Bolt Pattern Force Distribution
Determine the maximum bolt force in a circular bolt pattern subjected to direct shear and torsional moment using closed-form elastic analysis methods.
About This Calculator
This calculator finds the most heavily loaded bolt in a circular bolt group carrying an in-plane shear force and a torsional moment about the group centroid, then checks that bolt in shear. Method: the applied shear is shared equally between the bolts. The moment is resisted by the polar moment of the bolt group, J = n R², where R is half the pitch circle diameter, so each bolt carries a torsional force of M R / J = M / (n R). The calculator reports two values for the critical bolt: a conservative upper bound that adds the direct and torsional forces as if they acted in line, and the vector resultant if they act at right angles. The conservative value is compared with the design shear resistance of one bolt to EN 1993-1-8 Table 3.4, α_v f_ub A_s / γ_M2, with one shear plane through the thread. Inputs are the number of bolts, the pitch circle diameter, the applied shear and moment, the bolt’s ultimate strength and tensile stress area, the shear factor α_v (0.6 for grades 4.6, 5.6 and 8.8, or 0.5 for 4.8, 5.8, 6.8 and 10.9), and the partial factor γ_M2 (1.25 in the UK National Annex). Assumptions and limits: rigid connected plates, bolts of one size on a single pitch circle, elastic load sharing, and loads in the plane of the joint. Bolt tension from out-of-plane moments, prying, slip resistance of preloaded joints and plate bearing are not covered. Typical uses: flange and coupling connections, slew ring and turntable bolting, sheave and winch drum mountings, and bolted brackets loaded off-centre.
Referenced Standards
- Budynas and Nisbett, Shigley’s Mechanical Engineering Design (bolt groups in shear)
- BS EN 1993-1-8, Table 3.4 (bolt shear resistance)