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Figure 10. Comparisons between numerical and experimental force-displacement curves for rafter 190 x 225 mm under fwr = 1.5 MPa.

in the rafter of 1.0 MPa, the linear trend was followed up to about a transverse load of 1.6 kN, which is about 30% higher than the experimental value (Figure 9). As the rafter compression level increases (e.g. 1.5 MPa), the linear trend was followed up to a transverse load of 1.2 kN, and resulted very close to the experimental value (Figure 10).

Again, differences between numerical and experimental diagrams in terms of initial stiffness are found for low axial compressive stress (e.g. 1.0 MPa), because of the regularity in the numerical representation of the facing surfaces, which contrasts the reality of hand-sawn indentations. This may explain also the better agreement of results for higher compression values (e.g. 1.5MPa), that partially mitigate effects of local irregularities before that rotation of the rafter was experienced.

Results in terms of moment vs rotation curves for joint members are illustrated in Figure 11 for axial stress levels in the rafter equal to fwr = 1.0 MPa and 1.5 MPa. It can be observed that the numerical response is in good agreement with those provided by Parisi & Piazza (2000). Besides, the rotational elastic stiffness is not affected by the rafter axial compression level, in accordance with the reference FE model.

Figure 11. Comparisons of moment vs rotation curves for joint members 200 x 200 mm for fwr = 1.0 MPa and
Figure 12. Contour of the compressive stress along the grain (values in N/mm2). Rafter 200 x 200 mm - fwr = 1.5 MPa.

A sketch of the principal compressive stresses is plotted in Figure 12, where the compressed zone are due to the rotation mechanism of the joint.

2.3 Sensitivity analysis

A key point related to the reliability ofnumerical analysis is to know the influence of material data on the structural response. A sensitivity analysis of the results depending on the friction coefficient and the compres-sive level fwr in the rafter is herein presented. The model sensitivity with respect to the material parameters and the skew angle have been also assessed, but not reported herein for sake of brevity. The sensitivity of the analysis with respect of the compressive strength in the rafter has been illustrated in Figure 11.

A comparisons in terms of friction coefficient is given in Figure 13 with reference to a rafter cross section 200 x 200 mm. In particular, two values of the friction coefficient were accounted: |x = 0.3 and |x = 0.4.

Figure 13 illustrates results in terms of momentrotation plots. From Figure 11 it can be observed that variation of fwr did not alter the response of the plain joint in the elastic part (rotational stiffness remains almost identical). Increase of friction factor |i results in

Figure 13. Results of sensitivity analysis for |l = 0.3 and | = 0.4 for joint members 200 x 200 mm - fwr = 1.5 MPa.

an increase of the slope of the first part of the response of about +10% (Figure 13).

2.4 Connections of the Royal Palace in Caserta

In the present section, numerical analyses of the joints of the timber truss of the Royal Palace in Caserta are presented. In particular, the behaviour of connections was investigated by using the calibrate model above discussed. The analyses accounted the joints between: the rafters and the main chord, the king post and the rafter, the diagonal strut and the rafter, the diagonal strut and the king post. Due to the lack of experimental data, the Chestnut wood class C30 is used for joint elements in compliance to prEN 338 standard (1985).

The constitutive law of the wood elements was reproduced according to an orthotropic elasticity approximation. Mean values of the elastic Young' s moduli parallel and orthogonal to the grain were E; = 10000 MPa and E2 = 640 MPa, respectively. In addition the shear modulus G12 = 600 MPa and the Poisson's coefficient u12 = 0.4 have been assumed. Proper boundary conditions were considered and contact points type Normal are used to model the interface between the truss elements. The elastic stiffness of each contact element was estimated as EA/L, in accordance with Equation (1). In addition, a value of |i = 0.4 is assumed.

In this work, any interaction mechanism between the main and secondary rafters has been accounted for. It is worth noting that for accurate evaluation of deformation behaviour of the joint, the partial composite action between the rafters should be properly modeled. Conversely, the effect of the metal stirrup at the truss heel has been included in the finite element model by using a set of linear spring elements. The spring elements were placed diagonally with the chord grain direction (1-axis) within the joint, and their stiffness was derived based on formulation available in literature (Gelfi et al. 1998). The analyses were carried out under plane stress conditions and the Modified fwr = 1.5 MPa.

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