Maximum Principal Tensile Stress Research Articles

Response of existing lining subjected to closed blasting in zero-spacing twin tunnels and its damping measures

The blasting excavation of a new tunnel significantly impacts the lining of existing tunnels during the construction of zero-spacing twin tunnels. In this study, a field test was first carried out to study the vibration velocity of an existing lining in zero-spacing twin tunnels. LS-DYNA software was then employed to investigate the dynamic response characteristics under various blasting factors. Finally, the use of damping layer was considered to analyze its effects on the dynamic response of the existing tunnel lining. The maximum vibration velocity was found at the hance adjacent to the new tunnel, with a value of 17.51 cm/s in the tests. The maximum principal tensile stress(PTS) from the simulation was also shown at the same hance of the existing lining to have an intensity of 3.27 MPa. Additionally, the blasting of the rock mass close to the existing tunnel in the first step would result in a higher PTS intensity of 3.54 MPa within the lining, compared to the blasting of the rock mass away from the existing tunnel in the first step. However, the cumulative stress disturbance caused by the former to the lining was smaller than that of the latter. The maximum PTS at the hance was also found to linearly decrease with the reduction of the excavation footage and the maximum PTS was 2.3 MPa at an excavation footage of 0.9 m. The damping layer of the existing tunnel would contribute to a significant reduction of PTS. Therefore, a damping layer thickness of 2.5 cm was suggested in the study considering the effects of the damping and mechanics of the lining.

Obstructed swelling and fracture of hydrogels.

Obstructions influence the growth and expansion of bodies in a wide range of settings-but isolating and understanding their impact can be difficult in complex environments. Here, we study obstructed growth/expansion in a model system accessible to experiments, simulations, and theory: hydrogels swelling around fixed cylindrical obstacles with varying geometries. When the obstacles are large and widely-spaced, hydrogels swell around them and remain intact. In contrast, our experiments reveal that when the obstacles are narrow and closely-spaced, hydrogels fracture as they swell. We use finite element simulations to map the magnitude and spatial distribution of stresses that build up during swelling at equilibrium in a 2D model, providing a route toward predicting when this phenomenon of self-fracturing is likely to arise. Applying lessons from indentation theory, poroelasticity, and nonlinear continuum mechanics, we also develop a theoretical framework for understanding how the maximum principal tensile and compressive stresses that develop during swelling are controlled by obstacle geometry and material parameters. These results thus help to shed light on the mechanical principles underlying growth/expansion in environments with obstructions.

Fracture Simulation of Concrete Beams to assess softening behavior by varying different fractions of Aggregates

Simulating the concrete fracture unlike other elastic and brittle materials quite different due to its quasibrittleness. The present research focussed on assess softening behavior by varying different fractions of aggregates and cement matrix in micro details. Extended Finite Element Method (XFEM) for crack modeling implemented for simulating and visualizing crack propagation through Cement matrix, Interfacial Transition Zone (ITZ) and Aggregates . This approach permits the initializing crack by from enrichment zone and propagation of crack through element by traction separation law .The crack formation initiates when the maximum principal tensile stress reaches the tensile strength. The work involves creating python script for iterative process of random distribution of aggregates with in the matrix using Monte Carlo method and creating Cohesive zone element for zero thickness ITZ. introduces a finite element modeling technique for investigating multiscale fracture characteristics. This approach encompasses multiple levels of analysis, including the generation of aggregate particles using a Monte Carlo method implemented via a Python script. Additionally, we replicate the Interfacial Transition Zone (ITZ) between aggregate and mortar in the model. The load-deflection curves can be used to assess the softening behavior of concrete and suggest the realistic fraction of coarse aggregate in mix proportion to impart more ductility to beams.

Vibration-assisted material damage mechanism: From indentation cracks to scratch cracks

Vibration-assisted grinding is one of the most promising technologies for manufacturing optical components due to its efficiency and quality advantages. However, the damage and crack propagation mechanisms of materials in vibration-assisted grinding are not well understood. In order to elucidate the mechanism of abrasive scratching during vibration-assisted grinding, a kinematic model of vibration scratching was developed. The influence of process parameters on the evolution of vibration scratches to indentation or straight scratches is revealed by displacement metrics and velocity metrics. Indentation, scratch and vibration scratch experiments were performed on quartz glass, and the results showed that the vibration scratch cracks are a combination of indentation cracks and scratch cracks. Vibration scratch cracks change from indentation cracks to scratch cracks as the indenter moves from the entrance to the exit of the workpiece or as the vibration frequency changes from high to low. A vertical vibration scratch stress field model is established for the first time, which reveals that the maximum principal stress and tensile stress distribution is the fundamental cause for inducing the transformation of the vibration scratch cracking system. This model provides a theoretical basis for understanding of the mechanism of material damage and crack propagation during vibration-assisted grinding.

