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Metal fatigue is a problem in the use of metals in their applications, especially when they are exposed to cyclic or repetitive loads. This study analyzes the effect of round, rectangular and spherical cross-sections on fatigue failure of ST 60 steel. By providing a fatigue test load of 150 N and a rotating speed of 1500 rpm and a test specimen installation position with a distance of 70 cm, it was found that the round cross-section broke when experiencing 26,471 cycles, the rectangular cross-sectional shape broke when experiencing 115,515 cycles and the hollow round shape broke when experiencing 201,983 cycles. The largest shear stress is generated by a spherical cross-section with a value of 247.7 N/mm2 and the lowest is by a material with a hollow spherical cross-section with a value of 194.478 N/mm2. Normal stress and the highest shear stress are produced specimens with a spherical cross-sectional shape, this is because the spherical cross-section has a tendency to spread normal stress evenly over its surface.

A model based on the Element Free Galerkin (EFG) method in the framework of linear elastic assumptions was developed to determine the distribution of interfacial stress in a concrete beam reinforced with FRP plates. In this model, the behavior of the adhesive layer between the surfaces is considered like a linear spring using its elastic properties, and MLS approximation functions are used to approximate the total displacement fields. In addition, the results were calculated and presented under the condition of complete adhesion between the surfaces. The results of the model were compared with the FEM model in Abaqus software for concrete beam and FRP panel. The results show that the EFG method has a good agreement with the outputs of the Abaqus model. To conclude this work, a parametric study was performed. It shows how the thickness of the adhesive layer and the FRP plate affect the shear and normal stress values of the adhesive. [ABSTRACT FROM AUTHOR]

This study analyzes a concrete dam using Abaqus software at different water storage levels (60m, 70m, and 80m). The dam sections are designed based on these levels using approved equations by the United States Bureau of Reclamation. Static and dynamic forces, including seismic components, are calculated for worst-case scenarios. The analysis considers cases with and without galleries, varying the dam base width. Stresses (vertical, shear, and main) are calculated and presented as curves for comparison. The study examines the impact of reservoir water levels, additional base parts, and galleries on dam stability. Findings show that galleries significantly affect stress distribution, causing stress concentrations near openings. Normal stress is uniform except at the gallery, where it decreases. Maximum water storage leads to slight increases in normal stress. Without a gallery, normal stress increases until a certain distance, then decreases towards the pre-toe region, with maximum stress at the toe. The length of the additional base has a limited effect on normal stress. The presence of a gallery affects principal stress distribution, with higher values near the toe region for higher storage levels. The shear stress distribution is more uniform without a gallery. These findings demonstrate the complex interaction of factors in concrete dam stress behavior. Proper consideration of these factors is crucial for design, analysis, and maintenance to ensure structural integrity and performance. Further analysis considering material properties, loading conditions, and dam geometry would enhance understanding and facilitate precise design and safety assessments.

In this analytical study, we are concerned about the influence of stresses produced due to a moving load on an elastic plate (which is not traveling with a moving load) under gravity lying over a semi-infinite water medium with hydrostatic stress. The elastic property of the plate is considered to be orthotropic. The water and elastic medium are bonded with an irregular interface. The type of irregularity is considered parabolic type. To discover the displacement field, the perturbation approach has been employed to solve the governing differential equations with variable coefficients. Due to moving load, closed-form normal and shear stresses are established for both elastic plate and semi-infinite water medium. The variation of non-dimensionalized shear and normal stresses with various parameters, such as gravitational coefficient, hydrostatic stress, and irregularity factor, is discussed through numerical computation and graphical demonstration. Moreover, some remarkable observations have been performed to study the influence of the frictional coefficient and depth factor on the shear and normal stresses of both mediums. Some particular cases also have been discussed for the validation of the problem. [ABSTRACT FROM AUTHOR]

The hydraulic and mechanical coupling characteristics of fracture networks under normal stress and shear stress were studied in this paper. The hydraulic and mechanical coupling model of the fracture network comprehensively considers the normal stress, shear stress, seepage pressure and roughness characteristics. Based on the boundary conditions and reasonable assumptions, COMSOL Multiphysics software was used to develop the hydraulic and mechanical coupling finite element model of the fracture network with different intersection points under normal stress and shear stress, focusing on the study of the effect of normal stress and shear stress on the fracture permeability. The degree of permeability change caused by the normal stress and shear stress is different. The shear stress has a significant influence on the fracture permeability, and when the normal stress is low, the relationship between the fracture permeability and shear stress can be described by a linear relationship. Then, the influence of the number of intersection points in the fracture network on the average fracture width, average water pressure, average seepage velocity and seepage passage of the fractured rock mass was analyzed. The number of intersections in the fracture network has little influence on the average fracture gap width and average water pressure but has a great influence on the flow velocity. The analysis in this paper is very helpful to understand the seepage characteristics in rough fractures under normal stress and shear stress. [ABSTRACT FROM AUTHOR]

