Generally, for a given loading condition, the bending moment in a beam varies throughout its length due to which the maximum normal/bending stress at every section is different. For a given allowable stress (fixed by the material and Factor of Safety), the maximum bending stress will be maximum where the bending moment is maximum, and will be equal to the allowable. Everywhere else the maximum bending stress will be below this allowable value.
To save material we can vary the section modulus such that the maximum bending stress at every section remains the same, equal to allowable stress. such a beam will have, at every cross section, the same value of max bending stress and hence will be fully stressed.
Such beams are also called beams of uniform strength. Even though I get why they are called fully stressed beams, I don't understand why they are called beams of uniform strength.
Strength to my understanding is the capability of a structure to bear loads. The larger the loads it can carry the higher is its strength. I don't understand how to use this definition with the concept above.