Temperature gradient effect on high-speed railway frame structure yard based on fluid-solid coupling analysis

As the frame structure can effectively save the lower space and optimize overall layout of the yard, it was first applied in the railway double-layers yard in Beijing Fengtai, including the elevated high-speed yard and the ground common-speed yard. To identify the most unfavorable temperature gradient effect on railway frame structure yard, the present study combined with CFD (Computational Fluid Dynamics) and FEM (Finite Element Method) to analyze the temperature gradient and corresponding temperature stress of the structure, and utilizes ray tracing method to analyze the shielding effect between components of structure under the sunlight. The results show that, the temperature gradients of the slab need to be focused. Both positive and negative temperature gradients are observed in the vertical direction of the slab at the end of September (autumn equinox), which are 80.95℃/m and −29.85℃/m, respectively. Under the most unfavorable temperature gradient, the maximum principal tensile stress of the structure lies at the junction of positive and negative temperature gradients of the slab, accounting for 45.6% of the concrete tensile strength, which is the controlling index of the frame structure.

Crack extension mechanism and scratch stress field model of hard and brittle materials caused by curvature effect

Inhibition of subsurface crack growth under contact loading is key to enhancing the service performance of brittle materials. However, the understanding of crack extension mechanism under complex conditions is still limited. In this paper, scratch experiments and stress field analysis were used to investigate the damage evolution of glass materials induced by the curvature effect of abrasive trajectories. A cycloid or trochoid analytical model was developed to identify curvature-sensitive paths. On this basis, Curvature scratching experiments were conducted on the self-developed scratching experimental platform. The results revealed that surface cracks appeared outside the scratch grooves at the maximum curvature. Scratches with higher curvature peaks demonstrated less depth of crack initiation, and deeper cracks were induced inside the scratch. A novel finite-length, curved stress field model is proposed to evaluate the damage evolution from the inner and outer sides of the scratch. Based on the theory of maximum principal stress and tensile stress, the mechanism of crack extension under the curvature effect is revealed. This study improved the understanding of abrasive scratching and cracks extension under broad physical conditions.

Research on Mechanical Characteristics and Load-bearing Behavior of Nodes of Steel Fiber Concrete Arch Bridges

Steel fiber reinforced concrete (SFRC) is a new type of composite material formed by dispersing discontinuous short steel fibers in a uniform and random direction throughout the concrete, which has excellent properties of tensile, shear and high toughness, can effectively improve the load-bearing capacity of arch bridges. In this paper, the mechanics of SFRP in the nodal structure of an arch bridge is initially explored by means of indoor model tests and numerical simulation studies. The results show that the maximum principal tensile stress occurs at the intersection of arch rib, arch foot and tie beam, and the maximum principal compressive stress occurs at the connection between arch rib and arch seat, which should be considered in the design. In this paper, we hope to understand the characteristics of the force and bearing capacity of this type of structure to provide a reference for similar projects.

Plastic shrinkage of 3D printed concrete under different self-weight of upper layers

The material properties of 3D printed concrete determine its fragility in preventing plastic shrinkage cracking due to the presence of restraint. Residual friction at the bottom that is positively related to the self-weight of the upper layers is a potential source of constraint that may cause cracking. The present study investigates the effect of self-weight of upper layers on plastic shrinkage of bottom printed concrete at early age. The corresponding surface moisture, bleeding rate, evaporation rate, capillary pressure development, and plastic shrinkage strain of printed concrete specimens under different upper self-weight are determined. It is found that increased self-weight of upper layers can significantly yield more early-age surface moisture and higher bleeding rate of the concrete at the bottom. The increased self-weight of upper layers can induce water to migrate and accumulate on the sides of the printed elements. However, as the self-weight of upper layers reduces the equivalent pore radius, the self-weight of upper layers would still facilitate the development of capillary pressure and further causes larger free plastic shrinkage strain. And when there is friction at the bottom, the horizontal plastic shrinkage is significantly limited by the constraint of the self-weight of upper layers, and the restraint strain increases with the upper self-weight. The maximum principal tensile stress results are calculated by two-dimensional plane strain field on the observation surface, which indicates that the specimen bears a greater risk of plastic shrinkage cracking with larger self-weight of upper layers.

