Results Summary

Calculation

Bolt Group Geometry





# of rows

:3​







Spacing of rows

:30 mm​







# of columns

:2​







Spacing of columns

:50mm​







Total number of bolts

:6​





Bolt group geometry, with bolt tags





x_centroid

:15mm​







y_centroid

:50mm​



Bolt group centroid





I_p

:1.14e+4mm4​





Polar second moment of area

In-plane Loads





F*x

:50 kN​







F*y

:100 kN​







ex

:0.2 m​







ey

:0.1 m​







M*z

:10 kN m​







M*1

:15kN m​



Notes



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



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

Explanation



Beam to column connection

Bolt capacity

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.



Exert from Australian Guidebook for Structural Engineers



Exert from Australian Guidebook for Structural Engineers

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.



Exert from Steel Designers' Handbook

Analysis of bolt groups

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



$(F_x^{\ast },F_y^{\ast },M_z^{\ast })$

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



$F_x^{\ast },F_y^{\ast }$

and a resolved moment



$M_1^{\ast }$

.



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,



$V_f^{\ast }$

is:



$V^*_{f} = \sqrt{[V^*_x]^2+[V^*_y]^2}\\ \text{for:}\\ V^*_x = \dfrac{F^*_x}{\text{n}} - \dfrac{M^*_1y_n}{I_{p}} \\ V^*_y = \dfrac{F^*_y}{\text{n}} + \dfrac{M^*_1x_n}{I_{p}}\\ M^*_1 = F^*_x e_y + F^*_ye_x-M^*_z$

Where:

1. 
   

   $V_x^{\ast },V_y^{\ast }$
   are the x- & y-axis design forces in each bolt
2. 
   

   $x_n,y_n$
   are the horizontal and vertical distances, respectively, from bolt to bolt group centroid

1. 
   

   $M_o^{\ast }$
   is the resolved in-plane moment about the group centroid

1. 
   

   $n$
   is the total number of bolts in the bolt group
2. 
   

   $I_p$
   is the polar second moment of area of the bolt group



The bolt group centroid coordinates



$(\bar{x},\bar{y})$

are given by:



$\bar{x}=\dfrac{\sum x_i}{n}\\\bar{y}=\dfrac{\sum y_i}{n}$

Where:

1. 
   

   $x_i,y_i$
   are the coordinates of the bolts

1. 
   

   $n$
   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



$V_o^{\ast }$

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



$e$

, results in a moment



$M_o^{\ast }$

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,



$N_{tf}^{\ast }$

is:



$N^*_{tf,i} = \dfrac{M^*_o y_i}{\sum{[y_i(y_i+y_c)]}}\space \dfrac{1}{n_{\text{col}}}$

Where:

1. 
   

   $M_o^{\ast }=V_o^{\ast }e$
   is the resolved out-of-plane moment about the bolt group centroid

1. 
   

   $y_i$
   is the vertical distance of a bolt to the NA

1. 
   

   $y_c$
   is the distance from the NA to the compression force, which we conservatively assume is the y-coordinate of the bolt group centroid
2. 
   

   $n_{\text{col}}$
   is the number of columns in the bolt group



Assumptions of bolt group analysis for out-of-plane loading used in this calculator



1. The centroid of the bolt group is evaluated based on the inputted bolt group geometry.
2. All applied loads
   

   $(F_x^{\ast },F_y^{\ast },M_z^{\ast },V_o^{\ast })$
   are calculated as a concentrated resultant load
   

   $(F_x^{\ast },F_y^{\ast },M_1^{\ast },M_o^{\ast })$
   at the centroid of the bolt group.
3. The resultant loads are distributed to each bolt by calculating the shear force
   

   $V_f^{\ast }$
   and tension force
   

   $N_{tf}^{\ast }$
   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
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