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Example 1:Flexural stress calculation using transformed area method for rectangular beam with double layer of reinforcing bars

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 to resisting of tension. figure 2 shows the section after transformation 
Transformed area for first layer=As*n=2*8=16in2
Transformed area for second layer=As*n=4*8=32in2

figure 2

Neutral axis can be calculated by equalling moment of area from both parts as shown below 
x=8.77 in
moment of inertia for transformed area=

flexural stress for compression zone. y at extreme compression equal 8.77in=0.73ft


flexural stress for tension zone for y at bottom layer equal 12.23in=1.019ft


flexural stress for tension zone for y at the center of reinforcing steel layer equal 20-x=20-8.77=11.23in=0.9358ft



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