The latter matrix is the utilization tensor. The largest eigenvalue of this tensor is the utilization (unity check), which can be displayed in a contour plot of a structure for all load combinations related to the ultimate limit state. For example, the stress at some location in a structure is formula_40 = 4 N/mm², formula_41 = -10 N/mm², formula_42 = 3 N/mm², formula_43 = 3 N/mm², formula_44 = -7 N/mm², formula_45 = 1 N/mm². The reinforcement yield stress is formula_12 = 500 N/mm². The proposed reinforcement is formula_3 = 1.4%, formula_6 = 0.1%, formula_9 = 1.9%. The eigenvalues of the utilization tensor are -20.11, -0.33 and 1.32. The utilization is 1.32. This shows that the bars are overloaded and 32% more reinforcement is required. Combined compression and shear failure of the concrete can be checked with the Mohr-Coulomb criterion applied to the eigenvalues of the stress tensor of the brittle material.  formula_50 ≤ 1,   where formula_51 is the largest principal stress, formula_52 is the smallest principal stress, formula_53 is the uniaxial compressive strength (negative value) and formula_54 is a fictitious tensile strength based on compression and shear experiments. Cracks in the concrete can be checked by replacing the yield stress formula_55 in the utilization tensor by the bar stress at which the maximum crack width occurs. (This bar stress depends also on the bar diameter, the bar spacing and the bar cover.) Clearly, crack widths need checking only at the surface of a structure for stress states due to load combinations related to the serviceability limit state.