Strength Reduction Factor Research Articles

Substantiating the rock mass control parameters based on the geomechanical model of the Severny Katpar deposit, Kazakhstan

Purpose. The research purpose is to develop a geomechanical model for ensuring the safety of mining operations by determining the optimal slope angles and probabilistic assessment of the stability of the open-pit walls. Methods. Three-dimensional geomechanical models for surface mining of deposits have been developed based on calculations of the stability factor (safety factor SF) of the open-pit walls in the Rocscience program to determine the rock mass stress-strain state at the end of mining using the finite element method. The geological wireframe model (GWM) has been built on the basis of the available geological sections, horizon plans and the results of the engineering-geological surveys using the Surpac geoinformation system. Findings. Strength reduction factor (SRF) has been determined taking into account the physical-mechanical properties of rocks that constitute the near-wall mass. An assessment of the stability of walls according to the selected geological sections is given, taking into account the projected contour of the Severny Katpar open-pit walls. The calculation of the projected contour stability of the open-pit walls by several different methods has revealed that the open-pit walls are generally stable. The open-pit parameters at the end of mining have been determined. Originality. For the first time, it has been determined that in the Southern and South-Western area of the Severny Katpar open-pit wall in the horizons +700…+400, there is a decrease in SF from 1.18 to 1.41 due to the predominant occurrence of siltstones and tectonic disturbances of the walls. Practical implications. The mathematical calculation results of the stability of the projected contour walls in the Severny Katpar open pit have been generalized. In addition, a geological and structural wire-frame model of the deposit has been developed, which makes it possible to ensure the safety of mining operations in the open pit.

Effect of Stacking Sequence on Long-Term Creep Performance of Pultruded GFRP Composites.

Pultruded glass-fibre reinforced polymer (pGFRP) composites are classified as lightweight material, which exhibit high strength-to-weight ratio for structural usage. This composite material has been applied as cross-arm members in transmission towers due to its ability in thermal and electrical insulation. However, the influence of the stacking sequence of pGFRP composite on its mechanical performance has not been fully covered in the literature to explain the long-term durability of the current cross-arm designs. The study expected to evaluate five fiber layers with various stacking sequences in terms of quasi-static and creep tests in a four-point bending mode. The creep test was performed for 1440 h (60 days). These composites were fabricated using the pultrusion process in the form of a square hollow structure. Later, it was cut into composite coupons with various sizes depending on the test conducted. The results showed that nine layers with 0°/45°/0°/−45°/0°/−45°/0°/45°/0° had the ultimate flexural strength. This stacking sequence configurations seemed to be optimally manufactured in continuous roving fibre by alternating between 0° and ±45° fiber orientations. Additionally, the S-9 pGFRP composite sample showed that it had a low-creep deflection with high elastic and apparent creep moduli in 1440 h. In terms of strength reduction factor, this configuration was recorded as the highest. The findings showed that the nine layers of pGFRP composites with alternation of 0° and ±45° fiber orientations were highly suitable for structural application at transmission towers for a long-term operation.

Strength capacity of hollow clay blocks structural masonry - Flange, Chases, and slenderness effects

Unplanned chases made in structural masonry for the passage of pipes can compromise the overall strength of the structure. This interference does not have clearly established and uniform criteria in Brazilian and international standards for assessing the deformability and consequent safety reduction of the walls. The present study evaluates numerically, by using the Finite Element Method (FEM) and fitting procedures, the effect of chases in masonry walls elements, proposing a method to preview walls strength reductions with the presence of chases. Thus, an additional criterion for the reduction factor (R) due to the masonry slenderness is presented. The contribution of the flanges is also evaluated for different height/length ratios. The simplified approach of disregarding the chase thickness of the wall determine its slenderness (λ), and consequently the strength reduction factor (R), was invalidated in the present study, considering that the numerical models provided lower reduction coefficients for any wall group studied. The slenderness of the walls considering the residual wall thickness in the chase region must be limited to 33.

Actual weld profile fatigue performance by digital prototyping of defected and un‐defected joints

AbstractThis paper considers the effects of the actual weld profile on the fatigue behavior of welded joints by means of the implicit gradient approach. Different types of geometrical approximation are considered in the analysis. In order to define the fatigue strength reduction factor of the actual weld profile, FE analyses have been considered based on a three‐dimensional scan of the welded joints. Furthermore, the fatigue behavior of butt‐welded joints with a discontinuous undercut is considered, and a comparison has been made with experimental data taken from the literature.

