Shear lag effect

Net-tension failures can be avoided or delayed by increased joint flexibility to spread the load transfer over several lines of bolts. Composite materials are generally more brittle than conventional metals, so loads are not easily redistributed around a stress concentration such as a bolt hole. Simultaneously, shear-lag effects caused by discontinuous fibers lead to difficult design problems around bolt holes. A possible solution is to put a relatively ductile composite material such as S-glass-epoxy in a strip of several times the bolt diameter in line with the bolt rows. This approach is called the softening-strip concept, and was addressed in Section 6.4. 

The shear lag effect caused by a finite thickness of the bond layer can be taken into account starting from strain beam theory. The shear lag in the bond layer causes a reduction of the effective length and width of the sensor considered in the following equation [84] ... 

Shear lag effects when for outstanding flange elements... 

For platelets that are in relative isolation, the largest stress appears to occur towards the centre of the platelet. As shown quantitatively by Sheng and Boyce et al. [39], this indicates that the load-transfer from matrix to platelet is mainly through interface shear stress, giving rise to the classical shear-lag effect [44] along the length of the platelet. One can also clearly see that the stress in the platelets is affected by the presence of other nearby platelets (platelet-platelet interaction). 

The initial beam cross section is the gross cross section. However, for wide flanges, either of concrete or steel, effective widths must be introduced to consider shear lag effects (Fig. 5). Although effective widths vary along the length of the bridge, they are smaller at internal supports... 

This type of analysis is based on the study of stresses and strains in adhesive joints. By considering the stress state in single lap joints, which are commonly used in industry and have a simple geometry, it can be seen that a complex state of stress is present in adhesive joints. When loaded in tension, the shear stresses in the adhesive layer in single lap joints have a nonuniform distribution owing to the differential straining of the adherends. This shear lag effect, as shown inO Fig. 25.9, causes maximum stresses at the ends of the overlap. 

The results presented in Section 4.3.6 suggest that the shear lag models based on a single fiber composite is inadequate for modelling a composite with a high fiber f). From the experimental viewpoint, to measure the relevant fiber-matrix interface properties, the fiber volume fraction in single fiber pull-out tests is always very low (i.e. Ff <0.01). This effectively means that testing with these specimens has the... 

Darby et al [42] investigated the effect of broken or cut plies in a 6k XAS reinforced PES matrix. To calculate the stress distribution of a break in a single carbon fiber under tension, the shear lag method of Cox [43] was used and the ineffective length of a single broken fiber... 

Stress distribution shear lag solution D A DILLARD Stresses in shear joints Creep A D CROCOMBE Occurrence protection against creep failure Durability creep rupture D A DILLARD Creep under sustained stress Durability fatigue D A DILLARD Effect of cyclic loads... 

The effective length and width of a piezoceramic sensor depends on both the sensor and layer properties. Sirohi and Chopra [84] describe how to determine those effective quantities. In general this is to say that the smaller the thickness and stiffness of a sensor, the smaller the shear lag losses. 

Siriruk A, Weitsman YJ, Penumadu D (2009a) Polymeric foams and sandwich composites material properties, environmental effects, and shear-lag modeling. Compos Sci Technol 69 (6) 814-820... 

Fig. 12. (a) The shear lag model for a single lap joint is fonnulaled using the indicated terms and the differential elements. Bending in the adherends is specifically ignored, (h) Exaggerated dcfomiaiions of loaded lap joints illustrating the effect of adherend extensibility on adhesive shear stress, t, and adherend axial stresses, ct. After Adams and Wake [1 Ij,... 

Shear stress is normalized by Pco, effectively showing the shear lag stress distributions for joints of various length holding a constant load... 

Volkersen [28] presented a continuum mechanics approach to analyse the shear-lag configuration of the single lap joint. However, there were limitations to his analysis, most significant of which was its failure to account for the effect of the bending moments induced by the eccentricity of the applied load. Nor did it account for the adherend shearing, and it predicted the maximum shear stress to occur at the free surface at the end of the joint overlap. As this is a free surface, the shear stress here should, in practice, be zero. 

Bascom and Jensen [67], used an approach similar to that of Drzal and coworkers. Wimolkiatisak et al. [70] found that the fragmentation length data fitted both the Gaussian and Weibull distributions equally well. Fraser et al. [71 ] developed a computer model to simulate the stochastic fracture process and, together with the shear-lag analysis, described the shear transmission across the interface. Netravali et al. [72], used a Monte Carlo simulation of a Poisson-Weibull model for the fiber strength and flaw occurrence to calculate an effective interfacial shear strength X using the relationship ... 

In this paper, the macroscopic nanofiber network properties are determined by multiscale modeling approach. On the first stage, effective fiber properties determined by homogenization procedure using modified shear lag model, while on the second stage the point-bonded stochastic fibrous network properties at macro scale determined by volumetric homogenization approach. 

The discrete atomic nanotube structure replaced the effective hollow cylinder having the same length and outer diameter as a discrete nanotube with effective Young s nanotube modulus determined from atomic structure [7], The stress transfer between fiber and matrix in RVE was determined using modified shear-lag model [8], For example, in the region laxial component of stress tensor (dimensionless form) for fiber matrix has the following form... 

Where a is the axial normal stress uniformly applied owz = L. X is shear-lag parameter, and Ef are elastic modules of CNT and matrix respectively. For the known stress and strain distribution under RVE we can calculate elastic effective properties quantifications [7]. The effective module > can be calculated as follow... 

The remarkable properties of electrospun CNTs nanocomposites continue to draw attention in the development of multifunctional properties of nanostructures for many applications.. Multiscale model for calculation macroscopic mechanical properties for fibrous sheet is developed. Effective properties of the fiber at microscale determined by homogenization using modified shear-lag model, while on the second stage the point-bonded stochastic fibrous network at macroscale replaced by multilevel finite beam element net. Elastic modulus and Poisson s ratio dependence on CNT volume concentration are calculated. Effective properties fibrous sheet as random stochastic network determined numerically. We conclude that an addition of CNTs into the polymer solution results in significant improvement of rheological and structural properties. 

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