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UNIVERSITY OF GREENWICH
DEPARTMENT OF CIVIL ENGINEERING
BRIDGE DESIGN AND ASSESSMENT
BRIGDE ASSESSMENT ACCORDING TO BA 16/97 AND BD 21/01
BY
BELLO IDRIS
MSC CIVIL
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CONTENTS LIST
y Introductiony MEXE Methody Mechanism Methody Pippard-MEXE Methody Conclusiony References
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Introduction
Masonry bridges have been for a long time, in the U.K a choice option for Engineers settingout to achieve the task of building a bridge. Some 40,000
(1)masonry arch bridges are in
continual use by highways, railways and waterways, most of which are over 100 years old.
Due to the availability of steel, masonry bridges have been replaced by metal bridges for
obvious reasons of better load bearing capacity and aesthetics.
From January 1999 the European Commission Directive 96/58/EEC requires (2) all trunk road
bridges to be capable of 40 tonne axle loadings. This is a prerequisite so as to ensure that a
minimum safety zone is achieved to avoid any unforeseen circumstances.
The purpose of this project is to investigate the procedures of bridge assessment by methods
following the guidelines set out in the BA 16/97 and BD 21/01 The Assessment of
Highways Bridges and Structures.
MEXE Method
The most widely used method for masonry arch assessment is the Military Engineering
Experimental Establishment (MEXE) method that was evolved from Pippards 1930s(3)
work
during the 1930s. Pippard started off from his observation that a slight spread of the
abutments would cause the formation of hinges, or pins, at the abutments. His analysis was an
elastic one of the parabolic two-pin arch with live loads acting at the centre. He derived two
expressions for the safe live load on a bridge, W1 and W2.
During the war Engineers found(4)
that Pippards expression ofW2 can be simplified into anomogram so that a provisional axle loading can be read off immediately. It is then
multiplied by a number of modifying factors, to give the final axle loading. However slight
alterations in the depth of fill alter the provisional axle loading greatly; thus it is the problem
with the MEXE method that requires a need for a better method of assessment.
During the course of this project we will examine the MEXE method as presented by the
ASSARC software made available via the web.
The results, etc obtained are displayed below.
Comment [B1]: ref
Comment [B2]: Ref
Comment [B3]: ref
Comment [B4]: ref
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--------------------------------------------------------------------------
* ASSARC 10.0 *
Assessment of Masonry Arch Bridges (c) MSW SoftwareMEXE Assessment to BA16/97 Date: 29/11/2010
--------------------------------------------------------------------------
Bridge Name - 12.75 MEXE
Bridge Reference No - BELLO IDRIS
ARCH DIMENSIONS (Segmental):
Clear span parallel to the axis of the arch - 12.75 m
Rise of the arch barrel at the crown - 4.250 m
Rise of the arch barrel at the quarter points - 3.470 m
Barrel thickness (adjacent to the keystone) - 0.280 m
Average depth of fill over the crown (incl surfacing)-
0.200 m
Fig 1 Arch Barrel Properties
MEXE AXLE LOADS:
Provisional - 6.231 tonnes
Modified - 2.996 tonnes
CENTRIFUGAL EFFECTS: non-applicable
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Fig 2 Arch Barrel Shape
MODIFYING FACTORS:
Span/Rise Factor - 1.00
Profile Factor - 0.83
Barrel Factor - 1.20
Fill Factor - 0.70
Material Factor - 0.99
Joint Width Factor - 0.90
Joint Mortar Factor - 0.90
Fig 3 MEXE Results
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Joint Depth Factor - 0.90
Joint Factor - 0.73
Condition Factor-
0.80
ASSARC 10.0 Date: 29/11/2010
RESULTS OF MEXE ASSESSMENT to BA16/97
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MAXIMUM PERMITTED GROSS AXLE AND BOGIE WEIGHTS:
< assuming no axle lift-off >
per Axle per Bogie
(tonnes) (tonnes)
Single axle 5.10 5.10
Double axle bogie 3.00 5.99Triple axle bogie - 2.6m spread 2.25 6.74
less than 40 tonne requirements
WEIGHT RESTRICTIONS:
A 3 TONNE WEIGHT RESTRICTION IS REQUIRED
Bridge must be CLOSED to Fire Engines
Fig 4 MEXE Weight Restrictions
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The Mechanism Analysis
The method depends on the formation of four hinges to cause failure of the arch. The shapeof masonry arch is a statically indeterminate one which turns determinate when the hinges
form in arch ring due to failure loads(5)
. The arch is assumed to be rigid and loads are moved
across the span to find the collapse load for that load position. Once the locations have been
determined the set of equations from below can be used to determine the thickness of arch
ring (d) required for the given loading. The failure mode of the arch is the set of hinge
positions that require the lowest collapse load.
B
C
A
D
Fig 5 Profile of Beam Mechanism
The equations are formed merely by taking moments and are shown below:-
Again the assessment for this method was carried out using the ASSARC software with the
results presented below.
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--------------------------------------------------------------------------
* ASSARC 10.0 *
Assessment of Masonry Arch Bridges (c) MSW Software
Modified Mechanism Analysis to BD21/01 Date: 29/11/2010
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Bridge Name - MECHANISM 12.75
Bridge Reference No - BELLO
BARREL PROFILE - Segmental (Single Span)
Clear Span - 12.75 m
Rise at Crown - 4.250 m
Barrel Thickness-
Crown-
0.280 m- Springings - 0.280 m
Depth to mortar in Barrel - 0.012 m
Height of effective haunches - 0.000 m
Width of carriageway - 7.200 m
Min distance from carriageway
to edge of barrel - 0.800 m
No of Barrel Segments used in Analysis - 30
Characteristic Strength of Masonry of Arch Barrel - 8.60 N/sq mm
Fig 6 Arch Barrel with Surface Profile
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ROAD SURFACE PROFILE: Horizontal.