Damage-based strength reduction factor spectra of structures subjected to bidirectional ground motions

The current research on the damage-based strength reduction factor has been completely based on the inelastic single-degree-of-freedom systems that are more suitable for two-dimensional analyses. Therefore, it is necessary to construct damage-based strength reduction factor spectra for systems subjected to bidirectional ground motions. In this study, an inelastic single-mass bi-degree-of-freedom (SMBDOF) system subjected to the orthogonal bidirectional ground motions with the hysteretic property of two-dimensional yield-surface plasticity function is presented, and the x-component of the system is used to construct the damage-based strength reduction factor spectra of the system ( R b spectra). The Park-Ang damage model is used to determine the constant damage index of the R b spectra. In addition, 178 ground motion records for site classes C, D, and E are considered as ground excitations of the SMBDOF system to construct the mean R b spectra with the format of R b- D- T for a given ductility capacity and R b- μ u- T for a given damage level. The R b spectra of the SMBDOF system is compared with the corresponding R spectra of the SDOF system. Statistical analysis considering different values of the natural period, ductility capacity, damage index, period ratio, and site condition is conducted. Analysis results show that the coupling of two-component responses of an inelastic system could increase the strength demand of the system in certain cases; the trend of the R b spectra presented in this study is approximately consistent for different site classes, but the spectral values have the characteristic of site conditions. Therefore, the influence of the period ratio should be considered because a large period difference between two components of the SMBDOF system could aggravate seismic damage in certain situations. Based on the statistical analysis, the expression of R b spectra curves with a period ratio γ = 1 is derived using the regression analysis, and the correction expression is obtained considering the influence of the period ratio on the R b spectra. Then, the construction procedure of the R b spectra is introduced. The predicted R b spectra obtained by the proposed procedure is compared with the actual mean spectra, and comparison results indicate a good match.

Estimation and Application of Strength and Stiffness Reduction Factors of Liquefiable Soil

The reduction of soil strength and stiffness caused by soil liquefaction is an important issue in designing pile or shallow foundations on liquefiable soils. In practice, strength and stiffness reduction is considered via a reduction factor ([Formula: see text]) approach in seismic design. Different sets of values of [Formula: see text] are available according to the factor of safety against liquefaction ([Formula: see text]) of the liquefiable soil; these ([Formula: see text]) values are usually calculated using simplified liquefaction analysis procedures. Each set of [Formula: see text] is calibrated and constructed for specific simplified liquefaction analysis procedures or soil conditions. Thus, engineers have difficulty in selecting [Formula: see text] when using a simplified liquefaction analysis procedure without a corresponding set of [Formula: see text]. In this study, values of [Formula: see text] for simplified liquefaction analysis procedures commonly used in Taiwan are obtained using a single element test via FLAC program and UBCSAND model. In addition, a novel application of [Formula: see text] is introduced to improve the usability of the simplified numerical procedure used to predict the liquefaction-induced settlement of a shallow foundation. Simulation results show that the simplified numerical procedure with [Formula: see text] approach yields a convincing and conservative result.

Assessment of end-two-flange web crippling strength of roll-formed aluminium alloy perforated channels by experimental testing, numerical simulation, and deep learning

This work presents a deep-learning model referred to as a deep belief network (DBN) to investigate the end-two-flange (ETF) web crippling behaviour of roll-formed aluminium alloy lipped channels (both unfastened and fastened to the supports) with centred and offset web circular holes. A total of 1,080 data points was generated for training the DBN, using an elasto-plastic finite element model that was validated using 30 new experimental results presented in this paper. When the DBN predictions were compared to the experimental results, they were found to be 5% conservative on an average. A parametric analysis was then carried out using the DBN predictions, to study the effects of hole size, hole position, section thickness, and the bearing plate on web crippling strength of perforated roll-formed aluminium alloy channels. The DBN predictions were utilised to evaluate the performance of the current design rules of American Iron and Steel Institute (AISI 2016), Australian and New Zealand Standards (i.e., AS/NZS 1664, AS/NZS 4600:2018), and Eurocode (CEN 2007). The current design standards were demonstrated to be over conservative in predicting the web crippling strength of roll-formed aluminium alloy perforated channels. From the parametric analysis, new web crippling strength and web crippling strength reduction factor formulae for roll-formed aluminium alloy perforated channels were proposed. Additionally, a reliability analysis revealed that the proposed equations accurately predicted the ETF web crippling strength of roll-formed aluminium alloy perforated lipped channels.

