Yield-Line Theory (YLT) has been in wide spread use since the 1960's.YLT allows determining of the upper-bound bending resistance of reinforced concrete slabs using the concept of virtual work.YLT can be used for two purposes in the design of sprayed concrete support: the determination of quality assurance demands for the sprayed concrete or in the design of adequate sprayed concrete layer thickness against a bending failure. The square slab energy absorption test (EN 14488–5) and the round panel flexural toughness test (ASTM C1550- 12a) are used. Solutions for both tests are given and conversion equations are derived. Testing results produced during normal quality assurance testing process in Länsimetro project (Finland) are shown for comparison. Finally, the merits and draw-backs of the test types are discussed.
As long ago as 1908, the Danish codes for reinforced concrete structures specified a beam analysis that can be characterized as a modified yield-hinge theory, and in 1921, the Yield-Line Theory (YLT) for slabs proposed by Danish engineer Aage Ingerslev came into use. (Johansen 1972) In 1931, Knud Windstrup Johansen gave the concept a geometrical meaning as lines of relative rotation of rigid slab parts. (Braestrup 2007) In 1943, Johansen published his thesis Brudlinietheorier (Yield-line theory) in Danish. 19 years later it was translated into English and released asYield-line theory (Johansen 1962), which is the recommended source for the reader.
The term "yield-line" (brudlinie) was coined by Ingeslev in 1921 to describe lines in the slab along which the bending moment is constant. (Braestrup 2007) According to Holmgren (1993) reinforced concrete slabs are normally designed using Yield-Line Theory. The YLT is a widely used method in order to determine the bending resistance of reinforced concrete slabs.
YLT is an upper bound method to determine the plastic moment resistance using the concept of virtual work. The slab is divided into rotating parts by yielding regions which are approximated as yield-lines and the virtualwork is calculated for both internal and external actions. The sum of these virtual works must be zero to maintain equilibrium. When the yield-lines are fully developed, the slab becomes a mechanism and fails.