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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



lj
:0 mm​



kr
:1.0​


Bolt splice



Threads?
:Included​


Threads included or excluded



n
:1​


Shear planes



μ
:0.3​


Slip factor (for 8.8/TF bolts only)



Bolt Group Geometry

In-plane Loads

Out-of-plane Loads

Single Bolt Capacities

Bolt Group Check



V*f_max
:126.7kN​



N*tf_max
:20.5kN​


Bolt Group Analysis



ϕ
:0.8​


Capacity factor



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

Bolts in combined shear and tension

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

Out-of-plane Loading

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