107 results found
Afshan S, Yu JBY, Standing JR, et al., 2017, Ultimate capacity of a segmental grey cast iron tunnel lining ring subjected to large deformations, TUNNELLING AND UNDERGROUND SPACE TECHNOLOGY, Vol: 64, Pages: 74-84, ISSN: 0886-7798
Einpaul J, Vollum RL, Ramos AP, 2017, On the distribution of shear forces in non-axisymmetric slab-column connections, Pages: 841-848
© Springer International Publishing AG 2018. The majority of punching tests, based on which the provisions for slab-column connections in design codes are developed, were performed on symmetric test specimens where the support reaction was centric with respect to the supported area. However, most slab-column connections in practice are subjected to asymmetric loading. This may lead to non-uniform distribution of bending moments, deformations and shear forces on a control perimeter around the column or transfer of bending moments between the slab and the column. A non-linear finite element approach was developed in this research to investigate the distribution of internal forces around the columns in non-axisymmetric connections. The focus of this paper is on analyzing the interaction between redistributions of bending moments and shear forces while maintaining the equilibrium of internal forces in the slab. Selected test specimens from the literature were modelled with different types of asymmetric loading. The modelling results show that shear redistribution along the perimeter of the connection, which would lead to a more uniform shear distribution, is possible only in certain cases depending on the bending moments and flexural capacity of the slab. It is also shown that uneven distribution of shear forces can also occur in connections with no eccentricity, being related to the non-linear flexural behavior of the slab. The results obtained from the analyses are compared to the approaches suggested in the design codes or by other authors.
Micallef M, Vollum R, 2017, The Effect of Shear and Lap Arrangement on Reinforcement Lap Strength, Structures, Vol: 12, Pages: 253-264
© 2017 Institution of Structural Engineers The paper is concerned with the design of tension laps in reinforced concrete structures. The most recent design recommendations for laps are found in fib Model Code 2010 which is likely to influence the next revision of EN-1992. This is of concern to UK industry since laps designed to Model Code 2010 can be significantly longer than laps designed to EN-1992 which UK designers already consider excessive compared with previous UK code requirements. Unlike the previous UK code, BS8110, EN-1992 requires adjacent laps to be offset by 0.3 of the lap length which complicates reinforcement detailing. The paper describes an experimental programme which was undertaken to assess the influence on lap performance of increasing lap length beyond that required for bar yield, shear and staggering of laps. The influence of shear was assessed by comparing the performance of laps of the same length positioned in zones of uniform and varying bending moment. Reinforcement strains were monitored and detailed measurements of crack development and crack widths were obtained with digital image correlation. Results show that very long laps are inefficient with the central half contributing little to force transfer between bars. Shear was found to have no significant influence on lap strength while lapping only 50% of bars at a section increased forces in the lapped bars leading to premature bond failure. Test results are compared with EN-1992 predictions, which are shown to be conservative for the tested laps.
Micallef M, Vollum RL, 2017, The behaviour of long tension reinforcement laps, Magazine of Concrete Research, ISSN: 0024-9831
Over time, the length of reinforcement laps required by design standards has increased significantly. By way of illustration, fib Model Code 2010 can require over twice the lap length required by the superseded UK code BS8110:1997. The need for this increase is debatable since, outside the laboratory, there is no evidence that laps designed to BS8110 are unsafe. The paper describes an experimental programme which was undertaken to compare failure modes of beams with laps of varying length loaded in four point bending. Tested laps are classified as “short”, “long” and “very long” with “long” laps just sufficient to develop reinforcement yield. The “very long” laps were between 1.5 and 2.0 times the length of the “long” laps. Tested laps were between bars of equal as well as mixed diameter with diameters ranging between 16 mm and 25 mm. Instrumentation included strain gauges and digital image correlation which was used to record crack development. Bond failure was very sudden and brittle in “short” laps. The failure modes of both “long” and “very long” laps were ductile due to flexural reinforcement yield. However, bond failure occurred subsequent to yield in “long” laps including at least one 25 mm diameter bar.
