Single Degree Of Freedom Analysis Research Articles

ANCHORAGE DESIGN FOR BLAST-RESISTANT WINDOWS

This paper presents a summary of experimental research on the performance of blast-resistant window anchors and the development of a design procedure for the anchors. The experimental results, obtained from forty-six window tests conducted under simulated blast loading using a shock tube are reported. Two analysis procedures that were developed for anchor design are described. The first procedure involves a two-degree-of-freedom dynamic analysis. The second procedure involves a single degree of freedom analysis that can be implemented manually. The development of both methods is presented for the anchorage design of windows subjected to blast loads.

Improved analysis for impact response prediction of reinforced concrete structures considering stress wave propagation and time dependent shape function

In the design of reinforced concrete (RC) structures subjected to impulsive loading, usually an equivalent Single-Degree-of-Freedom (SDOF) system is derived based on a constant deflection shape assumption corresponding to static-loading condition. It is commonly known that this idealized assumption may not necessarily lead to accurate predictions of structural responses. This paper presents an improved analytical approach to predict the dynamic response of RC beams with consideration of stress wave propagation effect in the beam in the initial stage upon impact load application, and time-dependent shape function for SDOF analysis. The response of a structural component is divided into two phases: local response phase which is calculated using governing equations of stress wave propagations; and global response phase analyzed using the equivalent SDOF systems with considerations of time-dependent deformation shapes. Laboratory drop-weight impact tests are performed on RC beams, which are used to validate the developed method. Further validation is carried out against existing testing results by other researchers, demonstrating the proposed approach offers more accurate predictions of RC beam responses under impact loading compared to the conventional SDOF method.

Blast performance and analysis of reinforced concrete beams subjected to corrosion of the longitudinal reinforcement

AbstractThis research has investigated the effect of reinforcement corrosion on the flexural response of reinforced concrete beams subjected to blast loading. Five beams, with and without corrosion, were tested under blast loads using a shock‐tube. The corroded specimens were subjected to an accelerated corrosion regime prior to testing, with a mass loss of up to 22% in the longitudinal steel reinforcement over the mid‐span or full‐span regions. A companion set of two beams was tested under quasi‐static four‐point bending. The results from the static tests show that corrosion of the longitudinal reinforcement decreased the strength and ductility, and ultimately changed the failure mode from ductile to brittle. Under blast loading, the steel corrosion increased maximum displacements and support rotations, reduced blast capacity, increased damage and fragmentation, and led to more brittle failure as the % mass loss increased. The effects of corrosion on blast response were moderate when the steel was corroded over the full‐span region. Furthermore, the blast response of the beams was predicted using dynamic inelastic single‐degree‐of‐freedom (SDOF) analysis, with the resistance functions developed using 2D finite element modeling, while accounting for the reduction in steel stress–strain properties and corrosion‐induced cracking. The SDOF analysis showed acceptable results in terms of ability to predict maximum displacements of the flexural‐governed beams (corroded and un‐corroded).

Blast retrofit of one-way reinforced concrete members using externally bonded FRP and FRP anchorage

This paper presents the results of nine as-built and carbon fiber reinforced polymer (CFRP) retrofitted reinforced concrete panels subjected to simulated blast loading using a pneumatically operated shock tube. The objective of the study was to characterize the blast response of CFRP retrofitted reinforced concrete panels, with and without supplemental mechanical anchorage applied to the CFRP. The results indicate that retrofitting can significantly increase the strength and stiffness of reinforced concrete flexure members and greatly enhance the displacement time-history response over non-retrofitted members. Debonding of the externally bonded CFRP was the failure mode for all retrofitted members. FRP anchors, designed to prevent or delay debonding failures through mechanical end-anchorage, were found to substantially enhance the performance of panels experiencing critical diagonal crack debonding. However, the FRP anchors were found to have no substantial effect on retrofit performance for the case plate-end interfacial debonding failures. In addition, the displacement time-histories for as-built and FRP retrofitted panel obtained through detail single degree of freedom analysis were found correlate well with those obtained experimentally. Finally, a discussion on the practical considerations of using externally bonded FRP retrofits to resist blast loads and recommendations for protective design are presented.

