SME
Machine Design · Problem type
Bolt preload and tightening torque
Use this for “An M12 bolt (Aₜ = 84.3 mm², proof strength 600 MPa) is tightened for reuse with K = 0.2. Find the preload and the wrench torque.”
This is an example. Type your own values to start a new problem.
Fᵢ (kN)
=
c
×
Aₜ (mm²)
×
Sₚ (MPa)
T (N·m)
=
K
×
Fᵢ (kN)
×
d (mm)
Formulas
Fᵢ
=
c
×
Aₜ
×
Sₚ
1,000
37.935
=
0.75
×
84.3
×
600
1,000
T
=
K
×
Fᵢ
×
d
91.044 = 0.2 × 37.935 × 12
Assumptions
•
The preload is Fᵢ = cAₜSₚ: c = 0.75 for a reusable joint, 0.9 for a permanent one.
•
The torque factor K is about 0.2 for plain, dry steel threads.
•
Aₜ in mm² times Sₚ in MPa gives N; kN times mm gives N·m.
Step-by-step
WE KNOW
d = 12 mm, Aₜ = 84.3 mm², Sₚ = 600 MPa, c = 0.75, K = 0.2
FIND
preload (Fᵢ), tightening torque (T)
Step 1 · Find preload (Fᵢ)
Use Fᵢ = c × Aₜ × Sₚ ÷ 1,000
The
proof
load
is
Aₜ
times
Sₚ;
the
bolt
is
tightened
to
the
fraction
c
of
it
(÷
1000
gives
kN).
Fᵢ
=
0.75
×
84.3
×
600
1,000
Fᵢ
=
63.225
×
600
1,000
Fᵢ
=
37,935
1,000
Fᵢ = 37.935 kN
Step 2 · Find tightening torque (T)
Use T = K × Fᵢ × d
The wrench torque grows with the preload and the bolt size.
T
=
0.2
×
37.935
×
12
T
=
7.587
×
12
T
=
91.044
N·m
Check
Put the numbers back in. Both sides should match.
37.935
=
0.75
×
84.3
×
600
1,000
✓
91.044 = 0.2 × 37.935 × 12 ✓
Topic check
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