#round 3 "Bolt Pattern Force Distribution 'This calculator determines the maximum bolt force in a circular bolt pattern subjected to direct shear and torsional moment. The analysis uses closed-form elastic methods suitable for preliminary design and verification. "References 'Ref 1: Budynas, R.G. and Nisbett, J.K., 2008, Shigleys Mechanical Engineering Design, 8th Edition, McGraw-Hill "Inputs '

Bolt Pattern Geometry

' Number of bolts in pattern -'n_b = ? {6} ' Pitch circle diameter -'PCD = ? {200}mm '

Applied Loading

' Applied shear force on bolt group -'V_app = ? {60000}N ' Applied torsional moment about group centroid -'M_app = ? {3000000}N*mm '

Bolt Properties

' Bolt ultimate tensile strength -'f_ub = ? {800}MPa ' Bolt tensile stress area -'A_s = ? {245}mm^2 "Calculations '

'Click to expand/collapse detailed calculations '

Bolt Pattern Geometry

R = PCD/2 ' Bolt radius from centroid -'R '

[Geometry]

Polar Moment of Bolt Group

'For a circular pattern with all bolts at the same radius R: J_bolt = n_b*R^2 ' Polar moment of bolt group -'J_bolt '

[Ref 1, Ch. 8]

Direct Shear per Bolt

'The applied shear is distributed equally among all bolts: V_direct = V_app/n_b ' Direct shear force per bolt -'V_direct '

[Ref 1, Ch. 8]

Torsional Shear per Bolt

'The torsional component at each bolt due to the applied moment: V_torsion = M_app*R/J_bolt ' Torsional shear force per bolt -'V_torsion '

[Ref 1, Ch. 8]

Maximum Combined Bolt Force

'Conservative upper bound assuming worst-case vector alignment: F_max = V_direct + V_torsion ' Maximum bolt force, conservative -'F_max '

[Ref 1, Ch. 8 - algebraic sum]

'Vector resultant assuming perpendicular components: F_resultant = sqr(V_direct^2 + V_torsion^2) ' Vector resultant bolt force -'F_resultant '

[Ref 1, Ch. 8 - vector sum]

Bolt Shear Capacity

'Single bolt shear capacity based on 0.6 times ultimate tensile strength: F_v = 0.6*f_ub*A_s ' Single bolt shear capacity -'F_v '

[Ref 1, Ch. 8]

Utilization

'Using conservative maximum force: util = F_max/F_v ' Bolt shear utilization -'util '

"Results 'Bolt Pattern: 'Number of bolts: 'n_b 'PCD: 'PCD 'Bolt radius: 'R 'Applied Loading: V_app M_app 'Force Components per Bolt: V_direct V_torsion 'Maximum Bolt Force - Conservative: F_max 'Note: This is the conservative upper bound assuming worst-case alignment of direct and torsional force vectors. 'Maximum Bolt Force - Vector Resultant: F_resultant 'This is the vector resultant assuming perpendicular force components. 'Bolt Capacity: F_v 'Utilization: util '

Assessment

#if util ≤ 1 '

PASS - Bolt Shear Capacity

Utilization = 'util' is less than or equal to 1.0

Maximum bolt force of 'F_max' is within the single bolt shear capacity of 'F_v'

#else '

FAIL - Bolt Shear Capacity

Utilization = 'util' is greater than 1.0

Maximum bolt force of 'F_max' exceeds the single bolt shear capacity of 'F_v'

Increase number of bolts, PCD, bolt grade, or bolt size.

#end if "Conclusion 'A circular bolt pattern with 'n_b' bolts on a PCD of 'PCD' has been analyzed for an applied shear of 'V_app' and torsional moment of 'M_app' per Ref 1. The direct shear per bolt is 'V_direct' and the torsional shear per bolt is 'V_torsion'. The conservative maximum bolt force is 'F_max' giving a utilization of 'util' against a single bolt shear capacity of 'F_v'.

Bolt Pattern Force Distribution

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