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Bolt Group Calculator to AS 4100's banner

Bolt Group Calculator to AS 4100

Verified by the CalcTree engineering team on August 8, 2024

This calculator analyses and checks each bolt in a bolt group for in-plane and of-of-plane loading. The bolt group is analysed using the Instantaneous Centre of Rotation (ICR) concept. The shear force, tension (pull-out) force and combined action in each bolt is then checked to validate the bolt group.
All calculations are performed in accordance with AS4100-2020.

Calculation

Assumptions

This calculator:
  1. Assumes the plate elements being joined by bolts behave rigidly in the plane of the bolt group
  2. Assumes all bolts in the bolt group are the same size
  1. Considers all bolt coordinates relative to an origin which defined by the bottom left corner bolt in the bolt group
  2. Will display the results of up to 10 bolts. For bolt groups with more bolts, use the spreadsheet directly.
  3. Does not account for grade 10.9 bolts, hence
    
    in the bolt shear capacity equation
  4. Does not consider increased bolt tensions due to prying actions
  1. Does not calculate the crushing capacity of the ply material from bolt bearing, or the bearing capacity of the ply material from bolt tear out
  2. Assumes standard holes for 8.8/TF bolts shear capacity check (i.e.
    
    ). That is, slotted and oversized holes are not take into account.
  3. Will check the serviceability limit state if 8.8/TF bolts are selected. Therefore, serviceability loads should be inputted if 8.8/TF bolts are selected. To check 8.8/TF bolts in the ultimate limit state, the user can select 8.8/TB bolts which have the same properties as 8.8/TF bolts in ULS.
  4. Conservatively assumes the neutral axis is at the same position as the bolt group centroid, which is used when calculating the tension in each bolt due to out-of-plane loading.


Bolt Properties



Bolt grade
:8.8​



Tensioning spec
:S​



Bolt type
:8.8/S​



fuf
:830MPa​


Bolt category

Australia uses two categories of bolts and three tensioning specifications.
Bolt category:
  1. 4.6 bolts are made from a low carbon steel. The value
    
    .
  1. 8.8 bolts are made from a high-strength, heat-treated, medium carbon steel. The value
    
    .
Bolt tensioning specifications:
  1. "S" is a snug-tightened bolt
  2. "TB" is a fully tensioned bolt using the bearing types
  3. "TF" is a fully tensioned bolt using the friction type
The applications for the bolt types are provided below.
👉Note if 8.8/TF bolts are selected, this calculator provides results for the serviceability limit state check, see Explanation section below. To check 8.8/TF bolts in the ultimate limit state, the user can select 8.8/TB bolts which have the same properties as 8.8/TF bolts in ULS.


lj
:0 mm​



kr
:1.0​


Bolt splice

For bolted splice connections (also known as lap connections),

is the distance from the first to the last bolt on each side of splice.
Length of bolted connection,

This distance affects the reduction factor

in the bolt shear capacity equation as per Table 9.2.2.1 of AS4100. For values of

, the shear capacity is reduced to account for uneven shear distribution, which occurs in connections where plates behave in a more flexible manner.
Table 9.2.2.1 of AS4100

For non-splice connections,

and

.


Threads?
:Included​


Threads included or excluded

A bolt will either be classed with "threads included" which is standard practice, or "threads excluded" which is non-standard practice. Therefore the

or

will become zero in the bolt shear capacity equation, respectively.
The shear capacity is greater if the bolt has threads excluded.


n
:1​


Shear planes

The number of shear planes:
  1. = 1, when two plates are bolted to each other
  2. = 2, when there are two plates on one side sandwiching the inside plate
Shear planes: n=1 (left) and n=2 (right) [Source]

The number of shear planes has symbol

for bolts with threads included, or

for bolts with threads excluded.


μ
:0.3​


Slip factor (for 8.8/TF bolts only)

The design value of the slip factor (aka the coefficient of friction) depends on the surface preparation for the category 8.8/TF bolts in the serviceability limit state.
👉Note if 8.8/TF bolts are not selected, this parameter is not applicable and won't affect the calculation.
The Steel Designers' Handbook provides a table of

values, see below.
We provide three options for

in this calculator:

.


