Theoretical wall stresses and insert loads in a bin-hopper with a conical insert using the differential slice method

The wall stresses and insert load in a three-dimensional bin-hopper with a conical insert were investigated theoretically using the differential slice method. The placements of a conical insert for different kinds of hopper half-angle, insert half-angle and friction coefficient were determined by using the method of Johanson. Moreover, the effects of the hopper half-angle, insert half-angle, internal friction angle and wall friction angle upon the wall stress and insert load were demonstrated. The maximum stress peak of normal wall stress in a bin-hopper with an insert is found at the apex of the conical insert instead of at the transition point of the bin-hopper and decreases with increasing insert half-angle. Additionally, for a fixed value of hopper half-angle, the insert load (i.e. the total vertical force on the insert) increases with increasing insert half-angle in the active state, but decreases with increasing insert half-angle in the active/passive state. Employing the results obtained using the differential slice method, the wall stress and insert load in a bin-hopper with a conical flow corrective insert may be further understood.