Carbon Fibre Plates can be bonded to the tension faces of concrete structures to provide additional strength. Failure often takes place in the concrete layer just below the adhesive, either by peeling at the ends or by a crack propagating from an existing shear crack in the concrete. The conventional methods of analysis use finite elements to model the CFRP, the concrete and the adhesive. But the exact shape of the adhesive layer is unknown, and there is a singularity in the stress concentration at the interface. Furthermore, the condition of the interface is unknown, and unknowable - it is impossible to say if there are small voids in the adhesive and the exact surface texture cannot be known. Our analysis applies fracture mechanics principles - we assume that a crack is present and the method asks whether a propagation of the crack requires additional energy (in which case it will only propagate slowly as the load increases), or releases energy (in which case it will fail catastrophically). 

The stress-rupture performance of aramid fibres governs the allowable stresses that can be applied to them when used as prestressing tendons for concrete. Such tendons would have design lives of 120 years, so we clearly cannot wait that long to obtain the relevant test data. This project, undertaken by by Nadun Alwis, has evaluated various strategies for using accelerated testing. It has been concluded that the Stepped Isothermal Method can be used to produce test results in reasonable time scales. The method can also produce master curves for the creep response of the fibres.

In a joint research project with the Herchel Smith Laboratory for Medicinal Chemistry, the techniques have been determined to enable the study of the fracture state of hardened concrete samples. The technique is non-destructive, which enables multiple scans to be made of the sample at different loading stages. It has been shown that the internal structure of concrete can be determined in the first 10 hours after casting, and fractures can be studied in wet samples. If registration markers are present, the two images can be combined to show how the fractures relate to the aggregate distribution. At the moment the method is useful for the study of the meso-structure of small concrete samples, but it is intended to extend the work to larger samples. For more details ...

In association with the Educational Trust of the Institution of Structural Engineers, we are producing teaching material for use in schools.  A study carried out for the trust showed that the biggest drop-off in the numbers studying the physical sciences occurs immediately after GCSE level.  It was recognised that many school teachers were not sufficiently familiar with engineering, but would be willing to use material if it were available.  Thus the objective is to show pupils in their final GCSE year how relevant physics is to modern life; we have produced three modules with the general theme of "Stadium Roof Design", which takes pupils through a Design Decisions Activity (aimed at DT Resistant Materials Syllabus), Emirates Stadium Structural Analysis (aimed at Mathematics and Physics - Forces and Motion), and Cantilever Roof Design (covering Physics, Maths and DT material).  Other modules are in preparation.  The material can be freely downloaded and is intended for use by the teacher without additional help.

There were three inventions that gave us the bicycle wheel as we know it today - each is associated with an application of prestressing to a structural system. The first and most obvious is the tensioned spokes - the rider's weight is carried from the forks to the ground not by hanging off the top spokes, but by reducing the pretension in the lower spokes - only a couple of spokes are carrying the load at any one time. The second is the pneumatic tyre, where the compressive load is carried to the ground by reducing the tension in the sidewall. The air pressure in the tyre does not change when the load is applied. The final prestressing system is the tyre cord, which is shorter than the perimeter of the rim. The cord is thus in tension, holding the tyre on the rim, which enables the pretension in the sidewalls to be reacted. A paper describes these systems and the tests that were carried out.

The Koror-Babelthuap Bridge in Palau collapsed on 26th September 1996, at around 5:45 in the afternoon, about 90 days after work had been carried out to eliminate excessive deflection due to creep during the 19 years since it had been built. The collapse was catastrophic, killing two people and injuring four more, and occurred under virtually no traffic load during benign weather conditions. Services passing through the bridge between the country's two most populated islands were severed; this caused the government to declare a state of national emergency and request international aid for the thousands of people left without fresh water or electricity. Why did a major structure collapse so soon after engineering intervention. Was the repair at fault or was the original construction at fault? A study has been carried out to investigate the various possibilities, and the conclusions, which have been published, are surprising. 