Bolt Group Geometry



# of rows
:4​



Spacing of rows
:50 mm​



# of columns
:2​



Spacing of columns
:50mm​



Total number of bolts
:8​

Bolt group geometry, with bolt tags



x_centroid
:25mm​



y_centroid
:75mm​


Bolt group centroid

The bolt group centroid coordinates

are given by:

xˉ=∑xinyˉ=∑yin\bar{x}=\dfrac{\sum x_i}{n}\\\bar{y}=\dfrac{\sum y_i}{n}
Where:
  1. 
    
    are the coordinates of the bolts
  1. 
    
    is the total number of bolts in the bolt group


I_p
:3.00e+4mm4​



Polar second moment of area

The polar second moment of area of the bolt group,

is given by:

Ip=Ix+Iyfor:Ix=∑xn2Iy=∑yn2I_{p}=I_x+I_y\\\text{for:}\\I_x=\sum x_n^2\\I_y=\sum y_n^2
Where:
  1. 
    
    are the horizontal and vertical distances, respectively from bolt to bolt group centroid
  1. 
    
    are the second moment of areas about the weld group centroid in the x- and y-axis.
👉Note, since we assume all bolts in the bolt group are the same size, each bolt has a section area of 1. Therefore the second moment of areas about the centre of each bolt is negligible, and the added second moment of areas due to the offset between the bolt group centroid and the center of each bolt are the terms that remains in

.

In-plane Loads



F*x
:100 kN​



F*y
:200 kN​



ex
:0.2 m​



ey
:0.1 m​



M*z
:10 kN m​



M*1
:40kN m​


Notes

  1. input the design actions
    
    using the sign convention in the image below, hence:

M1∗=Fx∗ey+Fy∗ex−Mz∗M^*_1 = F^*_x e_y + F^*_ye_x-M^*_z
  1. 
    
    and
    
    are the force eccentricities from the bolt group centroid. Refer to the coordinates of the bolt group centroid in order to determine your
    
    and
    
    .
Bolt group loaded by in-plane actions: (a) initial in-plane actions, (b) resolved actions about group centroid


Out-of-plane Loads



V*o
:100 kN​



e
:0.3 m​



M*o
:30.0kN m​


Notes

A shear force

applied out-of-plane to the bolt group at an eccentricity

, results in a moment

which then induced axial forces in the bolts.
Bolt group loaded by out-of-plane actions: (a) initial out-of-plane actions, (b) resolved actions about centroid


Single Bolt Capacities



Chosen bolt type
:Threaded 8.8/S Bolt in Single shear​

0​
104​
163​
234​
373​
Single shear​
0​
59.3​
92.6​
133​
214​


Bolt Group Check



V*f_max
:126.7kN​



N*tf_max
:20.5kN​


Bolt Group Analysis

The bolts furthest from the bolt group centroid will be the most loaded.
The in-plane design force per bolt,

is:

Vf∗=[Vx∗]2+[Vy∗]2for:Vx∗=Fx∗n−M1∗ynIpVy∗=Fy∗n+M1∗xnIpM1∗=Fx∗ey+Fy∗ex−Mz∗V^*_{f} = \sqrt{[V^*_x]^2+[V^*_y]^2}\\ \text{for:}\\ V^*_x = \dfrac{F^*_x}{\text{n}} - \dfrac{M^*_1y_n}{I_{p}} \\ V^*_y = \dfrac{F^*_y}{\text{n}} + \dfrac{M^*_1x_n}{I_{p}}\\ M^*_1 = F^*_x e_y + F^*_ye_x-M^*_z
The out-of-plane design tension force per bolt,

is:

Ntf,i∗=Mo∗yi∑[yi(yi+yc)] 1ncolN^*_{tf,i} = \dfrac{M^*_o y_i}{\sum{[y_i(y_i+y_c)]}}\space \dfrac{1}{n_{\text{col}}}
Read our Explanation section below for further details about bolt group analysis.


ϕ
:0.8​


Capacity factor

The capacity reduction factor

is always 0.8, as per Table 3.4 of AS4100, except for 8.8/TF bolts in serviceability limit state,

is 0.7.


Minimum required bolt
:M24​

Evaluation of each bolt in the bolt group is provided below:

0​
0​
105​
0​
​
​
​
SAFE​
SAFE​
2​
0​
50​
62​
0​
​
​
SAFE​
SAFE​
SAFE​
3​
0​
100​
74​
7​
​
​
SAFE​
SAFE​
SAFE​
4​
0​
150​
127​
20​
​
​
​
SAFE​
SAFE​
5​
50​
0​
88​
0​
​
​
SAFE​
SAFE​
SAFE​
6​
50​
50​
22​
0​
​
SAFE​
SAFE​
SAFE​
SAFE​
7​
50​
100​
47​
7​
​
SAFE​
SAFE​
SAFE​
SAFE​
8​
50​
150​
113​
20​
​
​
​
SAFE​
SAFE​
​
​
​
​
​
​
​
​
​
​
​
​
​
​
​
​
​
​
​
​
👉Note,

are the bolt coordinates from an origin point defined by the bottom left bolt and are in

. The design loads

are in

.

