# Bolt Group Capacity Software

The SkyCiv Bolt Group Capacity Calculator is designed to aid structural engineers in the calculation of individual bolt forces and capacities for combined shear and tension loads.

This tool carries out a comprehensive check of loads in any axis/direction in order to resolve bending moments, shear forces and axial forces into equivalent in-plane and out-of-plane forces on the bolt group. The tool can check the bolt group for the following modes of failure:

- Bolt Shear Capacity
- Bolt Tension Capacity
- Combined Tension and Shear Capacity
- Bearing and Tearout Capacity
- Bolt Setout Requirements

The tool also allows for both elastic and plastic analysis and can assess the utilisation of the bolt group in accordance with the AS4100:2020.

The calculation results have been independently verified against the *Australian Guidebook for Structural Engineers* and *Joints in Steel Construction: Moment-Resisting Joints to Eurocode 3.*

## About the Bolt Group Capacity Calculator

## How Do Individual Bolts Resist Forces?

Bolts are individually capable of resisting tension and shear forces. Although theoretically bolts could also take moments and compression forces, bolts have a small section modulus that means moment resistance is relatively small and connection details often have compression forces resolved through plate-to-plate contact.

Most design standards in the world only describe the capacity of a bolt in tension and shear since bolts are only expected to take these types of loads.

## Bolt Shear Strength

Bolt shear strength is the capacity of a bolt to resist forces that attempt to cause the bolt to slide along a plane perpendicular to its axis. Most bolted connections rely on a bolts shear capacity in order to provide stability in the connection. For example, bolted splice connections are almost exclusively subject to shear forces.

## How Are Shear Forces Distributed Between Bolts?

In-plane forces are resolved in the bolt group through shear. The bolt group is modelled to evenly distribute direct in-plane forces and take torsion forces proportional to the distance from the bolts instantaneous point of rotation (ICR) which can generally be taken as the centroid. Therefore, the bolts with the highest shear forces are always bolts furthest from the ICR.

The design bolt shear force can be calculated by finding the bolt shear force in each of the in-plane directions and then combining them into a resultant shear force. The bolt shear capacity for a single bolt can then be compared to the critical bolt shear that develops for a single bolt within the group.

## Calculating Bolt Shear Strength

Bolt shear strength can generally be calculated with the following general equation:

V_{f} = 0.6 * f_{uf} * A

where:

- f
_{uf}is the minimum tensile strength of the bolt - A is the cross sectional area being intersected for a bolt

## Calculating Bolt Shear Strength to AS 4100:2020

The AS 4100 more specifically calculates bolt shear strength with the following equation:

ϕV_{f} = ϕ * 0.62 * f_{uf} * k_{r} * k_{rd} * (n_{n} * A_{c} + n_{x} * A_{o})

where:

- ϕ = 0.8
- f
_{uf}is the minimum tensile strength of the bolt - k
_{r}is a reduction factor for bolted lap connections - k
_{rd}is a reduction factor to account for reduced ductility of grade 10.9 bolts - n
_{n}is the number of shear planes with threads intercepting the shear plane - A
_{c}is the cross sectional area of bolts through its threads (known as core, minor or root area of bolt) - n
_{x}is the number of shear planes without threads intercepting the shear plan - A
_{o}is the nominal plain shank area of the bolt

## Example Bolt Shear Strength Calculation to AS 4100:2020

For a grade 4.6 M12 bolt with a minimum tensile strength of 400 MPa with 1 shear plane intersecting the shank of the bolt we can calculate the shear capacity as:

ϕVf = 0.8 * 0.62 * 400 MPa * 1 * 1* ( 0 * Ac + 1 * 113 mm^{2}) = 22.4 kN

## Calculating Bolt Shear Strength to EN 1993-1-8:2005

The EN 1993-1-8:2005 (EC3) calculates the bolt shear capacity as:

F_{v,Rd} = α_{v} * f_{ub} * A * β_{lf} / γ_{M2}

where:

- α
_{v}= 0.6 for grade 4.6, 5.6 and 8.8 bolts and 0.5 otherwise - f
_{ub}is the bolt ultimate tensile strength - A is the cross sectional area of the bolt
- A = A
_{s}(tensile area of bolt) if the shear plane passes through the bolt threads - A = Ag (gross cross sectional area of bolt) if the shear plane does not pass through the bolt threads

- A = A
- β
_{lf}reduction factor for bolted lap connections - γ
_{M2}= 1.25

## Example Bolt Shear Strength Calculation to EN 1993-1-8:2005

For a grade 4.6 M12 bolt with a minimum tensile strength of 400 MPa with 1 shear plane intersecting the shank of the bolt we can calculate the shear capacity as:

ϕVf = 0.6 * 400 MPa * 113 mm2 * 1 / 1.25 = 21.7 kN

## Calculating Available Bolt Shear Strength to AISC 360-16

The AISC 360-16 calculates the available bolt shear capacity for allowable strength design (ASD) as:

_{Rn / Ω = Fnv * Ab / Ω }

_{and calculates the available bolt shear capacity for load and resistance factor design (LRFD) as:}

ϕ * R_{n} = ϕ * F_{nv} * A_{b}

where:

