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	<title>reinforced concrete columns &#8211; Science</title>
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	<title>reinforced concrete columns &#8211; Science</title>
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		<title>Basalt Fiber Wraps Give Aging Concrete Columns a Seismic Second Life</title>
		<link>https://scienmag.com/basalt-fiber-wraps-give-aging-concrete-columns-a-seismic-second-life/</link>
		
		<dc:creator><![CDATA[Beatrice Stafford]]></dc:creator>
		<pubDate>Thu, 01 Oct 2026 16:11:11 +0000</pubDate>
				<category><![CDATA[Earth Science]]></category>
		<category><![CDATA[basalt fiber]]></category>
		<category><![CDATA[Basalt fiber reinforced concrete columns]]></category>
		<category><![CDATA[basalt fiber wrap for concrete reinforcement]]></category>
		<category><![CDATA[cost-effective earthquake retrofit solutions]]></category>
		<category><![CDATA[cyclic loading]]></category>
		<category><![CDATA[disturbed stress field model]]></category>
		<category><![CDATA[ductility]]></category>
		<category><![CDATA[durability of basalt fiber in structural applications]]></category>
		<category><![CDATA[Earthquake engineering]]></category>
		<category><![CDATA[earthquake-resistant structural upgrades]]></category>
		<category><![CDATA[energy dissipation]]></category>
		<category><![CDATA[finite element analysis]]></category>
		<category><![CDATA[flexure-controlled columns]]></category>
		<category><![CDATA[FRP]]></category>
		<category><![CDATA[full-scale testing of basalt fiber wraps]]></category>
		<category><![CDATA[hybrid BFC-FRP system for seismic resilience]]></category>
		<category><![CDATA[improving ductility and energy dissipation in concrete columns]]></category>
		<category><![CDATA[reinforced concrete columns]]></category>
		<category><![CDATA[seismic retrofit]]></category>
		<category><![CDATA[seismic retrofitting for aging buildings]]></category>
		<category><![CDATA[seismic safety enhancement for old buildings]]></category>
		<category><![CDATA[shear-controlled columns]]></category>
		<category><![CDATA[strengthening reinforced concrete structures with basalt fiber]]></category>
		<category><![CDATA[volcanic basalt fiber in structural engineering]]></category>
		<guid isPermaLink="false">https://scienmag.com/?p=223498</guid>

					<description><![CDATA[Researchers in South Korea show that wrapping reinforced concrete columns with basalt fiber-reinforced polymer composites can multiply their strength, ductility, and seismic energy dissipation in large-scale cyclic tests.]]></description>
										<content:encoded><![CDATA[<p>When a major earthquake strikes a city, the buildings that collapse are often not new ones but older reinforced concrete structures designed decades ago under codes far less demanding than those in force today. Their columns, the vertical members that carry entire buildings, can fail in a brittle, explosive manner when the concrete cover spalls and the internal steel reinforcement buckles. A research team in South Korea now reports that a wrapping system built from volcanic basalt fiber can dramatically change how these vulnerable columns behave under the repeated shaking of a quake, boosting strength, ductility, and energy dissipation in specimens tested at full structural scale.</p>
<p>The study, published in the Bulletin of Earthquake Engineering by Ju-Seong Jung of Chungwoon University and colleagues at Hanyang University&#8217;s Innovative Durable Building and Infrastructure Research Center, proposes a hybrid system the authors call BFC-FRP: a combination of prefabricated basalt fiber sheets and fiber-reinforced polymer panels applied to the surface of reinforced concrete columns. Basalt fiber, drawn by melting volcanic rock at high temperature, has attracted growing attention in structural engineering because it offers a favorable balance of mechanical performance, chemical stability, and cost compared with the glass and carbon fibers that have traditionally dominated the retrofit market.</p>
<p>To test the concept, the team fabricated seven large-scale columns, each with a square cross section of 350 by 350 millimeters and a clear height of 1.5 meters, dimensions representative of real building columns rather than miniature laboratory proxies. Three of the specimens were detailed to fail in shear, the most dangerous failure mode because it is sudden and brittle, while four were designed to be flexure-controlled, meaning their response is governed by bending and tends to be more ductile. Every column was then pushed sideways under reversed cyclic lateral loading, the laboratory equivalent of the back-and-forth motion an earthquake imposes, while a constant axial load corresponding to a ratio of 0.10 pressed down from above.</p>