Micallef M, Vollum RL, Izzuddin BA, 2017, Investigating the need for long laps in reinforced concrete elements, Pages: 1549-1557
© Springer International Publishing AG 2018. The current Eurocode 2 (EN 1992-1-1) detailing rules can lead to considerably greater lap and anchorage lengths than previous design recommendations such as the superseded British Standard BS 8110-1. Moreover, fib Model Code 2010 (MC 2010) requires even longer laps than EN 1992-1-1. This research is motivated by complaints from industry that designing to the current EN 1992-1-1 detailing rules leads to numerous construction issues such as reinforcement congestion, as well as cost and sustainability implications, with no apparent justification. This paper presents the experimental programme which was conducted by the authors with a view to justifying reduced lap lengths more commensurate with previously proven UK experience. To this end, a series of three point bending (3PB) and four point bending (4PB) tests were designed and tested in the Structures Laboratory at Imperial College London to investigate bond stress distributions along laps of different lengths consisting of lapped reinforcing bars of the same or different bar diameters. In particular, experiments were aimed at quantifying the effectiveness of very long laps in transferring forces between two lapped bars. The 3PB tests were aimed at investigating whether anchorage capacity of laps is enhanced at high shear locations.
Micallef M, Vollum RL, Izzuddin BA, 2017, Crack development in transverse loaded base-restrained reinforced concrete walls, ENGINEERING STRUCTURES, Vol: 143, Pages: 522-539, ISSN: 0141-0296
Micallef M, Vollum RL, Izzuddin BA, 2017, Cracking in walls with combined base and end restraint, MAGAZINE OF CONCRETE RESEARCH, Vol: 69, Pages: 1170-1188, ISSN: 0024-9831
Pamplona MKY, Ferreira MP, Vollum RL, 2017, Bearing capacity of partially loaded concrete elements, Pages: 604-611
© Springer International Publishing AG 2018. There are numerous situations where compressive loads are introduced into members over small areas. The stress distribution in these zones, which are depicted D for disturbed, is non-uniform. The flow of compressive stresses into the surrounding member induces transverse tensile stresses which can cause premature splitting failures. D regions are typically designed using the strut-and-tie method (STM). The STM design recommendations provided by ACI 318(2014), fib Model Code (2010) (2013) and Eurocode 2(2004), limit bearing stresses to admissible values which depend on a strut efficiency factor (β s ). This paper uses a database with 162 tests on partially loaded concrete prisms without and with crack-control reinforcement to evaluate these provisions and to discuss the influence of parameters like the concrete strength (f c ), the crack-control reinforcement ratio (p), concentration ratio (b/a) and aspect ratio (h/b). It also presents results of four tests on diamond-shaped concrete prisms carried out to evaluate the effect on resistance of increasing p. Experimental results show that crack-control reinforcement increases both ductility and resistance. Existing design provisions are shown to be conservative.
Setiawan A, Vollum R, Macorini L, 2017, Nonlinear finite element analysis of reinforced concrete flat slabs subjected to reversed-cyclic loading, Pages: 814-822
© Springer International Publishing AG 2018. Flat slabs are only permitted to be used as gravity-load carrying systems in regions of high seismicity because of poor resistance to lateral deformation and punching shear under reversed cyclic loading. This paper considers the influence of reverse cyclic loading on the punching resistance of internal slab column connections without shear reinforcement. Currently, ACI 318-14 determines the deformation capacity of slab-column connections using a best-fit line based on test data from relatively thin slabs, with average thickness of 110 mm, and flexural reinforcement ratios of around 1%. Consequently, the ACI 318-14 (2014) design recommendations require further validation for slab thicknesses and reinforcement ratios outside this range. A possible tool for doing this is the mechanically-based critical shear crack theory (CSCT) of Muttoni (2008). The model is based on considerations of equilibrium and kinematics for an isolated axis-symmetrical slab. The model gives good predictions of punching resistance under concentric loading but its applicability to the design of flat slabs subject to reversed-cyclic loading requires further consideration. The paper presents the results of a parametric study which was carried out with the finite element program ATENA (Cervenka et al. 2007) in order to obtain an improved understanding of the influence of cyclic degradation on punching resistance. Maximum slab rotations are shown to increase under cyclic loading with a consequent degradation in unbalanced moment resistance and ultimate slab rotation. This finding is consistent with the predictions of the CSCT.
