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The single most important design objective for a structure or a component of a structure is the provision of adequate strength. The consequences and costs of strength failures are large and therefore the probability of such failures must be very small.19768
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The satisfaction of concrete and steel stress limits at service loads does not necessarily
ensure adequate strength and does not provide a reliable indication of either the actual
strength or the safety of a structural member. It is important to consider the non-linear
behaviour of the member in the over-loaded range to ensure that it has an adequate structural
capacity. Only by calculating the ultimate capacity of a member can a sufficient margin
between the service load and the ultimate load be guaranteed.
In the 1950s and 1960s, there was a gradual swing away from the use of elastic stress
calculations for the satisfaction of the design objective of adequate strength. The so-called
ultimate strength design approach emerged as the most appropriate procedure. The ultimate
strength of a cross-section in bending Mu is calculated from a rational and well established
flexural strength theory, which involves consideration of the strength of both the concrete and
the steel in the compressive and tensile parts of the cross-section. The prediction of ultimate
flexural strength is described and illustrated in this chapter. When Mu is determined, the
design requirements for the strength limit state (as discussed in Section 1.7.6) may be checked
and satisfied.
In addition to calculating the strength of a section, a measure of the ductility of each section
must also be established. Ductility is an important objective in structural design. Ductile
members undergo large deformations prior to failure, thereby providing warning of failure
and allowing indeterminate structures to establish alternative load paths. In fact, it is only with
adequate ductility that the predicted strength of indeterminate members and structures can be
achieved in practice.4.2 Flexural behaviour at overloads
The load at which collapse of a flexural member occurs is called the ultimate load. If the
member has sustained large deformations prior to collapse, it is said to have ductile behaviour.
If, on the other hand, it has only undergone small deformations prior to failure, the member is
said to have brittle behaviour. There is no defined deformation or curvature which
distinguishes ductile from brittle behaviour. Codes of practice, however, usually impose a
ductility requirement by limiting the curvature at ultimate to some minimum value, thereby
ensuring that significant deformation occurs in a flexural member prior to failure. Since beam
failures that result from a breakdown of bond between the concrete and the steel
reinforcement, or from excessive shear, or from failure of the anchorage zone tend to be
brittle in nature, every attempt should be made to ensure that the region of maximum moment
is the weakest link. The design philosophy should ensure therefore that a member does not fail
before the required design moment capacity of the section is attained.
Consider the prestressed concrete cross-section shown in Figure 4.1. The section contains
non-prestressed reinforcement in the compressive and tensile zones and bonded tensile
prestressing steel. Also shown in Figure 4.1 are typical strain and stress distributions for four
different values of appliedmoment. As the applied moment M increases from typical in-service levels into the overload
range, the neutral axis gradually rises and eventually material behaviour becomes non-linear.
The non-prestressed steel may yield if the strainε st exceeds the yield strain (ε y=fy/Es), the
prestressed steel may enter the non-linear part of its stress-strain curve asε p increases, and the