Capacitiy of Existing Concrete Joist System

[marinaman]

I've been asked to look at an existing one-way concrete joist system. It was built in 1953.

I have a good set of the original construction documents. The f'c is listed to be 3,000 psi minimum and the reinforcing steel is indicated to be intermediate billet with an allowable tensile stress of fs = 20,000 psi.

I was just thinking about something here.....if the nominal moment of resistance was governed by the following equation:

Mn = (As)(Fy)(d - a/2).....and I know Fy for intermediate billet steel is 40,000 psi.......I'm thinking to myself if 20,000 psi should be used for Fy instead of 40,000.

My thinking is that this Mn equation is defining the internal couple inside a beam, with d-a/2 being the lever arm. If the allowable steel tensile stress is only 20,000 psi, shouldn't that be in the equation instead of Fy at 40,000 psi?

 

[HeavyCivil]

Depends on whether you're doing your calcs ASD or LRFD.

Most people would use LRFD, except maybe old-timers. In which case you'd use 40ksi and multiply by Phi. Then back off your load factors when you report the load capacity to your client.

 

[BAretired]

No. The original design was based on WSD (Working Stress Design) wherein plain sections remain plain, etc. The formula you are quoting (there should be a [φ] factor added) is a USD (Ultimate Strength Design) formula.

To check the original design, you could factor the loads and use USD with Fy = 40 ksi.

BA

 

[msquared48]

For 1953, I agree with BA. Definitely WSD.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[marinaman]

Thanks guys. I appreciate the input.

Thanks BA.....I know that the factor needs to be added when I do my analysis.....I was just trying to break this down to the moment arm and the force.

I do wonder, in my mind, when the fs = 20,000 would come into play? When determining bending capacity (using factored loads, etc) we're using yield strengths of steel in the equations (Fy and not fs).....and not going back and considering that the allowable tensile in the steel is 20,000psi.

That allowable tensile stress is bothering me.

 

[JAE]

Just because the original design was perhaps based on ASD doesn't mean you have to check it with ASD. The fy = 20,000 psi simply reflects a steel with Fy = 40,000 psi. You can choose to check either as your current local code probably accepts both methods.

 

[msquared48]

I believe that USD was first introduced in the 1963 ACI code, along with the concept of load factors, and the phi factor. Prior to this code, WSD ruled.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask