Securing
nut
Table 1 shows the overall lengths
ofthe
members and their effective length
of28
mm (2 x
14
mm)
longer, allowing
for the joint at each end
of
the member. Figure 3 shows this more clearly.
Member Effective
Member Length
Length The experiment that you
Number mm)
mm) use them
n
1
2 3 4 5 6
112
14 experiment 1 needs two of these
and 7
experiment 2 needs all seven
experiment 3 needs all seven
8 9 10and11
93
121
experiment 3 needs all four
12 and 13 42 70
experiment 3 needs both
14 and 15
17 198
experiment 1 needs one
able 1 Labelled Members
Member Length
Figure 3 Member Lengths and Effective Lengths
4 Fit the frame into the supports using the pins, checking they pass through both sides. Ensuring the free (roller)
support is
in
the middle of its travel, fine adjust the support positions. Tighten the supports using a 6 mm A/FAllen
key .
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TecQuipment Pin Jointed Frameworks: Student Guide
5. Adjust the position of the load cell until the hole
in
the fork reaches the hole of the loading position . Make sure it is
also
in
the correct angular position. Tighten the load cell using the 6 mm A/F Allen key Secure the fork using a pin.
6. Make sure the Digital Force Display is on . Connect the mini DIN lead from Force Input I on the Digital Force
Display to the socket marked Force Output on the left-hand side of the load cell.
7
With no load on the load cell (the pin should turn) roughly zero the reading using the control on the front
of
the load
cell.
8. Make sure the Digital Strain Display is on . Connect the strain gauges to the strain display, matching the number on
the lead to the number on the socket. Leave the gauges for 5 minutes to warm
up
and reach a steady state.
9. Apply a preload of I 00 Nand again zero the load cell . Carefully apply a load of 500 Nand check the frame is stable
and secure. Return the load to zero.
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xperiment
:
Forces in a Warren Girder
You need
7
off 2mm
members 140
effective length) for his
experiment
100 l l
- 9 0
TecQuipment Pin Jointed Frameworks: Student Guide
~ ) - - - - - - - - - - - - - - - ~ ~ - - - ~ - - ~
Figure 6 Layout Of Experimental Warren Girder
E
A
D
F
B
•
c
140 mm
Figure 7/dealised Warren Girder Setup
Warren girders are common structures They are usually used for simple bridges and
n
cantilevered form for crane
booms
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TecQuipment Pin Jointed Frameworks: Student Guide
As well as looking at the forces in each one of the members, we will also look into the relationship between the load and
the vertical deflection of one of the joints.
How to Set p the Equipment
Fit the dial indicator to the arm which swings from the pivoting support as in Figure 7). Slide the indicator and rotate
the arm until the indicator stylus rests on the joint . Ensure the indicator has enough travel.
ocking
nut
Figure DTI Mounting Arm Assembly
Washer
Make sure the equipment is set up properly. Apply a preload of 100 N in the direction of loading) and zero the load cell.
Carefully apply a load of 500
and
check the frame is stable and secure. Return the load to zero and carefully zero the
indicator this may take a few tries as the indicator
is
very sensitive
Apply loads in the increments as in Table 4 recording the strain and indicator readings.
Load
AD AE AF BD
CF
DE EF
N)
0
1
2
300
400
500
Table
5
Member Strains
(Jt )
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TecQuipment Pin Jointed Frameworks Student Guide
Load AD
AE AF
BD CF DE EF
N)
0 0 0
0
0 0 0 0
1
2
3
4
5
able rue Member Strains t
Calculate the equivalent member forces at 500 N to complete the table. You will need the following information: Young s
modulus
is
the ratio
of
stress to strain, that
is;
where:
E = Young s modulus (Nm-
2
)
cr = Stress in the member (Nm-
2
)
= Displayed strain.
And
where:
F = Force in member
A = Cross-sectional area of member.
E
F
j
A
Ask your lecturer for the nominal diameter
of
the rods or measure them yourself using a micrometer (to the nearest
0.01 mm).
Equivalent member forces at 500 N.
Rod diameter= mm and
E steel
= 210 GNm-
2
.
Select one boom (a compression member) and one tie a tension member). Plot a graph from
of
Load (N) against Strain
f.LE) on same axis. Comment on your graph.
Using a suitable method calculate the theoretical member forces for the framework with a load
of
500 N. Compare the
experimental and theoretical results. Plot a graph
of
Load (N) against Joint Deflection (mm) and comment on the
resulting graph.
