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Example 09: flexural stress for reinforced beam using transform area method(SI units)

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determine the flexural stresses for the beam shown in figure 1 using the transformed-area method. (Mn=130Kn.m, n=9)
Figure 1







Transform area=As*n
TA=650*4*9=23,400mm2

To calculate the neutral axis location we need to equal moments around the neutral axis as shown in figure 2

X*350*(X/2)=23,400*(530-X)
175*(X^2)+23,400X-12,402,000=0
X=207.62mm

now we can calculate the moment of inertia using the parallel axis theorem
I=Ic+A*(d^2)
I=(350*(207.62^3))/12+350*207.62*(103.81^2)+23,400*(322.38^2)
I=3,476,064,887.554mm^4

bending stress at extreme compression fiber, y=207.62mm
Mn=130 kn.m=130,000,000n.mm
fc'=(M*y/I)
fc'=(130,000,000*207.62/3,476,064,887.554)
fc'=7.76Mpa

bending stress at the center of reinforcing steel, y=322.38mm

fs=n*M*y/I
fs=9*(130,000,000*322.38/3,476,064,887.554)=108.50Mpa
Figure 2


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