<p>The strengthening scheme varied along two experimental axes. The first was coverage: some columns received strengthening only in the end regions, where damage typically concentrates, while others were wrapped over their full surface. The second was the arrangement of the prefabricated basalt fiber sheets and the FRP panels, allowing the researchers to compare how different configurations of the composite layers influenced confinement of the concrete and restraint of the longitudinal reinforcement. This systematic variation is what gives the study its practical value, because retrofit budgets rarely allow blanket coverage, and engineers need to know whether partial wrapping is enough.</p>
<p>The results for the shear-critical columns were striking. Full-surface BFC-FRP strengthening increased the ultimate strength by approximately 1.5 times compared with the unstrengthened control specimen, but the more important gain was in deformation: the displacement reached at ultimate strength grew by a factor of 2.0 to 2.6. In seismic terms, that transformation matters more than raw strength. A column that can keep carrying load while being pushed far sideways gives occupants time to evacuate and prevents the soft-story collapse mechanism that has killed thousands of people in recent earthquakes worldwide, from Turkey and Syria to Morocco and Japan.</p>
<p>For the flexure-controlled columns, which started from a more forgiving baseline, the retrofit delivered different but equally consequential improvements. The ultimate displacement increased by roughly 1.4 times, and the ductility ratio, a normalized measure of how much inelastic deformation a member can sustain before losing capacity, nearly doubled. Most notably, the energy dissipation capacity, which quantifies how much seismic energy the column can absorb and dissipate through hysteretic behavior in each loading cycle, rose by approximately 2.4 to 2.5 times. Since earthquake-resistant design fundamentally relies on structures dissipating energy rather than simply resisting force, this multiplication of dissipative capacity is arguably the study&#8217;s headline finding.</p>
<p>Alongside the physical tests, the researchers built nonlinear quasi-static cyclic finite element models of the columns using the disturbed stress field model, a mechanics-based formulation for reinforced concrete developed at the University of Toronto and implemented in analysis software widely used for shear-dominated members. The modeling work serves a purpose beyond reproducing the experiments: if a numerical framework can reliably predict how a wrapped column will deform and dissipate energy, engineers can extend the findings to configurations that were never tested, and design codes can eventually incorporate the strengthening system with confidence.</p>
<p>The models performed well. They reproduced both the load-displacement envelopes and the energy-dissipation responses of the tested columns with average deviations of approximately 10 percent, a level of accuracy that is respectable for nonlinear analysis of reinforced concrete, a material whose cracking, crushing, and bond-slip behavior is notoriously difficult to capture. The authors note that these results demonstrate the proposed BFC-FRP system can improve the deformation and energy-dissipation capacities of both shear- and flexure-controlled columns within the tested conditions, a carefully scoped conclusion that reflects the bounded nature of laboratory evidence.</p>
<p>The work sits within a broader and urgent engineering challenge: seismic strengthening of existing buildings. International guidelines, including documents from the American Concrete Institute and the Japan Building Disaster Prevention Association, already recognize externally bonded FRP systems as a legitimate retrofit strategy, but the field continues to search for materials that lower cost and improve sustainability. Basalt fiber fits that agenda well because its raw material is abundant volcanic rock, requiring no energy-intensive precursor chemistry of the kind needed for carbon fiber. Recent studies have explored basalt composites for repairing earthquake-damaged and corroded beam-column joints, for strengthening precast bridge piers, and even for confining columns built with recycled brick aggregates, suggesting a rapidly maturing research ecosystem.</p>