Seismic design of self-centering bridge piers considering soil-structure interaction

This paper presents the seismic design method for self-centering (SC) bridge piers considering soil-structure interaction (SSI) based on the inelastic displacement ratios (CR). The pier is simplified to a single-degree-of-freedom (SDOF) system characterized by flag-shaped hysteretic behavior. The cone model is adopted to simulate the dynamic behavior of the elastic homogeneous soil half-space below the foundation. Firstly, nonlinear time history analyses are conducted by subjecting the soil-structure interaction systems to 20 synthetic ground motions matched to the design response spectra. The effects of different parameters including the fundamental period of the fixed-base superstructure Tfix, strength reduction factor R, secondary stiffness ratio α, energy dissipation ratio of the flag-shaped model β, structure-to-soil stiffness ratio a0, and the height of the pier hs on the inelastic displacement ratios are studied. The analysis results show that the inelastic displacement ratio of the self-centering pier is generally underestimated when SSI is ignored. Specifically, the analytical relationship among CR, R, and Tfix is developed through regression analysis and used to estimate the inelastic displacement demands of the soil-structure systems during the design process. Next, the effects of soil on the elastic structural base shear force are investigated using the base shear effect coefficient RSSI and a simple equation is developed through regression analysis to estimate the RSSI value. A seismic design procedure of the self-centering piers considering soil-structure interaction is then proposed. Finally, a design example demonstrates the application of the proposed.design procedure, and 12 natural ground motions are used to perform nonlinear time history analyses of the designed self-centering pier. The analysis results verify the effectiveness of the proposed seismic design method.

Historic subsurface dimension stone quarry and the stability of its galleries as a function of pillar width and thickness of cover bed

There are historic subsurface dimension stones in the capital of Hungary (Budapest) that were excavated in porous limestone. The stability of these subsurface openings is important, since most of them are located in urban areas, where existing buildings or new structures are planned to be built. The paper presents a detailed study considering the geometry of the system and the mechanical parameters of the limestone. The geometry of the cellar system was obtained using terrestrial laser scanning (TLS). The cover beds are few meters in thickness, and the width of the pillar is between 2.50 and 3.98 m, according to the measurements. The rock mass parameters which were used in the calculations were obtained from laboratory tests. A finite element (FEM) software Rocscience (RS2) were applied to model the stability of the galleries. Calculations were made for various geometries taking into account the thickness of cover beds and the width of pillars. Altogether 70 models were made. A surface load of 150 kN/m2 was also applied to model the buildings. New relationships between cover bed thickness, pillar width and displacements are outlined to compare these results to previous works. The strength reduction factor was also calculated for all geometries, indicating the changes in the stability of these underground quarries and pointing out the importance of cellar geometries.

Web crippling design of cold-formed high strength steel SHS and RHS at elevated temperatures

This study investigates the web crippling capacities of cold-formed high strength steel (CFHSS) hollow structural section members at elevated temperatures. A numerical investigation on square and rectangular hollow sections (SHS and RHS) undergoing web crippling was performed at various temperatures from 21 °C to 1000 °C. Finite-element (FE) models were firstly developed to replicate the available web crippling tests on CFHSS SHS and RHS members. After validation, extensive parametric studies with 784 specimens covering all four codified web crippling load cases in the current cold-formed steel design specifications were performed. The reductions of web crippling capacities at elevated temperatures were compared against the corresponding yield strength and elastic modulus reduction factors of the materials. The suitability of available web crippling design provisions in current codes of practice and literature to CFHSS sections at elevated temperatures was evaluated. Comparison results reveal that the direct strength method (DSM) previously proposed by the authors at ambient temperature could be extended to elevated temperature conditions and would provide rather consistent and reliable predictions than other existing provisions. A modified DSM is put forward in this paper and it is found that the modified DSM is suitable for web crippling design of the CFHSS sections at both elevated and ambient temperatures, and moreover, can also be used for cold-formed stainless steel SHS and RHS of various grades. Therefore, the modified DSM is recommended to be used for web crippling design of CFHSS and stainless steel SHS and RHS at elevated and ambient temperatures.

