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Example 10: 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.
Figure 1







Transform area=As*n
TA=1006*4*9=36,216mm2

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

300*X*(X/2)=36,216*(420-X)
150*X^2+36,216X-15,210,720=0
X=219.83mm


now we can calculate the moment of inertia using the parallel axis theorem
I=Ic+A*(d^2)
I=(300*(219.83^3))/12+219.83*300*(109.915^2)+36,216*(200.17^2)
I=2,513,437,241.55mm4

The maximum moment for simply supported beam located at the center and equal M=(W*(L^2))/8
M=(20*(8^2))/8
M=160KN.m=160,000,000n.mm

bending stress at extreme compression fiber, y=219.83mm

fc'=(M*y/I)
fc'=(160,000,000*219.83/2,513,437,241.55)
fc'=13.99Mpa

fs=n*M*y/I
fs=(9*160,000,000*200.47)/2,513,437,241.55
fs=114.85Mpa

Figure 2







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