Effects of temperature - Concrete Structures: Stresses and Deformations - page 357

q cr = h ( T − T a ) (10.9)

where

q cr = q c + q r (10.10)

For analysis of temperature distribution over the thickness of a slab or
a wall, it is su

ed one-dimensional form of
Equations (10.1) and (10.2), by dropping out the term involving x (or y ).
Numerical solution of the di

cient to employ a simpli fi

erential Equation (10.1), subject to the
boundary condition expressed by Equation (10.2), gives the temperature dis-
tributions at various time intervals. Finite di

ff

ff erence or fi nite elements 8

methods may be employed.

10.5 Material properties
From the preceding sections, it is seen that a number of values related to
thermal properties of the material are involved in heat transfer analyses. For
concrete, the material properties vary over wide ranges, depending mainly on
composition and moisture content.
Table 10.1 gives several material properties which may be employed for
analysis of temperature distribution and the corresponding stresses in bridge
cross-sections.
The following values may be employed for the convection heat transfer
coe F) ), based on a wind speed of 1 m/s

(3 ft/s) for all surfaces of a box-section bridge, except for the inner surfaces of
the box, where the wind speed is considered zero.

cient h c (W/(m 2 ° C) )(or Btu/(h ft 2 °

W/ (m 2

° C)

Btu/(h ft 2

° F)

Top surface of concrete deck
Asphalt cover
Bottom surface of a cantilever
Inner surfaces of box
Outside box surface

8.5
8.8
6.0
3.5
7.5

1.5
1.6
1.1
0.6
1.3

10.6 Stresses in the transverse direction in a
bridge cross-section
In Section 10.3 we discussed analysis of self-equilibrating and continuity
thermal stresses in the direction of the axis of a bridge. Equally important
stresses occur in the transverse direction in a closed box cross-section.