Approximate seismic performance of full and partial self-centering systems based on spectral analysis of SDOF systems

This paper presents a performance evaluation of full and ‘partial’ self-centering (SC) systems based on spectral analysis of Single Degree of Freedom (SDOF) systems. The primary objectives are to quantify the structural performances of the full and ‘partial’ SC systems, with a wide spectrum of structural parameters under near-fault (NF) and far-field (FF) earthquakes, and to assess the accuracy of the prediction models derived from SDOF analysis to approximate the seismic performances of multi-story frame buildings. More than 1.45 million statistical response results are processed and discussed. Among other important findings, it is shown that ‘partial’ SC systems appear to be a desirable option that could control the acceleration and residual displacement responses without inducing a notable increase in the maximum displacement. Based on the available data, two sets of prediction models about the inelastic displacement demand and residual displacement response are proposed. Finally, the accuracy of the prediction models to approximate the seismic performances of multi-story frame buildings is investigated by the comparison of the responses computed from a series of braced frames with various parameters and that calculated from prediction models. The results imply that the prediction models from SDOF analysis are capable of predicting the seismic performances of the corresponding multi-story frame buildings.

Improved resistance functions for RC elements accounting for compressive and tensile membrane actions

Membrane actions commonly present in reinforced concrete elements as a result of restrained boundary conditions and geometry of deformations, which could substantially improve the ultimate flexural load-resistance as compared to that using yield line theory. Nevertheless, most current design manuals do not consider membrane effect because of a short of proper analysis method. This paper proposed an improved resistance model for RC (reinforced concrete) elements which considers both compressive and tensile membrane actions. Firstly, the derivation of the proposed membrane model was presented in detail. It was then validated with available testing data, in which good agreement was found on the load-deflection relationship of RC element between the estimation using the proposed model and testing data. Combining with the equivalent SDOF (single-degree-of-freedom) analysis method, the dynamic responses of structural elements subjected to blast loads could be more accurately predicted as compared to the common elastic-perfectly-plastic resistance assumption in design guides. The proposed method was further verified with existing field blast testing results. Parametric studies were then carried out to examine the influences of critical design parameters for membrane behaviors including reinforcement ratio, span-to-depth ratio, and restraint stiffness. Last but not the least, based on the proposed analytical method a series of diagrams for modifying the design loading capacity estimated by UFC (Unified Facilities Criteria) design guides without considering the membrane effects were derived for more accurate and easy predictions of loading capacities in engineering applications.

Predicting the self-centering behavior of hybrid FRP-steel reinforced concrete beams under blast loading

An inelastic single-degree-of-freedom (SDOF) dynamic analysis model is developed to predict the entire displacement time-history of concrete beams reinforced with hybrid mixtures of fiber reinforced polymer (FRP) and steel reinforcing bars subjected to blast loads. Hybrid FRP-steel reinforced concrete members exhibit strong self-centering tendencies which promote blast resilience through reductions in residual damage, repair cost, and facility downtime after a terrorist bomb attack or accidental explosion. FRP bars provide an internal restoring force that activates self-centering behavior after the inertial loads are removed, while the conventional steel reinforcement and concrete dissipate energy by their inelastic response. The SDOF model is equally applicable to all-steel, all-FRP, and hybrid FRP-steel reinforced concrete flexural members, incorporating all the relevant parameters of flexural response, nonlinearity, and self-centering that have been observed to play an important role in blast tests. These parameters include the type, size, spacing, arrangement, and material properties of longitudinal and transverse reinforcement, as well as concrete properties and section geometry. The effect of these parameters is described in terms of nonlinear resistance functions capturing the inbound and rebound flexural response, plastic hinge formulations to account for crack bridging provided by FRP bars, and a hysteretic model for the combined effects of self-centering behavior and stiffness degradation due to accumulated damage from progressively increasing repeated blast tests. A new response parameter, known as the Blast Self-Centering Index (BSI), is proposed to evaluate and assess the residual displacements of all-steel, all-FRP, and hybrid FRP-steel reinforced concrete beams predicted by SDOF analysis. The model has been verified extensively against data obtained from explosively driven shock tube blast experiments.