Strength Reduction Factor for Circular Reinforced Concrete Columns

Strength Reduction Factor for Circular Reinforced Concrete Columns

Numerical Analyses of Tunnel Outlet Slope at Leuwikeris Dam, West Java, Indonesia

The excavated slope of the diversion tunnel outlet at the Leuwikeris Dam was designed based on core test data and the Circular Failure Chart (CFC) method. Stability of the excavated slope under static and seismic loads has not been verified using a different method. The objective of this research was to evaluate performance of the excavated slope under static and seismic loads using the finite element method (FEM). Stability analyses of the natural slope were also carried out to assess the improved stability of the slope after excavation. Geological mapping, examinations of drill cores and borehole logs, and laboratory tests were conducted to characterise the soils and rocks comprising the tunnel outlet slope. The rock masses were characterised using the Geological Strength Index (GSI) for the input parameters of the Generalised Hoek-Brown criterion. The slope stability analyses under static and seismic loads were performed using the finite element-based computer package RS2. The results show that the diversion tunnel construction site consists of residual soil and very poor to fair quality andesite breccia rock and tuff breccia with thin claystone intercalation. The groundwater table was located approximately 40 m below the ground surface. In general, the seismic load reduced stability of the slopes. The critical strength reduction factor (SRF) values of the natural portal slope, which had 40º inclination, were 3.6 and 1.45 under static and seimic loads, respectively. Meanwhile, the SRF values of the excavated slope, which had seven benches and 55 to 74º inclinations, were 3.83 and 1.78 under static and seismic loads, respectively. The natural and excavated slopes were considered stable under static and seismic loads and met the stability criteria specified by the National Standardization Agency (2017). The slope design increased the slope FS values by 6% and 20% under static and seismic loads, respectively.

A Numerical Analysis of the Leakage Characteristics of an Embankment Dam Slope With Internal Erosion

Leakage is a common defect of embankment dam slopes, and is usually accompanied by internal erosion. This study establishes a mathematical two-phase seepage coupling model that explicitly considers the effects of internal erosion. With the help of finite element software COMSOL Multiphysics®, we use this model to study the characteristics of fluid seepage, the fraction of leakage volume that is made up of migrated fine particles (migrated fine particles volume fraction), porosity, permeability, and displacement in the leakage process of a three-dimensional embankment dam slope, as well as to study the influence of the water level and leakage outlet size on the aforementioned features. Our results show that water seepage velocity gradually increases with time, especially at the downstream leakage outlet. Therefore, the erosion and migration of fine particles occur primarily at the downstream leakage outlet, resulting in a significant increase in the migrated fine particles volume fraction, porosity, and permeability. In addition, the maximum migrated fine particles volume fraction, the maximum porosity, and the maximum permeability in the slope increase nonlinearly with time. Curves for maximum displacement with a strength reduction factor can be divided into three stages: the early stable stage, the midterm nonlinear growth stage (creeping state), and the later rapid growth stage (instability state). We also find that the rise of the water level promotes the erosion and migration of fine particles on the slope and that the maximum migrated fine particles volume fraction and the maximum porosity increase with the water level. The values of the strength reduction factor for the creeping state decrease as the water level rises. Furthermore, the larger the size of the downstream leakage outlet, the larger the maximum migrated fine particles volume fraction and maximum porosity. However, the relationship between maximum displacement and strength reduction factor is nearly unaffected by the size of the leakage outlet.

Structural fuse design of bolted steel frame with low yield point angle steel connection components

