The Bolt Pattern Force Distribution Calculator allows for applied forces to be distributed over bolts in a pattern. See the instructions within the documentation for more details on performing this analysis. See the reference section for details on the equations used.

Options:

Inputs

Input the details for the pattern, then click the "Calculate Results" button:

Individual bolt locations are below, for reference:

Plot Display Units:

Display Units

Display results in:

Results

The results of the force distribution analysis are detailed below. Refer to the force distribution reference section for details on how these results were derived.

The applied forces and moments are translated to the centroid of the pattern.

The forces at the centroid are simply the sum of the applied forces:

F_{c.x}

=

sum of the forces in the X-direction

F_{c.y}

=

sum of the forces in the Y-direction

F_{c.z}

=

sum of the forces in the Z-direction

The moments at the centroid are:

M_{c.x}

=

moments at centroid about X-axis

M_{c.y}

=

moments at centroid about Y-axis

M_{c.z}

=

moments at centroid about Z-axis

Pattern Properties Summary

The properties of the pattern are detailed below:

A_{cmb}

=

combined area of bolts in the pattern

x_{c}

=

X-coordinate of the pattern centroid

y_{c}

=

Y-coordinate of the pattern centroid

I_{c.x}

=

centroidal moment of inertia about X-axis

I_{c.y}

=

centroidal moment of inertia about Y-axis

I_{c.p}

=

centroidal polar moment of inertia

See full result details on the other tabs (above).

Pattern Properties

This section details the properties of the bolt pattern. These pattern properties determine how the applied forces distribute among the individual bolts.

Pattern Properties Summary

The properties of the pattern were calculated based on the areas and locations of the bolts:

A_{cmb}

=

combined area of all bolts in the pattern

x_{c}

=

X-coordinate of the pattern centroid

y_{c}

=

Y-coordinate of the pattern centroid

I_{c.x}

=

centroidal moment of inertia of the pattern about the X-axis

I_{c.y}

=

centroidal moment of inertia of the pattern about the Y-axis

I_{c.p}

=

centroidal polar moment of inertia of the pattern

Bolt Pattern Geometry

The pattern properties are determined based on the pattern geometry. The specified bolt sizes and locations are shown in the table below, as well the distances of the bolts from the pattern centroid:

Bolt #

Ptrn #

Ptrn Type

Thread

Area

Location

Distance from Centroid

θ

x

y

r_{c.x}

r_{c.y}

r_{c.xy}

Bolt Pattern Centroid

Applied forces and moments are translated to the pattern centroid before distributing forces among individual bolts. The bolt pattern is treated as if it were a beam, where the centroid of the pattern is like the neutral axis of the beam.

The pattern centroid is calculated as:

where A_{i} is the bolt area and x_{i} and y_{i} are the x- and y- bolt locations, respectively.

Bolt Pattern Moment of Inertia

The moments of inertia of the pattern about the x- and y- axes are calculated as:

where A_{i} is the bolt area and r_{c.x,i} and r_{c.y,i} are the x- and y- distances of the bolt from the centroid, respectively.

The polar moment of inertia of the pattern about the centroid is calculated as:

The applied forces and moments are translated to the centroid of the bolt pattern. Once forces and moments at the centroid are calculated, they can be used to calculate the forces acting on individual bolted joints.

Centroid Location

The location of the pattern centroid is:

x_{c} =

y_{c} =

Applied Forces & Moments

The applied forces are listed below:

Force #

Force Value

Location

Distance to Centroid

F_{x}

F_{y}

F_{z}

L_{x}

L_{y}

L_{z}

R_{c.x}

R_{c.y}

R_{c.z}

The applied moments are listed below:

Moment #

Moment Value

M_{x}

M_{y}

M_{z}

There are no moments applied to this bolt pattern.

Forces & Moments at Pattern Centroid

The applied forces and moments are translated to the centroid of the pattern. Once forces and moments at the centroid are calculated, they can be used to calculate the forces acting on individual bolted joints.

The forces at the centroid are simply the sum of the applied forces:

F_{c.x}

=

sum of the forces in the X-direction

F_{c.y}

=

sum of the forces in the Y-direction

F_{c.z}

=

sum of the forces in the Z-direction

The moments at the centroid are:

M_{c.x}

=

moments about X, translated to centroid

M_{c.y}

=

moments about Y, translated to centroid

M_{c.z}

=

moments about Z, translated to centroid

The forces at the centroid are calculated as the sum of all applied forces:

The moments at the centroid are calculated as the sum of all applied moments, plus the sum of the cross product of each applied force with the vector from the centroid to the location of that applied force:

Individual Bolt Forces

This section details the axial and shear forces acting on each individual bolted joint in the pattern.

Bolt Force Summary

The resultant axial and shear forces at each bolt are given below:

The bolt forces were calculated based on the geometry of the pattern as well as the forces and moments at the centroid of the pattern, as seen below.

Bolt Pattern Geometry

Bolt #

Thread

Area []

Dist. from Centroid []

θ []

r_{c.x}

r_{c.y}

r_{c.xy}

Forces & Moments at Centroid

Forces at centroid:

F_{c.x}

=

F_{c.y}

=

F_{c.z}

=

Moments at centroid:

M_{c.x}

=

M_{c.y}

=

M_{c.z}

=

Axial Force Calculation

The axial forces on each bolted joint are shown in the table below. The equations used to calculate each axial force component are shown to the right.

Bolt

Area []

Axial Forces []

P_{ax} total

P_{z.FZ}

P_{z.MX}

P_{z.MY}

Z-force on bolt due to direct force in Z

Z-force on bolt due to MX about centroid

Z-force on bolt due to MY about centroid

The total axial force on an individual bolted joint is the sum of the axial force components:

P_{axial} = P_{z.FZ} + P_{z.MX} + P_{z.MY}

Shear Force Calculation

The shear forces on each bolted joint are shown in the table below. The equations used to calculate each shear force component are shown to the right.

Bolt

Area []

Shear Forces []

P_{shr} total

P_{x.FX}

P_{y.FY}

P_{xy.MZ}

P_{x.MZ}

P_{y.MZ}

X-force on bolt due to direct force in X

Y-force on bolt due to direct force in Y

XY-force on bolt due to MZ about centroid

P_{x.MZ} = P_{xy.MZ} · sinθ

X-force on bolt due to MZ about centroid

P_{y.MZ} = −P_{xy.MZ} · cosθ

Y-force on bolt due to MZ about centroid

The total shear force on an individual bolted joint is calculated as the vector sum of the X- components plus the Y- components:

Bolt shear forces are displayed below. Applied forces and moments are shown in blue, and resultant shear forces on the individual bolts are shown in red.

Download Report

Save a formatted Word document to your computer detailing the inputs and results of the analysis.

Download Inputs File

Save all input data to a file. You can later upload this file to pick back up where you left off.

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