Simplified stability analysis of quasi-brittle notched columns

The stability of columns made of quasi-brittle materials, loaded by an eccentric force at the top and edge notched at their base, is studied. Actually, columns are often made of quasi-brittle materials, as it happens for stone columns of historical monuments. They are frequently cracked or notched at the base, as this region is both more solicited and exposed to impacts that can chip them. Besides, columns are often slender, so that geometrical instability can also occur. Therefore, simplified methods of analyzing the instability due to both column geometry and fracture are useful, as the both can occur contemporarily. A simplified analysis of the instability of notched slender columns is then illustrated, by also avoiding the use of finite elements. This appears to be an advantage, because an easy analysis, although approximated, allows a faster check of the column stability, as well as an intuitive comprehension.