Analysis of early-age mechanics and crack of the base plate on the bridge in summer based on eXtended FEM

Based on the eXtended Finite Element Method (XFEM), taking the base plate of the double-block ballastless track on the new high-speed railway bridge in the southeastern coastal area as the research object, the finite element model of the base plate was established to investigate the early-age mechanical properties and cracks under the high-temperature environment in summer. The on-site tests of temperature monitoring and crack observation were carried out on the base plate at an early age to validate the correctness of the model. The influence of the groove radius, anti-cracking rebar mesh, and curing methods on the mechanical properties of the base plate was further analyzed. As the age increases, the principal tensile stress in the groove exceeds the standard value of the concrete tensile strength, and the crack appears at the groove first. Increasing the radius of the chamfer can effectively reduce the maximum principal tensile stress in the groove, where the reduction rate is 15.80% and 31.11% respectively when the radii are 200 mm and 300 mm compared with the radius of 100 mm. The horizontal and vertical anti-cracking rebars in the groove have a significant reduction effect on the maximum principal tensile stress in the groove, of which horizontal laying is the most effective. A reasonable selection of curing methods is conducive to reducing the early-age cracking risk in the grooves, with plastic film covering curing being one of the more favorable methods. This paper provides a certain reference value for studying the early-age mechanical behavior of the base plate on the bridge and the influencing factors of the cracks at the groove.

Experimental and finite element investigations on hydration heat and early cracks in massive concrete piers

The concrete hydration heat and different construction methods directly affects the early crack resistance of massive concrete structures and may lead to concrete cracks. In this work, the hydration heat test and finite element simulation were conducted to investigate the early cracking resistance and the main influencing factors of the massive concrete bridge pier. The size of the bridge pier was 8 m (length) × 4 m (width) × 22.5 m (height), and the pier was poured in two layers (8.5 m/14 m) with an interval of 37 h. The internal temperature of the pier was tested 16 days after the concrete pouring using pre-buried temperature sensors, and the crack expansion on the surface of the pier was continuously observed during the test period. The test obtained a maximum concrete temperature of 64.25 °C after 100 h after the concrete pouring, and 3 cracks were found on the surface of the pier. The pier simulation model is established according to the actual situation in the test, The maximum temperature inside the bridge pier obtained from the simulation is 61.73 ℃, and the temperature field development pattern and the crack expansion on the pier surface were basically consistent with the test, which confirmed the reliability of the simulation method. Besides, the simulation process found that the maximum main tensile stress on the surface of the bridge pier was 2.77 MPa, which was mainly distributed near the interface of the 2 layers, indicating that the layered pouring scheme adopted in the test was improper. The effect of layered casting schemes on the early cracking resistance of massive concrete has rarely been discussed, and further simulations revealed that: the maximum main tensile stress can be reduced by gradually improving the number of layers, layer height and interval between each layer. By changing the original layered pouring scheme to 3 layers with an interval of 3 days between each layer, the maximum principal tensile stress is reduced to 1.50 MPa, and early cracking of the bridge pier can be avoided. This work provides a general numerical analysis method with high accuracy, parameterization and quantification for early crack control of massive concrete structures in a multi-factor complex environment.

