Bending Moment Capacity Research Articles

Improved Moment Strength Prediction of Composite Steel Plate Girders in Positive Bending

This paper contains an alternate method for the calculation of the predicted positive bending moment capacity of composite steel girders. The 2000 interim version of the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design Bridge Design Specifications has extended the applicability of the provisions for the design of composite plate girders in positive bending to include 485 MPa high performance steel. Observations made during numerical studies performed in conjunction with this extension demonstrated a need for a more comprehensive study encompassing a larger and more diverse set of parameters. This paper provides a summary of the analytical and experimental work that was carried out to develop provisions for predicting the ultimate strength and assuring the ductility of composite girders constructed using 250, 345, or 485 MPa steels. The new provisions outlined in this paper are more accurate and require less calculation. The recommended equations...

Probabilistic analysis of bending moment capacity of titanium pipes

Statistical measures of bending moment capacity of titanium pipes exposed to high external pressure differences are developed. Variations in relevant geometry and material parameters are found from laboratory tests. These quantities are input to non-linear finite element shell models of the pipe. Maximum bending moment capacities estimated by the non-linear finite element analyses are compared with some experimental results. A response surface approach is applied in order to reduce the required number of non-linear shell analyses. The bending moment capacity is expressed as a function of the basic parameter. With statistical distributions fitted to the uncertain input parameters, the response surface enables estimation of probability distributions for the bending moment capacity for a titanium pipe subjected to high external pressure.

Elastic method for design of 3-D steel structures subject to fire

The elastic method previously developed for the design of steel structures subject to a fire for a 2-dimensional framework has been extended to a 3-dimensional one. In the method for a 2-dimensional framework, only bending about the major axis is a primary condition for design consideration. In this context, the deterioration of the bending moment capacity of a steel member subject to increasing temperature is related to the elastic bending moments attained due to the actions of both the static loading and the thermal loading. The relationship can be established for each member in terms of the unknown limiting temperature which can be solved. The lowest of the limiting temperatures of all members is the critical one for the whole structure. In extending this design method to a 3-dimensional framework, failure criteria beyond pure bending are used to appropriately reflect the state of force interactions in the members. This approach is reasonable as, in reality, structural members in a 3-dimensional framework are subject to different forces attributable to their ultimate failure at increasing temperature. In this paper, axial-bending interaction, including bending about both axes, is adopted as the failure criteria although other failure criteria, if required, can easily be incorporated into the design. In the examples given, it is shown that the limiting temperature of the structure decreases as the complexity of the failure criteria increases.

Experimental characterization of FRP composite-wood pile structural response by bending tests

A special prefabricated fiber reinforced polymer (FRP) composite shield or jacket was developed to repair wood piles in the field. Two types of load-transfer mechanisms between the wood pile and the FRP composite shield were developed and tested: (1) cement-based structural grout; and (2) steel shear connectors with an expanding polyurethane chemical grout. The objective of this paper is to characterize the structural response of full-size pre-damaged wood piles repaired with the FRP composite shield system. A three-point bending test procedure was used to simulate the response of a pile subjected to lateral loads. The load-deformation response, deflected shape profile, relative longitudinal displacements (slip), strain distribution, ultimate bending moment capacity and mode of failure were evaluated. Wood piles were pre-damaged by reducing approximately 60% of the cross-section over a portion of the pile. It was found that a pre-damaged wood pile repaired using the FRP composite shield with cement-based grout exceeded the bending capacity of a reference wood pile. The repair system using the FRP composite shield with steel shear connectors and polyurethane grout did not fully restore the bending capacity of a reference wood pile; however it can be used for marine borer protection when wood damage is not critical.

Probabilistic study of the behavior of steel frames with partially restrained connections

The reliability of steel frames with type PR (partially restrained) connections is dependent on the variability in the moment–rotation characteristics of the connections. In this paper, the contribution of this source of variability to the uncertainty in frame deformation is examined using stochastic finite element analysis to compare the effect of initial connection stiffness to that of bending stiffnesses of the beams and columns. The PR connections have top and seat angles connecting the beam and column flanges, and double web angles connecting the beam web to the column flange. A stochastic finite element analysis is used to develop system fragilities, which depict the probability of exceeding three limit states related to the maximum horizontal displacement, maximum interstory drift ratio and elastic bending moment capacity as a function of lateral force. The effect of the variability in initial connection stiffness on frame response is sufficiently important to require careful consideration in performance-based design.