Direct normal form analysis of oscillators with different combinations of geometric nonlinear stiffness terms

Nonlinear oscillators with geometric stiffness terms can be used to model a range of structural elements such as cables, beams and plates. In particular, single-degree-of-freedom (SDOF) systems are commonly studied in the literature by means of different approximate analytical methods. In this work, an analytical study of nonlinear oscillators with different combinations of geometric polynomial stiffness nonlinearities is presented. To do this, the method of direct normal forms (DNF) is applied symbolically using Maple software. Closed form (approximate) expressions of the corresponding frequency-amplitude relationships (or backbone curves) are obtained for both e and e2 expansions, and a general pattern for e truncation is presented in the case of odd nonlinear terms. This is extended to a system of two degrees-of-freedom, where linear and nonlinear cubic and quintic coupling terms exist. Considering the non-resonant case, an example is shown to demonstrate how the single mode backbone curves of the two degree-of-freedom system can be computed in an analogous manner to the approach used for the SDOF analysis. Numerical verifications are also presented using COCO numerical continuation toolbox in Matlab for the SDOF examples.

Performance-based seismic design of multi-story CBFs equipped with SMA-friction damping braces

This paper focuses on the performance-based seismic design (PBSD) methodology of multi-story concentrically braced frames (CBFs) equipped with a novel brace, i.e., the shape memory alloy (SMA)-friction damping brace (SMAFDB). The fundamental response characteristics of the framing structure are first understood through nonlinear response history analysis on the equivalent single-degree-of-freedom (SDOF) systems. The parameters varied in the SDOF analyses are the period of vibration (T), the strength reduction factor (R), and the normalized friction slip displacement (μf). The seismic response indexes of interest are the peak displacement, the ductility, the residual displacement and the peak acceleration. Relationships are built between the seismic response indexes and parameters of T, R and μf. Then, the SDOF-based results are explored to develop the PBSD methodology, which defines the peak interstory drift, the peak floor acceleration and the residual interstory drift as the performance targets. To demonstrate and validate the proposed design methodology, the six-story prototype CBFs equipped with SMAFDBs are designed and then subjected to ground motions associated with hazard levels of design basis earthquakes (DBE) and maximum considered earthquakes (MCE). The performance evaluation results indicate that the frames can be effectively designed to meet the targeted performance objectives at the DBE level. It also indicates that the frames maintain seismic-resisting capacity at the MCE level.

Experimental evaluation of OSB-faced structural insulated panels subject to blast loads

This paper reports the results of an experimental program to quantify the blast protection provided by as-built and strengthened structural insulated panels (SIP) subjected to short-duration uniform pressure loads in a blast load simulator facility. SIPs are used in residential and light-commercial buildings. The SIPs used in this study had an overall thickness of 117 mm with 11 mm thick oriented strand board (OSB) facers and a 95-mm thick polyurethane closed-cell foam core. This type of sandwich panel provides improved energy efficiency and reduced construction time. A total of eight panels were tested in four different configurations: (1) as-built SIP design with standard connections, (2) as-built SIP design with strengthened roof connection, (3) flexural strengthened SIP using galvanized steel straps with strengthened roof connections, and (4) flexural strengthened SIP using fiber reinforced polymer (FRP) wallboard with strengthened roof connections. Each panel in this experimental program was 1.2 m by 2.4 m and was tested independently. The panels were subjected to two to five incrementally increasing pressure-impulse combinations. The first was a low pressure shot to verify the elastic performance of the SIP. The magnitude of the pressure-impulse combination for the subsequent shots increased until ultimate failure of the panels. By strengthening the roof connection, the as-built panels withstood a 27% larger impulse. The steel strap and FRP flexural strengthening with the strengthened roof connections led to a three-fold and five-fold increase in impulse resisted, respectively, when compared to the as-built SIP with standard connections. The results of the experimental study were validated using single-degree-of-freedom (SDOF) models. The SDOF analysis included an elastic resistance function for each panel configuration. The SDOF analysis estimated displacements 9% larger than the experimental results on average. The analytical model was more conservative for the lower pressure shots indicating that one-way behavior of SIPs subjected to shortduration uniform pressure loads may be reasonably estimated using fundamental bending mechanics. Overall, the results of the experimental and analytical study indicated simple strengthening methods may be used to significantly improve the blast resistance of SIPs.

