The research, conducted by Ghazi Bahroz Jumaa of the Civil Engineering Department at the University of Garmian in the Kurdistan Region of Iraq, tackles one of the most safety-critical questions in reinforced concrete design: how much shear force can a beam resist before it fails catastrophically? Shear failure is notoriously brittle and sudden, unlike the gradual, warning-giving flexural failure that designers prefer to govern. For beams without stirrups, the closed steel hoops that normally provide shear reinforcement, the entire resistance must come from the concrete itself, making accurate prediction of that resistance a matter of structural life and death.

The heart of the problem lies in the messy, heterogeneous nature of RCA. When old concrete is crushed, each recycled particle is a composite: natural stone wrapped in a layer of adhered mortar that is often weaker, more porous, and riddled with micro-cracks from the crushing process. In a loaded beam, diagonal cracks propagate through the concrete web, and the rough crack faces resist sliding through a mechanism engineers call aggregate interlock. Weaker, more irregular recycled particles interlock less effectively, and the old mortar attached to them introduces additional weak zones. The result is a material whose shear behavior is inherently more variable than that of natural-aggregate concrete, and whose performance depends on the percentage of recycled content, a variable that most established design equations were never formulated to include.

Existing design provisions, such as those in the American Concrete Institute’s ACI 318 code and Europe’s Eurocode 2, were calibrated decades ago on natural-aggregate concrete. When applied to RCA beams, they can be either unconservative or wastefully conservative, and the experimental literature over the past two decades, from studies by Han and colleagues in 2001 through work by Rahal and Alrefaei, Ignjatović and co-workers, and many others, has documented a wide scatter in measured shear strengths. Empirical equations such as the classic Zsutty formulation, dating back to 1971, capture broad trends but struggle with the added complexity of recycled content. This is precisely the kind of nonlinear, multi-variable prediction problem where machine learning has begun to shine.

Jumaa assembled a database of 179 experimental RCA beam specimens drawn from published laboratory studies spanning more than two decades. Each specimen was characterized by the key parameters that govern shear capacity: beam width, effective depth, the shear span-to-depth ratio, the longitudinal reinforcement ratio, the concrete compressive strength, and, crucially, the percentage of recycled concrete aggregate replacing natural stone. The measured shear capacities ranged from small laboratory beams failing at around 12 kilonewtons to massive 400-millimetre-wide specimens carrying more than 860 kilonewtons, giving the models a rich and demanding training landscape.

Five machine learning algorithms were trained and compared under a rigorous validation protocol: k-Nearest Neighbors, Random Forest, Support Vector Machines, Gaussian Process Regression, and Artificial Neural Networks. Rather than relying on a single train-test split, which can flatter a model by luck of the draw, the study employed a 10-fold cross-validation scheme repeated 20 times. In this procedure the data are repeatedly shuffled and divided into ten subsets; the model trains on nine and is tested on the held-out tenth, with the process cycled through all folds and then repeated from scratch twenty times to average out randomness. This is the gold standard for demonstrating that a model’s accuracy reflects genuine learning of underlying physics rather than memorization of individual specimens.

The results were striking. Support Vector Machines emerged as the top performer, achieving a coefficient of determination of 0.933, meaning the model explained more than 93 percent of the variance in measured shear strength, with a root mean square error of 29.98 kilonewtons and a mean absolute error of just 13.08 kilonewtons. Gaussian Process Regression followed closely with an R-squared of 0.912 and the lowest mean absolute error of the trio at 11.81 kilonewtons, while Artificial Neural Networks achieved an R-squared of 0.892. All three outperformed both the newly proposed empirical equations, including a modified Zsutty equation and an ACI 318-style equation incorporating RCA content, and the traditional design codes themselves. Support Vector Machines, which work by mapping inputs into a high-dimensional feature space where a maximum-margin boundary separates the data, proved especially adept at handling the nonlinear interactions between beam geometry, material strength, and recycled content.

Beyond raw accuracy, the study included a parametric analysis that interrogated how the trained models respond when individual variables change, a crucial sanity check for any data-driven engineering tool. The machine learning predictions reproduced physically sensible trends: shear capacity increased with beam depth and width, and decreased as the recycled aggregate content rose, consistent with the known degradation of aggregate interlock in RCA concrete. This alignment between statistical learning and structural mechanics matters enormously, because a black-box model that contradicts physical intuition would be dangerous to trust, no matter how impressive its error metrics appear on paper.

The practical implications reach well beyond the laboratory. As governments worldwide push circular-economy mandates and green building standards, the volume of RCA entering structural applications is set to grow sharply, and the fib Model Code 2020 and the next generation of Eurocode 2 are actively working toward codified design rules for recycled aggregate concrete structures. Reliable predictive tools are the prerequisite for such codification: engineers need confidence that a beam designed with, say, 50 or 100 percent recycled coarse aggregate will carry its intended shear load with the same margin of safety as a conventional beam. A validated machine learning model, trained on nearly two hundred real experiments, offers exactly that confidence, and could inform both code committees drafting new provisions and practitioners evaluating existing structures built with sustainable materials.

The study also fits into a broader movement sweeping through structural engineering, in which data-driven methods complement, and sometimes surpass, hand-derived empirical formulas. Researchers have already applied neural networks and related techniques to predict the shear capacity of fiber-reinforced polymer concrete beams, the compressive strength of lightweight and recycled concretes, and bond strength in reinforced concrete members. What distinguishes the present work is its focus on the specific, under-addressed case of stirrup-free RCA beams and its head-to-head comparison of five algorithms under a demanding cross-validation protocol. As Jumaa notes in the paper, the work represents a step forward in using machine learning to enhance structural engineering, with the potential to make a significant impact in the field of sustainable materials. If the construction industry is to recycle its own waste at scale, it may well need algorithms, as much as new mix designs, to make the resulting structures safe.

Subject of Research: Machine learning prediction of shear strength in reinforced recycled aggregate concrete beams without stirrups

Article Title: Shear strength prediction of reinforced recycled aggregate concrete beams without stirrups using soft computing and empirical methods

Article References: Jumaa, G. B. (2026). Shear strength prediction of reinforced recycled aggregate concrete beams without stirrups using soft computing and empirical methods. Neural Computing and Applications, 38(19), Article 771. https://doi.org/10.1007/s00521-026-12488-z

Image Credits: AI Generated

DOI: 10.1007/s00521-026-12488-z

Keywords: machine learning, recycled concrete aggregate, shear strength, reinforced concrete beams, stirrups, Support Vector Machines, artificial neural networks, Gaussian Process Regression, ACI 318, Eurocode 2, sustainable construction, structural engineering

The research, led by Giorgio Monti of Sapienza University of Rome together with Dario De Domenico of the University of Messina, Qingcong Zeng of Zhejiang University, and Giuseppe Quaranta, also of Sapienza, addresses a deceptively simple question: for a rectangular concrete column facing a known axial load, bending moment, and shear demand, exactly how much transverse reinforcement, the stirrups and cross-ties wrapped around the section, is required? The answer matters because transverse reinforcement does double duty. It confines the concrete core, allowing the section to keep deforming after the outer cover has spalled away, and it acts as the shear-resisting web of an internal truss. More stirrups generally mean more ductility and more shear strength, but the two demands scale differently with axial load, geometry, and the severity of the expected seismic cycling.

The heart of the new framework is a strain-based description of two limit states. The first, called Damage Limitation, marks the point at which the longitudinal tension steel first yields while the concrete cover is still intact. The second, Near Collapse, describes the section at the brink of failure, which can arrive by two distinct routes: rupture of the tension reinforcement, or crushing of the confined concrete core after the cover has spalled. By writing sectional equilibrium and strain compatibility in dimensionless form, the authors derive closed-form expressions for the concrete and steel strains at each of these states, and from those strains they compute the curvature ductility capacity, the ratio of the curvature at Near Collapse to the curvature at Damage Limitation.

What makes the formulation unusual is its branch-exact structure. Depending on whether the compression steel and the compression concrete are in their elastic or plastic ranges, the equilibrium equations resolve into four distinct constitutive branches, each with its own closed-form solution. The method identifies which branch is physically admissible for any given column and selects the corresponding strain solution, so the answer is not an approximation averaged across regimes but an exact solution of the idealized section model. The concrete is treated as a no-tension, bilinear material whose strength and ultimate strain are amplified by confinement, with amplification factors left in a general form so that designers can plug in the provisions of whatever code they follow, including the second-generation Eurocode 2 demonstrated in the paper.