<p>For practitioners, the Korean team&#8217;s findings offer a concrete, quantified case for considering basalt-based wrapping when assessing older building stock, particularly in regions where shear-critical columns from pre-modern-code construction remain common. The demonstration that full-surface wrapping can more than double the deformability of brittle shear-critical columns, while partial schemes remain available where budgets constrain coverage, gives retrofit designers a tested menu of options. As with any laboratory campaign, the caveats are real: the tests covered a single axial load ratio, one column size, and specific composite arrangements, and fire performance of FRP-strengthened members remains a recognized consideration in practice. But the combination of large-scale testing, systematic parameter variation, and validated numerical modeling makes a persuasive case that volcanic rock, spun into fiber and bonded onto concrete, can help the world&#8217;s aging buildings stand up to the next big shake.</p>
<p><strong>Subject of Research:</strong> Seismic retrofit of reinforced concrete columns using basalt fiber-reinforced polymer composites</p>
<p><strong>Article Title:</strong> Experimental and numerical investigation on the seismic performance of reinforced concrete columns retrofitted with basalt FRP composites</p>
<p><strong>Article References:</strong> Jung, J.-S., Lee, B.-G., Kim, K., &amp; Lee, K.-S. (2026). Experimental and numerical investigation on the seismic performance of reinforced concrete columns retrofitted with basalt FRP composites. <em>Bulletin of Earthquake Engineering</em>. <a href="https://doi.org/10.1007/s10518-026-02653-z" rel="noopener noreferrer">https://doi.org/10.1007/s10518-026-02653-z</a></p>
<p><strong>Image Credits:</strong> AI Generated</p>
<p><strong>DOI:</strong> <a href="https://doi.org/10.1007/s10518-026-02653-z" rel="noopener noreferrer">10.1007/s10518-026-02653-z</a></p>
<p><strong>Keywords:</strong> basalt fiber, FRP, seismic retrofit, reinforced concrete columns, cyclic loading, ductility, energy dissipation, finite element analysis, disturbed stress field model, shear-controlled columns, flexure-controlled columns, earthquake engineering</p>
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		<post-id xmlns="com-wordpress:feed-additions:1">223498</post-id>	</item>
		<item>
		<title>Machine Learning Predicts How Earthquake-Damaged Concrete Columns Will Behave Next</title>
		<link>https://scienmag.com/machine-learning-predicts-how-earthquake-damaged-concrete-columns-will-behave-next/</link>
		
		<dc:creator><![CDATA[Violet Maxwell]]></dc:creator>
		<pubDate>Thu, 01 Oct 2026 01:12:04 +0000</pubDate>
				<category><![CDATA[Earth Science]]></category>
		<category><![CDATA[aftershock resilience]]></category>
		<category><![CDATA[Bulletin of Earthquake Engineering]]></category>
		<category><![CDATA[cyclic loading response of damaged columns]]></category>
		<category><![CDATA[damage-induced reduction factors]]></category>
		<category><![CDATA[data-driven seismic damage prediction]]></category>
		<category><![CDATA[earthquake engineering and structural health monitoring]]></category>
		<category><![CDATA[Earthquake-damaged concrete columns]]></category>
		<category><![CDATA[energy dissipation in damaged structures]]></category>
		<category><![CDATA[finite element simulation of earthquake effects]]></category>
		<category><![CDATA[hysteretic behavior]]></category>
		<category><![CDATA[Ibarra-Medina-Krawinkler model]]></category>
		<category><![CDATA[Machine learning]]></category>
		<category><![CDATA[Machine learning in earthquake engineering]]></category>
		<category><![CDATA[post-earthquake damage]]></category>
		<category><![CDATA[post-earthquake structural assessment]]></category>
		<category><![CDATA[rapid evaluation of building safety after earthquakes]]></category>
		<category><![CDATA[reinforced concrete column hysteresis behavior]]></category>
		<category><![CDATA[reinforced concrete columns]]></category>
		<category><![CDATA[seismic assessment]]></category>
		<category><![CDATA[SHAP]]></category>
		<category><![CDATA[stiffness degradation in reinforced concrete]]></category>