Depth of Fill (including surfacing) at the Crown - 0.200 m
Depth of surfacing-
0.100 m
CENTRIFUGAL EFFECTS: non-applicable
DEAD LOAD PARAMETERS:
Assumed Unit Weights x partial load factors:
Barrel - 21.00 x 1.15 kN/cu m
Fill - 19.00 x 1.20 kN/cu m
Surfacing - 23.00 x 1.75 kN/cu m
Fig 7 Material Properties
LATERAL EARTH PRESSURE ON BARREL:
A Rankine-Bell Lateral Pressure Distribution is assumed
Angle of internal friction - 35.00 deg
Cohesion - 0.00 kN/sq m
Coefficient of Active Pressure, Ka - 0.27
Coefficient of Passive Pressure, Kp-
3.00
Coefficient of Pressure at Rest, Ko - 0.43
Partial factor on active pressure effects - 1.50
Partial factor on passive pressure effects - 1.50
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ASSARC 10.0 Date: 29/11/2010
RESULTS OF ANALYSIS FOR AW BOGIES to BD21/01
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Assumptions:
Partial Factor for Live Load (crit. axle) - 3.40
(other axles) - 1.90
Partial Factor for Material Strength - 1.00
Condition Factor - 0.80
Centrifugal Effects Factor - 1.00
Assessment Load Effects Factor - 1.00
Vehicle width - 2.50 m
Width of Load Contact Area - 300.0 mm
Load Dispersion (Horizontal: Vertical) - 1 : 2
Fig 8 Lateral Pressure Distribution
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MAXIMUM PERMITTED GROSS AXLE AND BOGIE WEIGHTS:
(incorporating axle weight conversion factors in accordance with
BD21/01 Table 6.2)
< assuming no axle lift-off >
per Axle per Bogie
(tonnes) (tonnes)
Single axle 6.17 6.17
Double axle bogie - 1.0m spread 4.28 8.55
Double axle bogie - 1.3m spread 4.50 9.01
Double axle bogie - 1.8m spread 4.91 9.81
Triple axle bogie - 2.6m spread 4.20 12.60
Triple axle bogie - 2.8m spread 4.39 13.16
* less than 40 tonne requirements
Fig 9 Mechanism Results
WEIGHT RESTRICTIONS:
A 7.5 TONNE WEIGHT RESTRICTION IS REQUIRED
Fire Engines are restricted to Group 2
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Fig 10 Mechanism Weight Restriction
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Pippard-MEXE
This method utilises the sample load bearing capacity calculations inserted in the Annex F
(6)
of the BD 16/97. The method allows for calculation of single axle and double axle allowable
loads using information obtained from a plane frame computer program. Such programs
analyse structural dimensions in an elastic non-linear manner to obtain values for bending
moments and axial forces as well as shear forces if the need be. In this case, the Structural
Analysis and Design (S.A.N.D) software was used for analysis of the frame. A load of
1000kg was applied across the span in order to gain a behaviour pattern of the arch. The co-
ordinates used were those obtained from the ASSARC software in order to exemplify the
similarities in physical and geometric properties of the arch.
These barrel co-ordinates are shown below along with the results of this method as calculated
by hand.
Comment [DHL5]:ref
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Single
Double
1.8m
Triple
2.6m
Per Axle
(tonnes)
Per
Bogie
(tonnes)
Per Axle
(tonnes)
Per
Bogie
(tonnes)
Per Axle
(tonnes)
Per
Bogie
(tonnes)
MEXE 5.1 5.1 3 5.99 2.25 6.74
Mechanism 6.17 6.17 4.91 9.81 4.2 12.6
Pippard-
MEXE 133.5 78.5
As seen from the results, errors from the S.A.N.D program calculations for the live load were
incorrect. Therefore as a result the values obtained for Pippard-MEXE calculations were
wrong. This notwithstanding, I was able to verify that the results for the method in question
are less than values of the ASSARC based methods which goes to show that the values in
terms of real work calculations have to be regarded closely.
Conclusion
The condition of highway structures is determined by visual inspection. There are five main
types of inspection which are undertaken at different frequencies. These inspections cover a
range of detail, from a cursory check for obvious defects, through to a close examination of
particular areas or defects causing concern. The quality of data collected depends on theability of inspectors to observe and accurately record details on visible defects.
This could be affected by many factors, such as the environmental conditions, and the
knowledge and experience of the inspectors.
Strengthening methods that have been applied successfully and found to be useful include
using(7)
plastic based fibres as a reinforcement tool on the intrados of the arch. Also, increasing the width of concrete beams by placing additional concrete and reinforcement can
be undertaken to enhance the load bearing capacity of bridges.
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REFERENCES
1.
Ashurst, D. AnAssessmentof RepairandStrengtheningTechniquesContractor Report, 19922. BA 16/97, TheAssessmentof Highway BridgesandStructures Highways Agency, 19973. Thorne, A.Assessmentofa Masonry Bridge University of Exeter, 20034. Wang, J.MEXE MethodForMasonryArch BridgeAssessment, University of the West
England, 2010
5. Thorne, A.Assessmentofa Masonry Bridge University of Exeter, 20036. 16/97, TheAssessmentof Highway BridgesandStructures Highways Agency, 19977. Task Group Report,Enhancingthe Capacity of Concrete Bridges , Cement & Concrete
Industry Publication, 2008