Of course, an exact branch-by-branch solution is a verification tool, not a design shortcut. To make the method usable at a drawing board, the authors introduce compact approximations of the governing strains and then perform something mathematically ambitious: they invert the ductility relationship. Instead of calculating how much ductility a given column has, the equations directly output the transverse reinforcement ratio needed to achieve a prescribed curvature ductility demand. For the practically common case of symmetric longitudinal reinforcement, typical in seismic columns because earthquakes reverse the loading direction, this inversion collapses into a single closed-form expression involving the axial load ratio, the confinement effectiveness coefficients, and the target ductility.

Validation was carried out on two fronts. First, the compact strain expressions were compared against the branch-exact solutions across 57,767 admissible parameter combinations spanning realistic column sizes, reinforcement layouts, and axial load levels. The median absolute error was about one percent, and the vast majority of cases fell within five percent of the exact value, with the largest deviations confined to a small subset of cases governed by an elastic-elastic branch that the compact form does not reproduce. Second, and more decisively, the entire curvature formulation was tested against an independent fiber-section numerical analysis on a random sample of 1,000 mechanically admissible column sections. The branch-exact equations matched the numerical curvatures and ductilities with maximum relative errors below 0.14 percent, and the compact design version reproduced curvature ductility with a mean absolute relative error of about 2.1 percent, with nearly 86 percent of cases within five percent.

The second half of the framework tackles shear through a variable-angle truss model, enhanced by a machine-learning-assisted calibration published by some of the same authors in 2022. In this model, shear capacity is the smaller of two resistances: the force at which the stirrups yield, and the force at which the diagonal concrete strut between cracks crushes. The concrete contribution depends on the aspect ratio of the member, the axial stress, and crucially on the displacement ductility demand, because repeated inelastic cycling degrades the concrete’s ability to carry shear, an effect the model captures through an inverse-square dependence on ductility. The authors also added an extrapolation-control bound so that the machine-learned coefficients are not stretched beyond the experimental database that calibrated them, which included 119 rectangular column tests and 373 beam tests.

The payoff of combining the two models is an explicit map of which requirement governs. Because the final transverse reinforcement is simply the larger of the ductility-controlled and shear-controlled values, the designer can see analytically where the transition occurs, and the transition is anything but intuitive. Increasing the axial load makes the ductility problem worse: it reduces curvature ductility capacity, so more confinement steel is needed. Yet the same axial load, normalized over the gross section, strengthens the concrete shear strut and reduces the reinforcement demanded by shear. In the paper’s worked example, the two curves cross at an axial load ratio of roughly 0.25; below that value the design is shear-governed, above it the design is ductility-governed. No sequential checking procedure reveals this competition so cleanly.

The authors are careful about boundaries. The closed-form ductility inversion applies only within a formally defined domain where the assumed sequence of limit-state events holds, and the shear inversion is valid only within the calibration ranges of the underlying truss model, with strut inclination parameters between one and five. The formulation addresses solid rectangular sections under uniaxial bending and does not cover biaxial response, torsion, or the progressive deterioration of cover spalling during cyclic loading. The curvature ductility demand and the displacement ductility demand that feed the two halves of the procedure are distinct quantities, and the paper stresses that they must be derived consistently from the preceding structural analysis rather than through any universal conversion.

Even within those limits, the study offers something the field has lacked: a direct, mechanically interpretable design equation for the reinforcement that must simultaneously deliver deformation capacity and shear resistance in earthquake-exposed columns. Because every quantity is dimensionless, the influence of each parameter, axial load, confinement effectiveness, steel ratio, geometry, is visible in the algebra rather than buried in iteration. The authors point toward extending the framework to asymmetric reinforcement layouts, biaxial loading, and richer experimental validation, but the immediate message is already striking. Two requirements that codes have long kept in separate chapters can, with the right mathematics, be solved together, exactly, and on a single sheet of paper.

