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nominal flexural moment for reinforced concrete beam

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The nominal or ultimate flexural moment for reinforced concrete beam represents the ultimate moment that a beam can carry. moments generated by service load shall be less than the nominal moment of the beam. at this stage, reinforcing steel assumed to yield. concrete stress will not vary linearly from the neutral axis. compressive stress will be similar to that shown in figure 1. for simplification concrete compressive stress transferred into a rectangular shape with a constant stress of 0.85fc' and depth a.





Figure 1

as the steel assumed to yield. a tensile force equal T=As.fy, where As is the cross-section area of reinforcing bar and fy is the yield stress of reinforcing bar.
concrete compression force equal C=0.85fc'.a.b where a is the depth of concrete compressive stress block and b the width of the reinforced concrete beam.

C must be equal to T to maintain the equilibrium.  the moment is equal to the magnitude of the force multiplied by the perpendicular distance between its line of action and the axis of rotation. in our case the perpendicular distance between the force is d-a/2. 

Mn=As.fy(d-a/2)

Example: Determine the nominal moment strength of the beam shown in figure 2. fy=420Mpa. fc'=20 Mpa, As=1935.50cm2. 

T=C
As.fy=0.85fc'.a.b
1935.5*420=0.85*20*a*350
a=136.6mm

Mn=As.fy(d-a/2)
=420*1935.5(550-136.6/2)
=391,578,747n.mm=391.58kn.m


Figure 2



More examples
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7



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