### strains for flexural reinforced concrete members

strains for concrete and steel for flexural member varies directly with distance from the neutral axis. this is applicable for shallow members. for deep members with a depth equal to 0.25 or more of clear span length, this will not be applicable. ACI10.2.3 stating that the maximum usable strain in concrete at extreme fiber can be assumed to be 0.003. at the strain of 0.003 concrete assumed to reach it is flexural capacity. for reinforcement steel of grades 60 (yield strength of 60,000psi) or grade420 (yield strength of 420 Mpa) and for all prestressed reinforcement the strain may be assumed to be 0.002 at balance condition. if we calculate strain for reinforcement steel at the yield point.

εs=0.00207 so the strain is very close to the assumed 0.002

Figure 1

Example: determine the values of a, c and εt for the beam shown in figure 1. fy=60,000psi, fc'=3000psi.

Figure 1

a=(Asfy)/(0.85fc'*B)
=(3*60,000)/(0.85*3000*14)
=5.04in
a=β1*c
β1=0.85
a=5.04/0.85=5.93in
from trinagle similarities

εt/(d-c)=0.003/c
εt=0.003(d-c)/c
εt=0.003(21-5.93)/5.93
εt=0.00762

Example(si units): determine the values of a, c and εt for the beam shown in figure 1. fy=420 mpa, fc'=21 Mpa.

Figure 1

a=(Asfy)/(0.85fc'*B)
=(1935*420)/(0.85*21*355)
=128.25mm
a=β1*c
β1=0.85
a=128.25/0.85=150.88
from trinagle similarities

εt/(d-c)=0.003/c
εt=0.003(d-c)/c
εt=0.003(533-150.88)/150.88
εt=0.0076