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Example 3:Flexural stress calculation using transformed area method for rectangular beam

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assume the section for beam shown in figure 1 cracked calculate the flexural stresses for the given load or moment using transformed area method.





Figure 1

Transform Area=As*n
As=6*1.0=6in2
Transform Area=6*8=48in2

neutral axis location as shown in figure 2
16*X*(X/2)=(28-X)*48
8X^2+48X-1344=0
X=10.30in

moment of inertia
I=Ic+Ad^2
=(16*10.3^3)/12+16*10.3*5.15^2+48*17.7^2
=20865.78in4=1.006ft4

Figure 2

the figure no 3 showing the shear and moment diagram for the beam in this example. from moment diagram. maximum moment =400 k-ft

Figure 3


flexural stress at extreme compression. y=10.30 in=0.86ft
fc=M*y/I
=400*0.86/1.006=341.28k/ft2=2370psi


flexural stress at cetner of reinforcing steel. y=17.70 in=1.475ft
fs=nM*y/I
=8*400*1.475/1.006=4691.85k/ft2=32,582psi






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