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SUMMARY:The effect of stereotomy on the shape of the thrust line and the m
 inimum thickness of masonry arches - Professor Nicos Makris - University o
 f Patras\, Greece
DTSTART:20131101T150000Z
DTEND:20131101T160000Z
UID:TALK47582@talks.cam.ac.uk
CONTACT:Lorna Everett
DESCRIPTION:More than a century ago Milutin Milankovitch presented a remar
 kable formulation for the thrust-line of arches that do not sustain tensio
 n\, and by taking radial cuts and a polar coordinate system he published f
 or the first time the correct and complete solution for the theoretical mi
 nimum thickness\, t\, of a monolithic semicircular arch with radius R.\n\n
 In this seminar we show that Milankovitch’s solution\, t/R=0.1075\, is n
 ot unique and that it depends on the stereotomy exercised. The adoption of
  vertical cuts which are associated with a cartesian coordinate system yie
 lds a neighboring thrust-line and a different\, slightly higher value for 
 the minimum thickness (t/R=0.1095) than the value computed by Milankovitch
 . We show that this result can be been obtained with a geometric and a var
 iational formulation.\n\nThe Milankovitch minimum thrust-line derived with
  radial stereotomy and our minimum thrust-line derived with vertical stere
 otomy are two distinguishable\, physically admissible thrust-lines which d
 o not coincide with R. Hooke’s catenary that meets the extrados of the a
 rch at the three extreme points. Furthermore\, the seminar shows that the 
 catenary (the “hanging chain”) is not a physically admissible minimum 
 thrust-line of the semicircular arch although it is a neighboring line to 
 the aforementioned physically admissible thrust-lines. The minimum thickne
 ss of a semicircular arch that is needed to accommodate the catenary curve
  is t/R=0.1117―a value that is even higher than the enhanced minimum thi
 ckness t/R=0.1095 computed in this work after adopting a vertical stereoto
 my\; therefore\, it works towards the safety of the arch.\n\nAs in the cas
 e of gravity loads\, the value of the minimum horizontal acceleration that
  is needed to convert an arch into a four-hinge mechanism depends on the d
 irection of rupture at the imminent hinge locations. Vertical ruptures yie
 ld the minimum rupture acceleration.\n\n
LOCATION:Cambridge University Engineering Department\, LR5
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