an orthotropic continuum model for the analysis of masonry structures

TNO-95-NM-R0712 1995 37For the numerical analysis linear plane stress continuum elements (4-noded) and constant strain trianglesin a cross diagonal patch with full Gauss integration are utilised. A regular mesh of 24 × 154-noded elements is used for the panel and 2 × 15 cross diagonal patches of 3-noded triangles areused for each ßange. The properties of the composite material are obtained from Ganz andThŸrlimann (1982). The elastic properties read E x = 2460 N/mm 2 ,E y = 5460 N/mm 2 , ν xy = 0. 18and G xy = 1130 N/mm 2 . The inelastic parameters for the panel read f tx = 0. 05 N/mm 2 ,f ty = 0. 25 N/mm 2 , α = 1. 66, α g = 1. 0, G fx = 0. 02 N/mm, G fy = 0. 02 N/mm, f mx = 1. 87 N/mm 2 ,f my = 7. 61 N/mm 2 , β =−1. 05, γ = 1. 2, G fcx = 5. 0 N/mm, G fcy = 10. 0 N/mm and κ p = 0. 0008.The inelastic parameters that control the shape of the yield surface are obtained from a least squaresÞt from the experimental results but no data are available for the post-peak range. It is noted that, inthe ßanges, a stack bond masonry is used and different material properties must be considered. Theinelastic parameters for the ßanges read f tx = 0. 68 N/mm 2 , f ty = 0. 25 N/mm 2 , α = α g = 1. 0,G fx = 0. 05 N/mm, G fy = 0. 02 N/mm, f mx = 9. 5 N/mm 2 , f my = 7. 61 N/mm 2 , β =−1. 05,γ = 3. 0, G fcx = 10. 0 N/mm, G fcy = 10. 0 N/mm and κ p = 0. 0008. Finally, note that the selfweightof wall and top slab is also considered in the analysis.5.2.1 Wall W1The results of the numerical analysis are given in Fig. 38 to Fig. 44. The comparison betweenexperimental and numerical results, in terms of load-displacement diagrams, is given in Fig. 38. Inopposition to the Þrst example shown in the present report, good agreement is found between bothresults. This is due to the distributed nature of the process prior to collapse. The behaviour of thewall is depicted in Fig. 39 to 44 in terms of total deformed mesh, incremental deformed mesh,cracked Gauss points and minimum principal stresses contour. Note that the center node of thecrossed diagonal patch is not shown in the meshes to obtain a more legible picture. For the samereason the contour of minimal principal stresses is shown instead of the representation at eachGauss point. The comparison between experimental and numerical behaviour results is more difÞcultbut reasonable agreement seems to be found. Immediately after starting loading the structure,extensive diagonal cracking of the panel is found, see Fig. 39. Upon increasing deformation crackingtends to concentrate in a large shear band going from one corner of the specimen to the other,see Fig. 40 and Fig. 41. This is accompanied by ßexural cracking of the right ßange and, at a laterstage, also the left ßange, see Fig. 42 and Fig. 43. At ultimate stage, see Fig. 44, a well deÞned failuremechanism is formed with a Þnal shear band going from one corner of the specimen to theother and intersecting the ßanges. This means that cracks rotate signiÞcantly since initiation governedby MohrÕs circle to failure in a sort of shear band, which agrees extremely well with theexperiments (see Fig. 37a,b).300.0Horizontal force F [kN]200.0100.0ExperimentalNumerical0.00.0 4.0 8.0 12.0Horizontal displacement d [mm]Fig. 38 - Load-displacement diagram for wall W1 (low conÞning pressure)