There are many 18th and 19th century buildings which cantilevered stone staircases. They are made of brittle stone of unknown quality; they are often on means of escape and sometimes in public buildings, but the mechanism by which they carry load is uncertain. There is a widespread belief that they work by carrying forces down the flight to the base, with the wall providing only torsional restraint, but some flights are very long and there are some which spiral down many storeys. There are also horizontal cantilevered landings which cannot behave in this way. Engineers are being asked to sign certificates to say that these staircases are "safe" which means putting their PII on the line. Our study, in conjunction with Price and Myers has involved tests on stine in torsion and also dynamic tests on staircases and landings in a Cambridge college.

Fibre Reinforced Polymers and aramid ropes have been identified as suitable materials for reinforcing and prestressing concrete. Much research has been carried out over the last 20 years, but the take-up by industry has been very slow. The problem appears to be economic, but this topic is rarely addressed by researchers, who concentrate on the purely technical issues. This project, undertaken by Iannis Balafas, looks at the optimal design constraints, the rates of corrosion in structures reinforced with steel, and traffic delay costs. It has been shown that, if whole-life costing and realistic discount rates are used, it is worthwhile spending a little more on non-corroding materials when structures are first built. The image on the left shows part of a design chart for finding the optimal geometry. 

It is known that bones grow in response to stress and decay when not used. They are also known to be near-optimal structures with relatively low factors of safety by normal structural standards. Athletes have more bone mass in the limbs they use most (e.g. the serving arm of tennis players) and people with broken legs need to exercise to prevent loss of bone structure. But what are the rules that govern this behaviour? Biology must reflect structural mechanics - our research seeks the rules that have to be adopted to allow bone growth to be stable with the minimum requirement for genetic coding. The images show sections obtained by Saumarez showing various rib cross-sections - he showed that they were optimal for the loadings to which they were subjected.

The articulation of the elbow joint is complex. The forearm can be flexed relative to the upper arm, and also twisted. One can also carry significant loads in many of these orientations. Designing a mechanical engineering joint with the same freedoms is extremely complex, as robot designers have found; the image on the right shows a crude (and unworkable) representation as a mechanical system. The aim of this project is to determine the shapes of the mating surfaces and the positions that the bones take up as the various degrees of freedom are exercised. This involves structural engineering (in the load paths), mechanics (following the motion), computer vision (to determine the shapes of the mating surfaces) and computer modelling (to put all the components together). It thus requires an understanding of many aspects of engineering, as well as biology.

The increased use of FRP reinforcement has raised technical questions regarding the behaviour of the concrete. Because FRPs have no ductiility themselves we must ensure that the complete section shows some ductility and gives warning of failure. This can partly be achieved by the cracking behaviour of the concrete, but we must ensure that the concrete srushes before the FRP snaps, and that as much energy as possible is absorbed in the compression zone. Slightly paradoxically, development of new tension materials focusses attention on the failure mechanisms of concrete. In this work we are studying how concrete failures are localised. This image shows strain distributions (measured optically). Two large cracks are visible, as is the localised failure region at the top of the right-hand crack.

To determine the behaviour of beams and columns which buckle an accurate description of the 3D buckled state is required.  If the pre-buckling deformations are significant the post-buckling rotations are not adequately expressed as vectors and a more accurate analysis is required.  Direction cosines, Euler angles and finite rotations have all been tried, but have varying problems.  With Joan Lasenby of the Speech Vision and Robotics group we have been applying the principles of geometric algebra to these problems.  Geometric algebra is a consistent method of specifying orientation in multiple dimensions and is based on Clifford Algebra.  We have shown that these techniques can be aplied successfully to these problems.

When an indeterminate beam is constructed in stages the bending moment due to the dead load differs from that which would be appplicable if the beam was built in a single operation.  Because concrete creeps, the distribution of bending moments changes over the next few months.  Conventional wisdom says that the bending moment diagram always lies somewhere between the "as-built" diagram and the "monolithic" bending moment.  It is then possible to check that the structure is satisfactory under these two extremes.  But is this always the case.  Are there combinations of constructions sequence and temperature which can mean that this assumption is not safe?

FRP reinforcement used as tension elements in beams are brittle, which implies that the concrete in the compression zone must be made more ductile to avoid sudden failure.  One way of achieving this is by providing confining spirals of aramid reinforcement to keep the concrete in a state of triaxial compression.  If this sort of reinforcment was used in the compression zone, which is rectangular, there would be three types of confinement - the normal zone, which is confined by a single spiral; a doubly confined zone where spirals overlap, and an area in the cover outside the spiral which is unconfined.  What are the relevant governing equations?  The image shows a block with all three types of confinement.  Final failure occurs when the AFRP yarns failed in tension.