Effect of tension and compression on dynamic alveolar histomorphometry

Here, we tested the hypothesis that tensile and compressive stresses generated in the alveolar bone proper regulate site-specific cellular and functional changes in osteoclasts and osteoblasts. Thirty-two 13-week-old male mice were randomly divided into four groups: two experimental groups with vertical loading obliquely from the palatal side to the buccal side of the maxillary molar (0.9 N) 30 min per day for 8 or 15 days and unloaded controls (n = 8). Calcein and alizarin were administered 8 and 2 days before euthanization, respectively, to detect the time of bone formation. Undecalcified sections parallel to the occlusal plane were prepared on the palatal root and the surrounding alveolar bone in the middle of the root length. The alveolar perimeter was divided into 12 equal regions for site analysis, and the bone histomorphometric parameters were obtained for each region. Data from in vivo microfocus computed tomography were used to construct animal-specific finite element models. 2D stress distribution images were overlain on histology images obtained from the same location. Significant differences in the total perimeter between groups and between loading and unloading in each region were statistically analyzed (α = 0.05). Osteoclast counts and the alizarin label ratio were significantly higher in the loaded group than in the unloaded group in regions where the maximum von Mises and principal tensile stresses were the highest along the perimeter. The label ratio of calcein was significantly lower in the 8-day loaded group than in the unloaded group, indicating that the calcein-labeled surface was resorbed by osteoclasts that appeared during the loading period. The effect of loading was mitigated by an increase in the maximum principal compressive stress. We conclude that bone resorption and bone formation are functions of site-specific tension and compression in the alveolar bone proper, confirming our hypothesis. This finding is critical for the advancement of diagnosis and treatment planning in clinical dentistry.

Performance and strength analysis of concrete-encased steel plate walls under tensile-flexural-shear load

When located at the base of a building experiencing high-intensity earthquakes or bi-directional earthquakes, shear walls may be tensile, resulting in tensile-flexural-shear (TFS) stress states after lateral load coupling. The Chinese code proposes the embedded steel to counteract such issues, but there are few relevant studies. Six concrete-encased steel plate (CES) walls were tested under the TFS load to investigate the effects of axial tensile ratio and steel content on seismic behavior. The results showed that TFS specimens failed in tensile flexural-shear mode. Compared to the tension-free specimen, TFS specimens with an axial tensile ratio of 2.5 had 21%, 56%, and 40% lower shear strength, initial lateral stiffness, and ductility. Comparatively, increasing the steel content in the boundary elements effectively reduced the strengthening effect of steel and the brittle fracture potential of boundary elements induced by TFS load, thus enhancing the overall behavior by 15–19%. Furthermore, the failure mechanism was proposed based on the development of deformation and strain. It demonstrated that the maximum principal tensile stress in the web caused severe shear strength degradation and highlighted the importance of the dowel action through the crack interface, depending on the variables. Through the comparative analysis of the shear strength design formulas for eccentric tensile CES walls, the steel proportion was proposed as a modified factor in Chinese code for better estimation.

Cohesive fracture evolution within virtual element method

The paper presents a numerical procedure for the nucleation and evolution of cohesive fracture in two-dimensional bodies. The procedure is based on the development of a 12-node virtual element. Initially, the construction bases of the virtual element method (VEM) are illustrated, with specific reference to a four sides 12-node element. The recovery of the stress via complementary energy within the single element is described. The fracture is introduced in the two-dimensional body by splitting the virtual element, called parent element, into two slave elements joined by a cohesive interface. Thus, a damage interface model characterized by bilinear softening and accounting for mode I, mode II and mixed mode of fracture is presented. Then, the numerical procedure for crack nucleation and evolution is proposed. The crack direction is individuated by the maximum tensile principal nonlocal stress computed averaging on the mesh, by means of a weight function, the stress field evaluated via complementary energy within each element. Once the direction is determined, the (parent) 12-node element is split into two (slave) elements joined by the interface. Several numerical applications are developed, illustrating the performance of the 12-node element and the its accuracy in evaluating the stress field. Then, computations concerning typical fracture tests are performed, comparing the obtained results with available experimental evidences and with the ones carried out by using different numerical techniques.

Structural and thermal performance of a novel form of cladding panel: the I-beam beetle elytron plate

To develop a non-bearing prefabricated straw sandwich concrete wallboard (I-beam beetle elytron plate: IBEPsc), the effect of certain structural parameters (e.g. panel thickness, T, number of I-cores, N, and core height, h) on mechanical and thermal insulation performance was investigated using the finite-element method, with the following results. (a) Bearing capacity of the IBEPsc is controlled by the maximum principal tensile stress; the optimal structural parameters of the IBEPsc for a self-insulated wall with a large safety margin are presented. (b) The consideration of strips as opposed to whole plates and the selected upper bearing constraint type have little influence on the mechanical properties. In practical applications, the strips and whole plates can be reasonably selected according to engineering needs, and these components can be connected with the main structure by conventional mortar. (c) According to qualitative analysis and comparison with common I-shaped thermal insulation walls, the IBEPsc requires the least material and weight while ensuring a sufficient safety margin in terms of mechanical and thermal insulation performance. Hence, biomimetic techniques can play a key role in breaking through the limitations of traditional structures. This paper can help direct the application of beetle elytron plates in prefabricated wallboards.

