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KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
To understand tilt & angular distortion appears to be quite simple. However, since late 1950s’
many reference professionals and academics have been trying to derive relationships between tilt & angular distortion and the risk of damage to buildings.
Regarding instrumentation, more often than not it looks like there are several options to
monitor tilt & angular distortion. A good understanding of the behaviour of the structure is needed, together with careful planning and design for instrumentation and monitoring.
This article presents the basic concepts to help decide how to monitor tilt taking into
consideration the most common issues encountered and the type of data sought.
Angular Distortion in Structures:
Point vs. Linear Monitoring - considerations
In regard to tilt & angular distortion, this articles covers the following points: • Definitions and (typical) values for tilt and angular distortion • Accuracy: MEMS & Electrolytic, ATS • Point tilt meter vs. linear tilt beam • Calculation • Pictures • Summary • References
NOTE: There is still ongoing discussion about tilt & angular distortion in relation to
building and structural damage.
KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
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Item Definition
Tilt
ω
Tilting, ω, normally describes the rigid body rotation of the
whole superstructure or of a well defined part of it. Normally
it is not possible to ascertain the tilt unless details of the
superstructure and its behaviour are known. Even then it can
be difficult when the structure itself flexes. Burland & Wroth
(1975), Settlement of Buildings and Associated Damage.
Angular Distortion or Relative Rotation
β = δ / l
Angular distortion, β, is the ratio of the differential settlement
δ and the distance l between two points. Skempton &
MacDonald (1956), The Allowable Settlements of Buildings.
Relative rotation, β, is the rotation of the straight line joining
two reference points relative to the tilt. Burland & Wroth
(1975), Settlement of Buildings and Associated Damage.
DEFINITIONS AND (TYPICAL) VALUES FOR TILT AND ANGULAR DISTORTION
NOTE: It is crucial to understand beforehand the range of tilt & angular distortion that will
possibly cause unacceptable damage to the structure.
β = δ / l
Dimensionless
β = δ / l
mm/m
β = δ / l
Percentage %
β = δ / l
arc sine 360°
β = δ / l
arcsecond
β = δ / l
arcminute
1/100 10.0mm / 1m 1.00% 0.573° 2062.8arcsecond 34.4arcminute
1/150 6.6mm / 1m 0.66% 0.382° 1375.2arcsecond 22.9arcminute
1/200 5.0mm / 1m 0.50% 0.286° 1029.6arcsecond 17.2arcminute
1/300 3.3mm / 1m 0.33% 0.191° 687.6arcsecond 11.5arcminute
1/500 2.0mm / 1m 0.20% 0.115° 414.0arcsecond 6.9arcminute
1/1000 1.0mm / 1m 0.10% 0.057° 205.2arcsecond 3.4arcminute
Typical Values for Angular Distortion β = δ / l
KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
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NOTE: It is not always easy to understand the difference between tilt and angular
distortion at first glance onsite.
ω
Building showing tilt ω, Ciudad de México, June 2017. Tilting around 1/250 or bigger is
noticeable to the naked eye.
DEFINITIONS AND (TYPICAL) VALUES FOR TILT AND ANGULAR DISTORTION
KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
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NOTE: Structural angular distortion may come with rigid body tilt or with differential
settlement.
Maximum angular distortion β over a certain distance l, Ciudad de México, June 2017.
β = δ / l
δ
l
DEFINITIONS AND (TYPICAL) VALUES FOR TILT AND ANGULAR DISTORTION
KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
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ACCURACY: MEMS & ELECTROLYTIC, ATS
NOTE: Accuracy needed, type of readings output and long-term stability are factors to
consider when choosing tilt measuring equipment.
Item Considerations Remarks
MEMS Tilt Meter
MEMS: Micro-Electro-
Mechanical Systems, polysilicon
springs suspend the MEMS
structure above the substrate
such that the body of the
sensor -”proof mass”- can move
in xy.
Designed to be installed in
either vertical or horizontal
position to measure tilt.
Uniaxial or biaxial options:
range ±5°, ±10°, ±15°.
Accuracy: ±0.02mm/m (range ±5°),
±0.035mm/m (range ±10°), ±0.065mm/
m (range ±15°), or ±0.0125%FS
Excellent thermal stability; unit fitted with
a thermistor.
Output: +/- Volt; 4-20mA; RS-485/BUS
The digital RS-485 output signal
provides high accuracy with the
advantage of being able to create a
digital BUS system where all sensors
can be linked together, reducing cable
quantities.
Electrolytic Tilt Meter
Electrolytic: Sensor’s liquid
includes an electrolyte that
conducts electrons between a
common connection and left
and right electrodes.
Designed to be installed in
either vertical or horizontal
position to measure tilt.
Uniaxial or biaxial options:
range ±5°, ±10°, ±15°.
Accuracy: ±0.035mm/m (range ±5°),
±0.09mm/m (range ±10°), ±0.09mm/m
(range ±15°), or ±0.025%FS
Vibration resistant.
Unit fitted with a thermistor.
Output: RS-485/BUS
The major advantage of the new
electrolytic tilt meter systems is their
long term stability.
Automatic Total Stations
Survey equipment like
monitoring total stations is
often used to monitor
movements from mini prisms
on structures.
3D measurements.
Accuracy: ±1mm, or lower than.
Reading frequency: around 20 minutes
per full set of prisms –control and
reference-.
To achieve higher monitoring
frequencies and accuracies, it is highly
recommendable for ATS systems to be
complemented with MEMS or
electrolytic tilt meters.
ATS systems imply higher purchasing,
installation and maintenance costs.
KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
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ACCURACY: MEMS & ELECTROLYTIC, ATS
NOTE: Structural tilt monitoring equipment and its distribution onsite must be chosen
bearing in mind jobsite conditions and the decision-making data needed.
Type of sensor /
equipment
Affected by temperature
and weather-related
changes
Affected by vibration
MEMS tilt meter
LOW HIGH
Electrolytic tilt meter HIGH
LOW
Automatic Total
Stations HIGH HIGH
KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
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POINT TILT METER vs. LINEAR TILT BEAM
NOTE: Anchoring point tilt meters and linear tilt beams in joints and/or mortar should be
avoided by all means.
Using a point tilt meter or a linear tilt beam (uniaxial/biaxial) is a function of:
f: fabric of the structure f: structural continuity
f: stiffness of the structure f: expected deformation wavelength
General criteria is detailed in the table below, as specified in the references cited at the end of this
f: fabric of the
structure
f: structural
continuity
f: stiffness of
the structure
f: expected
deformation
wavelength
Point tilt meter Linear tilt beam
(length on
request)
Masonry - - short - X
Brick - X
Cast-iron bolted
lining tunnels
- X
Mass concrete X -
Reinforced
concrete
X -
Structural steel or
similar + + long X -
With the means available at the jobsite and right after installation is finished, it is highly recommendable to accurately survey xyz point tilt meters as well as the starting and end points of a tilt beams’ chain. This will be really useful to calculate and understand deformations.
Point tilt meters are used to monitor tilt on structures at individual locations. Linear tilt beams have a defined gauge (beam) length so that changes in tilt can be simply converted to millimetres of movement.
KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
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CALCULATION
NOTE: Sine of the angle is common practice in the structural and geotechnical industry to
calculate movement; tangent of the angle may be used too for angles ranging 0° ↔ ±15°.
Item Considerations Remarks
Measurand
The physical quantity unit
measured in tilt is degrees
(360°).
In the structural and geotechnical
industry, usual tilt ranges are ±5°, ±10°,
±15° Full Scale FS; other ranges are
available upon request.
Measurements in degrees are used in
different calculations knowing the
length of the linear tilt beams or
assuming a certain wavelength for the
deformation when using tilt meters,
degrees 360° can be easily converted
into mm/m.
Sign convention
Sign convention must be
agreed before installation of
any type of tilt meters.
It is common practice to install tilt
sensors so A+ points towards the
expected direction of maximum
movement, both for the uniaxial and the
biaxial options.
Not understanding the directions of
movement may lead to tremendous
errors in the interpretation of
deformation as well as in the
implementation of any remedial
measures.
KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
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NOTE: It is crucial to foresee convenient onsite conditions before installing tilt meters.
PICTURES
Point tilt meters monitoring a reinforced concrete structure –dam-.
Point tilt meters and prisms -ATS– monitoring a building neighboring excavation works.
Point tilt meter
Prism
Prism
ATS
KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
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PICTURES
Linear tilt beams monitoring vertical –higher- and horizontal –lower- movement in a brick wall.
NOTE: Clean and tidy installations favour reliable readings.
Linear tilt beams
KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
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PICTURES
Chained linear tilt beams monitoring horizontal movement in a cast-iron bolted lining tunnel.
NOTE: Using tilt beam chains requires accurate surveying of both end points.
Chained linear tilt beams
KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
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TYPE OF STRUCTURE Rigid body / structure A good understanding of the behaviour of the structure is
needed.
Options to monitor tilt & angular
distortion
Careful planning and design for instrumentation design
and monitoring.
CONCEPT Tilting ω ↔ Angular distortion β Rotation ω ↔ ratio of differential settlement δ and dis-
tance l between two points
MESURAND Basic engineering unit Degrees (360°)
VALUES (TYPICAL) Expected values Anticipated range of tilt & angular distortion affecting the
structure.
TYPE OF TILT SENSOR Readings possibly affected by onsite
conditions
MEMS tilt meter ↔ Electrolytic tilt meter.
Weather related changes and vibration.
TYPE OF INSTALLATION Fabric and structure Point tilt meter @ individual location.
Linear tilt meter @ beam length.
CALCULATION A+ ↔ A-
Range 0° ↔ ±15°
Main foreseen direction of movement.
sin α –common practice in the industry-.
NOTE: Positive installations need planning and good care onsite.
SUMMARY
KNOWLEDGE ARTICLE MC, GC, TL 31/01/2018 V1.0
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NOTE: Since late 1950s’ many professionals and academics have been trying to derive
direct relationships between tilt & angular distortion and the risk of damage to buildings.
REFERENCES
Boone, S. J. (2001). Assessing construction and settlement-induced building damage: a return to fundamental principles. Proceedings, Underground Construction, Institution of Mining and Metallurgy, London, pages 559—570. Burland, J. B., Broms, B. B. and De Mello, V. F. B. (1978). Behaviour of foundations and structures. Building Research Establishment, London. Burland, J. B. and Wroth, C. P. (1974). Settlement of Buildings and Associated Damage. British Geotechnical Society’s Conference on the Settlement of Structures, Cambridge, April 1974. Frank, R. (2011). Geotechnical aspects of building design (EN 1997). Eurocode 2, Background and Applications, Brussels. Mair, R. J., Taylor, R.N. and Burland, J. B. (1996). Prediction of ground movements and assessment of risk of building damage due to bored tunnelling. Geotechnical Aspects of Underground Construction in Soft Ground, Mair & Taylor (eds.), Rotterdam. Skempton A W and MacDonald D H (1956). The allowable Settlements of Buildings. Structural and Building Division Meeting, Structural Paper No. 50, London.
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