Remote measurement of large deflections in fire tests

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Remote measurement of large deflections in fire tests

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THl

B92

1

no. 84

I

c. 2 I

- - - -

REMOTE MEASUREMENT

OF

LARGE

DEFLECTIONS

IN

FIFCE TESTS

by

T.T.

Lie and J . E . Berndt

-- P l V l S l Q N O F B U I L D I N G R E S E A R C H

-

N A T I O N A L R E S E A R C H C O U N C t L Q T T A W A C A N A D A Ottawa

(3)

REMOTE MEASUREMENT O F

LARGE

DEFLECTIONS

EN

FIRE TESTS

by

T . T . Lie and J . E . Berndt

In experimental investigations of the fire resistive properties

of structural elements it i s often nece a s a r y to measure large deflections of t e s t specimens. The simplest a n d m o s t commonmethod of d e t e r - m i n i n g deflections makes u s e a£ a calibrated tape or rule. Taking such measurements during the course of a fire t e s t has, however, become

hazardous and difficult owing t o the increasing u s e of materials that

develop combustion products that may be toxic or reduce visibility.

Remote recording of the deflections is therefore desirable. Such a remote recording system must

a) record deflections of up to 2 0 in, as a function of

t h e ;

b) be reliable at temperatures in a range f r o m room

temperature to about 1 50

OF;

c ) be capable of u s e in an environment of dense smoke;

d)

be

small (so that it can be i n s e r t e d between hydraulic

jacks such as those used in the laboratory of DBR/NRC

for applying a load during a fire t e s t ) .

A survey of the literature indicates that although n u m e r o u s versions of

displacement-measuring devices have evolved there are none tbat completely

satisfy the above requirements.

An

attempt has t h e r e f o r e been made

t o design and construct an appropriate device.

In general, t w o methods are used for measuring large dis- placements [ 1 3 ,

i.

e , optical and electro-mechanical. Because of

the possibility of s m o k e development during a t e s t , optical methods w e r e n ~ t considered in this case. Of the various electro-mechanical techniques one was chosen in which the displacement of a certain point

on a t e s t specimen could be converted into an electrical signal with the aid of a linear potentiometer, Such conversions are described in

References 2 , 3 and 4.

A d e v i c e was constructed that could measure displacements in

(4)

(Figure l ) , simple to operate,

and

can be constructed at a low cost (approximately $ 2 0 f o r material and 7 hours of labour, based on the

construction of five units by DBR/NRC).

DESCRIPTION

OF

DEVICE

The device is shown in Figure 1. Components include: I , Aluminum frame.

2 . Pulley onto which a steel wire, 0 . 0 1 -in. diameter, is wound. The s t e e l w i r e i s connected at the point where displacement is

t o be measured. The cavity of the pulley contains a spring f r o m

a

standard 8-ft steel measuring tape. The

spring

keeps the wire taut as it unwinds from the pulley. The maximum force

exerted by the spring i s 1 2 5 g .

3 . C o v e r plate of aluminum that prevents the spring from escaping

from the cavity.

4. S c r e w w i t h a slot t o f i t t h e end of the tape spring.

5. Nut to lock the screw (paint 41 and thus the end of the tape spring.

Locking is done by tightening the nut against the frame [I).

6 .

Magnet t o

fix

the device at a suitable location during the test.

7. S c r e w to attach the magnet ts the frame (point 1 ) .

8 . Three-pin plug used t o connect a three-wire cable to the potentiometer (point

9).

9 . Ten-turn l i n e a r potentiometer (resistance 1 kfl f 3 per cent, tem- perature coefficient 11.11 x

IO'~/F

deg, temperature range - 8 5 to

185"F, linearity 0 . 2 5 per cent). The potentiometer is fastened to the f r a m e (point 1) with the aid of the nuts (points 10 and 1 2 ) and toothed lock washer (paint I I ) . The pulley (point 2) is secured to

the shaft of the potentiometer by means of f i e screw (point 1 3 ) .

PERFORMANCE AND CE-XARAGTERETIGS

A potentiometer (ELD) is placed in an arm of a Wheatstone Bridge (Figure 2 ) . A suitable range f o r

VM

is 100rnV,as this corresponds to

the normal range of output of t h e m a c o u p l e s used in f i r e t e s t s . Thus the same meters, usually multipoint recorders, can be used f o r rneasur

-

ing both temperature and deflection.

(5)

The

maximum

deflection of interest in f i r e t e s t s is about 20 in.