- ϕ = 0.75 for LRFD design
- Ω = 2 for ASD design method
- F
_{nv}is the nominal shear strength from Table J3.2, typically:- If shear plane includes threads (N) then F
_{nv}= 0.450 * F_{u} - If shear plane excludes threads (X) then F
_{nv}= 0.563 * F_{u} _{where Fu}is the bolt ultimate tensile strength

- If shear plane includes threads (N) then F
- A
_{b}is the gross cross sectional area of the bolt

## Example Bolt Shear Strength Calculation to AISC 360-16

For a Group A (Fu = 120 ksi) 1" diameter bolt with 1 shear plane intersecting the shank of the bolt (X) we can calculate the shear capacity as:

ϕ * Rn = 0.75 * 0.563 * 120 * 1^2 * π / 4 = 39.8 kip

Rn / Ω = 0.563 * 120 * 1^2 * π / 4 / 2 = 26.5 kip

## Bolt Shear Strength Chart

Users can create there own bolt shear strength charts using the SkyCiv QD Bolt Group Capacity Calculator for different standards globally.

A user can specify inputs in the QD to match project requirements and generate a set of common capacities that can be used as a reference for projects. For example by using three runs of the AS 4100:2020 Bolt Group Capacity a simple table can start to be constructed.

Size | Grade | Shear Plane | ϕVf |
---|---|---|---|

M16 | 8.8 | Thread Included (N) | 59.3 |

M20 | 8.8 | Thread Included (N) | 92.7 |

M24 | 8.8 | Thread Included (N) | 133.5 |

## Bolt Tension Strength

Bolt tension strength refers to a bolts ability to resist pulling or *tensile *forces along its axis. This strength is particularly critical when a bolt group is required to resist moments since moments are generally resolved by a bolt taking tension forces at some lever arm distance away from the point of rotation.

## Calculating Bolt Tension Strength

Bolt shear strength can generally be calculated with the following general equation:

N_{tf} = A_{s} * f_{uf}

where:

- A is the tensile stress area of the bolt
- f
_{uf}is the minimum tensile strength of the bolt

## How Are Tensile Loads Distributed Between Bolts?

Forces due to axial loads are considered to be uniformly distributed across all bolts.

Forces due to applied moments are distributed based on either plastic or elastic analysis.

Tension or compression forces may develop in bolts, however since compression forces in reality are expected to be resolved by plate-to-plate contact only the critical tension force is adopted for design checks.

The maximum bolt tension can be found be combining the bolt tension forces that develop through axial loading and moments. The bolt tension capacity for a single bolt can then be compared to the critical bolt tension that develops for a single bolt within the group.

A bolt group can better resist forces than individual bolts since moments can be resolved by having bolts take tension (or compression) forces at some lever arm distance. This utilises the bolts capacity in tension to resolve moments in order to compensate for its small section modulus.

For example a single M12 bolt with a yield strength of 240 MPa and a tensile strength of 400 MPa would have a 0.04 kN.m moment capacity. However, the bolt has a tension capacity of 27 kN (for AS 4100:2020) and if we couple two M12 bolts together at a spacing of 100 mm we can resolve a 2.7 kN.m moment. This gives a moment capacity 30x larger than if we just used the moment capacity of the individual sections.

## Calculating Bolt Tension Strength to AS 4100:2020

The AS 4100 calculates bolt tensile strength as:

ϕN_{tf} = ϕ * A_{s} * f_{uf}

where:

- ϕ = 0.8
- A
_{s}is the tensile stress area of the bolt (from AS 1275) - f
_{uf}is the minimum tensile strength of the bolt

## Example Bolt Tension Strength Calculation to AS 4100:2020

For a grade 4.6 M12 bolt with a minimum tensile strength of 400 MPa we can calculate the tensile capacity as:

ϕN_{tf} = 0.8 * 84.3 mm^{2} * 400 MPa = 27 kN

## Calculating Bolt Tension Strength to EN 1993-1-8:2005

The Eurocode 3 calculates the bolt tensile strength as:

F_{t,Rd} = k_{2} * f_{ub} * A_{s} * / γ_{M2}

where:

- k2 is 0.63 for countersunk bolts and 0.9 otherwise
- A
_{s}is the tensile stress area of the bolt (from AS 1275) - f
_{ub}is the minimum tensile strength of the bolt - γ
_{M2}= 1.25

## Example Bolt Tension Strength Calculation to EN 1993-1-8:2005

For a grade 4.6 M12 bolt with a minimum tensile strength of 400 MPa we can calculate the tensile capacity as:

F_{t,Rd} = 0.9 * 84.3 mm^{2} * 400 MPa / 1.25 = 24.3 kN

## Calculating Available Bolt Tension Strength to AISC 360-16

The AISC 360-16 calculates the available bolt tension capacity for allowable strength design (ASD) as:

_{Rn / Ω = Fnt * Ab / Ω }

_{and calculates the available bolt tension capacity for load and resistance factor design (LRFD) as:}

ϕ * R_{n} = ϕ * F_{nt} * A_{b}

where:

