The key difference in the standard approaches is the selection of the point about which the pattern is assumed to pivot: (It should be noted that if all of the bolts in the pattern are the same size, then (Mr/I)♺ simplifies to Mr / Σ r 2 ). There are several standard approaches to distributing axial loads among the bolts in a case like this, all of which involve calculating the moment of inertia of the pattern about some bending axis and then using (Mr/I)♺ to distribute the loads. Loading of this type is analogous to a shaft under a combined shear and torsion load. In this case the bolts are loaded in shear only (no axial loads), and the shear loads are due to a combination of the direct shear force and the induced moment. Therefore, it induces a torsional moment about the Z-axis (perpendicular to the plane of the pattern) that will tend to rotate the pattern about its centroid. The load is eccentric because it does not act through the centroid of the pattern. The figure below shows a pattern with an eccentric shear load that is applied in the plane of the pattern. Two common loading conditions are discussed in the next two sections, followed by a discussion of the generalized approach for distributing applied loads over a bolt pattern. The reason for this is that not all of the load applied to a bolted joint is actually seen by the bolt, as discussed here. Note that we maintain the distinction that the forces are distributed to individual bolted joints rather than individual bolts. Likewise, shear forces are distributed based on the pattern's area, A, and polar moment of inertia, I c.p. Axial forces are distributed over a bolt pattern based on pattern's area, A, and moments of inertia, I c.x and I c.y. The forces and moments at the centroid are then resolved into axial and shear forces acting at the individual bolted joints. Applied loads are translated to the centroid of the pattern (analogous to the neutral axis of a beam or shaft). The distribution of forces and moments over a bolt pattern is similar to the analysis of a beam or a shaft. Bolt Pattern Calculator Overview and Discussion.
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