Bolts distributed about a bolt circle are often called upon to resist an external bending moment as shown in the figure. The external moment is

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Bolts distributed about a bolt circle are often called upon to resist an external bending moment as shown in the figure. The external moment is 12 kip? In and the bolt circle has a diameter of 8 in. The neutral axis for bending is a diameter of the bolt circle. What needs to be determined is the most severe external load seen by a bolt in the assembly.
(a) View the effect of the bolts as placing a line load around the bolt circle whose intensity F′b, in pounds per inch, varies linearly with the distance from the neutral axis according to the relation F′b = F′b, max R sin θ . The load on any particular bolt can be viewed as the effect of the line load over the arc associated with the bolt. For example, there are 12 bolts shown in the figure. Thus each bolt load is assumed to be distributed on a 30 arc of the bolt circle. Under these conditions, what is the largest bolt load?
(b) View the largest load as the intensity F'b,max multiplied by the arc length associated with each bolt and find the largest bolt load.
(c) Express the load on any bolt as F = F max sinθ, sum of the moments due to all the bolts, and estimate the largest bolt load. Compare the results of these three approaches to decide how to attack such problems in the future.