Temperature load on the pier (from superstructure) is based on the amount of longitudinal movement in superstructure applied to the pier. The movement of a pier depends on the overall arrangement of piers, spans, bearing and skew in addition to temperature rise/fall and the coefficient of thermal expansion.

Substructure can do temperature load generation for two types of bearings. These are:

• Fixed bearings
• Expansion bearings

For fixed bearings, Substructure only considers column stiffness to determine the thermal force.

Expansion bearings could be specified in the program.

• Elastomeric
• Sliding (plates)
• Rockers

Following table provides information as what items are considered in generation of thermal loads in the program.

For sliding bearings, Substructure computes the thermal force as a fraction of total dead load.

Fs = µ (DL)

where:

Fs = Total thermal load on the pier

α Coefficient of friction between sliding parts in the bearing

Program defaults to a value of 0.06

DL = Total dead load on the pier

For rocker bearings, Substructure computes the thermal force which is a fraction of total dead load on the pier and also depends on the radius of the pin and the rocker.

Fr = 0.25 DL (r / R)

where:

Fr = Total thermal load on the pier

DL = Total dead load on the pier

R = Radius of rocker

r = radius of rocker pin

In case of Elastomeric bearing pads, thermal movement will be resisted by the flexibility of the bearings and columns.

The total movement of the superstructure at the pier is,

Δ_s = Δ_b + Δ_c

where:

Δ_s = Superstructure longitudinal movement at the top of the pier

Δ_b= Shear flexibility of elastomeric bearing pad

Δ_c= Bending flexibility of the pier column

The total deformation in superstructure based on change in temperature is,

Δ_s = α Δ T L

where:

α = Coefficient of thermal expansion

Δ T = Change in temperature

L = Contributing length of superstructure

The movement of the column when a thermal force is applied is,

Δ_c = T H³ / (3 E_c L_c)

where:

T = Thermal Force, K (N)

H = Distance from top of footing to top of cap, in (mm)

E_c = Modules of elasticity of concrete, ksi (MPa)

I_c = Inertia of pier columns in4 (mm4)

The movement of the column when a thermal force is applied is,

Δ_b = T t / (n A G)

where:

T = Thermal Force, K (N)

t = total Elastomer thickness (without steel laminates), in (mm)

n = number of steel semi forced elastomeric bearing

A = bearing area of elastomeric bearing

G = Shear modules of elastomer, ksi (MPa)

Substructure determines the thermal force on the pier using the above mentioned equations for movement of bearings and columns. Any contribution from footings/pile is ignored.

The point of zero movement, any hinges or construction joints should be considered while deciding about the contribution length for thermal movement.

For thermal generation, program either considers all bearings on a pier to be fixed or expansion. It considers the longitudinal movement of the bridge only which is the case for straight bridges or bridges with small skew. In case of large skew transverse flexibility may need to be considered which is not considered in the program. User should compute the loading manually for those or any other cases not covered and input directly. It does not check any unbalanced thermal force on the bridge. Substructure only generates the forces on the bearings and does not do any bearing design. User should check to see that bearing forces generated are not more than the capacity of the bearing.