The Bolted Joint Analysis calculator allows for stress analysis of a bolted joint, accounting for preload, applied axial load, and applied shear load. See the instructions within the documentation for more details on performing this analysis. See the reference section for details on the methodology and the equations used.

Inputs

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

Bolt Inputs:

Joint Type:

Inch Metric

Size Chart

Clamped Parts:

(add washers and plates to the joint)

Type:

Washer

Plate

Cylinder

Help

Material:

Create Material

Thickness:

OD:

Display Units

Display results in:

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Results

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

Results Summary Joint Properties Installation Forces & Stresses Clamped Parts

Results Summary

Summary tables of results are shown below. These tables give the factors of safety for the joint and for the clamped parts. Any factors of safety of at least 1 are shown in green, and below 1 are shown in red. It is up to the discretion of the engineer to determine the appropriate factor of safety to use in design.

Joint Summary

The table below summarizes the factors of safety for the joint corresponding to the nominal, maximum, and minimum bolt load (the bolt load varies based on preload uncertainty and relaxation).

	FS_{thread shear bolt}	FS_{thd shear internal}
Nominal:
Max Bolt Load:	---	---
Min Bolt Load:	---	---

Clamped Parts Summary

The table below summarizes the factors of safety for each clamped part in the grip.

	FS_{pull thru}	FS_{pin bearing}	FS_{bearing, top surface}	FS_{bearing, bot surface}

See full result details on the other tabs.

Joint Properties

This section details the properties of the bolted joint components.

Inputs

Joint Type	Tensile Force	Shear Force	Bolt Material	Thread Size	Preload %	Torque Coefficient	Preload Uncertainty	Preload Relaxation

Materials List

(Material Properties)

	Elastic Modulus	Tensile Yield Strength	Shear Yield Strength	Bearing Yield Strength

Bolt Properties

(Thread Dimensions)

Material:
Thread Size:

d_nom	=	nominal diameter
TPI	=	threads per inch
P	=	pitch

d_m	=	minor diameter
d_p	=	pitch diameter

A_t	=	tensile stress area
A_s	=	minor (shear) area

L	=	length
L_t	=	thread length

d_head	=	head diameter

Clamped Parts List

	Grip Thk	Hole Dia	Width	Material

Bolt Length Calculation

Grip:		Grip length
Threaded Member:		Additional length to protrude through threaded member.
2 threads:		2 threads at the end to ensure full engagement
Total:		Length of the bolt before rounding up to the preferred size

The bolt length was rounded up to the preferred size of .

Joint Stiffness

(Joint Stiffness)

Bolt Stiffness

(Bolt Stiffness)

The individual stiffnesses of the shank and the threads in the grip are calculated as:

Stiffness of shank:
Stiffness of threads in grip:

Reference Values

A_nom	=
A_t	=
E	=
L_shank	=
L_thd.g	=

The bolt stiffness is calculated considering that the shank and threads in the grip act as springs in series:

Grip Stiffness

(Grip Stiffness)

The stiffness of each part in the grip is calculated based on a simplified pressure-cone method, as described here. The table below shows the stiffness for each part:

	Grip Thk	Hole Dia	Elastic Modulus	Stiffness

The grip stiffness is calculated considering that the parts in the grip act as springs in series:

Joint Constant

(Joint Constant)

The joint constant is the stiffness of the bolt relative to the total joint stiffness:

Joint Installation

This section details the parameters relevant to installation of the joint. A summary of the installation parameters is given in the table below:

Preload (% Yield)	Preload Force	Torque Coefficient, K_T	Install Torque

The nominal preload force is calculated as:

F_PL = %_yld · S_ty A_t =

Reference Values

%_yld	=
S_ty	=
A_t	=

The installation torque is calculated as:

T = K_T d_nom F_PL =

Reference Values

K_T	=
d_nom	=
F_PL	=

Bolt Forces & Stresses

This section details the force and stress analysis on the bolt itself.

Preload Force

The nominal preload force is calculated as:

F_PL.nom = %_yld · S_ty A_t =

Reference Values

%_yld	=
S_ty	=
A_t	=

Due to preload uncertainty, the actual preload applied to the bolt may be more or less than the nominal value. Due to preload relaxation, there will be some loss in the preload after the joint is installed.