Subject of Research: Analytical design of transverse reinforcement in reinforced concrete columns for simultaneous ductility and shear requirements under seismic loading

Article Title: Simultaneous analytical design of ductility and shear capacity in reinforced concrete columns

Article References: Monti, G., De Domenico, D., Zeng, Q., & Quaranta, G. (2026). Simultaneous analytical design of ductility and shear capacity in reinforced concrete columns. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02682-8

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02682-8

Keywords: reinforced concrete, seismic design, ductility, shear capacity, transverse reinforcement, confinement, curvature ductility, columns, earthquake engineering, closed-form equations, structural analysis, Eurocode 2

The research, published in Results in Engineering by Johannes Rathgen and Vincent Oettel of the iBMB Division of Concrete Construction, tackles a problem that has haunted bridge engineers for decades. Shear failure is among the most treacherous failure modes in structural concrete: unlike ductile flexural failure, which announces itself through large deflections and visible sagging, shear failure typically arrives suddenly and without significant warning, governed by the unstable propagation of diagonal cracks inclined toward the load. Design codes handle this uncertainty conservatively, and analyses of extensive experimental databases show that current approaches can substantially overestimate the danger for beams with little or no shear reinforcement. The German team’s calculations, for instance, underestimated the measured failure loads of three low-reinforced beams by factors approaching 1.85, confirming that the true reserve of these structures is often much larger than the codes admit. Monitoring, the authors argue, can unlock that reserve safely by revealing how a structure actually behaves under load.

To test that idea, the researchers cast six reinforced concrete beams spanning a deliberate range of shear reinforcement ratios, from one beam with no stirrups at all to others provided with between 1.3 and 8.1 times the minimum ratio required by the German National Annex to Eurocode 2. All beams used normal-strength concrete with a maximum aggregate size of 16 millimeters, B500B steel bars of 20 millimeters as longitudinal reinforcement, and B500A stirrups of 6 and 8 millimeters. Each beam was loaded to failure in three-point bending, with the load applied at midspan and a shear span of 90 centimeters, deliberately chosen to prevent direct load transfer to the supports. The material properties were carefully characterized on the day of testing: mean cylinder compressive strengths ranged from 36.3 to 56.5 newtons per square millimeter, and mean yield strengths of the reinforcement were determined by tensile testing according to EN ISO 15630-1.

The instrumentation was the heart of the experiment. The team used a LUNA ODiSI 6104 interrogator working on the principle of optical frequency domain reflectometry, a technique that turns a single polyimide-coated optical fiber into thousands of distributed strain measurement points with a gage pitch of just 0.65 millimeters, acquired at 1 hertz. Two contrasting sensor configurations were compared in the shear-critical regions near the supports. In one region, the fiber was bonded in an inclined loop at 45 degrees, aligned with the principal tensile stresses of the uncracked beam so that emerging shear cracks would cross it nearly perpendicularly. In the other region, the fiber ran in three horizontal sections parallel to the beam’s bottom surface, spaced 6 centimeters vertically. The horizontal layout is far simpler to install and requires no prediction of the expected crack pattern, but it sacrifices some sensitivity because inclined cracks intersect it at oblique angles. To keep the fragile fibers alive through large crack openings, the researchers bonded them with a slightly elastic UV-curing resin, allowing controlled debonding instead of catastrophic fiber breakage.

The results were striking. In the beam without shear reinforcement, which failed at 145 kilonewtons, the inclined sensor detected the critical shear crack at approximately 76 percent of the failure load and pinpointed its position to within a centimeter at sensor coordinate 8.2 centimeters. Continued loading produced a pronounced and largely continuous rise in measured strain, an unmistakable early indication of impending failure. In the beams with low shear reinforcement, the picture was even more encouraging: the crack that ultimately governed failure was first flagged at 58 percent of the ultimate load in one beam, 52 percent in another, and 77 percent in a third with an asymmetric stirrup arrangement. The team condensed these observations into a shear-failure warning index, defined as the ratio of the detection load to the failure load, offering a quantitative measure of how much warning a monitoring system can realistically provide before brittle collapse.