The single adhesive joint has many applications in the shipbuilding industry, where it offers the advantage of joining materials (adherents) with different properties and characteristics using an adhesive. However, one disadvantage of this type of joint is the stress concentration at the ends of the joint, which directly affect the adhesive. Another disadvantage is the possible difference between the coefficients of thermal expansion of the adherents of the joint. Through compilation and classification of the formulas found in various publications, this study presents a state-of-the-art review of an adhesive single-lap joint that can be used in marine applications. It will consider the types of materials used as the adhesive and as the adherents, the possibility of varying the thicknesses of the adherents and the thickness of the adhesive, and the recommended design factors for each proposed methodology. This study proposes formulas to estimate the stresses for joints with balanced thicknesses and extrapolates the results for non-balanced joints; also, an equation is derived to calculate the minimum overlap joint length for ship lengthening, allowing the design process to be simplified. The results are expected to facilitate the design of single-lap joints in marine applications, such as reinforcing composite panels and lengthening of hulls and superstructures.

Abstract Femoroacetabular impingement (FAI), together with its two main pathomechanisms, cam and pincer, has become a trending topic since the end of the 1990s. Despite massive academic research, this hip disorder still conceals obscure aspects and unanswered questions that only a question-driven approach may settle. The pathway that leads a FAI asymptomatic morphology through a FAI syndrome to a FAI-related osteoarthritis is little known. Contact mechanics provides a shareable and persuasive perspective: cam FAI is based on shear contact stress at joint level with consequent cartilage wear; pincer FAI, contrariwise, determines normal contact stress between acetabular rim and femoral neck and squeezes the labrum in between, with no cartilage wear for many years from the onset. Pincer prognosis is then far better than cam. As a matter of fact, cartilage wear releases fragments of extracellular matrix which in turn trigger joint inflammation, with consequently worsening lubrication and further enhanced wear. Inflammation pathobiology feeds pathotribology through a vicious loop, finally leading to hip osteoarthritis. The association of cam and pincer, possibly overdiagnosed, is a synergic combination that may damage the joint rapidly and severely. The expectations after FAI surgical correction depend strictly on chondral layer imaging, on time elapsed from the onset of symptoms and on clinic-functional preoperative level. However, preemptive surgical correction is not recommended yet in asymptomatic FAI morphology. Level of evidence V.

Sandwich-structured composites are extensively used in aerospace, transportation, marine, and automotive applications where mechanical performance and weight-saving features are extremely critical. Consequently, analyzing the mechanical properties including the elastic behavior of the sandwich structure is incumbent for the precise application of such composites. This paper deals with the stress analysis of a two-dimensional (2-D) rectangular sandwich-structured composite with the help of a robust numerical model. A finite difference (FD) scheme based on the displacement potential function is developed to investigate the stress-strain behavior of the sandwich structure under different loading conditions. The 2-D mixed-boundary-value elastic problem is solved by implementing special FD formulations inside the domain and at the boundaries. The mathematical intricacy of the interfaces of the sandwich structure is handled by employing modified FD formula structures. Results obtained from the FD model show that the two interfacial regions constitute the critical stress zones, and the material having a higher modulus of elasticity experiences higher stress. The proposed FD model is validated by comparing the FD results for stress distribution and displacement fields with the results obtained from a commercial finite element (FE) package. The comparison between the FE and FD results shows a good agreement which constructively establishes the proposed FD scheme as an accurate and reliable technique for conducting the structural analysis. [ABSTRACT FROM AUTHOR]

