A History of Research and a Review of Recent Developments

Civil bridges 201
Figure 8.6 Relationship between residual strength and initial strength for a given
loss of depth of a rectangular section.
truss, or the pylon of a cable-stayed bridge, assume that the section loss extends
over the entire length. This leads to m=3, because the second moment of area,
required in the calculation of buckling or compressive strength, will be
approximately proportional to the cube of the depth of the component.
For a very stocky compression member such as a masonry pier or abutment,
damage will only lead to m=3 if so much of the cross section is removed that
the remainder buckles as a slender strut. Otherwise, the order is more likely to
be m=1. The above discussion is illustrated in Figure 8.6, and from it we can
form a relationship between strength ratio and area ratio, as shown in Figure
8.7. This figure represents the simplest loading and the most elementary member
Figure 8.7 Relationship between strength ratio and area ratio. Permissible stress
design in the elastic range.