T o obtain 100 m V for

a

deflection of ZO in., each inch of deflection

should be converted into 5

m V

meter output voltage

VM. The

method

of calculating

VM

is described in Appendix A,

and

suitable values of

the bridge resistances and voltage

V,

f o r a sensitivity of

5 m V

per inch deflection, are given in Figure. 2 and Appendix A .

h practice the sensitivity of the circuit is adjusted to the desired value by varying the voltage

V.

Once the sensitivity is set, the output

voltage to the meter VM i s zeroed by varying the resistance between AD. At r o o m temperature the main errors in the displacements

measured by the device are caused by non-linearities of the bridge and

potentiometer (RD), and by the eccentricity and imperfect roundness of

the pulley. Calibration shows that the t o t a l error resulting from these causes i s l e s s than 3 per cent f o r deflections in the range of 0 . 2 5 to I in. and

less than 1 per cent for higher deflections. Another possible error is

that associated with defamation of the steel wire under dynamic f o r c e s

caused bymovement of the t e s t specimen. W h e n these forces are not

greater than approximately 150 g the e r r o r i s negligible.

In

fire t e s t s the rate

of

deflection of t e s t specimens is usually within t h s e limits.

At higher temperatures errors in displacement measurements

are mainly due to

a) change in the resistance of the potentimeter that converts displacement into electric current

(RD]

b) expansion of the pulley

c) expansion of the steel. wire.

These e r r o r s can be large, but they c a n be reduced by choice of suitable values f o r the potentiometer resistances and wire lengths. Because errors tend t o compensate for each 0 t h ~ ~ the t o t a l error c a n

be made negligibly small.

Change in the resistance of

RD

with temperature rise will cause

an increase in the reading of t h e meter

VM.

B y using small initial values of

a

and 0, f o r exasnple 0.05, the e r r o r can be made quite small,

This c a n be done by turning the pulley about one half turn caunter-

clockwise from i t s r e s t position and attaching the wire to the test specjmen.

A s shown in Appendix B , the meter w i l l then give in the range of deflections

of 1 to 20 in. a reading that is approximately 0 . 3 per cent too high when the ambient temperature r i s e s by 9 0 F deg ,

(6)

The err or due t o expansion of the aluminurn pulley and that

due to expansion of the steel wire tend to compensate each other. B y choosing suitable lengths f o r that part

of

the wire on the pulley

(ap)

and that between the pulley and the t e s t specimen

(a,),

the angular

position of the pulley can be made insensitive to temperature.

It

is

shown

in

Appendix C that this is true when fl

₌

_0.4375lo. Thus f o r P

a

value of

R

_P

= 2 5 in.

,

a suitable length f o r measuring deflections

of

fire t e s t specimens, A. should be approximately 57 in.

Def lectians of the specimen will alter the ratio of to Lo and

thus introduce

a

small error due t o temperature effect.

#

or an

ambient temperature r i s e of 90 F deg the e r r o r is of the order of

0 . 2 per cent

in

the range of deflections under study (0 to 20 in. ). This e r r o r causes t o o low a meter reading, and it practically compensates the error of 0.3 per cent due to change of resistance of the potentiometer with temperature. As a consequence, in the range of deflections from

1 to 20 in. and at temperatures up t o about 90 F deg above room tem-

perature the total error w i l l be approximately the same as that at r o o m temperature, i . e . less than 1 per cent.

REFERENCES

1 . W a r d , H. S . Some Reasons and Techniques for M e a s u r i n g L a r g e Structural Displacements. The Engineering Journal,

Vol.

54, No. 6 , 1971, p. 14-21.

2 . Lebow, M . J . S o m e Principles of Transducer Design. ISA

Transactions, Vol. 2,

No.

1,

1963,

p. 85-92.

3. Chudnovskii,

V.

Y. ,

M . P. K o r o l , and

V.

G . Zagorodnii. Converter f o r Large Linear Displacements. Measurement

Techniques, Vol. 13, No. 3, 1970, p. 339-340.

4. Burn, K. N. Instrumentation f o r a Consolidation Study of a Clay Deposit Beneath an Embanhnent. Geotechnique, Vol.

IX,

(7)

APPENDIX A ELECTRIGAL CIRCUIT

B y

applying Kirc?hofFs law to circuits

ABC,

ABD and BCD

(Figure

2) the equations f o r the currents t h o u g h these circuits can

be set up. Solving the equationsgivesthe current through the meter,

and f r o m this the voltage

V

between

B

and D can be derived. F o r a meter having a resistance%igh in comparison with the resistances

in the a r m s of the bridge, the voltage

VM

c a n be given by

T o obtain a reading of 100

m V

for a deflection of 20

in.,

various

cambinations of values of bridge resistances and supply voltage V can

be chosen.