The maximum value of preload accounts for the preload uncertainty, and is calculated as:

F_PL.max = (1 + %_uncrt ) · F_PL.nom =

The minimum value of preload accounts for the preload uncertainty as well as relaxation, and is calculated as:

F_PL.min = (1 − %_uncrt − %_relax ) · F_PL.nom =

Reference Values

F_PL.nom	=
%_uncrt	=
%_relax	=

The table below summarizes the preload values. The nominal value is the design target, and the min and max values account for preload uncertainty and relaxation.

	Nominal	Minimum	Maximum
Preload Force:

Bolt Load Diagram

The Bolt Load Diagram below shows the tensile load on the bolt as a function of applied tensile load on the joint. The dark blue line gives the nominal bolt load, and the light blue lines account for preload uncertainty and relaxation. The knee in the curve shows the point at which the joint separates.

Before joint separation, only a portion of the applied load is carried by the bolt, and the other portion acts to relieve compression in the clamped parts. The bolt load line in this region has a constant slope equal to the joint constant. After separation, all applied load is taken by the bolt and so the bolt load line has a slope of 1.

Joint Constant

The value of the joint constant is determined by calculating the stiffness of the bolt, k_bolt, and the stiffness of the clamped parts in the grip, k_grip. The once the stiffnesses are known, the joint constant is calculated as:

The joint constant for this joint was calculated in the Joint Properties tab as:

Joint Constant, C

Joint Separation

The separation force is the force that will result in separation of the joint. A summary of the separation force values and their corresponding factors of safety is given in the table below. The nominal and minimum values in the table correspond to the nominal preload and the minimum preload, respectively.

	Separation Force	FS_sep
Nominal:
Minimum:
Maximum:

The minimum separation force dictates the adequacy of the joint and is calculated below:

Reference Values

F_PL.min	=
C	=

The factor of safety on joint separation is calculated as the ratio of the separation force to the applied tensile load:

Reference Values

F_sep.min	=
F_t.app	=

Tensile Force on Bolt

The total (combined) tensile force on the bolt is the sum of the tension due to preload and the tension due to the applied load. The values of these tension components are dependent on whether the joint has separated. Refer to the Bolt Load Diagram above for a visual indication of joint separation. The combined tensile force on the bolt is calculated as:

The combined tensile forces on the bolt corresponding to the nominal, minimum, and maximum values of preload are given in the table below:

Separated?

Combined Tensile Force

Nominal:

Minimum:

Maximum:

Reference Values

F_PL.nom	=
F_PL.min	=
F_PL.max	=
C	=
F_t.app	=

The table below summarizes the tensile force components on the bolt. The nominal, minimum, and maximum values in the table correspond to the nominal, minimum, and maximum values of preload, respectively. Note that if the joint has not separated, the bolt will only take a portion of the applied tensile load.

	Separated?	Preload, F_b.PL	Applied Load, F_b.t.app	Total (Combined), F_b.t
Nominal:
Minimum:
Maximum:

Shear Force on Bolt

The shear force on the bolt is equal to the shear load applied to the joint:

F_b.s = F_s.app =

Reference Values

F_s.app

Bolt Stresses

The stresses in the bolt are calculated per the equations in the table below:

Preload Stress	Tensile Stress	Shear Stress	Von Mises Stress

where F_b.PL is the tensile force on the bolt due to preload, F_b.t.app is the tensile force on the bolt due to applied tensile load, F_b.s is the shear force on the bolt, A_t is the tensile stress area, and A_s is the minor (shear) area. The value n in the equation for von Mises stress is the load factor. The load factor is related to the factor of safety, with the difference being that it is a factor that is applied to the loads or stresses to ensure that the bolt stress remains below the allowable stress.

The stresses at the maximum bolt preload determine the adequacy of the joint. The preload stress at the maximum preload value is:

Reference Values

F_b.PL.max	=
A_t	=

The tensile stress due to applied tensile load at the maximum preload value is:

Reference Values

F_b.t.app.max	=
A_t	=

The shear stress due to applied shear load is:

Reference Values

F_b.s	=
A_s	=

The von Mises stress at the maximum preload value, considering a load factor of 1, is:

Reference Values

σ_PL.max	=
σ_t.max	=
τ_sh	=
n	=	1

The factor of safety when considering bolt stress is the value of the load factor, n, at which the von Mises stress equals the allowable stress (the bolt yield stress in this case). At the maximum preload value, the factor of safety is:

FS =

Reference Values

S_ty

The bolt stresses are summarized in the table below summarizes the tensile force components on the bolt. The nominal, minimum, and maximum values in the table correspond to the nominal, minimum, and maximum values of preload, respectively.