Bending Moment Capacity of Pipes

In this paper, the bending moment capacity for metallic pipes has been investigated to provide criteria for optimizing the cost effectiveness in pipeline seabed intervention design. An analytical solution for the ultimate load-carrying capacity of pipes subjected to combined pressure, longitudinal force, and bending has been derived and thoroughly compared against results obtained by the finite element method. The derived equations can be used for high-strength materials with isotropic as well as anisotropic stress/strain characteristics, and may be applied for pipelines, risers, and piping if safety factors are calibrated in accordance with appropriate target safety levels. [S0892-7219(00)00504-5]

Softening of Normal Strength and High-Strength Concrete Frames

In the 21st century, computing facilities will make it possible to opt on a regular basis for more accurate rigorous methods of analysis. A rigorous collapse load analysis requires a knowledge of the behaviour of plastic hinges up to advanced curvatures. Concrete sections characteristically soften, that is the bending moment capacity decreases with increasing curvatures after the end of the plastic plateau while steel sections undergo a hardening phase. Consideration of softening is essential in a rational analysis. In this paper, the important aspects of softening of concrete frame structures are reviewed. High-strength concrete (f'c>50 MPa) is a more brittle construction material than normal strength concrete. High-strength concrete sections show a steeper softening slope when compared with similar normal strength concrete sections. An example is presented to demonstrate that a HSC frame structure with steeper softening slopes will have a lower collapse load.

A Life Prediction Methodology for Thick Section Composites Used in Civil Infrastructure

As fiber-reinforced polymer (FRP) composites find application in highway bridge structures, methodologies for describing their long-term performance under service loading will be a necessity for designers. The designer of FRP bridge structures will be faced with out-of-plane damage and delamination at ply interfaces. The damage most often occurs between hybrid plys and dominates the lifetime response of a thick-section FRP structure. In this paper a model is developed to address these issues. The methodology employs the quadratic delamination initiation failure criteria, in conjunction with a delamination growth law to describe the out-of-plane damage under bending. These phenomena are combined with the critical element residual strength life prediction tool to determine remaining bending stiffness and moment capacity of a pultruded and hybrid FRP 20.3-cm-deep structural shape. The model successfully describes the onset of delamination prior to fiber failure and suggests that out-of-plane failure controls the life of the structure.

Variation of Bending Capacity Along the Lamina Length of a Grass, Imperata cylindrica var. major (Gramineae)

The aim of this paper is to investigate variation of the bending moment capacity along the lamina of a grass (Imperata cylindrica (L.) Raeusch. var. major (Nees) C. E.Hubb. ex C. E.Hubb. & Vaughan). It is postulated that the bending strength of the grass section is obtained predominantly from the midrib and that the grass lamina contributes little to the overall bending behaviour. By observing transverse sections of the midrib, it can be estimated that the thickness of the outer sclerenchyma zone is approx. 10% of the midrib diameter and that the pith parenchyma makes up most of the rest of the midrib. This observation is taken to be valid for the entire length of the lamina. A simple structural model of an elliptical tube is proposed for the midrib. Bending tests on the grass lamina have shown that the bending moment capacity is very low in the distal third, but increases linearly in the middle third and is generally constant in the proximal third. Using the structural model for the midrib, the results indicate that the maximum bending stress of the midrib remains fairly constant over the length of the grass.

大口径・大径厚比鋼管コンクリート柱の曲げ耐力評価

Bending moment capacity of large sized concrete filled steel tube having larger diameter-thickness ratio is studied. Seven specimens are tested under constant axial load. Test parameters are diameter (300, 600, 900mm) and diameter-thickness ratio (75, 100, 150). The following conclusions are odtained. (1) Scale effect of concrete is large for'bending moment capacity. (2) Confinement effect can be expected on condition that diameter-thickness ratio is under 150. (3) Ring stress of steel tube in tensile side at maximum strength is larger than in compressive side. (4) The applicability of proposed equation for confinement and scale effect is confirmed.

コンクリート充填円形鋼管柱の弾塑性曲げ性状 : その1 拘束効果と残留応力の影響

In this paper, inelastic flexural behavior of concrete filled circular steel tubular columns is described. In order to obtain the flexural behavior more accurately, uniform bending tests were conducted in wide range of axial load ratio by using thirteen specimens, half of which were annealed to remove residual stresses, including two hollow tube specimens. Analytical methods for estimating bending moment capacity and moment-curvature relationships with taking account of confinement effects between steel tube and infilled concrete are proposed. Comparing the analytical results with the experimental results, influence of the confinement effects and residual stresses in steel tube on the flexural behavior is discussed.

Structural Safety of Post-Tensioned Concrete Slab Bridges With Unbonded Tendons

The authors examine the structural safety of simply supported post-tensioned concrete slab bridges with unbonded tendons. Slab designs are in accordance with the American Association of State Highway and Transportation Officials (AASHTO) load factor design specifications, and service stresses and ultimate strength are both considered in the design. Probabilistic resistance models that consider variabilities in material properties and section dimensions are developed using simulation methods. Reliability for flexural capacity at ultimate limit state is measured in terms of the reliability index. Sensitivity analysis is conducted to study the effects of changes in span length and prestressing steel reinforcement ratio on stress in unbonded tendons, bending moment capacity, and reliability index. Results of the analysis revealed that statistical properties of bending moment capacity at ultimate are a function of the amount of prestressing steel. Furthermore, designs based on current AASHTO specifications result in considerable nonuniform safety for bridges having different span lengths and reinforcement indexes.