Fibre Reinforced Plastics can only really be useful if all the steel in a section is replaced.  Thus, the shear links have to be replaced as well as the flexural steel.  But our techniques for analysing beams with steel reinforcment rely on the steel yielding so that we can apply plasticity theory.  This is the fundamental assumption that underlies the truss analogy, although it is rarely stated.  There are many proposals for using truss models for FRPs, which allow for the brittle FRPs by limiting the strain to those of elastic steel.  This ignores the fact that the steel must be yielding to allow the truss model to work.  A revised analysis, based on elastic distributions, has been undertaken by Tim Stratford (now at the University of Edinburgh) to show that this can lead to unsafe predictions for the strength of beams in shear.

Boutiron Bridge near Vichy is probably the most important structure in the development of prestressed concrete, although it is a reinforced concrete arch. It was here that Freyssinet realised the importance of creep, and this led to the invention of the first practical system for prestressing. A few prestressed concrete bridges were built during World War II, and development took off after the war when the shortage of steel caused major problems. Very few details exist about these bridges and many are not recorded. An on-going project is to build up a database of these structures so that their condition can be assessed. For more details ...

Ceramics offer a number of advantages for many applications, but they are available in limited sizes, since they need to be fired, and they are brittle, so they need to be expensively toughened. Or do they? The photo on the left shows bathroom tiles, laid end to end, and containing a pretensioning wire. The joints are made with conventional tile adhesive from a DIY shop. The beam is then loaded in 4-point bending. Even in this poor photograph, the cracks on the tension face are clearly visible, but the fracture does not propagate through the beam. Even under this extreme loading, the beam can be unloaded with no residual deflection. Brittle?

Concrete beams are normally thought to be not susceptible to buckling, since the sections are much chunkier than steel sections. But the desire to increase the span of concrete bridges, and still to allow the transportation of the beams around the country, has led to the development of longer, deeper, narrower and heavier beams, and checks now need to be taken for stability. It has been shown that the beams are most susceptible to buckling when the beams are being lifted into place, since the beam can rotate and buckle about its minor axis without causing torsion. The beams also need to be checked when they are placed in position, before the top slab has been cast. This work has been undertaken by Chris Burgoyne and Tim Stratford, now at the University of Edinburgh.

To demonstrate the internal profiles of prestressing cables within a typical prestressed concrete bridge, a virtual reality model of the Torridge Bridge at Bideford in Devon has been constructed. The observer can fly over and through the bridge, and can make the concrete transparent to reveal the internal cable profiles. The construction sequence can also be followed. The work was carried out by a final year project student, James Stevenson, with assistance from Parson Brinckerhoff who supplied accurate bridge drawings.  For more details ...

The design of continuous prestressed concrete beams is complicated because the prestress sets up secondary moments. These need to be known before the cable can be designed, but cannot be determined until after the profile is known, which is paradoxical. Design of such profiles can thus be a hit and miss affair; guessing a profile, calculating secondary moments and checking if the profile is satisfactory. By developing Low's theory of the "third equation" (Procs ICE, 73, 351-364, 1982), a design procedure has been developed which leads sequentially through design of the cross-section to selection of the prestressing force and finally to determination of the cable profile. Very few assumptions need to be made and the process does not need complicated calculations.

Expert systems have been proposed for many applications. The claim is that by allowing a "knowledge engineer" to interview "domain experts", a system can be designed which will allow a computer to be used to make the decisions for itself. Quality is judged by the number of rules the system contains. Our conjecture is the opposite of that; we believe that the computer should be used to calculate what it can, using logic programming only where decisions have to be made. Quality in our expert system is measured by how few rules the system includes. We have shown that such a system can be applied to the design of continuous prestressed concrete viaducts, using earlier work on the design of the cable profiles.  The picture shows Grangetown Viaduct in Cardiff, designed by Benaim.  It was not designed by our software but is the sort of structure we have analysed.