We examine the reflection and transmission phenomena of quasi-longitudinal plane (QP) waves in an AlN-ZnO laminated composite structure. The structure is designed under the influence of the initial stresses in which one carrier piezoelectric semiconductor (PSC) half-space is in welded contact with another PSC half-space. The secular equations in the transversely isotropic PSC material are derived from the general dynamic equation, taking the initial stresses into consideration. It is shown that the incident quasi-longitudinal wave (QP-mode) at the interface generates four types of reflected and transmitted waves, namely, QP wave, quasi-transverse (QSV) wave, electric-acoustic (EA) wave, and carrier plane (CP) wave. The algebraic equations are obtained by imposing the boundary conditions on the common interface of the laminated structure. Reflection and transmission coefficients of waves are obtained by implementing Cramer's rule. Profound impacts of the initial stresses and exterior electric biasing field on the reflection and transmission coefficients of waves are investigated and presented graphically. [ABSTRACT FROM AUTHOR]

This study presents the development and validation of a fibre Bragg gratings (FBGs)‐based sensor system for the assessment of strain in the midpalatal suture in subjects using rapid palatal expanders (RPEs). The ex‐vivo experiments were made by means of positioning two RPEs in a porcine palatal region. The RPEs used were the Hyrax, a tooth‐borne expander and MARPE (microimplant‐assisted rapid palatal expansion), a bone‐borne expander. In order to define the regions in the palatal region for the sensors positioning, a finite‐element analysis was performed in a porcine head subjected to the loadings caused by an RPE. In addition, a strain transfer model was used to obtain a correction coefficient that approximates the strain estimated by the FBG to the actual strain in the structure under shear and normal stress. Results show high linearity in the sensors characterisation tests with the advantages of compactness, intrinsic safe operation and multiplexing capabilities of FBGs. In the RPE analysis, a higher strain was estimated in the anterior region, which is in accordance with the simulation and previously reported results, where MARPE showed a higher strain (with an exponential pattern) than Hyrax as the number of activations increase. [ABSTRACT FROM AUTHOR]

In order to explore the mechanical characteristics and stability of the reverse fault under the influence of mining, an inverse mechanics model has been built under work face mining conditions, according to the law of working surface pressure distribution. As a result, a theoretical calculation equation of the normal and shear stresses in the fault zone have been deduced to obtain the stress variation rule between the working surface and the fault layer, under distance conditions of 10, 30, 50, and 70m. With distance conditions of 10 and 30m, the working surface mining stress had an obvious effect on the reverse fault, resulting in a changing trend of firstly increasing, then decreasing, and increasing again in the normal and shear stresses of the fault zone as a whole. With distance conditions of 50 and 70m, the working face mining stress had little effect on the reverse fault; furthermore, the normal and shear stresses exhibited a changing trend of gradually increasing. At a later stage, a simulation of the above distance plans was conducted using the FLAC3D numerical simulation software. The results demonstrated that the influence range of the mining stress on the working face under the spacing distances of 10 and 30m included the fault zone, while under the distance conditions of 50 and 70m, the fault zone was excluded. On this basis, the fault zone stability was analysed under four types of spacing conditions by means of the Mohr Coulomb theory rule and fault activation determination. It is concluded that the fault zone stability was high, with increasing distances between the working face and fault zone. The least sufficient stability was located near the working face, where the fault zone stability was so poor that it is likely to result in impact fracture.

The single adhesive joint has many applications in the shipbuilding industry, where it offers the advantage of joining materials (adherents) with different properties and characteristics using an adhesive. However, one disadvantage of this type of joint is the stress concentration at the ends of the joint, which directly affect the adhesive. Another disadvantage is the possible difference between the coefficients of thermal expansion of the adherents of the joint. Through compilation and classification of the formulas found in various publications, this study presents a state-of-the-art review of an adhesive single-lap joint that can be used in marine applications. It will consider the types of materials used as the adhesive and as the adherents, the possibility of varying the thicknesses of the adherents and the thickness of the adhesive, and the recommended design factors for each proposed methodology. This study proposes formulas to estimate the stresses for joints with balanced thicknesses and extrapolates the results for nonbalanced joints; also, an equation is derived to calculate the minimum overlap joint length for ship lengthening, allowing the design process to be simplified. The results are expected to facilitate the design of single-lap joints in marine applications, such as reinforcing composite panels and lengthening of hulls and superstructures. [ABSTRACT FROM AUTHOR]

