Geotechnika - Fakulta stavební - Vysoké učení technické v Brně

74 12 th International Scientific Conference, April 20-22, 2009 Brno, Czech Republicsection. The concrete part of section is substituted with additive rectangular steel section adjoined toexisting steel one. In that case the section retains either its latitude or high proportion. Whenmaterials are also combined in section latitude direction as the case of all tunnel linings thesubstituted section merges in existing steel one. This mode doesn’t provide well for reverseestimation of stress state in the concrete parts of true section.Concept of rings cooperationThe analysis of section homogenization is derived from analytical formulas estimating strainstressin multiply cylinder wall (Bulytschev 1982). The load (normal, shear) put on the outer wallperiphery is redistributed in decrement way on single rings that assemble the wall structure section.On the inner wall periphery the load equates to known value e.g. zero as the case of tunnel lining(Fig.2). The stress in each partial ring layer is established on sustaining the radial andcircumferential displacements at interface between the adjoining ring layers. For each ring theredistribution coefficients are assigned. They depend on ring layer thickness and its deformationparameters.Fig. 2 Scheme of load redistribution on single rings of multiply cylinder wall structuresection.The load formulae on the outer ring periphery arep = pn = p0+ p2cos 2θ ; q = qn= q2sin 2θp 0 – radial symmetrical part of external load; p 2 – radial asymmetrical part of external load; q 2– shear part of external loadThe stresses on an interface of adjoining rings p k , q k are assignedpk=p ( k ) + p0⎛ p⎜⎝ q22( k)( k)2⎞ ⎡⎟ = ⎢⎠ ⎢⎣( k )cos 2θ;⎛p ⎜0 ( k ) =⎜⎝n∏i=k+1n∏i=k+1⎛ K⎜⎝KKppqp0qk() i= q⎞⎟ p⎟⎠02( k )sin 2θ() i K pq () i ⎞⎤⎛p2() () ⎟ ⎞⎟⎥⎜i Kqq i ⎥⎝q2⎠⎠⎦The coefficients K 0(i) , K pp(i) , K pq(i) , K qp(i) , K qq(i) , i=1,...,n represent load redistribution at ring i.On the first ring (i=1) they equal zero.