		<category><![CDATA[structural engineering]]></category>
		<category><![CDATA[structural performance prediction]]></category>
		<category><![CDATA[XGBoost]]></category>
		<guid isPermaLink="false">https://scienmag.com/?p=220662</guid>

					<description><![CDATA[Researchers built an XGBoost-based surrogate model, trained on over a thousand simulated column tests, that predicts the residual hysteretic behavior of earthquake-damaged reinforced concrete columns.]]></description>
										<content:encoded><![CDATA[<p>When a major earthquake strikes a city, the immediate question facing engineers is not just which buildings have collapsed, but which of the damaged ones can still be trusted. Reinforced concrete columns that have cracked, yielded, and lost stiffness during a mainshock may look deceptively intact, yet their capacity to survive a strong aftershock can be dramatically diminished. A new study published in the Bulletin of Earthquake Engineering tackles this problem with a combination of large-scale simulation and machine learning, offering a fast, data-driven way to predict how damaged columns will behave under further cyclic loading.</p>
<p>The research, led by Xiaohui Yu, Zenghui Li, Zihan He, Kuangyu Dai and Feng Fu, with affiliations spanning Guilin University of Technology, Zhengzhou University and City, University of London, focuses on the hysteretic behavior of reinforced concrete columns. Hysteresis describes the looping force–displacement curves a column traces as it is pushed back and forth past its elastic limit. These loops encode everything engineers need to know about a column&#8217;s energy dissipation, stiffness degradation and strength deterioration, but measuring them for real damaged structures is slow, expensive and often impossible after a disaster.</p>
<p>To build a foundation for their predictive models, the team first assembled a comprehensive database of 1,053 reinforced concrete column specimens tested under cyclic loading. For each column, the hysteretic response was simulated using the modified Ibarra–Medina–Krawinkler (I-M-K) model, a phenomenological framework widely used in seismic collapse assessment. The I-M-K model represents a column&#8217;s backbone curve — the envelope of its strength and stiffness — together with rules for cyclic deterioration, capturing how repeated inelastic cycles progressively erode yield strength, unloading stiffness, and post-capping behavior.</p>
<p>The central innovation lies in a two-stage simulation strategy designed to mimic what an earthquake actually does to a structure. In the first stage, a partial loading history drawn from the experimental data is applied to each intact column, producing a wide range of initial damage states, from hairline cracking to severe strength loss. In the second stage, the complete loading history is applied to these now-damaged columns, generating the full hysteretic response of a structure that has already been through a mainshock. This approach effectively turns one experimental record into many, allowing the researchers to explore the continuum between pristine and heavily damaged states without physically breaking hundreds of additional specimens.</p>
<p>From the simulated responses of the damaged columns, the researchers identified the backbone and cyclic deterioration parameters of the modified I-M-K model. By comparing the backbone parameters of damaged columns with those of their intact counterparts, they quantified damage-induced reduction factors, or DRFs, for key quantities including yield strength, elastic stiffness, strain hardening ratio, capping strength, and the chord rotation of the softening stage. These factors express, in precise numerical terms, how much of a column&#8217;s original capacity survives a given level of earthquake damage.</p>
<p>With the database of DRFs and deterioration parameters in hand, the team trained six different machine learning models to predict these values directly from a column&#8217;s initial damage state and its design parameters — inputs such as axial load ratio, longitudinal and transverse reinforcement ratios, concrete compressive strength, stirrup spacing, shear span-to-depth ratio, and cross-sectional dimensions. Rather than relying on a single arbitrary train-test split, the models were trained and tested across 1,000 random splits, a rigorous protocol that guards against lucky partitions and gives a robust picture of each algorithm&#8217;s true performance.</p>