Blast behavior of columns built with high-strength concrete and Grade 690 MPa high-strength reinforcement

As part of this study a series of columns built with high-strength concrete and Grade 690 MPa high-strength reinforcement are tested under blast loads using a shock-tube. The performance of the columns is compared to a control set of specimens built with Grade 400 MPa reinforcement. In addition to the effects of concrete and steel type, the effects of longitudinal steel ratio and seismic detailing are also investigated. The results show that concrete strength has limited effects on blast behavior. Conversely, use of high-strength bars significantly enhances column blast performance by reducing displacements and increasing blast resistance, with an ability to reduce the required amount of steel reinforcement. The results further demonstrate that increasing the longitudinal steel ratio and seismic detailing improve the blast behavior of columns built with conventional and high-strength bars. As part of the analytical study the blast response of the columns is predicted using nonlinear single degree of freedom analysis and finite element modelling.

Improved SDOF and numerical approach to study the dynamic response of reinforced concrete columns subjected to close-in blast loading

In this study, the blast performance of steel reinforced concrete (RC) columns was experimentally and analytically investigated. The experiments consisted of 11 one-half-scale columns subjected to different levels of blast loading using TNT explosives. The experimental results show that when the scaled distance is relatively large, less damage occurs to steel RC columns with higher axial loads than to columns with smaller axial loads at the same blast level. As the scaled distance decreases, the axial load increases the level of damage to RC columns. In addition, the equivalent single-degree-of-freedom (SDOF) approach for determining the dynamic response of RC columns against combined axial and blast-induced transverse loads was improved. Nonlinear section and member analyses were incorporated into the suggested SDOF method by considering the effect of axial load and complex features of the material behavior, the high strain-rate effect and the column geometry. The SDOF model was validated by comparing the maximum displacements obtained from the SDOF analysis with experimental data from blast testing of RC columns. Parametric studies were also performed to investigate the effects of axial load, the longitudinal reinforcement ratio, transverse reinforcement ratio, aspect ratio and boundary conditions. In order to consider the local damage effect, the numerical study was undertaken to investigate the effects of transverse reinforcement spacing on the blast resistance of RC columns using LS-DYNA.

A novel identification method for obtaining bending moment–curvature relations of wood stems based on digital image correlation and SDOF analysis

Bending moment–curvature relations (M-χ) are useful in many beam modelling approaches. It allows describing in a simple way the mechanical behaviour at the cross-section scale and can be used to model continuous beams as single degree of freedom systems dedicated to perform stochastic analysis. This paper focused on tree mechanical charaterisation and presents an identification method for obtaining bending moment–curvature relationships up to failure from Digital Image Correlation (DIC) and experimental three points bending tests. Due to wood intrinsic variability, the proposed identification method has been validated from a Finite Element (FE) model which aims at simulating precisely the bending response of a cylindrical stem. The refined FE model has been developed based on the geometry and the boundary conditions of the experimentally tested stems. M-χ curves are derived from the FE model and used within a Single Degree Of Freedom (SDOF) approach. At the stem scale, the prediction of the SDOF model (Force-Displacement) is compared to the FE model and lead to a good agreement. Then the approach is used to characterise fresh European beech samples allowing deriving their mechanical properties (longitudinal Young modulus, modulus of elasticity and modulus of rupture).

