The theory of magnetic-probe operation in a nonuniform field is given assuming that a probe has an arbitrary physical nature.Magnetic probes are often used, for example, in flaw detection, to investigate static magnetic fields that are nonuniform within the probe's working zone. Below we present a theory of probe operation in such situations.A similar problem was solved in [1] for a particular case, specifically, for a ferroprobe with cores whose diameters were much smaller than their lengths. The formulas that we derive in the present article are more general than those derived in [1], since they are based on the black-box method; i.e., it is assumed that the probe is "hidden" inside some mobile small-sized box that is accessible for examination and is connected with a flexible cable to an stationary electronic unit. The interior of the box and hence the probe's operating principle (whether the Hall effect or the ferroprobe effect, etc., is used) were considered unknown.
Bolts of the tension type alter the state of stress of the rocks which they support. Alteration of the state of stress of a body alters the conditions for its fracture under a given deformation and the limiting values of its breaking stresses. It is therefore important to study the magnitude and nature of the stress distribution caused by tension bolts in the peripheral rock and the relations between them and the stresses due to the weight of the rocks surrounding the working.Such an analysis was carried out for a vertical working (bolt supports are being increasingly used in such workings). The initial values of the quantities influencing the state of stress of the peripheral rock were taken to lie in the range most frequently encountered in actual shaft construction.To study the stress distribution around the working and around the bolts we used some results of the theory of elasticity [1][2][3][4]. After the vertical working has been driven, the state of stress of the rocks around it are given [1] by the following equations (Fig, 1):%::~'(h(1 r2~ )r' ; (2) %=k'fh 1+ r' 1' where o B, o r, and o 0 are the vertical and horizontal [radial and normal (peripheral)] stresses, H is the depth of the working, r 0 is the radius of the shaft, r is the distance from the axis of the shaft to the reference point, k is the coefficient of lateral thrust, and Y is the density of the rock, The stresses at the periphery of the cross section of the unsupported shaft (r = r 0) are z, := 0; % = 2), "/h.A tension bolt can be regarded as a system of two equal and opposite forces applied to the surface of a linearly deformable half-space (bearing plate) and within it (the anchorage of the bolt).According to Boussinesque [4], the stress at a point M at depth z', due to the action of a force P applied to the external face of a semiinifinite solid body (i.e., one having an infinite extent depthwise and sideways), is given by the following expressiom: P = = ~ Kz,;_ P --~K r ~r, 2~ , ;Perm' Polytechnic Institute.
The theory of magnetic-probe operation in a nonuniform field is given assuming that a probe has an arbitrary physical nature.Magnetic probes are often used, for example, in flaw detection, to investigate static magnetic fields that are nonuniform within the probe's working zone. Below we present a theory of probe operation in such situations.A similar problem was solved in [1] for a particular case, specifically, for a ferroprobe with cores whose diameters were much smaller than their lengths. The formulas that we derive in the present article are more general than those derived in [1], since they are based on the black-box method; i.e., it is assumed that the probe is "hidden" inside some mobile small-sized box that is accessible for examination and is connected with a flexible cable to an stationary electronic unit. The interior of the box and hence the probe's operating principle (whether the Hall effect or the ferroprobe effect, etc., is used) were considered unknown.
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