Femoroacetabular impingement (FAI), together with its two main pathomechanisms, cam and pincer, has become a trending topic since the end of the 1990s. Despite massive academic research, this hip disorder still conceals obscure aspects and unanswered questions that only a question-driven approach may settle. The pathway that leads a FAI asymptomatic morphology through a FAI syndrome to a FAI-related osteoarthritis is little known. Contact mechanics provides a shareable and persuasive perspective: cam FAI is based on shear contact stress at joint level with consequent cartilage wear; pincer FAI, contrariwise, determines normal contact stress between acetabular rim and femoral neck and squeezes the labrum in between, with no cartilage wear for many years from the onset. Pincer prognosis is then far better than cam. As a matter of fact, cartilage wear releases fragments of extracellular matrix which in turn trigger joint inflammation, with consequently worsening lubrication and further enhanced wear. Inflammation pathobiology feeds pathotribology through a vicious loop, finally leading to hip osteoarthritis. The association of cam and pincer, possibly overdiagnosed, is a synergic combination that may damage the joint rapidly and severely. The expectations after FAI surgical correction depend strictly on chondral layer imaging, on time elapsed from the onset of symptoms and on clinic-functional preoperative level. However, preemptive surgical correction is not recommended yet in asymptomatic FAI morphology. Level of evidence: V. [ABSTRACT FROM AUTHOR]

Copyright of Coal Science & Technology (0253-2336) is the property of Coal Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Highlights • Experimental assessment of the LWAC-to-NDC interfaces, with different surface roughness. • Influence of the normal stress and reinforcement ratio at the interface behavior. • The lightweight aggregates decrease the interface strength. • The rebars did not increase the maximum shear strength, contrary to codes predictions. • Proposal of expressions to predict the coefficients of cohesion and friction. Abstract This experimental study aims to characterize the behavior of LWAC-to-NWC interfaces, using a substrate of normal weight concrete (NWC) with different surface roughness and three lightweight aggregate concrete (LWAC) mixtures for the overlay, with a density ranging between 1500 and 1900 kg/m3 and a compressive strength varying between 45 and 75 MPa. The NWC-to-NWC interfaces were also tested to be used as reference, only one NWC with a compressive strength of 50 MPa was used. Two more parameters were considered in this study, the normal stress applied at the interface and the reinforcement ratio crossing the interface. Results were analyzed and compared with predictions according to Eurocode 2, fib Model Code 2010 and ACI 318-14, showing significant differences, mainly when LWAC is added, proving that the binding matrix strength is an important parameter in this analysis and that the cohesion component is underestimated by codes. It was also concluded that the incorporation of the lightweight aggregates decreases the interface strength and the rebars did not have a clear increase in the maximum shear strength, contrary to predictions of some codes. Expressions based on the roughness parameter are presented to predict the coefficients of cohesion and friction. [ABSTRACT FROM AUTHOR]

Due to stress concentration at the edges, fiber-fiber bonds under load are known to fail gradually inwards from the edges. In this paper, we propose a failure mechanism for fiber-fiber joints under load, based on the peak stresses occurring at the bond edges. We have modeled the mechanical testing of individual fiber-fiber joints using a finite element method (FEM) framework. The model is based on experimental results of fiber-fiber joint strength tests designed to induce each of the three modes in fracture mechanics: opening, sliding, and tearing. A parametric study of the peak load at the edges of the fibers was carried out in order to identify a failure mechanism. The peak stresses were not directly taken from the FEM models, as these values are highly discretization-dependent. Instead, the peak stresses were estimated from resultant forces and moments in the bond and an idealized geometry of the bonding region. The literature has, up to now, focused on shear load as a failure mechanism for fiber-fiber bonds. However, our findings indicate that pulp fiber joints are sensitive to normal stresses and insensitive to shear stresses. Hence, we suggest utilizing failure criteria related to normal stress in future work.

Abstract This paper presents the results of examination of shear properties of rockfills used for the construction of rockfill dams. Based on the results of a large number of experiments, mathematical model of the shear strength of the rockfill was derived, as a function of normal stress, initial compaction and uniaxial compressive strength of intact rock material. Using this model it is possible to make a realistic assessment of the shear strength of a rockfill for the Preliminary Design. The experimental data used for modelling were obtained by direct shear tests performed in the majority at the "Jaroslav Cerni" Institute for Development of Water Resources in Belgrade, Serbia. [ABSTRACT FROM AUTHOR]

The motivation for this work is a desire for a deeper understanding of the structural failures in a composite glider wing, which has been tested in the laboratories of the Institute of Aerospace Engineering, Faculty of Mechanical Engineering, Brno University of Technology. To understand the causes of the encountered failures, one has to consider the effects of all the stages in the design, manufacturing and testing of the wing. This paper focuses only on the design stage. The presented facts were obtained from a finite element analysis. The geometry used for the analysis is that of the tested specimens. This allows validating the results by the comparison of the deformation and strains measured during the laboratory tests. The analysis starts with a simple I-beam loaded by three-point-bending. In the next step a cantilever is added. Several more modifications follow, changing the I-beam to the wing. The case evaluation considers the interaction between normal (material direction 1) and inter-laminar shear stresses in the upper flange. The goal of this paper is to quantify the effect of each design change in the wing structure and loading on the stress plane σ1-τ31.

