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=n*As**

**As=4*.79=3.16 in2**

**Transform area=3.16*10=31.6in2**

**now we will determine the location of the neutral axis as shown in figure 2**

**12*X*(X/2)=(17.5-X)*31.6**

**6*X^2+31.6X-553=0**

**X=7.32 in**

**moment of inertia using parallel axis theorem**

**I=Ic+Ad^2**

**I=(12*7.32^3)/12+12*7.32*3.66^2+31.6*10.18^2=4843.67in4**

**=0.234ft4**

**now we will calculate the moment applied to beam**

**Maximum moment for simply supported beam**

**M=(W*L^2)/8**

**=(1.5*24^2)/8**

**=108K-ft**

**now we will calculate flexural stress at extreme compression fiber. y=7.32 in =0.61ft**

**fc=M*y/I**

**=108*0.61/0.234**

**=281.538k/ft2=1955.125psi**

**now we will calculate flexural stress at center of reinforcing steel. y=10.18 in =0.85ft**

**fs=nM*y/I**

**=10*108*0.85/0.234**

**=3923.076k/ft2**

**=27243.58psi**

*Figure 2*