Mining - Stress Distribution Around a Vertical Crack in a Mine Roof Beam

Models of photoelastic material were made to simulate a mine roof that had cracked over the edge of the pillars and at the center of the span. Models were restrained from moving laterally outward so they acted as flat arches. Uniform loading was approximated by loading the models along the bottom at eight points spaced equally along the span. It was found that for models with depth to span ratios of 1:3 to 1:6, the maximum stress at the top of the center crack could be calculated directly by the following formula: Elastic stresses in mine roofs composed of sedimentary beds are usually computed by assuming that the immediate roof bed acts as a fully restrained beam uniformly loaded by its own weight and by overlying strata. Very little work has been done to analyze stresses in roof beds or beams which contain vertical (normal to the span) or nearly vertical cracks. Yet every mining engineer has walked safely under roofs that show such cracks. As far back as 1933, Bucky' made model studies of the effect of vertical cracks on the behavior of horizontal strata. He did not make any analysis of the stresses but did show that a cracked beam will stand safely under certain conditions, and also showed that a beam restrained at the ends can crack over the supports and in the middle without collapsing as long as the ends of the beam are not free to move laterally outward. The beam, or rather, part of the beam, acts like a flat arch and supports itself by pushing outward at its supports. In 1941 Evans2 treated analytically the problem of a beam cracked along so many planes perpendicular to the axis of the beam that no tensile stress can operate. He named this type of beam a "voussoir-beam" by analogy to the voussoir-arch. In 1962 ~a~cocks~ modified Evans's solution by including the effect of the shear stress component of the resultant force at the abutment. This paper gives the results of a photoelastic study of the stresses in a beam containing vertical cracks in the center of the span and over the supports. A