Perhaps the most consequential finding concerns what happens after the load is removed. Because bridge inspections are performed under service loads rather than at the extreme levels that may have formed cracks, many shear cracks close up and become invisible to the naked eye. The fiber optic measurements, however, reliably detected and localized cracks even after they had largely closed upon unloading. This means the sensors can supply a structural record that visual inspection cannot, capturing evidence of past cracking events that would otherwise vanish. For the vast population of older bridges that show no visible distress despite calculated shear deficits, this capability could fundamentally change how condition assessments are made, replacing worst-case assumptions with measured structural response.

The study also revealed that detecting cracks is the easy part; classifying them is the real challenge. Flexural cracks form roughly perpendicular to the beam axis, while shear cracks incline at around 45 degrees, but a crack that begins as a benign flexural crack can gradually rotate and develop into the critical flexural-shear crack that destroys the beam. In one test, the top horizontal sensor section registered a crack at 63 percent of the failure load that looked entirely flexural; only when a rapidly propagating shear crack merged with it did the fatal crack emerge, becoming detectable in the lower sections at 77 to 79 percent of the failure load. The researchers therefore propose a conceptual two-step classification procedure: first, estimate crack inclination from the pattern of strain peaks across adjacent, closely spaced sensor sections of a loop-shaped fiber; second, track potentially critical cracks near the supports over successive load levels, watching for continuous strain growth that signals dangerous propagation.

That classification framework, the authors emphasize, remains a concept rather than a validated method, but it points toward something genuinely transformative: an automated, condition-based early warning system for shear-deficient bridges. Combined with predefined warning and action levels, the approach could drive a traffic-light scheme in which green indicates all measured strains remain within expected ranges, yellow triggers additional assessment, and red demands prompt investigation, weight restrictions, or closure. A fixed strain threshold of 1 per mille proved suitable under laboratory conditions for separating crack-induced strain peaks from measurement noise, and its simplicity makes it attractive for automated data evaluation, though the researchers caution that it is a configuration-specific criterion whose robustness under field conditions, varying materials, and environmental exposure still requires validation.

The broader implications reach well beyond the laboratory. Strengthening a deficient bridge with ultra-high performance concrete overlays or carbon fiber reinforced polymer strips demands long planning lead times, temporary closures, and considerable expense, while wholesale replacement is simply infeasible given limited personnel, machinery, and materials. Distributed fiber optic sensing, by contrast, can be installed on existing structures with minimal intervention and no major structural modification, enabling both long-term and large-scale monitoring of the regions where shear failure would begin. The study also found that sensor placement matters more than orientation: multiple horizontal sensor sections stacked near the support, particularly the lowest section in the tension zone, caught cracks earlier than expected, and the horizontal configuration avoids the complex principal-stress trajectory calculations that the inclined layout demands. Notably, no clear relationship emerged between the crack-to-fiber intersection angle and early detection performance, weakening the case for the more elaborate inclined installations.

Laboratory beams are not bridges, and the authors are careful about the limits of their work. Only four of the six tests ended in shear failure, some measurement data were lost to a defective remote module and sensor damage, and the findings apply strictly to the tested configurations and loading conditions. Long-term and variable loading, environmental effects, and full-scale field trials remain necessary before the method can be trusted on live structures. The Braunschweig team is already extending the work to haunched beams, whose tapered support regions alter the stress distribution and crack patterns in ways that complicate sensor placement. Still, the core message stands: light traveling through a fiber thinner than a human hair can reveal the silent, invisible cracks that precede one of structural engineering’s most sudden failure modes, and in doing so may help keep thousands of aging bridges open safely while the slow work of renewal catches up.

Subject of Research: Monitoring shear crack formation in reinforced concrete beams using distributed fiber optic sensors

Article Title: Experimental investigation of fiber optic sensors in shear-critical regions of reinforced concrete beams for monitoring shear behavior

Article References: Experimental investigation of fiber optic sensors in shear-critical regions of reinforced concrete beams for monitoring shear behavior. (n.d.). https://doi.org/10.1016/j.rineng.2026.113052

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113052

Keywords: fiber optic sensors, structural health monitoring, reinforced concrete, shear failure, bridge assessment, distributed fiber optic sensing, crack detection, Eurocode 2, shear reinforcement, concrete beams, early warning system, TU Braunschweig