It

c a n be verified by means of Equation ( 1 ) that for a pulley

with a diameter of 2 in. the above requirement c a n be satisfied by the following c m b i n a t i o n

a

_{w h e r e}_{b o i s}_the_initialvalue_{o f u}

0'

(approximately 0.05, corresponding to about one half turn counterclockwise

of the potentiometer

+

from its rest

position)

approximately 30.0 IT m V , adjustable.

In

practice,

V

is adjusted during the calibration of the device at a value

(8)

APPENDIX

B

ERROR

DUE TO

CHANGE

OF

RESISTANCE

OF

THE POTENTIOMETER

The error caused by a change in the resistance of the potentio-

meter of the device

RD

(Figure 2 ) can be calculated by means of Equation 1 ),

T o keep the error small it is essential to make the initial value

a

.

of

a

small. T h i s implies that B, which is adjusted so as t o equal

a0

to

make

VM

zero at the start of the t e s t , is small. a l s o ,

F o r R = 0 . 05, a temperature coefficient of resistance

RD

of

11. 11 x ~ O - ~ / F deg, a temperature rise of 90

F

deg and l -in. deflection

1

(a

=

0.05

+

lOrrD

,

where D is the diameter of the pulley) it follows

from Equation C1) that

Because at the initial temperature the voltage

VM

is 5

m V ,

the error resulting from a temperature rise in the potentiometer of 90 F deg is

thus 0.012675 m V , or roughly 0.3 per cent.

In

the s a m e way, f o r

a

deflection of 20 in. the e r r o r due t o a temperature rise of 9 0

F

deg i s

(9)

APPENDIX

G

ERROR D U E T O EXPANSION O F P U L L E Y AND W I R E WITH

NO

DEFLECTION

OF

THE TEST SPECIMEN

It

is a s s u m e d that the wire, with less than four turns wound

round the pulley, will slip over the pulley _{when it expands. This} assumption has been verified by heating only the pulley and observing

the change of the voltage

VM.

B y choosing suitable lengths of wire f o r t h e _{pulley and the wire}

between the pulley and t e s t specimen it is possible to make the zero

position of the pulley insensitive to temperature. The condition is that

at any temperature

1 9 - a = n i-r

D2

0 D

where

A s

=

the total wire length at the temperature under consideration .to

=

initial w i r e length between pulley and t e s t specimen

n

=

initial number

of

turns of s t e e l wire on the pulley

8

Dr = diameter of the pulley at the temperature under consideration.

A' can be written as

at

= A ₍₁_-t-

_a,

_T)

w h e r e

R

=: the length of the steel wire at r o o m temperature

as

=

the expansion coefficient of steel

T = temperafxre o f t h e w i r e .

Dt can be w r i t t e n as

where

D

=

the diameter of the pulley at r o o m temperature

aa

=

the expansion coefficient of aluminum.

(10)

n can be written as

0 A

where

= the length of the steel w i r e on the pulley at r o o m

temperature.

From Equations (2-51, it is possible to make the zero position of the pulley independent of temperature, when

- 6

- 6

or for

a

=

7 x 1 0 /F d e g a n d

m a =

2 3 x 10

/F

deg when

S

For

R

=

2 5 in., the length As of the _steel_{wire between pulley}_and

P

t e s t specimen should be 5 7 . 1 4 in. to make the zero position of the pulley insensitive t o temperature.

(11)

APPENDIX

D

ERROR

DUE

TO

EXFANSION

OF

PULLEY

AND WJRE WHEN TEST

SPECIMEN DEFLECTS

When there is deflection, the equation for the position of the pulley will be

where

t

=

the length of the steel wire between pulley and t e s t

specimen at time t after the start of the deflection

n

=

the number of turns of the steel wire on the pulley at

t

time t .

The movement of the pulley at time t i s no - nt turns. T h i s

will cause a change in t h e indication of the miflivolt meter of

Substitution

in

Equation

(8)

of

R

1'

-

4

n

=

2

a n d n 7 33

n D

t r D f gives

- 6

-6

F o r Ap = 25 in., I

=

57.14 in.,

a,

=

7 x 10 ]OF,

a

=

23 x 10

/OF,

a-

with a deflection of 1 in. ( B t = 58.14 in. ), the indication of the meter

becrrmes

G

=

4 . 9 8 9 6 8

m V .

This indicates a meter reading that is approximately 0 . 2 1 per cent too

low. In the same way it can be shown that f o r a deflection of 20 in, t h e meter reading will be approximately 0 . 1 9 per cent too low. The error