Basic methods of reinforcing steel structures - Assessment and Refurbishment of Steel Structures - page 125

original cross-section, reliability condition (4.17) ensures the reliability of the whole
cross-section, including the reinforcing elements. If the quality of the materials is
different, it is necessary also to check the outer region of the reinforcing elements using
the condition
(4.18)
We obtain the optimum reinforcement of a cross-section stressed by bending if the outer
regions of both original and reinforced cross-sections are equally used (see Figure 4.41).
This condition means that the design resistance value is reached simultaneously in both
outer regions. Applying this on condition that ƒ yd,1 = ƒ yd,2 = ƒ yd , we obtain the value of the
required ratio of cross-section heights ( h 1 ) before and ( h 2 ) after reinforcement:
(4.19)
However, in practice we hardly ever obtain the optimum height ratio in equation (4.19)
because equation (4.19) requires an excessive enlargement of the cross-section that
technically is not possible to attain. We usually propose the reinforcement so that the
height ratio before and after reinforcement is greater than that given in equation (4.19) so
that the stress in the reinforced part is decisive. In the less frequent case when the height
ratio is lower than that required by equation (4.19), the reinforcing part limits the
reliability.
In case of cross-sections of first and second classes, it is possible to use their plastic
reserve by partial or full plastification of the cross-section. We can reach the partial
plastification of the original cross-section if the condition of reliability chosen is just
equation (4.18), which controls the elastic state in the outer regions of the reinforcing part
of cross-section but ignores tensions in the outer regions of the reinforced part.