Analysis of an RC section under combined torsion and shear

breadmonkey

Hi,

I'm trying to figure out how to determine the torsional resistance of a section under combined torsion and shear. I have examples of how it's done for pure torsion and for combined torsion and bending but not for torsion and shear.

In the former two examples, I've been assuming that failure is due to combined yielding of stirrups, longitudinal reinforcement and concrete crushing. I then rearrange the following equation to get the value of cotθ:

Asl*fyd = T*Uk*cotθ/2*Ak

and then plug that value into the equation for Trd,max:

Trdmax = 2*v*fcd*Ak*t/(tanθ + cotθ)

which gives the answer.

However, when there is an applied shear force, I think I have to account for it in the actual derivation of the first equation above. Unfortunately, I'm not getting very far. I'm not even really sure how the section would fail under this type of loading.

Would anyone be able to shed some light on the situation or point me towards potentially helpful literature? I have "Reinforced Concrete Design to Eurocode 2" but it's pretty light on torsion and doesn't have what I'm after.

I hope what I've described what I'm on about. Any suggestions would be greatly appreciated!

EDIT: Is it the case that the presence of an applied shear force means that the stirrups will yield first? So I can then check how much area of steel is "taken up" by the applied shear force and subtract it from the total area of steel in the stirrups. Then I'd have an equivalent section that I could analyse as if it was under pure torsion. Then use the following equation to get cotθ:

T = 2*Ak*fyd*cotθ*(Asw/s)

alanucc

Kong & Evans is a good source for concrete theory

Eurocodus

Example 7.9 in "Reinfoced Concrete Design" (Mosley et al), the text which you refer is based on example 7.6. This covers bending, shear and torsion.