Page
Adjusted Member Strains ( )
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TecQuipment Pin Jointed Frameworks: Student Guide
Member Experiment force Theoretical force
N)
N)
AD
AE
AF
BD
CF
DE
EF
able
Comparison
f
Experimental and Theoretical Forces
lo d
N)
Joint deflection mm)
1
2
3
4
5
able 8 Joint Deflection
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TecQuipment Pin Jointed Frameworks: Student Guide
Experiment 3: Forces in
a Roof
Truss with
a
Central
and
Wind Load
You need 7 off 112 mm
members 4 off 93
mm
members and 2 off 42 mm
members
Figure 9 Layout
f
Experimental Roof Truss
Figure
1
Idealised Roof Truss
67
495
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TecQuipment Pin Jointed Frameworks: Student Guide
Roof trusses of he type we will examine are usually wooden and commonly used in domestic buildings. Generally, these
are built beforehand
off
site. They form a stable three-dimensional structure once fixed together using longitudinal
batons or purlins.
In service, a
roof
truss has to withstand many forces. We will look at two cases
of
loading and compare the forces created
in
the truss members. The first loading
is
central to the frame and acts downwards. This loading could be from a water
tank for instance. The second loading on the frame is at an angle as may be caused by a wind, for example.
Results
of
a Central load
Load N)
AE
AG H BE
BF Cl CJ OJ EF FG GH
HI
IJ
0
1
2
3
4
500
Table Member strains JLli)
Load N)
AE
AG
H
BE BF Cl CJ OJ
EF
FG GH HI
IJ
0 0 0
0 0 0 0 0
0 0
1
0 0
0
1
2
3
4
5
Table 1 True member strains w)
Make sure the equipment is set up properly set up for the central load first). Apply a preload of 100 N in the direction
of
loading) and zero the load cell. ,Carefully apply a load
of
500
Nand
check the frame
is
stable and secure. Return the
load to zero. Apply loads in the increments shown in Table 8, recording the strain readings.
Calculate the equivalent member forces at 500 N to complete the table. You will need the following information:
Young s modulus is the ratio of stress
1o
strain, that is,
j
c
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r
L
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where:
E
=Young s
modulus (Nm-
2
)
O = Stress in the member (Nm-
2
)
E =Displayed strain.
And
where:
F
=Force
in member;
=Cross-sectional area of member.
j
F
TecQuipment Pin Jointed Frameworks: Student Guide
Ask your lecturer for the nominal diameter of the rods or measure them yourself using a micrometer to the nearest
0.01 mm).
Equivalent member forces at 500
N
Rod diamete r=_ mm and Esteel = 210 GNm-
2
.
Member Experiment force Theoretical force
N) N)
AE
AG
AH
BE
BF
Cl
CJ
OJ
EF
FG
GH
HI
IJ
Table
omparison
o
experimental and theoretical forces
Set
up
as for the angled load then apply a preload of 100 N in the direction of loading) and zero the load cell. Carefully
apply a load of 500 N and check the frame is stable and secure. Return the load to zero.
Apply loads in the increments as in Table 11 recording the strain readings.
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TecQulpment Pin Jointed Frameworks: Student Guide
Results
or
an Angled Load
Load N)
AE
AG
H
BE
BF
Cl
CJ
0
100
200
300
400
500
Table 2
Member Strains ps)
Load N) E G H BE
BF
Cl
CJ
0
100
200
300
400
500
Table 3 True
Member Strains pli)
Calculate the equivalent member forces at 500 N to complete the table.
Equivalent member forces at 500 N
Rod diameter= _
mm
and Esteel = 210 GNm
2
.
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OJ
EF
FG GH
HI IJ
OJ
EF
FG
GH HI
IJ
Adjusted Member Strains (
)
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I
1
I
•
j l
•
I
•
J
TecQuipment Pin Jointed Frameworks: Student Guide
Member Experiment force Theoretical force
N)
N)
E
G
H
BE
BF
Cl
CJ
DJ
EF
FG
GH
HI
IJ
Table 4 omparison f Experimental and Theoretical Forces
Using a suitable method calculate the theoretical member forces for the framework with a load of 500 at each position.
Compare to the experimental and theoretical results.
Does the simplified pin joint theory predict the behaviour of he truss? There is one member of particular interest which
one
is
it and why?
Why is it important we always examine all of the load cases that a structure may be exposed to?
The roof truss structure may need to carry both
of
these loads simultaneously. How would we assess the total load in
each one of the members?
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