In order to realize the urgent requirement for damage control and rapid recovery of structural function after earthquake excitations using more convenient strategies, a bolted steel frame equipped with replaceable dissipative angle steel connection components was proposed. These angle steels with designed free deformation length were made of low yield point steels (LYP) which have superior ductility, dissipation capacity and fatigue performance. The plastic deformation was expected to be circumscribed within the LYP angle steels, which behaved as structural fuses to protect the primary frame members and were easy to be demolished and replaced. To achieve this desired damage control objective, the quantitative influence of the key factors on the seismic performance and the structural fuse effect was evaluated via extensive numerical parametric analyses. The design procedure of the corresponding sizes of LYP connection components to act as structural fuses was further summarized on account of energy dissipation behavior. The analysis results demonstrated that the larger the strength reduction factor (the smaller design resistance capacity coefficient), free deformation length and height of beam section promoted the structural fuse action of the LYP connection components. In terms of comprehensive consideration of structural ductility, load-carrying capacity, structural fuse performance and material efficiency, the design resistance capacity coefficient (the strength reduction factor) was suggested as αd=0.8∼1.0, and the free deformation length ranged from 0.67 to 1.1 times of beam width. The critical value of the design resistance capacity coefficient to achieve desirable structural fuse effect was formulated by integrating above-mentioned key influencing factors. Consequently, the design resistance capacity coefficient was required to be less than this critical value to realize sufficient damage control objective.

Effect of web perforations on end-two-flange web crippling behaviour of roll-formed aluminium alloy unlipped channels through experimental test, numerical simulation and deep learning

Aluminium alloy has recently become popular in New Zealand’s construction sector as a sustainable building material. However, in roll-formed aluminium alloy (RFA) channel beams, particularly those having web holes, cripples at points of concentrated or localised loading. In this paper, end-two-flange (ETF) web crippling behaviour of RFA unlipped channels having web holes was investigated using experimental tests, numerical simulations and a deep learning model referred as deep belief network (DBN). A total of 1080 data points was generated to train the DBN, using a finite element (FE) model that was validated using 30 new experimental results reported in this paper. Compared to the test data, the DBN predictions were conservative by around 6%. Using the DBN predictions, a comprehensive parametric study was undertaken which used the validated FE model in order to explore the effects of hole size, hole location, section thickness, and bearing plate on the web crippling strength of RFA channels having web holes. Web crippling strengths obtained from the DBN, tests and finite element analysis (FEA) were utilised to evaluate the performance of current design specifications from the American Iron and Steel Institute (AISI), Australian/New Zealand Standards (AS/NZS 1664; AS/NZS 4600:2018) and Eurocode (CEN 2006, 2007). It is shown that the current design rules are not reliable to predict the web crippling strength of RFA unlipped channels with web holes. As a consequence of the parametric analysis, new web crippling strength and web crippling strength reduction factor formulae for perforated RFA unlipped channels were proposed. A reliability analysis was then conducted, which confirmed that the proposed equations are capable of predicting the ETF web crippling strength of perforated RFA unlipped channels.

Effects of Substitution of Fine Aggregate with Recycled Asphalt Pavement on Compressive Strength of Normal Concrete

In this research, the compressive strength of concrete utilizing fine recycled asphalt pavement (fine RAP) as fine aggregate substitution for natural sand is investigated at weight percentages of 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 percent. The compressive strengths of concrete were designed according to ACI 211.1 standard for 18 MPa, 25 MPa, 32 MPa and 40 MPa at 28 days of curing. The compressive strengths of the concrete using fine RAP aggregate in this study were compared to the ones that use the natural aggregate in the same proportions. From the results of the tests, it was found that the compressive strength of concrete using fine RAP is dependent on the amount of Fine RAP used in the mix proportions. Test results also indicated that there is a systematic reduction in the compressive strengths with the increase in the weight percentages of the fine RAP. The relationship between the normalized compressive strength and the weight percentages of the fine RAP were proposed. Finally, a suggested strength reduction factor for the concrete using fine RAP as aggregate was also proposed.

Multiaxial fatigue life prediction model considering stress gradient and size effect

Stress gradient effect (SGE) and notch size effect (NSE) have important influences on the fatigue performance of engineering components. In this paper, a new multiaxial fatigue life prediction model is developed by considering the effects of both. Firstly, with the help of the coordinate transformation principle (CTP), the location of the dangerous critical plane is found according to the energy-critical plane (ECP) method, and the equivalent stress gradient factor (SGF) within the fatigue damage zone is calculated by analyzing the equivalent stress distribution on the critical plane. Secondly, considering the size of the notch, the effect of stress concentration at the notch is analyzed. Meanwhile, a size influence factor is introduced to characterize the NSE and construct a new fatigue strength reduction factor. Further, combining with the Manson-Coffin equation (MC equation), a new fatigue life prediction model for multiaxial notched components is proposed by considering SGE and NSE on fatigue damage. Finally, the experimental data of fatigue specimens with different notch sizes processed by En8 and GH4169 materials are used for model validation and comparison with other three classical models, and the results show that the prediction life of the new model for proportional and non-proportional loads is within two-fold dispersion band and the prediction ability is better than the other three classical models.

