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Input Data:

Bolt location X, Y (A correspond to the number of screws).

A 111141 mat cm 2^* :

X 33.5 33.5 78.5 78.5 41 mat mm * :

Y 4919491941 mat mm * :

Forces Fx, Fy, Fz & Positions X, Y, Z

F 1 el 110 - 14002500 - 31 mat N * :

F 2 el 234 789.0 789.0 - 31 mat N * :

F 3 el 00031 mat N * :

L 1 el 57901031 mat mm * :

L 2 el 7890331 mat mm * :

L 3 el 00031 mat mm * :

Moments in the axes of inertia

M 1 el 900031 mat N * m * :

M 2 el 00031 mat N * m * :

M 3 el 00031 mat N * m * :

Calculation:

A.cmb A sum : cm 2^4

x.c X A * A.cmb / : mm 56

y.c Y A * A.cmb / : mm 34

z.c 0 mm * :

r.cx X x.c - : mm 22.5 - 22.5 - 22.5 22.5 41 mat

r.cy Y y.c - : mm 1515 - 1515 - 41 mat

r.cxy r.cx 2^r.cy 2^+ sqrt vectorize : mm 27.04 27.04 27.04 27.04 41 mat

θ r.cy m / r.cx m / atan vectorize : ° 146.31 146.31 - 33.69 33.69 - 41 mat

In this case there is no problem, but the "corrct" unit is m, not mm.

I.cx r.cy 2^A * vectorize (sum : cm 4^9

C x.c y.c z.c 31 mat :

I.cy r.cx 2^A * vectorize (sum : cm 4^20.25

# vectorize vectorize

I.cp I.cx I.cy + : cm 4^29.25

Move coordinates to center point 0,0

Rc Rc L vectorize x.c y.c z.c 31 mat - : vectorize eval : mm 1561031 mat 2256331 mat 56 - 34 - 031 mat 31 mat

F.c F sum : N 12421893289 - 31 mat

M.c M sum : N m * 900031 mat

M.c M sum (Rc F † vectorize (sum (+ : N m * 110.551 - 19.46 11.814 31 mat

Z-force on bolt due to direct force in Z

F.zFZ F.c 3 el A * A.cmb / : N 822.25 - 822.25 - 822.25 - 822.25 - 41 mat

Z-force on bolt due to MX about centroid

F.zMX r.cy A * vectorize M.c 1 el I.cx / * : N 1842.5167 - 1842.5167 1842.5167 - 1842.5167 41 mat

Z-force on bolt due to MY about centroid

F.zMY r.cx A * vectorize M.c 2 el I.cy / * - : N 216.2222 216.2222 216.2222 - 216.2222 - 41 mat

The total axial force on an individual bolted joint is the sum of the axial force components:

F.ax F.zFZ F.zMX + F.zMY + : N 2448.5 - 1236.5 2881 - 80441 mat

X-force on bolt due to direct force in X

F.xFX F.c 1 el A * A sum / - : N 31 - 31 - 31 - 31 - 41 mat

Y-force on bolt due to direct force in Y

F.yFY F.c 2 el A * A sum / - : N 547.25 - 547.25 - 547.25 - 547.25 - 41 mat

XY-force on bolt due to MZ about centroid

F.xyMZ r.cxy A * vectorize M.c 3 el I.cp / * : N 109.22 109.22 109.22 109.22 41 mat

X-force on bolt due to MZ about centroid

F.xMZ F.xyMZ θ sin * vectorize : N 60.58 60.58 - 60.58 60.58 - 41 mat

Y-force on bolt due to MZ about centroid

F.yMZ F.xyMZ θ cos * - vectorize : N 90.88 90.88 90.88 - 90.88 - 41 mat

The total shear force calculated as the vector sum of the X-Y-components

F.shear F.xFX F.xMZ + (2^F.yFY F.yMZ + (2^+ sqrt vectorize : N 457.33 465.47 638.81 644.67 41 mat