Space Trusses: Probleemoplossing

Consider a tripod consisting of a tetrahedral space truss with a ball-and-socket joint at C.

If the height and lengths of the horizontal and vertical members are given, what force is acting on members BC and BA, considering that a tensile force is applied at D?

A free-body diagram is drawn, including all the reaction forces at A, B and C.

The moment equilibrium condition at joint C is applied. The distances are expressed in terms of position vectors in three dimensions.

Simplifying further and using the force equilibrium conditions, the vector components along i yield F_Ay. Similarly, equating the k coefficients to zero, gives F_Bx.

Finally, equating the j coefficients, give F_Ax.

Now, a free-body diagram at joint B is considered to calculate the forces F_BC and F_BA.

The forces F_BD, F_BC and F_BA can be expressed using the position vectors.

Applying the force equilibrium condition at joint B, and equating the coefficients of i, j and k unit vectors to zero, yields the forces along BC and BA.