Explanation

Connections in building structures use a minimum of two bolts and often more than eight bolts. The bolts used in a connection form a bolt group. A bolt group may be acted on by loads and bending moments in the plane of the bolt group (in-plane) or at right angles to it (out-of-plane).
A typical connection with a bolt group is a beam to column bolted connection.
Beam to column connection


Bolt capacity

Bolts are required to be checked individually for shear and tensile loads, as well as with a combined action check.
The shear and tensile capacities of bolts are both based on the minimum tensile strength

rather than the yield strength.
Explore the toggles below for the bolt capacity equations to AS4100.

Bolts in shear

As per Cl 9.2.2.1 AS4100, the shear capacity of a bolt

is given by:

ϕVf=ϕ 0.62 krfuf(nnAc+nxAo)\phi V_f=\phi \space 0.62 \space k_rf_{uf}(n_nA_c+n_xA_o)
Where:
  1. 
    
    is the capacity reduction factor and is always 0.8, as per Table 3.4 of AS4100
  2. 
    
    is the reduction factor for bolted splice connections
  3. 
    
    is the minimum tensile strength of the bolt
  4. 
    
    is the core area (at the root of the threads)
  1. 
    
    is the shank area of the bolt
  1. 
    
    is the # of shear planes in the threaded regions
  2. 
    
    is the # of shear planes in the unthreaded region
👉A bolt will either be classed with "threads included" which is standard practice, or "threads excluded" which is non-standard practice. Therefore the

or

will become zero in the equation above, respectively.

As per Cl 9.2.3.1 of AS4100, an additional serviceability limit state check must be performed for friction-type connections (i.e. for the /TF bolting category) where connection slip is intended to be prevented at serviceability loads. The shear capacity of a bolt for a friction-type connection,

is:

ϕVsf=ϕ μ nei Nti kh\phi V_{sf}=\phi \space \mu \space n_{ei} \space N_{ti} \space k_h
Where:
  1. 
    
    is the capacity reduction factor and is 0.7 in this "special" serviceability check as per Cl 3.5.5 of AS4100.
  1. 
    
    is the factor for hole type: 1.0 for standard holes, 0.85 for oversize holes and short slots, and 0.70 for long slotted holes. This calculator assumes
    
    .
  2. 
    
    is the slip factor, which is the coefficient of friction between plies and depends on the surface preparation of 8.8/TF bolts, varying from 0.05 to 0.35.
  3. 
    
    is the minimum bolt tension imparted to the bolts during installation, and is typically tabulated per bolt size
  4. 
    
    is the number of shear planes


Bolts in tension

As per Cl 9.2.2.2 AS4100, the tension capacity of a bolt

is given by:

ϕNtf=ϕAsfuf\phi N_{tf}=\phi A_sf_{uf}
Where:
  1. 
    
    is the tensile stress area of the bolt
  1. 
    
    is the minimum tensile strength of the bolt


Bolts in combined shear and tension

As per Cl 9.2.2.3 AS4100, the combined shear and tension bolt check is given by:

(Vf∗ϕVf)2+(Ntf∗ϕNtf)2≤1.0\left(\dfrac{V^*_f}{\phi V_f}\right)^2+\left(\dfrac{N^*_{tf}}{\phi N_{tf}}\right)^2 \leq 1.0
It is common for textbooks to tabulate bolt capacities per bolt size. See the below toggle for such capacities taken from Australian Guidebook for Structural Engineers and the Steel Designers' Handbook.

Design capacity for Class 4.6 and 8.8 bolts

Tensile and shear (threaded and non-threaded) ULS capacities per bolt size for 4.6/S, 8.8/S, 8.8/TB and 8.8/TF, based on a single shear plane.
Tensile and shear (threaded and non-threaded) ULS capacities per bolt size for 4.6/S, 8.8/S, 8.8/TB and 8.8/TF, based on a single shear plane.

Analysis of bolt groups

Bolt groups are subjected to in-plane and out-of-plane loading. Loads on individual bolts are calculated by using a bolt group analysis.
Explore the toggles below for details on how to analysis bolt group based on loading type.

