Throughout the several-hundred-year-long history of the concept of strength, inaccurate material strength as a result of the size effect and the inconsistency of strength theories have been two continuous and challenging issues, and have even been taken to be inherent attributes of material strength. Applying the structural stressing state theory and method, this study experimentally investigates the uniaxial load-bearing process of concrete specimens and reveals their stressing state mutation features at specific load levels. Exploration of this general feature resulted in the discovery of essential strength, which is basically without size effect. Then, biaxial and triaxial experiments with concrete specimens were conducted in order to obtain the results for various combinations of principal stresses on essential strength. Consequently, according to Yu's unified strength theory, the formula for strength of concrete was determined by fitting the relation between the combined principal stresses and the essential strength, which was verified by experiments carried out using natural marble specimens. Essential strength could promote the accuracy of strength indices, and the formula for strength might replace the existing strength theories for brittle materials. The initial solution of these two classic issues could make a new contribution to Yu's unified strength theory and its final goal, promoting related research on material strength and leading to a more rational use of material strength in practical engineering.
Keywords: concrete; essential strength; formula of strength; marble; specimen; stressing state.