Vella JP, Vollum R, Jackson A, 2017, Headed bar connections between precast concrete panels loaded in bending, Pages: 989-997
© Springer International Publishing AG 2018. As part of a wider study into headed bar connections, this research concerns tests on precast concrete specimens connected by means of a joint developed and patented by Laing O'Rourke, known as the "E6 joint". The joint consists of lapped headed bars that, along with additional vertical shear studs and transverse bars used as confining reinforcement, allow a narrow joint width of only 200 mm to be used. The first part of this research included testing of small scale joint specimens subjected to direct tension, while the specimens presented here are tested in flexure. Variables tested include; the concrete strength in the joint, vertical misalignment of the precast panels, and absence of shear studs. Results show that tests in bending achieve a higher ultimate capacity than calculated from strengths of corresponding direct tension tests, whilst showing similar failure mechanisms. The experimental results are used to validate a three dimensional non-linear finite element model (NLFEM) of the joint. A strut-and-tie model (STM) used to determine the E6 joint design strength has been found previously to give safe predictions for specimens in tension whilst not fully capturing the observed joint behaviour. The STM gives even more conservative results for specimens in bending. The results presented in this paper will be used in future research to further optimise the joint design and reduce the degree of conservatism associated with the design model.
Vella JP, Vollum RL, Jackson A, 2017, Investigation of headed bar joints between precast concrete panels, Engineering Structures, Vol: 138, Pages: 351-366, ISSN: 0141-0296
© 2017 Elsevier Ltd The paper addresses the design and behaviour of narrow cast in-situ joints between precast concrete elements in which continuity of reinforcement is achieved through overlapping headed bars. Using headed bars minimises the lap length required within the cast-in-situ joint region. Confining reinforcement in the form of transverse bars and vertical shear studs is also installed in the joint. The paper describes a series of tensile tests which were carried out to simulate the tensile zone of a joint loaded in pure flexure. The headed bars used in the tests were 25 mm in diameter with 70 mm square heads and yield strength of 530 MPa. The tests studied the influences of concrete strength, headed bar spacing, splice length, transverse reinforcement and confining shear studs on joint strength. A lap length of 100 mm in concrete with 28 MPa cylinder strength was found to be sufficient to develop the full strength of the headed bars. A strut-and-tie model (STM) is presented for determining joint strength. Analysis shows that the STM gives safe results even though it does not fully capture the observed joint behaviour. An upper bound plasticity model is found to give relatively good predictions of joint strength in most cases, although it also does not always capture the correct failure mechanism. The tests provide insights into joint behaviour which, in conjunction with numerical modelling, will facilitate the development of an improved design method. Widespread use of this system would lead to improvements in buildability, sustainability and health and safety in the construction of concrete structures.
Vella JP, Vollum RL, Jackson A, 2017, Numerical modelling of headed bar joints subjected to tension, Magazine of Concrete Research, Vol: 69, Pages: 1027-1042, ISSN: 0024-9831
Vella JP, Vollum RL, Jackson A, 2017, Flexural behaviour of headed bar connections between precast concrete panels, Construction and Building Materials, Vol: 154, Pages: 236-250, ISSN: 0950-0618
© 2017 Elsevier Ltd The use of headed bars in joints between precast concrete elements allows continuity of reinforcement to be achieved over very short splice lengths. The paper describes a series of flexural tests carried out on specimens consisting of pairs of precast elements connected by overlapping headed bars of 25 mm diameter. The headed bars overlapped by 100 mm within a 200 mm wide in situ concrete joint in which transverse bars and vertical shear studs were installed to provide confinement. This type of joint facilitates the construction of continuously reinforced slabs from precast elements thereby enabling significant reductions in overall construction time and improvements in construction quality due to off-site fabrication. The tests investigated the influence on joint strength, ductility and crack width of concrete strength, out-of-plane offset of precast planks and confining shear studs. Ductile failure with yield of 25 mm diameter high strength headed bars was achieved with joint concrete having a cylinder compressive strength of 39 MPa. A nonlinear finite element model is presented, which gives good predictions of joint strength as well as providing insight into joint behaviour.
Yu J, Standing J, Vollum R, et al., 2017, Experimental investigations of bolted segmental grey cast iron lining behaviour, TUNNELLING AND UNDERGROUND SPACE TECHNOLOGY, Vol: 61, Pages: 161-178, ISSN: 0886-7798
Albuquerque NGB, Melo GS, Vollum RL, 2016, Punching shear strength of flat slab-edge column connections with outward eccentricity of loading, ACI Structural Journal, Vol: 113, Pages: 1117-1129, ISSN: 0889-3241
Copyright © 2016, American Concrete Institute. All rights reserved. Thirteen tests were carried out to investigate the effect of outwards eccentricity on the punching resistance of flat slab edge column connections. The slabs measured 2350 x 1700 mm (92.5 x 66.9 in.) on plan and were 180 mm (7.1 in.) thick. One end of the slab was supported on a 300 mm (11.8 in.) square column with a boot at its base for imposition of eccentricity. The other end was supported on a fixed roller support that extended across the full slab width of 1700 mm (66.9 in.). Four point loads were applied to the unsupported slab edges. The tested variables were eccentricity and the areas of flexural, shear, and torsion reinforcement. Presented test results include reinforcement strains, displacements, rotations, crack patterns, failure modes, and ultimate loads. The ACI 318 design procedure for punching shear at edge columns with outwards eccentricity is shown to be overly conservative unless the interaction between punching shear and unbalanced moment is reduced as permitted by the code. The EC2 design procedure is unsatisfactory and a modification is proposed.
