Bolt Diameter in Shear Calculator: Single or Double Shear for a Sloping Member
The bolt diameter needed to carry a load in shear.
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How this calculator works
Enter the load in the member and its slope, as a rise and a run such as 2V:1H or as an angle.
Enter the number of bolts, whether each is in single or double shear, and the allowable shear stress.
The calculator splits the load into vertical and horizontal parts, finds the bolt diameter, and gives the next standard size with its shear stress. Or give the diameter to find the load the bolts can carry.
Formulas used
- F_v = P\sin\theta,\ F_h = P\cos\theta
- P = \tau\,\frac{\pi}{4}d^2\,n_b\,n_p
- d = \sqrt{\frac{4P}{\pi\,\tau\,n_b\,n_p}}
Worked example
With the default numbers in the calculator above:
- Vertical part of the load: 187.83 kN
- Horizontal part of the load: 93.91 kN
- Number of shear areas: 6.00
- Bolt diameter squared: 297.09 mm2
- Required bolt diameter: 17.24 mm
- Next standard bolt diameter: M20 (20 mm)
- Shear stress with that bolt: 111.41 MPa
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: Shear planes for each bolt Single shear (one plane).
- Vertical part of the load: 187.83 kN
- Horizontal part of the load: 93.91 kN
- Number of shear areas: 3.00
- Bolt diameter squared: 594.18 mm2
- Required bolt diameter: 24.38 mm
- Next standard bolt diameter: M30 (30 mm)
- Shear stress with that bolt: 99.03 MPa
Common questions
What is double shear?
A bolt in double shear is cut across two planes, for example a plate held between two straps. It has twice the shear area of the same bolt in single shear, so it carries twice the load.
Why is the load split into vertical and horizontal parts?
It shows how the load in a sloping member acts on the support. The bolts still carry the whole load P along the member, so the bolt size comes from P and not from either part alone.
Why does my textbook say 17.23 mm and the calculator 17.24 mm?
The textbook rounds the working along the way. The calculator keeps full precision to the end, and then gives the answer to two decimal places.
Is this a bolted connection design?
No. It is the shear check used in study problems. A real connection also checks bearing on the plates, tear-out, the thread in the shear plane, the bolt grade and the steel standard rules (AS 4100 in Australia).
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Standard strength of materials texts (bolts in single and double shear); AS 4100 for structural steel bolted connections.
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