Statically indeterminate

In statics, a construction is statically indeterminate when the static equilibrium equations are not sufficient to calculate the reactions on that construction.

The equations are

• Σ F = 0, the sum of the forces acting on the construction equals zero, this translates to

Σ H = 0, the sum of the horizontal forces equals zero

Σ V = 0, the sum of the vertical forces equals zero

• Σ M = 0, the sum of the moments equals zero

In the construction on the right the four unknown reactions are V_A, V_B, H_A and H_B. Since there are only three equations the set cannot be resolved for H_A and H_B; the construction is statically indeterminate.

Statically determinate

If the support at B is designed as a rolling support, the reaction H_B cannot occur, the construction becomes statically determinate and can be calculated using the three equations:

Σ H = 0;

H_A - F_h = 0, or H_A = F_h

Σ V = 0;

V_A - F_v + V_B = 0, or V_A + V_B = F_v

Σ M_A = 0;

F_v · a - V_B · (a+b) = 0, or V_B = F_v · a / (a+b)

and it follows that V_A = F_v · b / (a+b)

See also

statics, structural engineering, Otto Mohr, Hardy Cross.