Page 53 - Handbook of Civil Engineering Calculations, Second Edition

1.36 STRUCTURAL STEEL ENGINEERING AND DESIGN

FIGURE 22. Thick-walled cylinder under internal and ex-
ternal pressure.

3. Check the accuracy of the results
Use the relation s 1 r 1 s 0 r 2 [(r 2 r 1 )/(r 2 r 1 )](p 1 r 1 p 2 r 2 ). Substituting the known
values verifies the earlier calculations.

THERMAL STRESS RESULTING FROM
HEATING A MEMBER

A steel member 18 ft (5.5 m) long is set snugly between two walls and heated 80°F
(44.4°C). If each wall yields 0.015 in. (0.381 mm), what is the compressive stress in the
5
6
member? Use a coefficient of thermal expansion of 6.5 10 /°F (1.17 10 /°C) for
steel.
Calculation Procedure:

1. Compute the thermal expansion of the member without
restraint
Replace the true condition of partial restraint with the following equivalent conditions:
The member is first allowed to expand freely under the temperature rise and is then com-
pressed to its true final length.
To compute the thermal expansion without restraint, use the relation AL cL T,
where c coefficient of thermal expansion, /°F (/°C); T increase in temperature, °F
(°C); L original length of member, in. (mm); L increase in length of the member,
6
in. (mm). Substituting gives L 6.5(10 )(18)(12)(80) 0.1123 in. (2.852 mm).
2. Compute the linear restraint exerted by the walls
The walls yield 2(0.015) 0.030 in. (0.762 mm). Thus, the restraint exerted by the walls
is L w 0.1123 0.030 0.0823 in. (2.090 mm).