This project was undertaken with Janet Lees.  It was based on a paper presented at Vancouver in 1993.  This questioned the validity of trying to improve the bond of FRPs to concrete, since this can lead to premature snapping of the tendon.  Instead, we showed that it is better to partially bond the tendons to the concrete, which allows controlled movement.  It is possible to arrange matters so that the beam is almost as strong as a fully-bonded beam, and has the rotation capacity of a beam with unbonded tendons, as shown in the figure on the left.  Various papers have been published on this work.  Experiments; Bond Behaviour; Analysis.

Parallel-lay aramid ropes can be anchored by means of a barrel-and-spike termination, which grips the aramid fibres in an annular ring. Many tests have been carried out to determine the optimum shape and length of the barrel and spike, in association with Linear Composites Ltd. The exact shape of the spike is commercially confidential. Finite element analyses have been performed to model the stress-state as the spike, fibre and barrel are brought into contact and loaded until the fitting is secure. With terminations at both ends of a rope in a tension test, the rope normally breaks away from the termination.

Fibres used in ropes are brittle.  This makes them very susceptible to variability, since if one yarn is weak it will snap, shedding load to its neighbours.  The strength of an assembly is thus less than the sum of the strength of the whole.  This has major impacts on the conversion efficiency that can be achieved.  The work is complicated; quality control in yarn manufactire is important, as is careful assembly of the rope.  Additional slack introduced in assmebly effectively makes the yarns more variable, which in turn reduces the strength even further.  There are also important length effects - in long ropes a broken yarn can pick up load by friction from its neighbours.  The rope can thus be seen as a chain of variable elements, and a weakest link theory applies.  Many papers have been published with Amaniampong, Mills and Flory.

The behaviour of prestressed concrete beams in the vicinity of the anchorage has been investigated by looking at the behaviour of reinforced concrete blocks under patch loads applied to their ends.  Both upper- and lower-bound plasticity models have been used to compare with these results.  As a result we now have better understanding of the behaviour of the concrete in this region.  This work was undertaken by Tim Ibell, now at Bath University and Chris Burgoyne.  Tim has a web page describing the importance of the work.   Three papers have been published; Experimental; plasticity analysis; lower bound analysis.

Gripping FRP rods with conventional wedges causes stress-concentrations which can lead to premature failure of the rods.  By using expansive cements in an annular region between the FRP rod and an external steel tube, the FRP can be anchored without stress-concentrations, which allows the full strength of the rod to be achieved.  Once anchored, the rod can be linked to an external loading system, or coupled to another rod.  This work is a development of that carried out by Harada at the University of Nagasaki in Japan.  A paper describing the method has been published.

Very highly stressed pretensioning wire can be cast centrally into long concrete prisms, which can then be cut into shorter lengths and used as reinforcing bars. This could be a useful of using FRP bars with very high strain capacities, without the need for prestressing on site, since the pretensioning operation could be acrried out at specialist precast factories. There are some limits imposed by the need to prevent the pretenioned rod splitting, and bond must also be assured between the prism and the concrete, but tests have shown that the full strength of pretensioning wire can be utilised at strains normally seen in reinforced concrete structures. This project was undertaken as a final year undergraduate project by Graham Redman. 

To determine the St. Venant's Torsional Stiffness of a cross-section, engineers often assume that the cross-section is made up of a number of flat plates. That approach works well for steel sections, where the flat elements are thin in comparison to their width, but it does not work well for concrete sections where end effects are more important. There are particular problems associated with T-junctions and L-junctions, especially where the section has chamfers. A large proportion of the torsional stiffness comes from the junction. In this work, the stiffness of the junction is calculated separately, which can then be added to that of the adjacent flat plates. The error compared with exact calculations is much reduced, but the method can still be applied by hand calculation. The method is described in a paper which can be used as a design manual.

The Ilyushin Yield surface is frequently used to determine the full plasticity surface for steel plates loaded in tension and bending. Ilyushin's original analysis was too complicated, in the days before computers, so he proposed an approximation. His parametrisation of the surface led to numerical ill-conditioning, so his original analysis has never been used. However, we have shown that if different aparmtrisation is used, the ill-conditioning can be eliminated, so that an exact formulation can be used. The image shows the Ilyushin surface, in Q-space, as a continuous curved surface - the approximation uses two flat surfaces, which cause problems at the intersection, and does not give correct values.