<p>The verdict was clear: XGBoost, the gradient-boosted decision tree algorithm that has become a favorite in engineering applications, exhibited the best performance in predicting the hysteretic behavior of damaged columns. XGBoost builds an ensemble of decision trees sequentially, with each new tree correcting the errors of the previous ones, making it particularly adept at capturing the nonlinear interactions between design variables and damage states that govern structural response. To test that the model was not simply memorizing its training data, the researchers also evaluated it on three reinforced concrete column specimens outside the original database, examining its general applicability to unseen cases.</p>
<p>Crucially, the study does not treat its model as a black box. Using SHapley Additive exPlanations, or SHAP, a technique borrowed from cooperative game theory that attributes each prediction to the contributions of individual input features, the researchers interrogated what their model had learned. The analysis indicated that initial damage is the most influential feature governing the reduced hysteretic parameters — an intuitive but now quantitatively confirmed result, since the severity of pre-existing damage directly controls how much strength and stiffness remain for subsequent loading.</p>
<p>The practical implications extend well beyond the laboratory. After a damaging earthquake, engineers must rapidly decide whether a building is safe for occupancy, whether it needs retrofitting, or whether it should be demolished. Current post-earthquake assessment practice often relies on simplified damage indices, such as the Park–Ang damage index, and conservative assumptions that can lead to unnecessary closures or, worse, underestimated risk. A trained surrogate model like the one developed here could take measurable column properties and an estimate of sustained damage and return, in seconds, a full prediction of the residual hysteretic envelope — feeding directly into aftershock fragility analysis and resilience planning for entire building stocks.</p>
<p>The work also fits into a broader movement in earthquake engineering toward machine-learning-assisted seismic assessment, with recent studies applying similar methods to fragility estimation, drift capacity prediction, and parameter identification for nonlinear structural models. By releasing their column database as supplementary material and making the source code openly available on GitHub, the authors have lowered the barrier for other researchers to build on the approach. As cities in seismic regions face aging infrastructure and increasing exposure, tools that translate raw data into rapid, explainable predictions of residual capacity may become as essential to post-earthquake response as the seismometers that record the shaking itself.</p>
<p><strong>Subject of Research:</strong> Machine learning prediction of the residual hysteretic behavior of post-earthquake damaged reinforced concrete columns</p>
<p><strong>Article Title:</strong> Hysteretic behavior prediction of post-earthquake damaged reinforced concrete columns using machine learning</p>
<p><strong>Article References:</strong> Yu, X., Li, Z., He, Z., Dai, K., &amp; Fu, F. (2026). Hysteretic behavior prediction of post-earthquake damaged reinforced concrete columns using machine learning. <em>Bulletin of Earthquake Engineering</em>. <a href="https://doi.org/10.1007/s10518-026-02704-5" rel="noopener noreferrer">https://doi.org/10.1007/s10518-026-02704-5</a></p>
<p><strong>Image Credits:</strong> AI Generated</p>
<p><strong>DOI:</strong> <a href="https://doi.org/10.1007/s10518-026-02704-5" rel="noopener noreferrer">10.1007/s10518-026-02704-5</a></p>
<p><strong>Keywords:</strong> machine learning, XGBoost, reinforced concrete columns, hysteretic behavior, post-earthquake damage, seismic assessment, Ibarra-Medina-Krawinkler model, damage-induced reduction factors, SHAP, aftershock resilience, structural engineering, Bulletin of Earthquake Engineering</p>
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		<post-id xmlns="com-wordpress:feed-additions:1">220662</post-id>	</item>
		<item>
		<title>New Equations Design Earthquake-Resistant Columns for Ductility and Shear at Once</title>
		<link>https://scienmag.com/new-equations-design-earthquake-resistant-columns-for-ductility-and-shear-at-once/</link>
		