Temperature Effect of Concrete Hydration Heat under Atmospheric Wind Based on Fluid-Solid Coupling

Concrete inevitably gets subjected to the effects of atmospheric wind during pouring. It is a significant factor to predict the temperature stress and gradient of concrete structure during pouring. In this paper, the Computational Fluid Dynamics (CFD) and Finite Element Method (FEM) were used to analyze the temperature and stress generated by temperature gradient of mass cap concrete under the wind environment. Then, the reliability of the temperature value was verified by the field test. The analysis shows that the use of the fluid-solid coupling method allows considering not only the thermal movement and thermodynamic properties of wind (given by CFD), but also the thermal expansion and stress of the concrete structure (given by FEM). Because of the wind, temperature of the windward side of the concrete is lower than that of the leeward side. Highest temperature is located at the center biased towards the leeward side. Increase in the wind speed increases the temperature difference and the maximum principal tensile stress. However, the study shows that change in the wind direction has limited effect on the concrete temperature stress.

Modeling mixed mode cracking in concrete through a regularized extended finite element formulation considering aggregate interlock

Mixed mode cracking in concrete keeps being a challenging issue in computational fracture mechanics. While uncracked concrete develops cracks perpendicular to the direction of the maximum principal tensile stress, the crack edges will expectedly open, mutually slide, and transmit both normal and shearing stresses. In the present formulation, we replace the damage band with a regularized strain band by enriching the space of the approximating functions in compliance with the regularized extended finite element model developed by the authors. Our clue is that a discriminant factor to choose the appropriate expression of the regularized strain relies upon the concept of stress compatibility modified to consider aggregate interlock. In particular, we resort to a simplified phenomenological saw-tooth model of the crack surface asperities. We show the capability of the methodology to capture both structural behavior and crack paths in a set of bending tests carried out on concrete specimens. Though phenomenological, the resulting approach is novel, conceptually simple and reliable for it directly reproduces the expected kinematics and structural results.

Accurate Effective Stress Measures: Predicting Creep Life for 3D Stresses Using 2D and 1D Creep Rupture Simulations and Data

Operating structural components experience complex loading conditions resulting in 3D stress states. Current design practice estimates multiaxial creep rupture life by mapping a general state of stress to a uniaxial creep rupture correlation using effective stress measures. The data supporting the development of effective stress measures are nearly always only uniaxial and biaxial, as 3D creep rupture tests are not widely available. This limitation means current effective stress measures must extrapolate from 2D to 3D stress states, potentially introducing extrapolation error. In this work, we use a physics-based, crystal plasticity finite element model to simulate uniaxial, biaxial, and triaxial creep rupture. We use the virtual dataset to assess the accuracy of current and novel effective stress measures in extrapolating from 2D to 3D stresses and also explore how the predictive accuracy of the effective stress measures might change if experimental 3D rupture data was available. We confirm these conclusions, based on simulation data, against multiaxial creep rupture experimental data for several materials, drawn from the literature. The results of the virtual experiments show that calibrating effective stress measures using triaxial test data would significantly improve accuracy and that some effective stress measures are more accurate than others, particularly for highly triaxial stress states. Results obtained using experimental data confirm the numerical findings and suggest that a unified effective stress measure should include an explicit dependence on the first stress invariant, the maximum tensile principal stress, and the von Mises stress.

Analysis of Ground Settlement Caused by Double-line TBM Tunnelling Under Existing Building

