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Abstract Theoretical solution of bending moment and deflection about tight roof is a subject which has not been well solved in mining rock mechanics. Statically indeterminate times of the tight roof in the first weighting are one more higher than that in the periodic weighting. The coal seam and immediate roof are considered as an elastic ground to solve the deflection of the unit width tight roof in front of the coal face and over the gob at the middle part of working face which is under the combined action of uniform load，advanced supercharger load of the load peak and the support resistance is solved. Adopting some results of solution of tight roof?s bending moment and deflection before periodic weighting obtained by PAN Yue et al.，all coefficients of tight roof?s four parts deflection expressions which are on the satisfaction of all continuity conditions and natural boundary conditions are obtained. According to the expressions obtained，the tight roof deflection，bending moment curve and shear curve of the tight roof in the first weighting which was got by Matlab software?s calculation and drawing functions was connected smoothly during the inspection. The following conclusions can be drawn from the curve analysis：(1) The increase or the decrease of the load has an obvious effect on bending moment and deflection of the roof. (2) The support resistance could effectively reduce the bending moment and deflection of the roof before the mine face and hanging roof and the shear stress of the gob roof. (3) Characteristic length of the unit width roof is composed of strata rigidity and flexural rigidity of the roof. With the same load，the bending moment of roof is completely the same if the characteristic length is identical；but the bending moment of the roof is larger when the characteristic length is larger. (4) When the elastic foundation coefficient is smaller，the deflection(subsidence value) of the roof ahead of coal face is larger. When the flexural rigidity is smaller，the deflection(subsidence value) of the gob roof is larger. (5) The peak position of the bending moment lies ahead of the coal face. The position of the bending moment peak is closer to coal face with the condition of large roof load，small the supporting resistance and large the elastic foundation coefficient. The roof shear is largest at the both sides of roof-control area. In this paper the expressions of tight roof deflection and bending moment are only theoretical solutions under ideal roof model，which can be used to be aroused from the calculation example of the theoretical solutions and to obtain regularity understanding for the variation in the roof deflection and bending moment when the relational parameters are changed；and to make reasonable qualitative judgment on the changes of the mine roof status. Also the analytic solution can offer basis for further study about the fracture process of tight roof，the releases of the roof strain energy and the energy source of rockburst caused by the fracture of tight roof .
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Received: 16 December 2012
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2013, Vol. 32 
