Safety factors of beams subjected to pure bending

The reliability-based calibration of safety factors for the design of a simply supported steel beam, based on BS5950 (2000) is presented in this research work. The calibration was undertaken using a specialized computer program in Microsoft excel environment developed by the Joint Committee for Structural Safety (JCSS) CODE-CAL 2001. The design variables considered were modeled using the software, and the safety factors for the material, dead and live load were calibrated by varying the safety index. From the results obtained, mathematical prediction models were developed using a least square regression analysis for bending, shear and deflection modes of failure considered in the study. The results showed that the safety factors for material, dead and live load are not unique, but they are influenced by safety index and it was also shown that the safety factors for material, dead and live load vary from 0.61 to 1.15, 1.44 to 1.91 and 1.40 to 1.65 respectively for both bending and shear modes of failure. For deflection mode of failure, the results showed that the safety factors for material, dead and live load vary from 1.08 to 1.56, 1.10 to 1.17 and 0.83 to 1.25 respectively for target safety index (βt) of 2.0 to 4.5. The mathematical prediction models developed for both bending and shear modes of failure are the same. Therefore, it is recommended that the mathematical prediction models developed in this study for bending and deflection modes of failure could be used when designing a simply supported steel beam to BS 5950 (2000).

International Journal for Numerical Methods in Engineering, 2005

The paper shows the practical importance of the failure probability-safety factor method for designing engineering works. The method provides an automatic design tool by optimizing an objective function subject to the standard geometric and code constraints, and two more sets of constraints, that guarantee some given safety factors and failure probability bounds, associated with a given set of failure modes. Since a direct solution of the optimization problem is not possible, the method proceeds as a sequence of three steps: (a) an optimal classical design, based on given safety factors, is done, (b) failure probabilities or bounds of all failure modes are calculated, and (c) safety factors bounds are adjusted. This implies a double safety check that leads to safer structures and designs less prone to wrong or unrealistic probability assumptions, and to excessively small (unsafe) or large (costly) safety factors. Finally, the actual global or combined probabilities of the different failure modes and their correlation are calculated using a Monte Carlo simulation. In addition, a sensitivity analysis is performed. To this end, the optimization problems are transformed into another equivalent ones, in which the data parameters are converted into artificial variables. In this way, some variables of the dual associated problems become the desired sensitivities. The method is illustrated by its application to the design of a composite beam.

To avoid failure in most engineering designs, von-mises failure criterion must be met. This criterion requires that the stress a body is subjected to is less than the yield strength of the material of the body. In this analysis, a beam structure has been designed with CATIA software to ensure that the von-mises criteria is met. This was done with critical evaluation of the mass requirement and the pivot constraints on the body. The first load case considers a total force of 18kN while the second load case considers a force of 9kN. The final weight of the initial model was 19.989kg. The maximum von-mises stress obtained from the initial analysis for load case 1 was 1560MPa whereas, the maximum von-mises stress obtained from the initial analysis for load case 2 was 530MPa. For the final design analysis, weight of the final model was 14.329kg. The maximum von-mises stress obtained from the final analysis for load case 1 was 102MPa whereas, the maximum von-mises stress obtained from the final analysis for load case 2 was 101MPa. Hence, one of the methods that failure can be avoided in beam design is to ensure that the maximum allowable stress is not exceeded.

2018

This paper presents a safety classification of 14 different of glass beam designs based on experimental research, using the Integrated Approach to Structural Glass Safety (introduced by the author, [1], [2]). The design parameters included the number of layers (2 or 3), the level of prestress (annealed, heat strengthened, thermally tempered), and laminate type (PVB or SG). Additionally, steel reinforced glass beams were tested. Three different methods were applied to obtain complete redundancy curves (development of residual strength under increasing levels of damage): 4-point bending after no, partial, or full damage. The damage was applied by a custom made impact device consisting of a spring loaded flat steel head that impacted the edges of the glass layers of the beams. The resulting Element Safety Diagrams of each design is discussed. Relativized curves are used to compare the safety of the designs.

The reliability-based calibration of safety factors for the design of a simply supported steel beam, based on BS5950 (2000) was presented in this research work. The calibration was undertaken using a specialized computer program in Microsoft Excel environment developed by the Joint Committee for Structural Safety (JCSS) CODE-CAL 2001. The design variables considered were modeled using the CODE-CAL software, and the safety factors for the material, dead and live load were calibrated by varying the safety index. From the results obtained, mathematical prediction models were developed using least square regression analysis for bending, shear and deflection modes of failure considered in the study. The results showed that the safety factors for material, dead and live load are not unique, but they are influenced by safety index and it was also shown that the safety factors for material, dead and live load varies from 0.61 to 1.15, 1.44 to 1.91 and 1.40 to 1.65 respectively for both bending and shear mode of failure. The deflection mode of failure results showed that the safety factors for material, dead and live load varies from 1.08 to 1.56, 1.10 to 1.17 and 0.83 to 1.25 respectively for target safety index (β t) of 2.0 to 4.5. The mathematical prediction models developed for both bending and shear modes of failure are the same. Therefore, it was recommended that the mathematical prediction models developed in this study for bending and deflection modes of failure could be used when designing a simply supported steel beam to BS 5950 (2000).