TBM tunnelling is less used in the subway construction in prosperous city due to the limitation of the engineering geological conditions. The studies on the influence of the TBM construction on the existing buildings are also limited. Therefore, based on the engineering case of tunnel crossing existing building in the section of Haiboqiao ~ Xiaocunzhuang station of Qingdao Metro Line 1, the numerical model that simulates the construction process of TBM tunnelling in slightly weathered granite layer is established by three-dimensional finite difference software FLAC3D to analyze the influence of TBM tunnelling. The comparisons between ground deformations obtained by FLAC3D and field monitoring data in different construction stages of double-line tunnel have been made firstly to validate the numerical model. Then the ground settlement characteristics, differential settlement and the stress distribution of the existing building and the stress of segment structure have been analyzed. During TBM tunnelling under existing building, the settlement of the building as a whole tends to increase, with the maximum measured settlement of 5.45 mm and the maximum differential settlement of 1.58 mm, which meets the control standard of relevant codes. Ground settlement groove along the transverse and vertical sections occurs near the building and tunnels, and the settlement becomes smaller with the farther the distance from the building and tunnels. The settlement curve on the cross section changes dynamically and is approximately V-shaped, and its width is about 5 ~ 6 times diameter of the tunnel. For the same cross section, the range of the settlement groove after tunnelling right line increases obviously compared with that after tunnelling left line (first construction), the settlement values also increase, and the symmetrical axis of the settlement curve is shifted to the right. For the segment structure, the maximum principal tensile stress occurs inside the arch bottom of the tunnel, while the maximum principal compressive stress occurs near the arch top and arch waist, with obvious stress concentration. For the existing building, the maximum principle tensile stress occurs at the door opening of the wall on the first floor and the maximum principal compressive stress is at the corner of wall. They are less than the tensile strength and compressive strength of the segment structure and building respectively, and have enough safety margins. This paper can provide important practical reference for the deformation control and protection design of surrounding buildings for relative construction.

Axisymmetric BEM analysis of layered elastic halfspace with volcano-shaped mantle and cavity under internal gas pressure

This paper presents an axisymmetric BEM analysis of layered elastic halfspace with volcano-shaped mantle and cavity under internal gas pressure. The problem is of interest to understand the behavior of volcanoes, tectonic earthquakes and other oil and gas reservoirs. The volcano-shaped mantle ground topography and the internal spherical or ellipsoidal cavity are added to the conventional model of layered halfspace. The analysis uses the axisymmetric boundary element method (BEM) associated with the fundamental solution of a multilayered elastic fullspace subject to the concentrated ring-body force. The BEM is further verified for its high efficiency and accuracy by comparing its result with the analytical and FEM solutions for the problem of a homogeneous elastic halfspace whose spherical cavity is under internal pressure. The BEM is used to examine the effect of the volcano-shaped mantle, the cavity shape, the layered material properties and the internal pressure on the elastic behavior of the halfspace under the internal pressure loading within the cavity. The displacements and stresses at the external and internal boundaries and within the layered halfspace are presented and analyzed in detail. The presence of the volcano-shaped mantle can reduce significantly the swelling ground movement induced by the expansive pressure in the cavity in the layered halfspace. The cavity shape can have significant effect to the location and magnitude of the maximum tensile principal hoop stress on the cavity surface induced by its internal pressure.

Seismic cracking mechanism and control for pre-stressed concrete box girders of continuous rigid-frame bridges: Miaoziping bridge in Wenchuan earthquake as an example

The box girder of the Miaoziping Bridge, a three-span prestressed concrete continuous rigid-frame bridge, suffered a serious crack in its box section’s web near the 1/6 to 1/2 length of the side span and the middle-span length of 1/4 to 3/4, as a result of the 2008 Wenchuan earthquake, which also caused large lateral residual displacements at both ends of the side span. In this study, eight strong-motion records near the bridge site and two other records (El Centro and Taft) are selected as inputs for time-history analysis of the bridge. The cantilever construction process and initial stress of the box girder are considered in a bridge model for seismic numerical simulation. Further, the simulation results are compared with the actual earthquake damage. The cracking mechanism, influencing factors and control of the girder crack damage are discussed. The high-stress zones of the box girder agree with the seismic damage observed, even various seismic inputs are considered. The findings reveal that the maximum (principal) tensile stress of the girder exceeds the tensile strength of the concrete under the seismic excitations, and cracks occur. Under various input directions of ground motions, the proportion of the main girder stresses induced by the earthquake shows differences. After the failure of the shear keys in the transverse direction of the bridge, the stresses of the girder decrease in the mid-span. However, the beams at both ends of the side spans revealed large lateral displacements. Considering that the uplift of the beam ends, stress and axial torque of the girder’s side span are greatly reduced. Setting bi-directional friction pendulum bearings on the transition pier is an effective damping measure to control web cracking of the mid-span and lateral drifts of the beam ends.