Shear and moment diagram

Summary

Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam. These diagrams can be used to easily determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure. Another application of shear and moment diagrams is that the deflection of a beam can be easily determined using either the moment area method or the conjugate beam method. Convention Although these conventions are relative and any convention can be used if stated explicitly, practicing engineers have adopted a standard convention used in design practices. Normal convention The normal convention used in most engineering applications is to label a positive shear force - one that spins an element clockwise (up on the left, and down on the

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Glass fiber-reinforced polymer (GFRP) pultruded decks and sandwich panels currently represent two of the most extensive applications of FRP materials for load-bearing structural components in the bridge and building domains. Based on the state of the art, the global structural behavior of both systems has been fairly well investigated. Nonetheless, local effects governing in most cases the global behavior have been barely addressed. Selected local structural effects relevant to the global structural performance of pultruded GFRP bridge decks and GFRP-foam web-core sandwich structures are therefore investigated in this research. The effect of the core geometry of pultruded GFRP decks on the systemâs behavior in its transverse-to-pultrusion direction was experimentally investigated. The experimental work conducted on two deck designs with trapezoidal- and triangular-cell cross sections showed that the transverse structural performance depends on the cell geometry. Furthermore, the systemsâ transverse bending and in-plane shear stiffness were evaluated and the results indicated that a triangular core causes a more pronounced bi-directional behavior of the deck when it is subjected to concentrated loads. The local behavior of the web-flange junctions (WFJs) of the pultruded deck with trapezoidal cells was experimentally investigated regarding energy dissipation capacity and recovery subsequent to unloading. The experimental responses reported for two junction types with similar geometry and fiber architecture but different initial imperfections demonstrated that dissimilar imperfections could significantly affect WFJ behavior and change it from brittle to ductile. The time-dependent recovery and energy dissipation mechanisms of the WFJs exhibiting a ductile response were evaluated; the viscoelastic effects were found to be small in both cases. The rotational behavior of all WFJ types present in the trapezoidal-core deck was characterized. An experimental procedure based on three-point bending and cantilever experiments conducted on the web elements was developed and used for this purpose. The rotational stiffness, strength and failure modes of the WFJs differed depending on the web type, location of the WFJ within the deck profile, existing initial imperfections and direction of the applied bending moment. Numerical simulations of the full-scale deck were performed to demonstrate the validity of the experimental moment-rotation (M-Ï) relationships and simplified M-Ï curves provided. The effects of creep on the load-bearing behavior of GFRP-foam web-core sandwich structures were investigated. A study of the creep behavior of polyurethane (PUR) foams was conducted and showed that in order to assess the long-term structural performance of the sandwich system, the foam anisotropy, density and loading type should be considered. The creep behavior of web-core sandwich panels, and specifically the structural aspects affected by the web-core interaction, were analyzed using the GFRP-PUR sandwich roof of the Novartis Campus Main Gate Building as case study and currently available design guidelines. The resulting sandwich designs depended on the applied design recommendations. Finally, provisions for the cross-sectional design of the hybrid web-core were proposed.

EPFL2017

Static behaviour of earth block masonry: experimental testing and Finite Element Modelling

Angelo Garofano, Urs Müller

In this paper an extensive research campaign aimed to define the mechanical performance of earth block masonry panels is presented. Uniaxial compression and diagonal compression tests were performed. The test results confirmed the brittle behaviour of earth block masonry under uniaxial compressive load and showed that the failure of earth block masonry under shear load occurs by sliding of the earth blocks along the mortar joints after initial cracking in mortar joints and earth blocks. For diagonal compression test results showed that building technique practice is one of the key factors affecting the structural performances. Experimental behaviour was modelled with a non-linear model capable of describing cracking behaviour. Both micro-modelling and macro-modelling implementing isotropic or orthotropic material laws were used to assess the reliability of different modelling strategies. The model calibration was carried out by sensibility analysis of the input parameters to understand the influence of unit strength on the shear behaviour of masonry.

2014

Web buckling mechanism of pultruded GFRP bridge deck profiles subjected to concentrated load

Yuqing Liu, Congzhe Wang

The web's local buckling is a major failure type of pultruded glass fiber-reinforced polymer (GFRP) bridge deck subjected to concentrated wheel loads. Three kinds of external actions-that is, in-plane shear force, local compressive force and bending moment-are coupled at web. Besides, the couple ratio of those three external actions is changed due to varied wheel's loading position, resulting in a more complicated web buckling mechanism. Hence, a study of the web buckling behavior was firstly conducted through two experiments with different concentrated loading cases, namely mid-span loading and quarter-span loading. After then, parametric analysis of FE model with detailed simulated web-flange junctions (WFJ) were performed to reveal a more comprehensive understanding. The experimental results showed that both specimens went through buckling failure of middle web, post-buckling strengthening owing to structural redundancy, and final failure caused by crack propagation on the top flange. The parametric analysis showed that the compression buckling and shear buckling coupled together, and that the compression buckling is dominant. In addition, as the shear-span ratio decreased, the principal compressive stress and the shear buckling became more pronounced, and consequently the GFRP bridge deck's bearing capacity reduced.

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EPFL2017