Artificial heart valves may expose blood to flow conditions that lead to unnaturally high stress and damage to blood cells as well as issues with thrombosis. The purpose of this research was to predict the trauma caused to red blood cells (RBCs), including hemolysis, from the stresses applied to them and their exposure time as determined by analysis of simulation results for blood flow through both a functioning and malfunctioning bileaflet artificial heart valve. The calculations provided the spatial distribution of the Kolmogorov length scales that were used to estimate the spatial and size distributions of the smallest turbulent flow eddies in the flow field. The number and surface area of these eddies in the blood were utilized to predict the amount of hemolysis experienced by RBCs. Results indicated that hemolysis levels are low while suggesting stresses at the leading edge of the leaflet may contribute to subhemolytic damage characterized by shortened circulatory lifetimes and reduced RBC deformability.

The basic mechanical behavior of a nonprismatic concrete-encased beam with corrugated steel webs (CSWs) was investigated through a scalemodel experiment and finite-element model analysis. Because of the influence of variable cross sections and the concrete encasement, results of this study contradicted the assumption that CSWs bear all of the shear force in a nonprismatic beam. The inclined bottom flange resisted a significant portion of the shear force in the section under longitudinal bending moment. Shear stress in the CSW was uniformly distributed through the cross section when the CSWs were encased in concrete. In addition, the authors made the counterintuitive finding that the average shear stress in the CSW decreased gradually from the free end to themiddle support. In other words, the root section near the support did not exhibit the greatest stress concentration, even though this region had the maximumvertical shear force and the largest hogging bending moment. Last, normal strain in concrete flanges and the concrete web approximately obeyed the plane section assumption. The longitudinal bending moment was mainly balanced by the moment from coupled axial forces in the concrete flanges. In general, the CSWs encased in concrete were unable to provide sufficient bending strength. [ABSTRACT FROM AUTHOR]

Copyright of e-GFOS is the property of Electronic Journal of the Faculty of Civil Engineering Osijek-e-GFOS and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The motivation for this work is a desire for a deeper understanding of the structural failures in a composite glider wing, which has been tested in the laboratories of the Institute of Aerospace Engineering, Faculty of Mechanical Engineering, Brno University of Technology. To understand the causes of the encountered failures, one has to consider the effects of all the stages in the design, manufacturing and testing of the wing. This paper focuses only on the design stage. The presented facts were obtained from a finite element analysis. The geometry used for the analysis is that of the tested specimens. This allows validating the results by the comparison of the deformation and strains measured during the laboratory tests. The analysis starts with a simple I-beam loaded by three-point-bending. In the next step a cantilever is added. Several more modifications follow, changing the I-beam to the wing. The case evaluation considers the interaction between normal (material direction 1) and inter-laminar shear stresses in the upper flange. The goal of this paper is to quantify the effect of each design change in the wing structure and loading on the stress plane σ1-τ31. [ABSTRACT FROM PUBLISHER]

In the limit equilibrium framework, two- and three-dimensional slope stabilities can be solved according to the overall force and moment equilibrium conditions of a sliding body. In this work, based on Mohr-Coulomb (M-C) strength criterion and the initial normal stress without considering the inter-slice (or inter-column) forces, the normal and shear stresses on the slip surface are assumed using some dimensionless variables, and these variables have the same numbers with the force and moment equilibrium equations of a sliding body to establish easily the linear equation groups for solving them. After these variables are determined, the normal stresses, shear stresses, and slope safety factor are also obtained using the stresses assumptions and M-C strength criterion. In the case of a three-dimensional slope stability analysis, three calculation methods, namely, a non-strict method, quasi-strict method, and strict method, can be obtained by satisfying different force and moment equilibrium conditions. Results of the comparison in the classic two- and three-dimensional slope examples show that the slope safety factors calculated using the current method and the other limit equilibrium methods are approximately equal to each other, indicating the feasibility of the current method; further, the following conclusions are obtained: 1) The current method better amends the initial normal and shear stresses acting on the slip surface, and has the identical results with using simplified Bishop method, Spencer method, and Morgenstern-Price (M-P) method; however, the stress curve of the current method is smoother than that obtained using the three abovementioned methods. 2) The current method is suitable for analyzing the two- and three-dimensional slope stability. 3) In the three-dimensional asymmetric sliding body, the non-strict method yields safer solutions, and the results of the quasi-strict method are relatively reasonable and close to those of the strict method, indicating that the quasi-strict method can be used to obtain a reliable slope safety factor. [ABSTRACT FROM AUTHOR]