In-plane Loading

As per Cl 9.3 of AS4100, elastic analysis of weld groups for in-plane loading is permitted using the Instantaneous Centre of Rotation (ICR) concept. The ICR is the point at which the bolt group rotates about when subject to overall bolt group actions. The ICR enables us to calculate the distribution of loads to each bolt in a bolt group.
The method is not described further in AS4100, but is summarised below based on guidance in Steel Designers Handbook.
Analysis of the bolt group uses the ICR concept together with superposition. For a bolt group with in-plane design loading, a pure moment acting on a bolt group has the ICR positioned at the bolt group centroid. Whereas, when the same bolt group is subject to shear force only, the ICR is at infinity. Therefore, for bolt group seeing in-plane shear and moments, superposition of the two individual action effects means uniformly distributing shear forces to all bolts in the group while also assuming the bolt group rotation from moment effects occurs about the group centroid.
👉 Based on superposition of in-plane loading, the bolt group ICR is in the same position as the bolt group centroid.
Design actions

applied away from the centroid of the weld group may be treated as being applied at the centroid plus moments, with forces

and a resolved moment

.
Bolt group loaded by in-plane actions: (a) initial in-plane actions, (b) resolved actions about group centroid

The in-plane design force per bolt,

is:

Vf∗=[Vx∗]2+[Vy∗]2for:Vx∗=Fx∗n−M1∗ynIpVy∗=Fy∗n+M1∗xnIpM1∗=Fx∗ey+Fy∗ex−Mz∗V^*_{f} = \sqrt{[V^*_x]^2+[V^*_y]^2}\\ \text{for:}\\ V^*_x = \dfrac{F^*_x}{\text{n}} - \dfrac{M^*_1y_n}{I_{p}} \\ V^*_y = \dfrac{F^*_y}{\text{n}} + \dfrac{M^*_1x_n}{I_{p}}\\ M^*_1 = F^*_x e_y + F^*_ye_x-M^*_z
Where:
  1. 
    
    are the x- & y-axis design forces in each bolt
  2. 
    
    are the horizontal and vertical distances, respectively, from bolt to bolt group centroid
  1. 
    
    is the resolved in-plane moment about the group centroid
  1. 
    
    is the total number of bolts in the bolt group
  2. 
    
    is the polar second moment of area of the bolt group

The bolt group centroid coordinates

are given by:

xˉ=∑xinyˉ=∑yin\bar{x}=\dfrac{\sum x_i}{n}\\\bar{y}=\dfrac{\sum y_i}{n}
Where:
  1. 
    
    are the coordinates of the bolts
  1. 
    
    is the total number of bolts in the bolt group



Out-of-plane Loading

Out-of-plane loading is ultimately axial loading on bolt groups. A shear force

applied out-of-plane to the bolt group at an eccentricity

, results in a moment

which then induced axial forces in the bolts.
Bolt group loaded by out-of-plane actions: (a) initial out-of-plane action, (b) resolved moment about centroid

To determine how much axial load is in each bolt is not described in AS4100. We have summarised a method below based on guidance in Steel Designers Handbook.
From force/moment equilibrium principles, there are bolts which are not loaded since they are positioned in the bearing (compression) part of the connection. The bolts in the tension region have tension loads that can be evaluated by assuming a linear distribution of force from the neutral axis to the farthest bolts, as shown in the image above. However it is difficult to accurately determine where the neutral axis (NA) exists due to the bolt, plate and support flexibility. A conservative approach, adopted by this calculator, is to assume the NA is at the bolt group centroid line.
From equilibrium principles and the principle of proportioning from similar triangles
The out-of-plane design tension force per bolt,

is:

Ntf,i∗=Mo∗yi∑[yi(yi+yc)] 1ncolN^*_{tf,i} = \dfrac{M^*_o y_i}{\sum{[y_i(y_i+y_c)]}}\space \dfrac{1}{n_{\text{col}}}
Where:
  1. 
    
    is the resolved out-of-plane moment about the bolt group centroid
  1. 
    
    is the vertical distance of a bolt to the NA
  1. 
    
    is the distance from the NA to the compression force, which we conservatively assume is the y-coordinate of the bolt group centroid
  2. 
    
    is the number of columns in the bolt group
Assumptions of bolt group analysis for out-of-plane loading used in this calculator


In summary, the analysis of bolt groups follows these steps:
  1. The centroid of the bolt group is evaluated based on the inputted bolt group geometry.
  2. All applied loads
    
    are calculated as a concentrated resultant load
    
    at the centroid of the bolt group.
  3. The resultant loads are distributed to each bolt by calculating the shear force
    
    and tension force
    
    in each bolt, which is proportional to the distance from the bolt to the group centroid.
  4. The 'critical' bolt is considered to be the bolt furthest from the centroid, which is used for the design check on the overall bolt group.

References

  1. Australian Guidebook for Structural Engineers
  2. Steel Designers' Handbook
  3. Australian Standard AS 4100:2020

Related Resources

  1. Fillet Weld Group Calculator to AS 4100
  2. Steel Base Plate Designer to EC3
  1. Steel Baseplate Designer to AISC 360

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