Torsional Analysis Calculations

The force F_i on shear line line i is given by

max (F_i+, F_i-)

where

F_i+ = F_di + + F_ti+

F_i- = F_di - + F_ti-

where

• F_di is the direct component given by

F_di = F * K_i / S K_i,

where

• F is the total applied force in the direction parallel to the shear lines and
• K_i is the rigidity of shear line i

• F_ti is the torsional component given by

F_ti+ = T+ * K_i * d_i / (J_x + J_y)

F_ti- = T- * K_i * d_i / (J_x + J_y)

where

• d_i is the distance from the shear line to the center of rigidity CR
• J_x and J_y are the torsional rigidities, in the x- and y- directions, given by

J = S K_i * d_i ^a

• T is the torsion, given by

T+ = (CL - CR + ae) * F

T- = (CL - CR + ae) * F

where

• CL = Center of load = centroid of applied loads in force direction. For seismic loading, this is equivalent the center of the building mass at that level.
• CR = Center of rigidity, given by

CR = S K_i * l_i / S K_i,

where l_i is the distance to the shear line from the edge of the building.

• ae = accidental eccentricity, which is a proportion of the building width perpendicular to force direction. Diaphragm Flexibility Cases for the values for different design cases.

In the direction of loading, torsional forces add to the direct shear forces for some walls and subtract from the direct shear forces for other walls, depending on the direction of the torsional moment created by the difference in the center of load and rigidity.

Torsional analysis also creates torsional forces in shear lines orthogonal to the force direction. Unless we are designing for loads from both directions simultaneously, as we do for low-rise wind loads, the program discards the torsional forces in the orthogonal direction on the assumption they are smaller than the total force from torsional analysis of loads in that direction.