		<dc:creator><![CDATA[Violet Maxwell]]></dc:creator>
		<pubDate>Thu, 24 Sep 2026 22:35:47 +0000</pubDate>
				<category><![CDATA[Earth Science]]></category>
		<category><![CDATA[closed-form equations]]></category>
		<category><![CDATA[columns]]></category>
		<category><![CDATA[combined structural safety equations]]></category>
		<category><![CDATA[confinement]]></category>
		<category><![CDATA[curvature ductility]]></category>
		<category><![CDATA[ductility]]></category>
		<category><![CDATA[ductility and shear resistance]]></category>
		<category><![CDATA[Earthquake engineering]]></category>
		<category><![CDATA[earthquake engineering code improvements]]></category>
		<category><![CDATA[earthquake resilience in building columns]]></category>
		<category><![CDATA[earthquake-resistant building design]]></category>
		<category><![CDATA[Eurocode 2]]></category>
		<category><![CDATA[innovative structural engineering methods]]></category>
		<category><![CDATA[reinforced concrete]]></category>
		<category><![CDATA[reinforced concrete columns]]></category>
		<category><![CDATA[reinforced concrete structural analysis]]></category>
		<category><![CDATA[seismic design]]></category>
		<category><![CDATA[seismic design optimization]]></category>
		<category><![CDATA[seismic performance of concrete columns]]></category>
		<category><![CDATA[shear capacity]]></category>
		<category><![CDATA[single equation for ductility and shear]]></category>
		<category><![CDATA[structural analysis]]></category>
		<category><![CDATA[transverse reinforcement]]></category>
		<category><![CDATA[transverse reinforcement calculation]]></category>
		<guid isPermaLink="false">https://scienmag.com/?p=212903</guid>

					<description><![CDATA[Researchers have developed closed-form analytical equations that simultaneously design the transverse reinforcement of reinforced concrete columns for both curvature ductility and shear capacity, revealing how axial load pushes the two demands in opposite directions.]]></description>
										<content:encoded><![CDATA[<p>When an earthquake strikes a reinforced concrete building, the columns carrying its weight must survive in two very different ways at the same time. They need to bend and deform without shattering, a property engineers call ductility, and they must resist shear, the slicing force that can snap a column clean through. For decades, design codes have treated these two demands with separate, largely independent procedures, leaving engineers to check one, then the other, and hope the two answers do not quietly undermine each other. A new study published in the Bulletin of Earthquake Engineering argues that this piecemeal approach is no longer necessary, and it backs that claim with a set of closed-form equations that handle both requirements in a single, transparent calculation.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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&#8217;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.</p>
<p>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&#8217;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.</p>
<p>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.</p>
<p>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.</p>
<p><strong>Subject of Research:</strong> Analytical design of transverse reinforcement in reinforced concrete columns for simultaneous ductility and shear requirements under seismic loading</p>
<p><strong>Article Title:</strong> Simultaneous analytical design of ductility and shear capacity in reinforced concrete columns</p>
<p><strong>Article References:</strong> Monti, G., De Domenico, D., Zeng, Q., &amp; Quaranta, G. (2026). Simultaneous analytical design of ductility and shear capacity in reinforced concrete columns. <em>Bulletin of Earthquake Engineering</em>. <a href="https://doi.org/10.1007/s10518-026-02682-8" rel="noopener noreferrer">https://doi.org/10.1007/s10518-026-02682-8</a></p>
<p><strong>Image Credits:</strong> AI Generated</p>
<p><strong>DOI:</strong> <a href="https://doi.org/10.1007/s10518-026-02682-8" rel="noopener noreferrer">10.1007/s10518-026-02682-8</a></p>
<p><strong>Keywords:</strong> reinforced concrete, seismic design, ductility, shear capacity, transverse reinforcement, confinement, curvature ductility, columns, earthquake engineering, closed-form equations, structural analysis, Eurocode 2</p>
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