Results Summary
A summary of the results is shown below. Further details are given on the other tabs.
Bolt Force Summary
The resultant axial and shear forces at each bolt are given below:
Bolt # 
Ptrn # 
Ptrn Type 

Axial Force 
Shear Force 
The highlighted bolts should be analyzed with the Bolted Joint Calculator.
Forces & Moments at Pattern Centroid
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 Xdirection 
F_{c.y} 
= 

sum of the forces in the Ydirection 
F_{c.z} 
= 

sum of the forces in the Zdirection 
The moments at the centroid are:
M_{c.x} 
= 

moments at centroid about Xaxis 
M_{c.y} 
= 

moments at centroid about Yaxis 
M_{c.z} 
= 

moments at centroid about Zaxis 
Pattern Properties Summary
The properties of the pattern are detailed below:
A_{cmb} 
= 

combined area of bolts in the pattern 
x_{c} 
= 

Xcoordinate of the pattern centroid 
y_{c} 
= 

Ycoordinate of the pattern centroid 
I_{c.x} 
= 

centroidal moment of inertia about Xaxis 
I_{c.y} 
= 

centroidal moment of inertia about Yaxis 
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} 
= 

Xcoordinate of the pattern centroid 
y_{c} 
= 

Ycoordinate of the pattern centroid 
I_{c.x} 
= 

centroidal moment of inertia of the pattern about the Xaxis 
I_{c.y} 
= 

centroidal moment of inertia of the pattern about the Yaxis 
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:
It should be noted that these calculations are directly analogous to the calculation of the centroid of a cross section, moment of inertia of a cross section, and polar moment of inertia of a cross section.
Forces & Moments at Centroid
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:
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 Xdirection 
F_{c.y} 
= 

sum of the forces in the Ydirection 
F_{c.z} 
= 

sum of the forces in the Zdirection 
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:
Bolt # 
Ptrn # 
Ptrn Type 

Axial Force 
Shear Force 
The highlighted bolts should be analyzed with the Bolted Joint Calculator.
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} 

Zforce on bolt due to direct force in Z 

Zforce on bolt due to MX about centroid 

Zforce 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} 

Xforce on bolt due to direct force in X 

Yforce on bolt due to direct force in Y 

XYforce on bolt due to MZ about centroid 
P_{x.MZ} = P_{xy.MZ} · sinθ

Xforce on bolt due to MZ about centroid 
P_{y.MZ} = −P_{xy.MZ} · cosθ

Yforce 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.