Calculate bolt pull out force, diameter, length, or bond stress from any 3 values with unit conversions for in, mm, cm, ft, m, psi, kPa, and MPa.
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Bolt Pull Out Force Formula
The calculator uses the bonded surface area of a cylindrical bolt or anchor and multiplies it by the average bond stress. In base units, diameter and embedded length are in inches, bond stress is in psi, and force is in pounds-force.
F = pi*D*L*tau
Rearranged formulas used when a different value is missing:
D = F/(pi*L*tau)
L = F/(pi*D*tau)
tau = F/(pi*D*L)
- F = bolt pull out force
- D = bolt diameter
- L = embedded or bonded length
- tau = average bond stress, also called bond strength
- pi = 3.14159
If you leave force blank, the calculator finds the pull out force from diameter, bonded length, and bond stress. If you leave diameter, length, or bond stress blank, it rearranges the same equation to solve for that missing value. Unit selections are converted internally before the formula is applied, then the result is converted back to the unit you selected.
Common Unit Conversions for Bolt Pull Out Calculations
| Quantity | Conversion | Used as base unit |
|---|---|---|
| Diameter or length | 1 in = 25.4 mm = 2.54 cm | in |
| Length | 1 ft = 12 in, 1 m = 39.3701 in | in |
| Bond stress | 1 MPa = 145.038 psi, 1 kPa = 0.145038 psi | psi |
| Force | 1 lb-f = 4.44822 N, 1 kN = 224.809 lb-f | lb-f |
Inputs That Affect Pull Out Force
| Input change | Effect on calculated force | Reason |
|---|---|---|
| Double the diameter | Force doubles | Bonded circumference is proportional to diameter. |
| Double the embedded length | Force doubles | More length gives more bonded surface area. |
| Double the bond stress | Force doubles | The same area is assumed to resist twice the stress. |
Example
Example 1: Calculate bolt pull out force
Suppose a bolt has a diameter of 0.5 in, an embedded length of 4 in, and an average bond stress of 1,200 psi.
F = pi*0.5*4*1200
F = 7539.82 lb-f
The pull out force is about 7,540 lb-f, or about 33.54 kN.
Example 2: Calculate required embedded length
Suppose the target pull out force is 10,000 lb-f, the bolt diameter is 0.75 in, and the average bond stress is 1,500 psi.
L = 10000/(pi*0.75*1500)
L = 2.8294 in
The required bonded length is about 2.83 in.
FAQ
What does average bond stress mean?
Average bond stress is the assumed shear stress acting between the bolt surface and the surrounding material or adhesive. The calculator treats this value as uniform along the bonded length. Real pull out behavior can vary because of concrete strength, adhesive type, hole cleaning, edge distance, embedment depth, cracking, corrosion, and installation quality.
Is bolt pull out force the same as bolt tensile strength?
No. Pull out force is the force needed to break the bond or surrounding material around the embedded bolt. Bolt tensile strength is the force needed to fracture the bolt itself in tension. A connection can fail by pull out, bolt rupture, concrete breakout, adhesive failure, thread stripping, or another mode. The lowest applicable capacity controls the design.
Should the diameter be the nominal bolt diameter or the hole diameter?
Use the diameter of the bonded surface that is resisting pull out. For a plain cylindrical anchor, this is usually the bolt or anchor diameter. If you are modeling a threaded, deformed, or adhesive anchor, the correct effective diameter may depend on the test data or design method you are using.
