Introduction:
In civil engineering, structures can be classified as determinate or indeterminate based on the number of unknown forces and reactions that need to be solved to determine the equilibrium of the structure. Determinate structures have a unique solution for these unknowns, while indeterminate structures have multiple solutions.

Explanation:
- Definition of determinate and indeterminate structures:
- Determinate structures: These structures can be analyzed using the equations of static equilibrium to find the unknown forces and reactions. They have a unique solution.
- Indeterminate structures: These structures cannot be analyzed using the equations of static equilibrium alone. They have more unknown forces and reactions than the number of equations available. Multiple solutions are possible.

- Stress and deflection in determinate structures:
- In determinate structures, the stress and deflection can be calculated accurately using the equations of static equilibrium and the properties of the materials.
- The maximum stress and deflection are directly related to the applied load and the properties of the structure. As the load increases, the stress and deflection also increase proportionally.

- Stress and deflection in indeterminate structures:
- In indeterminate structures, the stress and deflection cannot be calculated accurately using the equations of static equilibrium alone.
- The presence of additional unknown forces and reactions in indeterminate structures introduces uncertainties in the calculations.
- Due to these uncertainties, the maximum stress and deflection in indeterminate structures are generally smaller compared to determinate structures for the same applied load.
- The presence of additional unknowns allows the indeterminate structure to redistribute the applied load among different elements, resulting in a more efficient load-bearing system.

- Reason for smaller stress and deflection in indeterminate structures:
- The redistribution of load in indeterminate structures allows for stress and deflection reduction in critical elements.
- The additional unknown forces and reactions provide more flexibility for load sharing, resulting in a more efficient load distribution.
- This redistribution of load helps in reducing the stress and deflection in critical regions of the indeterminate structure.

Conclusion:
In most cases, for a given maximum stress and deflection, indeterminate structures exhibit smaller values compared to determinate structures. The presence of additional unknown forces and reactions in indeterminate structures allows for a more efficient load distribution, resulting in reduced stress and deflection in critical regions.