"# Correction of Normal Load by Lid Displacement\n",
"Because the tie rods which measure the shear force produce an angle that is dependent on the current lid position, the normal force $F_N$ measured by the machine is not equal to the effective normal stress $F_{Neff}$. It has to be corrected with respect to the currently measured shear force $F_{S1}$ and the current angle $\\beta$, that is dependent on the current lid position $d_{lid}$.\n",
"\n",
"For this we use a simple decomposition of the resulting force $F_R=F_{s1}$ into the effective shear force $F_S$ and the normal force $F_N$ excerted by pulling on the lid at an oblique angle $\\beta$:\n",
"\n",
"$$F_R = \\sqrt{F_S^2 + F_N^2}$$\n",
"\n",
"$$F_S = F_R \\, cos \\, \\beta$$\n",
"\n",
"$$F_N = F_R \\, sin\\, \\beta$$\n",
"\n",
"The angle is defined by the length of the tie rods $l_{rod} = 412 \\,mm $ and the lid displacement $d_{lid}$ with respect to the reference point at zero lid displacement $d_0 = +\\,9\\,mm$. The usual range of lid displacement is a few millimeters upwards (negative) and downwards (positive).\n",