Comparison of Predicted and Experimental Behaviour of RC Slabs Subjected to Blast using SDOF Analysis

<p>Explosions emanating from terrorist attacks or military weapons cause damage to civilian and military facilities. Understanding the mechanical behaviour of reinforced concrete structures subjected to blast is of paramount importance for minimizing the possible blast damage. A full-scale experimental program consisting of six reinforced concrete slabs with compressive strengths of 60 MPa, 50 MPa and 40 MPa, measuring 1.0 m × 1.0 m × 0.08 m, and subjected to 2.7 kg of non-confined plastic bonded explosive, was conducted in blast test area of Science and Technology Aerospace Department (Brazilian Air Force). This paper compares experimentally measured peak displacement values with theoretical values. Theoretical analysis was carried out using single degree of freedom (SDOF) models. The comparison showed that SDOF analysis worked very well in predicting the reinforced concrete slab peak displacement against blast effects. Qualitative analysis after the experiments showed that the blast wave shape generated by the cylindrical explosive was not uniformly distributed on the slabs for the standoff distance of 0.927 m∕kg1/3.<br /><br /></p>

Blast performance evaluation of structural components under very near explosion

The single-degree-of-freedom (SDOF) analysis with elastic-plastic resistance is often used for design of protective structures subjected to blast loads. Several documents such as UFC 3-340-02 present design charts for the maximum responses of the elastic-plastic SDOF system. The SDOF design charts are available for far-field detonations but seldom for near-field detonations of high explosive in free air, noting that the focus of security design is the near-field. Further, the assumption of uniformly distributed load for the SDOF analysis may not be appropriate for the near-field detonations where blast pressure distribution varies significantly with distance and angle of incidence. In this paper, to resolve these issues, updated SDOF design charts including the response to the near-field detonations are suggested based on numerical calculations. These generated charts are verified with comparison to UFC 3-340-02 predictions and finite element analysis results of steel components. The recommendations and limitations for the utility of the SDOF design charts for blast assessment of steel components are provided with an emphasis on the near-field detonations.

A simplified model to predict blast response of CFST columns

In order to study the dynamic response of concrete-filled steel tube (CFST) columns against blast loads, a simplified model is established utilizing the equivalent single-degree-of-freedom (SDOF) method, which considers the non-uniform distribution of blast loads on real column and the axial load-bending moment (P-M) interaction of CFST columns. Results of the SDOF analysis compare well with the experimental data reported in open literature and the values from finite element modeling (FEM) using the program LS-DYNA. Further comparisons between the results of SDOF and FEM analysis show that the proposed model is effective to predict the dynamic response of CFST columns with different blast conditions and column details. Also, it is found that the maximum responses of the columns are overestimated when ignoring the non-uniformity of blast loads, and that neglecting the effect of P-M interaction underestimates the maximum response of the columns with large axial load ratio against close range blast. The proposed SDOF model can be used in the design of the blast-loaded CFST columns.

Approach to Developing Design Charts for Quantifying the Influence of Blast Wave Clearing on Target Deformation

AbstractIf a structural component is located close to the free edge of a building, clearing of the blast wave around the target edge may significantly influence the temporal characteristics of the applied pressure. Because of this, traditional analysis methods assuming a linear decaying load may not be valid, particularly if the blast event imparts a relatively large impulse from the negative phase. Treatment of this phenomenon is brief in the literature, and its influence is usually neglected. This article presents an approach to quantifying the influence of clearing on target deformation, through rigorous analysis of elastic–perfectly-plastic equivalent single-degree-of-freedom (SDOF) systems. The cleared load is evaluated for structural components situated at various distances from the free edge of a reflecting surface using the Hudson acoustic approximation. The results from the SDOF analyses are then used to draw up design charts for determination of the likely influence clearing may have on the desi...

