Bolt Connection Calculators

Metric Thread Tightening

Bolted connections are the most common type of detachable connections. The simplicity, versatility, high strength and accuracy of the mutual arrangement of parts make them irreplaceable. In this section, the calculations of some types of bolted connections and also forces and stresses in bolts under an arbitrary static load are provided.

In this calculation, a bolted connection consisting of a bolt with a metric thread of diameter d with a pitch h and two parts having a total thickness L in the junction is considered. The bolt is tightened applying torque T.

The connection is under a load with a tensile component F_H and shear component F_K. As a result of calculations, the tightening force F_t, tensile force F and equivalent stress σ acting in the bolt are determined. With a tight connection, the tensile force in the bolt is constant and F = F_t. If the loads F_H and F_K/μ exceed the tightening force, the connection becomes loose, and the safety factor K becomes less than one. In this case, bending stresses start to appear in the bolts due to the shear component of the load.

In this calculation the coefficient of friction μ is same for thread and for connecting surfaces.

Calculation of Metric Thread Tightening

Calculation Thread Tightening

INITIAL DATA

d - Thread outer diameter;

h - Thread pitch (see table below);

T - Tightening torque;

μ - Coefficient of friction (see table below). In this case it is same for the bolt and for connection elements;

F_н - External tensile load on the connection elements;

F_к - External shear load on the connection elements;

L - Thickness of the connection elements.

RESULTS DATA

F_t - Tightening force;

F - Tensile force;

σ - Maximal equivalent stress (von-Mizes) in threaded part of the bolt;

K - Safety factor of tightness. K >= 1 to ensure that there are no gaps and displacements in the connection.

Metric Imperial

Diameter of thread (d)

Pitch (h)

Torque (T)

Friction coefficient (μ)

Tensile load (F_H)

Shear load (F_k)

Connection thickness (L)

Tightening force in bolt (F_t)

Tensile force in bolt (F)

Equivalent stress (σ)

Safety factor (К)

BASIC FORMULAS

Connection tightening force:

F_t = [2T*cosα / d]*[1 / (2cosα*μ + sinα)];

α - angle of thread inclination.

Tensile load in bolt:

F = F_t;

Equivalent stress:

σ = F / (π*(d₀ / 2)²);

d₀ - smaller thread diameter;

Safety factor:

K is less from the ratios: F_t / F_H and [F_t - F_H] / F_K*μ

These formulas are applicable for the tight connection. The algorithm of the program takes into account a loose connection in the case of insufficient tightening torque.

INITIAL DATA

d - Thread outer diameter;

h - Thread pitch (see table below);

T - Tightening torque;

μ - Coefficient of friction (see table below). In this case it is same for the bolt and for connection elements;

F_н - External tensile load on the connection elements;

F_к - External shear load on the connection elements;

L - Thickness of the connection elements.

RESULTS DATA

F_t - Tightening force;

F - Tensile force;

σ - Maximal equivalent stress (von-Mizes) in threaded part of the bolt;

K - Safety factor of tightness. K >= 1 to ensure that there are no gaps and displacements in the connection.

METRIC THREAD SIZES

Thread	M2.0	M2.2	M2.5	M3.0	M3.5	M4	M4.5		M5
Pitch	0.4	0.45		0.5	0.6	0.7	0.75		0.8
Thread	M6	M8	M10	M12	M14	M16	M18		M20
Pitch	1.0	1.25	1.5	1.75	2.0		2.5
Thread	M22	M24	M27	M30	M33	M36	M39		M42
Pitch	2.5	3.0		3.5		4.0			4.5
Thread	M45	M48	M52	M56	M60	M64		M68
Pitch	4.5	5.0		5.5		6.0

COEFFICIENTS OF FRICTION

Friction contact materials	Surface conditions	Friction coefficient
Steel-Steel	Dry	0.15
Steel-Steel	Greased	0.11
Steel – Cast iron	Dry	0.3
Steel - Copper	Dry	0.36
Steel - Copper	Greased	0.19
Steel - Bronze	Dry	0.12
Steel - Bronze	Greased	0.09
Steel - Brass	Dry	0.35
Steel - Brass	Greased	0.19
Steel - Titanium alloy	Dry	0.3÷0.7
Steel - Aluminium alloy	Dry	0.61
Bronze - Bronze	Greased	0.1
Cast iron - Bronze	Dry	0.22
Cast iron - Bronze	Greased	0.08
Cast iron – Cast iron	Dry	1.1
Cast iron – Cast iron	Greased	0.1
Aluminium alloy - Aluminium alloy	Dry	1.2
Aluminium alloy - Aluminium alloy	Greased	0.3
Titanium alloy – Titanium alloy	Dry	0.5

OTHER CALCULATORS

AREA MOMENTS OF INERTIA

BEAM CALCULATORS

TORSION OF BARS

CIRCULAR FLAT PLATES

BUCKLING

ELASTIC CONTACT

IMPACT LOADS

NATURAL FREQUENCIES

PRESSURED SHELLS

FLUID DYNAMIC

COMPOSITES

SPRINGS

THREAD CONNECTIONS

SHAFT CONNECTIONS

BEARINGS

DRIVES

FATIGUE

HEAT TRANSFER