Soares LFS, Vollum RL, 2016, Influence of continuity on punching resistance at edge columns, Magazine of Concrete Research, Vol: 68, Pages: 1225-1239, ISSN: 0024-9831
© 2016 ICE Publishing: All rights reserved. The paper considers punching failure at edge columns of reinforced concrete flat slabs without shear reinforcement and unbalanced moments about an axis parallel to the slab edge. Edge column punching shear tests have been carried out on a variety of isolated and continuous specimens. The influence of eccentricity and continuity on punching resistance is assessed using existing experimental data, non-linear finite-element analysis and the critical shear crack theory as implemented in fib Model Code 2010 (MC2010). Relating punching resistance to the elastic unbalanced moment as done in MC2010 levels I to III is shown to be overly conservative for continuous slabs. The ACI 318 and Eurocode 2 practice of making the design punching resistance independent of the unbalanced moment is reviewed and shown to be reasonable, particularly for continuous slabs.
Amini Najafian H, Vollum RL, 2015, Closed-form analytical solution procedure for element design in Dregions, Numerical Methods in Civil Engineering, Vol: 1, Pages: 1-15
This paper presents a novel procedure for solving the equations system of the rotating crack model used for reinforced concrete. It is implemented in the programme NonOPt where it is used to optimise the reinforcement design of D regions. The procedure is based on solving explicit closed-form relations without the need to incrementally increase the applied loads. The solution procedure is based on a secant modulus approach and is developed initially on the basis that the stress-strain response of the steel and concrete is linearly elastic. Subsequently the effect of material nonlinearities is included and the solution procedure is adapted accordingly. A reinforcement design procedure for membrane elements is described along with some case studies. The design procedure minimises the amount of reinforcement required to satisfy predefined design constraints. Material nonlinearities are taken into account, stress and strain compatibilities are satisfied and the design considers both the ultimate and serviceability limit states through the application of appropriate design constraints.
Bilbao A, Izzuddin BA, Vollum RL, 2015, Enhanced nonlinear analysis of three-dimensional concrete structures using damage plasticity modelling, ISSN: 1759-3433
© Civil-Comp Press, 2015. This paper presents an improved numerical procedure for the nonlinear analysis of three-dimensional continuum concrete structures employing damage-plasticity constitutive modelling. Previous convergence difficulties when performing singlestep return mappings for larger strain increments necessitated resorting to substepping methods, at the cost of a greater computational expense when calculating the consistent algorithmic tangent stiffness. Quadratic convergence rate at the global level while maintaining the single-step return scheme for the constitutive model is achieved here with a potential reduction in the number of simultaneous equations and with the utilisation of a basic line search technique for particular cases. Initial singularity of the Jacobian matrix is thereby avoided, ensuring a reduction in the convergence measure towards the converged solution. The improved robustness of the enhanced algorithm is confirmed, and its performance at larger scale is demonstrated through two benchmark application examples.
Bilbao AB, Izzuddin BA, Vollum RL, 2015, Enhanced nonlinear analysis of three-dimensional concrete structures using damage plasticity modelling, ISSN: 1759-3433
©Civil-Comp Press, 2015. This paper presents an improved numerical procedure for the nonlinear analysis of three-dimensional continuum concrete structures employing damage-plasticity constitutive modelling. Previous convergence difficulties when performing single-step return mappings for larger strain increments necessitated resorting to sub-stepping methods, at the cost of a greater computational expense when calculating the consistent algorithmic tangent stiffness. Quadratic convergence rate at the global level while maintaining the single-step return scheme for the constitutive model is achieved here with a potential reduction in the number of simultaneous equations and with the utilisation of a basic line search technique for particular cases. Initial singularity of the Jacobian matrix is thereby avoided, ensuring a reduction in the convergence measure towards the converged solution. The improved robustness of the enhanced algorithm is confirmed, and its performance at larger scale is demonstrated through two benchmark application examples.