Materials

This paper investigates the ultimate flexural strength of reinforced concrete beams when affected by premature failure due to a rotational capacity of the first plastic hinge being consumed before the last plastic hinges reach their maximum possible moment. The paper provides a simple formula for predicting the ultimate load of a hyperstatically supported beam, taking into account the available ductility. The proposed formula is the result of calibration against the ultimate loads from a non-linear analysis on a variety of beams, with a wide spectrum of configurations and with concrete grades from 10.0 to 60.0 N/mm2. The formula in based on the plastic hinge model, making it easy to apply, and the ultimate bending moments allow for the actual rotational capacity, making predictions accurate.

International Journal of Innovative Research in Science, Engineering and Technology, 2017

The present method of designing rectangular reinforced concrete beam is based on limit state design philosophy which makes use of partial safety factors for material strength and load. The design variables being random, it becomes much more important to assess the level of safety in the probabilistic design situation. Beam being the vital most structural element, the probability of failure of a beam is linked to the overall safety of a structural system. With this in view, an attempt is made to assess the safety levels in terms of reliability index and probability of failure of the beam. A reinforced concrete frame is modelled in ETABS software, the moment and area of tension reinforcement values are extracted from the same software for statistical analysis. Resistance statistics for rectangular reinforced concrete beam are generated using the equations provided in IS 456-2000 code. The variables relating to geometry, material properties and loading are considered as random. Probability of failure is obtained by Monte Carlo Simulation technique which establishes the statistics of safety margin that is Resistance(R) > Action (S). The study investigates the reliability index and probability of failure of the rectangular reinforced concrete beam and plotting of the histogram and probability distribution curve. The entire reliability analysis was implemented through developing a program in MATLAB software.

Engineering Structures, 2015

Developments and advances in fabrication technology have led to a new generation of structural shapes, among them, the sinusoidal-web girder. Due to easy execution and potential for structural efficiency, the use of sinusoidal-web girder has been increasing significantly in several segments of civil engineering construction such as bridges, pedestrian walkways, hangars and industrial buildings. In spite of the advantages this type of structural component may offer, there are no design standards or specifications dealing with all the phenomena involved in the behavior of such beams, such as the resistance against lateral-torsional buckling (LTB). As a result, there is a need to develop design recommendations that properly address the flexural capacity of these elements. Following the current trend of semi-probabilistic codes (e.g. load and resistance factor design format), these recommendations shall be developed within the concepts and methods of Structural Reliability. In this paper, reliability-based design recommendations for sinusoidal-web beams for the limit state of LTB are presented. To this end: (i) an experimental investigation on the resistance of sinusoidal-web beams has been performed, (ii) a finite-element model has been developed and validated by experimental results, (iii) a theoretical model for the sinusoidal-web beam resistance prediction is proposed, (iv) a comprehensive program was established toward the assessment of both physical and epistemic uncertainties related to the basic variables, (v) reliability analyses are performed using First Order Reliability Method (FORM), and (vi) resulting implicit reliability levels are checked against current practice. It is shown that the implicit safety levels in the proposed recommendations are in agreement with current trends in structural engineering practice.

Revista IBRACON de Estruturas e Materiais

This paper presents an investigation on the safety of structural elements submitted to pure bending, produced in reinforced concrete, in steel and steel-concrete composites, and designed according to Brazilian codes NBR8681:2003, NBR6118:2007 and NBR8800:2008. The study allows a comparison of the relative safety of beams produced with these materials and designed using these codes. Comparative studies between the performances of different materials are difficult to find in the published literature. The present study shows that reliability indexes for reinforced concrete beams are satisfactory; however, results for steel beams are below limit values established in international design standards. Reliability indexes found herein for steel-concrete composite beams are intermediate to concrete and steel beams.

International Journal of Structural Integrity, 2013

Purpose – The purpose of this paper is to develop basic principles of deterministic structural integrity assessment of a component with a crack- or notch-like defect by including safety factors against fracture and plastic collapse in criteria equations of linear and nonlinear fracture mechanics. Design/methodology/approach – The safety factors against fracture are calculated by demanding that the applied critical stress should not be less than the yield stress of the material for a component with a crack or a notch of the acceptable size. Structural integrity assessment of the engineering components damaged by crack- or notch-like defects is discussed from view point of the failure assessment diagram (FAD). The methodology of the FAD has been employed for the structural integrity analysis and assessment of acceptable sizes of throw-thickness notch in a plate under tension and surface longitudinal notch-like defects in a pressure vessel. Findings – Basic equations have been presente...