- ϕ = 0.75 for LRFD design
- Ω = 2 for ASD design method
- F
_{nt}is the nominal tensile strength from Table J3.2, typically:- F
_{nt}= 0.75 * F_{u} _{where Fu}is the bolt ultimate tensile strength

- F
- A
_{b}is the gross cross sectional area of the bolt

## Example Available Bolt Tension Strength Calculation to AISC 360-16

For a Group A (Fu = 120 ksi) 1" diameter bolt with 1 shear plane intersecting the shank of the bolt (X) we can calculate the tension capacity as:

ϕ * Rn = 0.75 * 0.75* 120 * 1^2 * π / 4 = 53 kip

Rn / Ω = 0.75* 120 * 1^2 * π / 4 / 2 = 35.3 kip

## Bolt Tension Strength Chart

Similar to the bolt shear strength chart, a user can also use the SkyCiv QD Bolt Group Capacity Calculator to generate tension strength charts for a project. For example the following chart is constructed using three runs of the AS4100:2020 Bolt Group Capacity Calculator

Size | Grade | Shear Plane | ϕNtf |
---|---|---|---|

M16 | 8.8 | Thread Included (N) | 104 |

M20 | 8.8 | Thread Included (N) | 162.5 |

M24 | 8.8 | Thread Included (N) | 234 |

## Can Bolts Take Compression?

Models of bolt groups often allocate compression forces to bolts on the compression side of the connection.

Compression forces however, are generally expected to be resolved through plate-to-plate contact and connection details often mean that bolts will only be engaged in tension.

Therefore the bolt compression forces in modelling is an idealisation to simplify calculations, but if a bolt is actually required to take compression forces this is something that should be considered by the engineer.

Bolt compression forces can be found with the SkyCiv Bolt Group Capacity Calculator by reversing load directions and taking the tension force in the reversed model. An upper bound for the compression capacity can be found by using the tension capacity, however the compression capacity would need to account for the possibility of buckling.

## What is Block Shear?

The block shear failure mechanism can develop on a plate due to bolt holes reducing the section capacity of the plate.

In general we have a reduced effective area for tension and shear capacity on the plate due to the bolt holes cut in the plate.

Typically standards required that the tension capacity of a plate is assessed by calculating the plate yield strength by multiplying the gross area of the plate by the yield strength of the steel. When there are bolt holes the tension rupture strength of the plates should also be assessed by multiplying the net area of the plate by the ultimate tensile strength of the steel plate. That is:

- Tensile yielding capacity = F
_{y}* A_{g} - Tensile rupture capacity = F
_{u}* A_{n}

Similarly the plate shear capacity is calculated by taking the minimum of the gross area of the steel plate multiplied by 60% of the yield strength and the net area of the steel plate multiplied by 60% of the ultimate tension strength of the steel plate. That is:

- Shear yielding capacity = 0.6 * F
_{y}* A_{g} - Shear rupture capacity = 0.6 * F
_{u}* A_{n}

We also might have a combined failure of tension and shear on the plate which is referred to as block shear. All the bolt holes collectively rip out a section of the plate. Possible block shear failure mechanisms are shown in the image below.

## How to Calculate Block Shear Capacity

There are slight variations on how the capacity is calculated in standards around the world but they all are calculated through the same general approach of combining the capacity of the area failing in shear with the capacity of the area failing in tension.

Where tension stress on the section is non-uniform the tension capacity component of block shear is typically reduced by 50%.

The Eurocode calculates block tearing as:

- V
_{eff,Rd}= 0.577 * F_{y}* A_{nv}/ γ_{M2 }+ U_{bs}* F_{u}* A_{nt }/ γ_{M2}

AISC 360-16 calculates block shear as:

- LRFD: ϕ R
_{n}= ϕ (0.6 * F_{u}* A_{nv}+ U_{bs}* F_{u}* A_{nt}) ≤ ϕ (0.6 F_{y}* A_{gv}+ U_{bs}* F_{u}* A_{nt}) - ASD: Rn / Ω = (0.6 * Fu * Anv + Ubs * Fu * Ant) / Ω ≤ (0.6 Fy * Agv + Ubs * Fu * Ant) / Ω

The Australian Standard calculates block shear as:

- ϕ R
_{bs}= ϕ (0.6 * F_{uc}* A_{nv}+ k_{bs}* F_{uc}* A_{nt}) ≤ ϕ (0.6 F_{yc}* A_{gv}+ U_{bs}* F_{u}* A_{nt})

where:

- A
_{gv}= gross area subject to shear at rupture - A
_{nv}= net area subject to shear at rupture - A
_{nt}= net area subject to tension at rupture - F
_{u}& F_{uc}= minimum tensile strength of the steel plate - F
_{y}& F_{yc}= yield strength of the steel plate - k
_{bs}& U_{bs}= a reduction factor for non-uniform tension- 0.5 when tension stress is non-uniform
- 1.0 when tension stress is uniform

- γ
_{M0}= 1.0 - γ
_{M2}= 1.25 - ϕ = 0.75 for both AISC and AS
- Ω = 2.00

The Eurocode presents a simpler more conservative method for the calculation by using the net shear in combination with the yield stress.

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