Goodchild CH, Morrison J, Vollum RL, 2015, Strut-and-tie models: How to design concrete members using strut-and-tie models in accordance with Eurocode 2, Publisher: MPA The Concrete Centre
Soares LFS, Vollum RL, 2015, Comparison of punching shear requirements in BS 8110, EC2 and MC2010, Magazine of Concrete Research, Vol: 67, Pages: 1315-1328, ISSN: 0024-9831
This paper compares design provisions for punching shear at internal columns in the superseded British Standard BS 8110, Eurocode 2 (EC2) and fib Model Code 2010 (MC2010). MC2010 is based on the critical shear crack theory proposed by Muttoni, which relates shear resistance to the width of the so-called 'critical shear crack' which depends on slab rotation. Parametric studies are presented that show BS 8110 to require significantly less shear reinforcement within 1·5d (where d is the slab effective depth) of the loaded area than EC2 and MC2010, both of which have been extensively calibrated against test data. This raises the question of whether flat slabs designed to BS 8110 have an adequate factor of safety against punching failure. This question is explored using nonlinear finite-element modelling in conjunction with MC2010 Level IV. It is shown that punching resistance at internal columns can be increased significantly by restraint from the surrounding slab but the strength increase is variable and, in the case of uniformly loaded slabs, already largely included in BS 8110 and EC2.
Standing JR, Potts DM, Vollum R, et al., 2015, Investigating the effect of tunnelling on existing tunnels, Underground Design and Construction Conference, Publisher: IOM3, Pages: 301-312
A major research project investigating the effect of tunnelling on existing tunnels has beencompleted at Imperial College London. This subject is always of great concern during theplanning and execution of underground tunnelling works in the urban environment. Many citiesalready have extensive existing tunnel networks and so it is necessary to construct new tunnels ata level beneath them. The associated deformations that take place during tunnelling have to becarefully assessed and their impact on the existing tunnels estimated. Of particular concern is theserviceability of tunnels used for underground trains where the kinematic envelope must not beimpinged upon. The new Crossrail transport line under construction in London passes beneathnumerous tunnels including a number of those forming part of the London Underground network
Standing JR, Potts DM, Vollum R, et al., 2015, Research into the effect of tunnelling on existing tunnels, Pages: 515-520
© The authors and ICE Publishing: All rights reserved, 2015. Increasing demands for providing transport systems in the urban environment has led to many tunnelling projects being undertaken worldwide. Many of the cities where new tunnels are to be constructed already have a comprehensive underground network of tunnels for both transport and services. New tunnels often have to be aligned beneath these and frequently there are concerns that their construction may cause unacceptable deformations of Ibe existing tunnels, potentially hindering their serviceability and in the extreme threatening their stability. The Crossrail project, currently underway in London, involves tunnelling beneath numerous existing tunnels. It therefore has provided a great opportunity to study this complex boundary value problem. This paper describes the philosophy behind a comprehensive research project, run in conjunction with the Crossrail construction, which has an emphasis on the response of older tunnels lined with grey cast iron segments. There is a focus on how the Central Line tunnels responded to new twin tunnel construction beneath them. The five main strands of the research arc: field monitoring within and around the existing tunnels; numerical analyses of the field conditions; structural testing of a half-scale grey cast iron segmental ring; numerical analyses of the ring and two-segment tests performed; advanced laboratory testing of London Clay samples taken during installation of field instrumentation. These activities link into each other. Some preliminary results are presented and the main finding to date arc summarised.
Vollum RL, 2015, Concrete design guide No. 4: An introduction to strut-and-tie modeling, Structural Engineer, Vol: 93, Pages: 36-41, ISSN: 1466-5123
Strut-and-tie modeling is a simple method of modeling complex stress patterns in reinforced concrete as triangulated models. It is based on the same truss analogy as the design for shear in Eurocode 21 and can be applied to many elements, but is particularly useful where normal beam theory does not apply, or in places where plane sections do not remain plane, such as in deep beams, corbels and pile caps. EC2 provides information about the use of strut-and-tie modeling, which can be useful for engineers who want to take advantage of this useful analysis method.
