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Flexural stress calculation using transformed area method for rectangular beam

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           

first, we will calculate the transformed area of steel. the concrete below the neutral axis will not contribute in resisting of tension. figure 2 shows the section after transformation 
As=4*0.44=1.76in2
Transformed area=As*n=8*1.76=14.08in2

Figure 2

Neutral axis can be calculated by equalling moment of area from both parts as shown below 
14.08*(17-x)=(x/2)*(14*x)
239.36-14.08x=7x^2
7x^2+14.08x-239.36=0
x=4.92

moment of inertia for transformed section =(14*4.92^3)/12+4.92*14*2.46^2+14.08*12.08^2=2610.422in4=0.125886ft4


flexural stress for compression zone. y at extreme compression equal 4.92in=0.41ft

fc=(M*y)/I
fc=60*0.41/0.125886=195.414k/ft2=1357psi


flexural stress for tension zone. y at extreme tension equal 12.08in=1.0067ft
fs=n(M*y)/I
ft=(8*60*1.0067/0.125886)=3838.392k/ft2=26655.49psi









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