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Bolt Group Calculator to AS 4100's banner
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Bolt Group Calculator to AS 4100

This calculator allows the user to analyse and check each bolt within a bolt group to ensure compliance with the Australian Standard AS 4100. The user defines the bolt group geometry by inputting the number of rows and columns of bolts. Using user input loads, the calculator then checks the shear force and tension (pull-out) force in each bolt.
A typical connection with a bolt group is a beam to column bolted connection.
❗This calculation has been written in accordance with AS 4100.
Beam to column connection


Calculation

Inputs

Bolt Properties



Bolt grade
:8.8​



Bolt category / tightening method
:S​



Threads in shear plane?
:1​



Length of lap splice
:0mm​



Slip factor
:100​



Bolt Group Geometry



Number of rows in bolt group
:4​



Spacing between rows
:50mm​



Number of columns in bolt group
:2​



Spacing between columns
:50mm​



Width of baseplate
:100mm​



Depth of baseplate
:200mm​



Loads

In-Plane Load:


F*x
:100kN​



F*y
:200kN​



ey, F*x eccentricity,
:0.1m​



ex, F*y eccentricity
:0.2m​



M*z (kNm)
:30​

Note, ex & ey are the force eccentricities from the weld group centroid. Refer to Output --> Weld Group Geometry for the coordinates of the weld group centroid in order to determine your ex and ey.

Out-of-Plane Load:


V*o
:100kN​



e, V*o eccentricity
:0.3m​

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

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


Output

Bolt Properties



Bolt type
:8.8/S​



Capacity reduction factor, ϕ
:0.8​



Reduction factor for lap connections, kr
:1.0​



Minimum tensile strength of a single bolt, fuf
:830MPa​



Bolt Group Geometry



Total number of bolts
:8​


Location of the Instantaneous Centre of Rotation (ICR):


x coordinate of bolt group centroid, mm
:25.0mm​

x coordinate of bolt group centroid (mm)


y coordinate of bolt group centroid, mm
:75mm​

y coordinate of bolt group centroid, mm

Second moment of areas:


I_x
:25000mm4​



I_y
:5000mm4​



I_p
:30000mm4​




Loads

In-Plane Resultant Forces:


Resultant applied in-plane moment, M*1
:60.0kN m​

Out-of-Plane Resultant Forces:


Resultant applied out-of-plane moment, M*o
:30.0kN m​




Design Checks



Critical shear force applied on the bolt group, V*f
:180kN​



Critical tearout force applied on the bolt group, N*tf
:45kN​



Minimum required bolt
:M30​


Evaluation of each bolt in the bolt group:
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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 loading).
See below for tabulated bolt data and information about the analysis of bolt groups.

Analysis of bolt groups

To calculate the distribution of loads to each bolt in a bolt group, the Instantaneous Centre of Rotation (ICR) Method is used. The ICR is the point at which the bolt group rotates about when subject to overall bolt group actions. The method follows the following steps:
  1. The ICR (or centroid) of the bolt group is evaluated based on the inputted bolt group geometry.
  2. All applied loads (F*x, F*y, M*z & V*o) are calculated as concentrated resultant loads (F*x, F*y, M*1 & M*o) at the ICR of the bolt group.
  3. The resultant loads are distributed to each bolt by calculating the shear force, V*f and tension force, N*f in each bolt, which is proportional to the distance from the bolt to the ICR.
AS 4100 permits elastic analysis to determine the design actions in a bolt group. For flexibility on the bolt group arrangement and bolt spacing, this calculation adapts conventional ICR analysis to the AISC method which uses inelastic analysis.


The in-plane design force per bolt, Vf∗ (kN) is:Vf∗=[Vx∗]2+[Vy∗]2where forces in the welds, per unit length, are:Vx∗=Fx∗no. of bolts−M1∗yiIpVy∗=Fy∗no. of bolts+M1∗xiIpwhere xi and yi are the distances of each bolt from the centroid of the bolt group, Ip the polar second moment of area of the bolt group, andM1∗ the resolved in-plane moment about the bolt group centroid, is:M1∗=Mz∗−Fx∗ey+Fy∗ex\text{The in-plane design force per bolt, } V^*_f \text { (kN) is:} \\V^*_{f} = \sqrt{[V^*_x]^2+[V^*_y]^2}\\ \text{where forces in the welds, per unit length, are:}\\ V^*_x = \frac{F^*_x}{\text{no. of bolts}} - \frac{M^*_1y_i}{I_{p}} \\ V^*_y = \frac{F^*_y}{\text{no. of bolts}} + \frac{M^*_1x_i}{I_{p}} \\ \text{where } x_i \text{ and } y_i \text{ are the distances of each bolt from the centroid of the bolt group, } \\ I_{p} \text{ the polar second moment of area of the bolt group, and} \\ M^*_1\text{ the resolved in-plane moment about the bolt group centroid, is:}\\ M^*_1 = M^*_z -F^*_x e_y + F^*_ye_x
Bolt group loaded by in-plane actions: (a) initial in-plane actions, (b) resolved actions about centroid


The out-of-plane design force per bolt, Ntf∗ (kN) is:Ntf∗=Mo∗yi∑[yi(yi+yc)]where Mo∗=Vo∗e is the resolved out-of-plane moment about the bolt group centroid, and yc is the y-coordinate of the bolt group centroid.\text{The out-of-plane design force per bolt, } N^*_{tf} \text { (kN) is:} \\N^*_{tf} = \frac{M^*_o y_i}{\sum{[y_i(y_i+y_c)]}} \\ \text{where } M^*_o = V^*_oe \text{ is the resolved out-of-plane moment about the bolt group centroid, and}\\ \ y_c \text{ is the y-coordinate of the bolt group centroid.}

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



Geometry for Class 4.6 and 8.8 bolts

Snippet from source spreadsheet


Design capacity for Class 4.6 and 8.8 bolts

Snippet from source spreadsheet