Structural behaviour of back-to-back cold-formed steel channel sections with web openings under axial compression at elevated temperatures

This paper investigates the structural behaviour of cold-formed steel (CFS) back-to-back (BTB) channel sections subjected to axial compression at elevated temperatures. The stress-strain curves of G250 grade CFS channels at ambient and elevated temperatures were taken from the literature, where the temperature varied from 20 to 700 °C. A detailed parametric analysis comprising 1554 validated finite element models was studied to investigate the effect of section size, web openings and elevated temperature on the structural behaviour of such channel sections. Based on the parametric analysis results, the design equations for axial strength reduction factors for CFS BTB channel sections at elevated temperatures were proposed, which outperformed the equations available in the design guidelines of American standard (AISI S100-16) and Australian/New Zealand standard (AS/NZS 4600:2018). Reliability analysis was then conducted, the results of which showed that the proposed design equations could closely predict the axial strength of CFS BTB channel sections at elevated temperatures.

High-strain rate tension behavior of Fiber-Reinforced Rubberized Concrete

This paper investigates for the first time the high-strain rate splitting tension behavior of Fiber-Reinforced Rubberized Concrete (FRRC). Splitting tension tests were performed on Φ100-mm specimens. Quasi-static tests were carried out using conventional quasi-static loading with a compressive testing machine and dynamic high-strain rate tests with a Φ80-mm Split Hopkinson Pressure Bar (SHPB) for strain rates up to 10s−1. The experimental program comprises the characterization of Plain Concrete (PC), Fiber Reinforced Concrete (FRC), Rubberized Concrete (RuC), and FRRC with a full test matrix (a total of 240 specimens) covering fiber contents up to 1.5% and rubber volume substitution ratios up to 30%. A high-speed camera was used to capture the cracking development processes together with Digital Image Correlation (DIC). The addition of fibers enhances the deformation capacity with a marked increase in the tensile strength both for quasi-static and dynamic conditions while the substitution with rubber aggregates significantly reduces the tensile strength with a similar enhancement of the deformation capacity. For FRRC, a combination of the two effects was observed. FRC, RuC, and FRRC are characterized by marked strain rate dependency within the considered test range. Furthermore, data-driven models for compression and tension strength reduction factor (SRFc and SRFt) and tension Dynamic Increase Factor (DIF) are proposed for different types of FRRC. Finally, a discussion on the image-based damage development processes is provided based on the high-speed camera videos. This study indicates that FRRC has an excellent high-strain rate tension behavior reducing and controlling the crack propagation.

Buckling behavior of slender square concrete filled steel tubular columns strengthened with CFRP profile under combined compression and bending

An innovative stub composite column consisting of square concrete-filled steel tubular (SCFST) column internally strengthened with a I-shaped pultruded CFRP profile, referred to as SCFST-CFRP column, has been developed. Research studies have demonstrated that this new stub column has the higher axial load capacity and ductility with the less weight in comparison to the SCFST column. Considering the use of slender column in the engineered systems, this study investigated resistance and behavior of slender SCFST-CFRP columns under the combined compression and bending. In the experimental program, the combined loading tests were completed on nine groups of specimens with varied slenderness ratios and load eccentricities. The column buckling behavior was analyzed in terms of failure modes, moment-curvature response, peak loads, longitudinal strain response, and strength reduction factors. The results addressed the differences in buckling behavior between SCFST-CFRP column and SCFST column. Finite element models were created and validated to evaluate influences of critical structural parameters on column resistance and provide supplementary numerical data. In addition, the tested and simulated results were utilized to assess the applicability of existing design approaches, as suggested in the AISC-LRFD specification, the GB50936 code, and empirical equations provided by Han, for the SCFST-CFRP slender column under the combined compression and bending. Validation results identified that the GB50936 code provided relatively accurate predictions of the slender column capacities under the combined loads, while the predicted capacity was not safe for the column with a large slenderness ratio. An improvement in the GB50936 design method was conducted using the test and simulation data for the SCFST-CFRP column under the combined compression and bending.