Shear stress distributions in mono-symmetric tapered I-beams are incorrectly predicted by the conventional beam analysis method used for uniform beams. More accurate predictions are obtained by assuming that the normal stress trajectories vary linearly between plate edges, instead of parallel to the centroidal axis. Transverse shear stresses at the flange-web junctions of mono-symmetric tapered I-beams of constant depth are induced by gradients of the forces in the tapered flanges. The transverse shear stress distributions caused by axial force, moment, and shear force are constant, linear, and parabolic, respectively. Axial force induces non-zero principal axis shear stresses, while shear force induces non-zero normal stresses acting parallel to the centroidal axis. [ABSTRACT FROM AUTHOR]

Shear stress distributions in tapered web I-beams are incorrectly predicted by the conventional beam analysis method used for uniform beams. More accurate predictions are obtained by adopting the finding for wedges that the normal stress trajectories are radial instead of parallel. The shear stress distributions in web-tapered I-beams are influenced by the vertical components of the inclined flange forces (which are zero in uniform beams), as well as by the normal stress gradients in the flanges. The net web shear equal to the difference between the external shear and the vertical components of the inclined flange forces is resisted by the resultant of the vertical components of the normal stresses and the circumferential shear stresses. The circumferential shear stresses τ rθ have linear components due to axial force and parabolic components due to moment and shear. The magnitudes of these stresses are controlled by the normal stress gradients at the flange-web junctions and by the requirement that the web shear resistance must equal the net web shear force. [ABSTRACT FROM AUTHOR]

Frictional strength and heat flow of faults are two related subjects in geophysics and seismology. To date, the investigation on regional frictional strength and heat flow still stays at the stage of qualitative estimation. This paper is concentrated on the regional frictional strength and heat flow of the southern San Andreas Fault (SAF). Based on the in situ borehole measured stress data, using the method of 3D dynamic faulting analysis, we quantitatively determine the regional normal stress, shear stress, and friction coefficient at various seismogenic depths. These new data indicate that the southern SAF is a weak fault within the depth of 15 km. As depth increases, all the regional normal and shear stresses and friction coefficient increase. The former two increase faster than the latter. Regional shear stress increment per kilometer equals 5.75 ± 0.05 MPa/km for depth ≤15 km; regional normal stress increment per kilometer is equal to 25.3 ± 0.1 MPa/km for depth ≤15 km. As depth increases, regional friction coefficient increment per kilometer decreases rapidly from 0.08 to 0.01/km at depths less than ~3 km. As depth increases from ~3 to ~5 km, it is 0.01/km and then from ~5 to 15 km, and it is 0.002/km. Previously, frictional strength could be qualitatively determined by heat flow measurements. It is difficult to obtain the quantitative heat flow data for the SAF because the measured heat flow data exhibit large scatter. However, our quantitative results of frictional strength can be employed to investigate the heat flow in the southern SAF. We use a physical quantity P to describe heat flow. It represents the dissipative friction heat power per unit area generated by the relative motion of two tectonic plates accommodated by off-fault deformation. P is called 'fault friction heat.' On the basis of our determined frictional strength data, utilizing the method of 3D dynamic faulting analysis, we quantitatively determine the regional long-term fault friction heat at various seismogenic depths in the southern SAF. The new data show that as depth increases, regional friction stress increases within the depth of 15 km; its increment per kilometer equals 5.75 ± 0.05 MPa/km. As depth increases, regional long-term fault friction heat increases; its increment per kilometer is equal to 3.68 ± 0.03 mW/m/km. The values of regional long-term fault friction heat provided by this study are always lower than those from heat flow measurements. The difference between them and the scatter existing in the measured heat flow data are mainly caused by the following processes: (i) heat convection, (ii) heat advection, (iii) stress accumulation, (iv) seismic bursts between short-term lull periods in a long-term period, and (v) influence of seismicity in short-term periods upon long-term slip rate and heat flow. Fault friction heat is a fundamental parameter in research on heat flow. [ABSTRACT FROM AUTHOR]