	Preload Stress	Tensile Stress (App)	Shear Stress	Von Mises Stress	FS_yld
Nominal:
Minimum:
Maximum:

Thread Shear Results

Thread shear is considered for both the bolt (external) threads and the internal threads.

External Thread Shear

The thread shear area for the external thread is calculated by:

Reference Values

d_p.ext	=
L_E	=

The shear stress in the external threads in the nominal case (where preload equals the nominal value) is:

Reference Values

F_b.t	=
A_ts.ext	=

The factor of safety on external thread shear with respect to the shear yield strength, S_sy, of the thread material is:

Reference Values

S_sy	=
τ_ts.ext	=

Internal Thread Shear

The thread shear area for the internal thread is calculated by:

Reference Values

d_p.int	=
L_E	=

The shear stress in the internal threads in the nominal case (where preload equals the nominal value) is:

Reference Values

F_b.t	=
A_ts.int	=

The factor of safety on internal thread shear with respect to the shear yield strength, S_sy, of the thread material is:

Reference Values

S_sy	=
τ_ts.int	=

Thread Shear Summary

The table below summarizes the thread shear results:

	Thread Shear Force	Thread Shear Area	Thread Shear Stress	Thread Shear Allowable	FS_{thd shear}
External (Bolt) Thread
Internal Thread

Clamped Parts Results

Failure of the clamped parts must be investigated when analyzing a bolted joint. There are several principal failure mechanisms for the clamped parts which are described below.

Pull Through

The tensile force applied to the joint will act to pull the parts through one another. The relevant equations for analyzing pull through are:

Area	Stress	Factor of Safety
A_pt = πd_ot_p

In the table above, d_o is the outer diameter of the part pulling through, t_p is the thickness of the part being considered, F_t.app is the applied tensile force, and S_sy is the shear yield strength of the material for the part being considered.

The table below summarizes the pull through results. The part listed in the "Pull Thru Part" column is acting to pull through the part listed in the first column. Stresses and factors of safety are calculated per the equations above. The allowable stress is the shear yield strength of the part in the first column.

	Pull Thru Part	Force	Area	Stress	Allowable	FS

Pin Bearing

If the joint is loaded in shear, then the bolt may be pressed against the inner walls of the through-holes in the clamped parts. This is referred to as pin bearing, and the relevant equations are:

Area	Stress	Factor of Safety
A_pb = d_nomt_p

In the table above, d_nom is the bolt nominal diameter, t_p is the part thickness, F_s.app is the applied shear force, and S_by is the bearing yield strength of the material.

The table below summarizes the pin bearing results. Stresses and factors of safety are calculated per the equations above. The allowable stress is the bearing yield strength of the part.

	Force	Area	Stress	Allowable	FS

Bearing

The preload force will act to cause each part to bear on the adjacent parts. The relevant equations for analyzing bearing are:

Area	Stress	Factor of Safety

In the table above, d_o.min is the minimum outer diameter of the two parts bearing against one another, d_h is the through-hole diameter of the part being considered, and S_by is the bearing yield strength of the part being considered.

F_bear is the bearing force, and the value for the bearing force on a surface depends on the location of that surface with respect to the location of the applied tensile force in the joint. If the bearing surface is inside of the applied force locations, then the maximum bearing force that surface experiences is simply the preload force. If the bearing surface is outside of the applied force locations, then the bearing force is increased by the applied force:

where F_PL is the preload force and F_b.t.app is the portion of the applied tensile force taken by the bolt.

Bearing, Top Surface

The table below summarizes the bearing results, considering the top surface of each part. The part listed in the "Bearing Part" column is bearing on the part listed in the first column. Stresses and factors of safety are calculated per the equations above. The allowable stress is the bearing yield strength of the part in the first column.

	Bearing Part	Force	Area	Stress	Allowable	FS

Bearing, Bottom Surface

The table below summarizes the bearing results, considering the bottom surface of each part.

	Bearing Part	Force	Area	Stress	Allowable	FS

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.

Limitations of Analysis:

Due to the large variety of inputs required to perform a bolted joint analysis, several simplifying assumptions have been made in this analysis. These assumptions include:

Hardware dimensions are approximated based on standard sizes
For thread shear calculations, length of thread engagement is approximated (does not account for chamfers on end of bolt or around threaded hole in nut or in tapped part)
Shear yield strength and bearing yield strength of materials are approximated. Shear yield strength is estimated as 0.577·S_ty, and bearing yield strength is estimated as 1.5·S_ty (see Barrett, "Fastener Design Manual," NASA).

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