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6.11: Space Trusses: Problem Solving

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Mechanical Engineering

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Space Trusses: Problem Solving

6.11: Space Trusses: Problem Solving

A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. Due to its adaptability and capacity to withstand complex loads, the space truss is widely used in various construction projects.

Consider a tripod consisting of a tetrahedral space truss with a ball-and-socket joint at C. Suppose the height and lengths of the horizontal and vertical members are known.

Figure 1

Assuming that a tensile force is applied at joint D, a free-body diagram that includes all the reaction forces at A, B, and C joints can be drawn to determine the force acting on members BC and BA.

The moment equilibrium condition at joint C is applied, considering the distances expressed in position vectors in three dimensions.

Equation 1

Simplifying further and using the force equilibrium conditions, the vector components along i yield FAy as 6 N and along k give FBx as -7.2 N. Finally, equating the j coefficients gives the value of FAx as 6 N.

Now, consider the free-body diagram at joint B to calculate the forces FBC and FBA. The forces FBD, FBC, and FBA can be expressed using position vectors. The force equilibrium condition at joint B is applied.

Equation 2

Equating the coefficients of the i, j, and k unit vectors to zero yields the forces along BC and BA as zero.

Suggested Reading


Keywords: Space Truss Three-dimensional Truss Ball-and-socket Joint Tensile Force Reaction Force Moment Equilibrium Force Equilibrium Vector Components Free-body Diagram FBC FBA

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