Tension and compression re-bars in a concrete beam are connected by stirrups vertically tied together. If the space in between (this corresponds to web of an I-Beam) carrying shear load predominantly why are stirrups not placed along $\pm 45^0$ principal stress direction for better material economy ?

Such a design practice could be in aerospace engineering for lightweight construction but not found in the originating civil/structural construction practice ?


Unfortunately the situation is more complicated than dealing with the principal stresses (see this answer). The principal stress direction will only be $\pm 45^o$ when in a condition of pure shear. So for a beam this is at the neutral axis, away from the neutral axis the principal stress direction will change. This can be seen here:

enter image description here

Current concrete shear design takes a strut-and-tie approach. For this we assume a truss made from steel tension ties (reinforcement) and concrete compression struts: enter image description here]

In this image the dashed lines are in compression (which can be carried by the concrete), while the solid lines are in tension (which are carried by the reinforcement). According to Eurocode 2, the inclination of the compression structs is allowed to vary between $21.8^o$ and $45^o$, and depends on the shear present in the beam. This will vary along the length of the beam, resulting in the stirrup spacing changing.

Inclining the stirrups can achieve an increase in shear resistance. However, inclined stirrups are very unusual in practice. This is due to some of the disadvantages of inclined stirrups, for example:

  • During load reversal (during an earthquake, for example), you would end up with effectively no shear reinforcement - which could result in failure.
  • The extra expense/complication involved in placing inclined reinforcement is usually not worth the relatively minor increase in shear resistance.
  • In most design situations the extra cost/time/risk involved in developing a non-standard design is discouraged except when absolutely necessary.
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In days of old (not sure how old) stirrups did get installed at the ends of beams in an inclined fashion. I believe CHBDC currently still has clauses for it, but I never see it used for new design. I have used it however in evaluating old designs.

Additionally to inclined stirrups, it was also common practice at one point to bend some of the bottom longitudinal bars up at the end of the beams where moment was decreasing and they were no longer required. However since the shear was increasing some of this bent bar was also used for shear reinforcing.

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  • $\begingroup$ Thanks for your comments. Restating the question.. rarely does one build large loaded beams to carry pure bending moment when vertical stirrups can be justified as spacers in a distancing role between top/bottom fibers carrying tension/compression. Heavy vertical shear resolved as tension and compression should be taken by re-bars or stirrups depending on load. Why not make good use of stirrups which are present in an almost useless vertical direction? $\endgroup$ – Narasimham Nov 28 '18 at 5:36
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    $\begingroup$ bullet point 2 from mg4w answer. For the couple of extra stirrups you are going to save by inclining the stirrups, you will lose in terms of labour installing in the correct position and incline. Its not as efficient to install them vertically, but it is much more economical. $\endgroup$ – Forward Ed Nov 28 '18 at 5:42

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