Statically determinate structures are those structures where the forces acting on the structure can be determined by using the equations of static equilibrium alone. On the other hand, statically indeterminate structures are those structures where the forces acting on the structure cannot be determined by using the equations of static equilibrium alone. In such structures, additional equations are required to determine the forces.

Cost of Supports

The cost of supports in a structure depends on the number of supports required. Statically determinate structures require fewer supports than statically indeterminate structures. This is because statically determinate structures have a specific number of degrees of freedom, whereas statically indeterminate structures have more degrees of freedom.

In statically determinate structures, the number of supports required is equal to the number of unknown forces. For example, a simply supported beam has two supports, and the number of unknown forces (shear force and bending moment) is also two. Therefore, statically determinate structures require fewer supports, which leads to lower costs.

In statically indeterminate structures, the number of supports required is greater than the number of unknown forces. This is because the additional equations required to determine the forces also introduce additional unknowns, which require additional supports. Therefore, statically indeterminate structures require more supports, which leads to higher costs.

Conclusion

In conclusion, statically determinate structures require fewer supports than statically indeterminate structures, which leads to lower costs. This is because statically determinate structures have a specific number of degrees of freedom, whereas statically indeterminate structures have more degrees of freedom, which require additional supports. Therefore, statically determinate structures are more economical than statically indeterminate structures.