Vollum RL, Fang L, 2015, Shear enhancement near supports in RC beams, Magazine of Concrete Research, Vol: 67, Pages: 443-458, ISSN: 0024-9831
Shear strength is enhanced within the short shear span of reinforced concrete beams that are loaded on their upper side within a distance of around 2-2·5d of supports (where d is the beam effective depth). Eurocode 2 and fib Model Code 2010 (MC2010) account for this by reducing the design shear force, unlike the previous UK code BS 8110, which increases the shear resistance provided by concrete. Eurocode 2 and MC2010 also allow shear enhancement to be modelled using strut-and-tie models. Very few test data are available to assess the comparative merits of these approaches for the design of beams with multiple point loads within 2d of supports. Consequently, 12 beams were tested to investigate the influence of loading arrangement on shear resistance. Comparisons are made between the strengths of the tested beams and the predictions of BS 8110, Eurocode 2, MC2010, strut-and-tie modelling and nonlinear finite-element analysis. Significantly, the BS 8110 approach of enhancing shear resistance is found to give better strength predictions than the load reduction methods of Eurocode 2 and MC2010. Accuracy of the non-linear finite-element analysis and strut-and-tie model is broadly comparable, but the former requires calibration, unlike the latter.
Yu J, Standing J, Vollum R, et al., 2015, Stress and strain monitoring at Tottenham Court Road Station, London, UK, Proceedings of the Institution of Civil Engineers - Structures and Buildings, Vol: 168, Pages: 107-117, ISSN: 0965-0911
Ferreira MP, Melo GS, Regan PE, et al., 2014, PUNCHING OF RC FLAT SLABS WITH DOUBLE HEADED SHEAR REINFORCEMENT, ACI Structural Journal, Vol: 111, Pages: 363-374
Twelve slabs, of which eleven contained double-headed studs as shear reinforcement, were tested supported by central column and loaded concentrically. Their behaviour is described in terms of deflections, rotations, strains of the concrete close to the column, strains of the flexural reinforcement across the slab width and strains of the studs. All the failures were by punching, in most cases within the shear reinforced region. The treatments of punching resistance in ACI 318, Eurocode 2 and the Critical Shear Crack Theory are described and their predictions are compared with the results of the present tests and 39 others from the literature. The accuracy of predictions improved from ACI 318 to EC2 to CSCT, i.e. with increasing complexity. However the CSCT's assumptions about behaviour are not well supported by the experimental observations.
Goodchild C, Vollum R, Webster R, 2014, Improving the L/d method, Pages: 248-251
© 2014, Universities Press (India) Private Limited. All rights reserved. The span-to-effective-depth method (L/d method) is a very popular way of verifying the of limit state of deformation, which is often critical to commercial viability in commercial structures. Yet there have been many comments in the UK relating to the soundness of the L/d method given in Section 7.4.2 of Eurocode 2 (EN 1992-1-1) and repeated in Section 220.127.116.11.4 of Model Code 2010. This paper describes how background work has informed interpretation of the rigorous method of determining deflection to allow a spreadsheet to be written and be used to generate data, which were compared to data for the current L/d method and for a proposed modification of the current L/d method. However correlation of the methods is not good. Further work is considered necessary in order to address discrepancies and provide a practical method of verifying the limit state of deflection with greater confidence.
Vollum RL, Fang L, 2014, Shear enhancement in RC beams with multiple point loads, Engineering Structures, Vol: 80, Pages: 389-405, ISSN: 0141-0296
© 2014 Elsevier Ltd. Eurocode 2 (EC2) allows short shear spans in reinforced concrete beams with loads near supports to be designed using either its shear provisions or strut and tie models (STM). In the case of beams with loads applied on their upper side within a distance a v ≤. 2. d from the edge of supports, EC2 allows the contribution of these loads to the design shear force to be reduced by the multiple β=. a v /2. d≥. 0.25 (where d is the beam effective depth). Conversely, the previous UK code BS8110 increases the shear resistance provided by the concrete within 2. d of supports to v c /. β (in which v c is the concrete shear resistance in MPa) up to a maximum shear resistance of 0.8fcu or 5. MPa. The two methods are only equivalent for beams without shear reinforcement and single point loads within 2. d of supports. However, there is a lack of test data to assess the comparative merits of the two methods and STM for beams with multiple point loads within 2d of supports. Therefore, twelve beams were tested with up to two point loads within 2. d of supports. Significantly, BS8110 is found to give better estimates of shear resistance than the EC2 shear provisions. STM gives good predictions of shear resistance if strut strengths are calculated in accordance with the recommendations of the modified compression field theory (MCFT) but some unsafe predictions are obtained when using EC2 strut strengths.
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