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To save on material, I am requested to design a continuously supported beam with a maximum bending capacity that is half of its maximum bending moment and to strengthen the beam at certain intervals where its capacity is exceeded. What is a feasible strengthening scheme without changing the beam's overall dimensions significantly.

This beam is going to be used as a waling where stiffeners will be added at strut-waling connection. This is also the location where moment capacity will be exceeded.

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If your beam design is governed by yielding in bending (not lateral-torsional buckling/plate buckling, etc) then you need to increase the second moment of area (I) to increase the bending capacity.

Usually this is done by fastening additional plates to the beam, typically onto the flanges.

Here are some examples of such a strengthening strategy:

Bolting:

Bolting

Welding:

Welding

See this article on strengthening existing steel beams for more information.

A more elaborate and expensive method would be to use variable depth beams as is sometimes done with bridges:

Variable Depth

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  • $\begingroup$ Obviously, if reinforcing with C shapes like those shown in the bolting examples, one must check that the flanges of the C don't interfere with the surrounding structure. $\endgroup$
    – Wasabi
    Commented May 27, 2017 at 14:56
  • $\begingroup$ I observe that although this answer says 'not LT buckling', many of the examples shown will actually improve LT buckling governmed strength. $\endgroup$
    – achrn
    Commented Jun 18, 2017 at 19:39
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Castellated beam. Cut the web with torch, and re-weld web at higher flange distance.

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    $\begingroup$ Your suggestion is a) for the overall beam not for local strengthening and b) violates the "without changing the beam's overall dimensions significantly". $\endgroup$
    – AndyT
    Commented Jun 16, 2017 at 10:32

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