Over-Reinforced Concrete Beam Design ACI 318-08 Note: Over-reinforced typically means the tensile steel does not yield at failure. for this example, over-reinforced means the section is not “tension controlled” per ACI standards even though the steel does yield Given: • f’c= 6,000 psi • fy= 60 ksi Required: • De te rmin e th e nominal momen t ca pa ci ty , !Mn Assumptions: 1. Plain s ect ion s re main plain (ACI 31 8-0 8 se cti on 1 0. 2.2 ) 2. Max imum conc rete strain at ext reme compre ssi on fiber = 0.00 3 ( ACI section 10.2.3) 3. T ensil e st ren gth of c onc ret e is n egl ect ed ( 10.2. 5) 4. Compression ste el is neglecte d in this calculation. Friday, August 10, 12
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8/10/2019 004 LEER Over Reinforced Concrete Beam Design
With c, we can calculate the strain in the extreme tensile steel using similar trWith this strain calculated, we can check our assumption that the steel yieldsdetermine if the section is tension controlled.
First, let’s calculate dt, the depth from the extreme compression fiber to the etensile steel
dt = 24” - 1.5” - 0.5” - 1”/2 = 21.5”
c/!c = dt/(!c + !t)
!t = (dt x !c)/c – !c = (21.5” x 0.003)/8.261” – 0.003
"t = 0.0048
Now that we know the depth of the stress block, we can calculate c, the depthneutral axis.
From ACI 318 section 10.2.7.1 – a = "1 x c
"1 is a factor that relates the depth of the Whitney stress block to the depth oneutral axis based on the concrete strength. It is defined in 10.2.7.3
– Per ACI section 10.3.4 a beam is considered tension controlled if the strain in the extreme tension steel is greater than 0.
– The calculated steel strain in our section is 0.0048 which is less than 0.005 therefore this beam section is not tension con
– Per ACI section 10.3.5 !t at nominal strength for flexural members shall not be less than 0.004 (0.0048 is acceptable)
• The strain for our section is between the limit for compression controlled (.002 per ACI section 10.3.3) and the limit for tensionsections, 0.005. Therefore, we must interpolate to determine our $ factor in accordance with ACI 9.3.2.2