## 2 Shear Crack Propagation Theory (SCPT)  
The SCPT intends to provide a deeper understanding of shear in beams and slabs without shear reinforcement through analyzing the entire shear response (load history) of a member instead of solely focusing upon the fracture state. To this end, the mechanical theory considers crack propagation through the shear zone and is based on the requirement of the equilibrium for the bending and shear stress resultants in an intermediate state of the shear crack propagation. Besides the equilibrium of the forces within every load increment, the SCPT accounts for the material constitutive behavior, as well as the compatibility of the kinematic behavior. The shear failure process of RC members without shear reinforcement includes several interacting effects of the material behavior. These elementary effects within the shear critical region of a member are exemplarily sketched in Figure 1a. Effect (1) is the crack localization within the fracture process zone (FPZ). Effect (2) describes the crack propagation due to the increasing load. Both effects are interrelated with the biaxial concrete stresses at the propagating crack-tip. The biaxial stress state depends on the shear transfer through bending of the concrete teeth between adjacent flexural shear cracks, also known as cantilever action (3). Here, bending of the concrete teeth is mainly influenced by the difference of tension in the longitudinal reinforcement between two adjacent interacting cracks (called \(\Delta\)Fs) and the equilibrium conditions of the forces within the shear cracks at both sides. Assuming that all forces within both shear cracks are rotating around an assumed center of rotation, located in the middle between the two crack tips, the vertical stresses resulting from this (cantilever action) are called \(\sigma_{x}\) and are taken into account when calculating the biaxial stress state at the crack tip. With increasing the vertical stress \(\sigma_{\rm z}\), the crack propagation angle decrease. Effect (4) represents the shear transfer in the uncracked part of the concrete above the crack tip in combination with the effect of direct strutting. Effect (5) is the shear stress transfer resulting from aggregate interlock between two crack faces, while effect (6) comprises the transverse stiffness and strength of the flexural reinforcement and concrete cover known as the dowel action. Finally, effect (7) describes the crack bridging actions including tension stiffening, as well as bond behavior and delamination of the flexural reinforcement. To combine all the identified effects (1)-(7) relevant for RC members without shear reinforcement in one all-encompassing algorithm, the member is discretized as a system of interacting concrete teeth that are separated from each other by discrete propagating shear cracks but connected by a continuous concrete body representing the compression zone and uncracked tension zone (\"backbone\") (Figure 1a). In the next step, a biaxial shear crack propagation criterion (cohesive crack approach by [PERSON] [37] combined with [PERSON]'s fracture criterion [38]) is implemented to determine the crack propagation angle and crack extension, as well as the continuity of stresses at the transition between the compression zone and crack (vertical crack tip stresses resulting from cantilever action serve as the input information) (Figure 1a). The crack propagation criterion delivers the shear crack path defining the control section to formulate the compatibility and equilibrium conditions. The stress and strain fields within this control section are decomposed into four parts-namely the compression and uncracked tension zone, fracture process zone, frictional zone and crack bridging and dowel action zone. Considering the compatible kinematic model illustrated in Figure 1b allows assessing the strains in uncracked concrete parts and the flexural reinforcement, as well as the local opening and sliding deformations in the propagating shear crack based on the rotational degree of freedom \(\varphi\).