trusses-full-rc.pdf

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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



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.



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 .




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.

Page



xperiment

:

Forces in a Warren Girder

You need

7

off 2mm

members 140

effective length) for his

experiment

100 l l

- 9 0


~ ) - - - - - - - - - - - - - - - ~ ~ - - - ~ - - ~

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

Page 9




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 )

Page 1



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 ( )




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

Page 12




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

Page

3




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

Page 14

r

L

Adjusted Member Strains ( )



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


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

.


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.

Page

5



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

.

Page 16

OJ

EF

FG GH

HI IJ

OJ

EF

FG

GH HI

IJ

Adjusted Member Strains (

)



I

1

I

•

j l

•

I

•

J



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?

Page

7

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