Analysis of offshore wind turbine tower under environmental loads

ABSTRACTResearchers have started to use numerical methods in the fluid–structure interactive solutions with the advancing of computing technology. There are few studies investigating bidirectional fluid structure interaction (FSI) analysis due to requirements of high computer capacity. This insufficiency is attempted to be corrected in this study. Offshore wind turbine tower is selected to employ the method under environmental loads. To detect accuracy of the numerical analysis, the tower is modelled as a single-degree-of-freedom (SDOF) system. The equation of motion of the system is numerically integrated by using a fourth-order Runge–Kutta method. Time-varying lateral displacement of the tower and first natural frequency values are obtained from analysis. Afterwards, the structure and the environment are modelled in ABAQUS finite elements program. Bidirectional FSI technique is applied to the structure due to the interaction between ABAQUS/CFD-ABAQUS/Explicit. The accuracy of SDOF and bidirectional FSI analyses results is determined in the end.

Modeling Zero – Inflated Regression of Road Accidents at Johor Federal Road F001

This study focused on the Poisson regression with excess zero outcomes on the response variable. A generalized linear modelling technique such as Poisson regression model and Negative Binomial model was found to be insignificant in explaining and handle over dispersion which due to high amount of zeros thus Zero Inflated model was introduced to overcome the problem. The application work on the number of road accidents on F001 Jalan Jb - Air Hitam. Data on road accident were collected for five-year period from 2010 through 2014. The result from analysis show that ZINB model performed best, in terms of the comparative criteria based on the P value less than 0.05. Structural response of reinforced concrete (RC) elements for analysis and design are often obtained using the positive phase of the blast pressure curve disregarding the negative phase assuming insignificant contribution from the negative phase of the loading. Although, some insight on the effect of negative phase of blast pressure based on elastic single-degree-of-freedom (SDOF) analysis was presented before, the influence of negative phase on different types of resistance functions of SDOF models and on realistic finite element analysis has not been explored. In this study, the effects of inclusion of pulse negative phase on structural response of RC elements from SDOF analysis and from more detailed finite element analysis have been investigated. Investigation of SDOF part has been conducted using MATLAB code that utilizes non-linear resistance functions of SDOF model. Detailed numerical investigation using finite element code DIANA was conducted on the significance of the negative phase on structural response. In the FE model, different support stiffness was used to explore the effect of support stiffness on the structural response due to blast negative phase. RESULTS from SDOF and FE analyses present specific situations where the effect of large negative phase was found to be significant on the structural response of RC elements. © Owned by the authors, published by EDP Sciences, 2016 Language: en

Effect of Large Negative Phase of Blast Loading on Structural Response of RC Elements

Structural response of reinforced concrete (RC) elements for analysis and design are often obtained using the positive phase of the blast pressure curve disregarding the negative phase assuming insignificant contribution from the negative phase of the loading. Although, some insight on the effect of negative phase of blast pressure based on elastic single-degree-of-freedom (SDOF) analysis was presented before, the influence of negative phase on different types of resistance functions of SDOF models and on realistic finite element analysis has not been explored. In this study, the effects of inclusion of pulse negative phase on structural response of RC elements from SDOF analysis and from more detailed finite element analysis have been investigated. Investigation of SDOF part has been conducted using MATLAB code that utilizes non-linear resistance functions of SDOF model. Detailed numerical investigation using finite element code DIANA was conducted on the significance of the negative phase on structural response. In the FE model, different support stiffness was used to explore the effect of support stiffness on the structural response due to blast negative phase. RESULTS from SDOF and FE analyses present specific situations where the effect of large negative phase was found to be significant on the structural response of RC elements. © Owned by the authors, published by EDP Sciences, 2016 Language: en