Shear Capacity of sections with insufficient anchorage of stirrups

[kww2008]

Some old simply supported RC bridges have stirrups that are terminated prematurely and are not hooked around the bottom longitudinal bars. These stirrups are likely to fail in a pull-out mode before achieving their yield strength. How would one determine the shear strength of such sections when load rating these bridges? Ignoring the stirrup is likely to be too conservative.

 

[yakpol]

On beam elevation:
1. Draw a classic 45 degrees shear crack stating from the support.
2. Draw the stirrups crossing the crack.
3. For each stirrup measure the distance from bottom of stirrup to the crack, Lo.
4. Reduce stirrup yield strength proportionaly fs = fy(Lo/Ld), where Ld - development length by code formulas.
5. Calculate shear reinforcment contribution Vs = sum(fs*Av)

It's rational method, not conservative, increase safety factor to make it conservative.

Regards,

 

[kww2008]

Thank you Yakpol for the response.

As each of the stirrups has a different length, a different calculated yield strength, and hence a different force, would it not be more appropriate to calculate, assuming we have 3 stirrups crossing with N1=fs1*Av, N2=fs2*Av, N3=fs3*Av (N1<N2<N3):

Vs= max (N3, 2*N2, 3*N1) ?

 

[dik]

Appropriate approch... since the lines of principle stress are normal to the bottom of a rectangular beam. Catch the link:

http://nptel.iitm.ac.in/courses/IIT...lysis_Design_for_Shear_Torsion/Section5.1.pdf

 

[yakpol]

kww,
Your approach Vs= max (N3, 2*N2, 3*N1) assumes a chain reaction, allows no ductility. Which is right when development governs capacity of reinforcement. However, I did see published guidelines (seismic retrofit related) to sum the capacities of individual bars Vs = N1+N2+N3. Also you may want to ajust the crack shape as dik suggested.

Yakov

 

[hokie66]

I don't believe there is a rational, code based, method of calculating shear capacity when the stirrups depend on development length rather than anchorage. I think the calculations should be based on the depth of the beam, for shear purposes, being assumed to be only the depth above where the bars are developed.