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Bolt Preload Temperature Effects Formulae and Calculator

Fastener, Bolt and Screw Design Torque and Force Calculations

Bolt Preload Effects Due to Temperature Load Calculator and Equations

Joints with bolts, or other threaded fasteners, which are exposed to a temperature change after installation will have a change in preload. The change can either be an increase or decrease.

Preview Bolt Preload Effects Due to Temperature Calculator

The following equations assume no washer deformation and no gap exists.

Eq. 1

e B = α B L B ( T − T 0 ) + P E B ( L s A s + L r A r + L g 2 A r )

Eq. 2

e m = ( T − T 0 ) ( α a t a + α b t b + α c t c ) − P ( t a A a E a + t b A b E b + t c A c E c )

Eq. 3

e B = e M

Eq. 4

P T = ( T − T 0 ) ( α a t a + α b t b + α c t c − α B L B ) 1 E B ( L s A s + L r A r + L g 2 A r ) + ( t a A a E a + t b A b E b + t c A c E c )

PT will tension if T > T0 and αM > αB
(+) is tension in bolt, (-) would unload a preload bolt

If all three materials are the same, equation 4 becomes

Eq. 5

P T = ( T − T 0 ) ( α M t M − α B L B ) 1 E b ( t s A s + t r A r + t g 2 A r ) + t m A M E M

If gap exists, no preload in bolt, equations 4 and 5 become

Eq. 6

P T = − g + ( T − T 0 ) ( α a t a + α b t b + α c t c − α B L B ) 1 E B ( t s A s + t r A r + t g 2 A r ) + ( t a A a + t b A b E b + t c A c E c )

(+) is tension in bolt, (-) would unload a reloaded bolt

Eq. 7

P T = − g ( T − T 0 ) ( α M t M − α B L B ) 1 E B ( t s A s + t r A r + t g 2 A r ) + t M A M E M

(+) is tension in bolt, (-) would unload a reloaded bolt

Eq. 8

A M = 3 π D B 2 / 4

Eq. 9

LB = Ls + Lr + Lg / 2

Eq. 10

tM = ta + tb + tc

Partially Restrained Square Plate
Figure 1 - Partially Restrained Rectangle Plate

Bolt Nomenclature
Figure 2 - Bolt Nomenclature

Where

Ar = Section area of root of bolt
As = Section area of shank of bolt
Aa = effective area of material under thermal load = Ab = Ac
DB = bolt diameter
DM = Effective diameter of material thermal load on bolt; assumed to be 2 DB
eB = Deformation of bolt over length, LB
LB = effective bolt length
eM = Deformation of material over thickness, LM
LM = Materials thickness
g = gap
tM = Total material thickness
E = modulus of elasticity
T0 = Initial temperature
T = final temperature
α = Coefficient of thermal expansion
P = bolt preload
PT = Preload tension with temperature effects
Ea = modulus of elasticity material a
Eb = modulus of elasticity material b
Ec = modulus of elasticity material c

  • Bell Helicopter Structural Design Manual, 1977

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