Factors influencing the strength of continuous composite beams in negative bending

Continuous composite beams are widely used in multi-storey buildings and bridges. For the purpose of flexural strength calculations, such beams may be divided into two distinct regions, namely regions of positive bending and negative bending. The flexural strength of composite beams in positive bending is governed by the strength of the concrete and the steel beam and simple calculations based upon fully plastic stress blocks provide acceptable accuracy in predicting ultimate bending moment capacities. In regions of negative bending moments, however, local and lateral instabilities of the steel section and cracking of the concrete influence not only the ultimate bending strength of the composite section, but also the ability of the section to redistribute bending moment by absorbing inelastic rotations. The factors influencing the behaviour of composite beams in negative bending and their relationship to the section geometry and span lay-outs are discussed in this paper. A theoretical model is presented which provides a basis for assessing the influence of the distortional restraint of the slab on the steel beam. The theoretical models are compared to experimental results obtained from tests on composite beams. The model is then used as a basis for an interactive design approach that also considers local flange and web buckling.

Ductility of Non-Compact Steel Bridge Beams

Since the fifties, composite construction in steel bridges has been used in simple as well as in continuous structures. Composite construction incorporates the concrete deck with the top flange of the supporting rolled beams or welded plate girders. The final result consists of the two components from different materials acting as a unit. The composite action can be accomplished by mechanical bond between the flange and deck in the form of welded channels, studs, or other devices. Either shored or unshored construction can be specified. Composite construction for highway bridge design is most economical for spans in the range of 40-50 ft. and longer. The increase in the moment of inertia of the composite section helps in reducing deflection due to live load and impact. For shorter spans, the saving in steel weight does not usually pay for the additional weight of the shear connections and labor involved. Composite steel girder bridges in the United States are usually designed using the Load Factor Design procedure of AASHTOs Standard Specifications for Highway Bridges. Current AASHTO allows the bending moment capacity of compact sections in positive bending to be based on the full plastic moment. The moment capacity at first yield is used, however, for non-compact sections. In most practical cases, the full plastic moment of composite sections is significantly larger than the yield moment.

Optimization of Reinforced Fibrous Concrete Beams

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梁スカラップの有無が箱形断面柱に溶接接合されるH形鋼梁端部の力学的性状に及ぼす影響

When H-shaped steel beams are connected to box columns, it can be considered that bending moment capacities of beam webs are reduced, because the out-of-plane stiffnes of the column flange in a joint panel decreases as the width-to-thikness ratio of the column flange increases. On the other hand, the presence of scallops at a beam web brings partial loss of cross section at a beam end, and the beams with scallops might reach failure at an early stage. In this study, three-point bending tests using cross-shaped specimens of beam-to-column connections are performed, and finit element method analysis are carried out. The effect of beam scallops and the width-to-thikness ratio of the flange in a joint panel on mechanical behaiviors of the steel beam end are investigated.

Stiffness Matrix for Elastic‐Softening Beams

Softening, the decrease of bending moment capacity of a section at advanced curvature, may occur at locations within a statically indeterminate reinforced concrete structure prior to the attainment of maximum load. The stiffness matrix for an elastic flexural member with a softening portion is derived, employing the necessary assumption of a finite softening or discontinuity length. For positive values of the softening parameter the stiffness values are as for a beam with a prismatic haunch. For negative values of the parameter stiffness coefficients become unstable at the critical softening parameter for a fixed-end beam. The derived stiffness coefficients allow use of standard frame analysis programs without special treatment for softening. An example of softening at the base of one column of a portal frame is given, showing the effect of softening on sway displacement. The frame demonstrates instability at the critical softening parameter for the particular position and length of the softening hinge.

Load‐Deflection Curves For Elastic‐Softening Beams

Softening, the decrease of bending moment capacity of a section at advanced curvature, may occur in a statically indeterminate reinforced concrete structure prior to the attainment of maximum load. Critical softening is that value of negative stiffness for a first formed hinge at which a structure cannot sustain increased load. The bending-moment versus softening parameter and load-deflection relationships for uniformly loaded fixed-end beams are derived, for sub-critical, critical and super-critical softening of first and second formed hinges. Corresponding load-deflection curves are presented, for particular values of hinge length and softening parameter.

Critical Softening of Hinges in Portal Frames

Softening behaviour, or decrease in bending moment capacity at far advanced curvature, is assumed to occur over a finite hinge length, or discontinuity length, at any point in a single-bay portal frame. The critical softening parameter, acr, is defined as that ratio of falling-arm slope to elastic slope on the moment-curvature diagram for the hinge, at which the structure as a whole cannot sustain increased load, however redundant it may still be. Formulae are derived for acr for the first formed hinge in fixed base portal frames. The critical softening parameter is found to be inversely proportional to the member-length : hinge-length ratio, m. For realistic values of m, appropriate formulae for acr are found to be quite accurate. For given frame geometry ``soft points'' at which acr is a minimum may be found for each member.