$\Sigma M_{R2} = 0$

$12R_1 = 9(2000)$

$R_1 = 1500 \, \text{lb}$

$\Sigma M_{R1} = 0$

$12R_2 = 3(2000)$

$R_2 = 500 \, \text{lb}$

**Maximum fiber stress:**

$(\,f_b\,)_{max} = \dfrac{Mc}{I} = \dfrac{4500(12)(2)}{\dfrac{2(4^3)}{12}}$

$(\,f_b\,)_{max} = 10,125 \, \text{ psi}$ *answer*

**Stress in a fiber located 0.5 in from the top of the beam at midspan:**

$\dfrac{M_m}{6} = \dfrac{4500}{9}$

$M_m = 3000 \, \text{lb}\cdot\text{ft}$

$f_b = \dfrac{My}{I}$

$f_b = \dfrac{3000(12)(1.5)}{\dfrac{2(4^3)}{12}}$

$f_b = 5,062.5 \, \text{ psi}$ *answer*

Hi

When putting values in formula

4500- max moment ->ok2- half depth -> ok2*(4- moment of inertia -> ok^{3})/12but what is the

12above line?can u help me?

Conversion of lb-ft to lb-in.

Hi

Actually they have just converted the unit of the moment from lb-ft to lb-in by multiplying 12 because other parameters are in inch and as you know 1 ft=12 inch so 4500 lb-ft=4500*12 lb-inch.

Hello. How did they get the 6 in M/6 = 4500/9 ?

That is by ratio and proportion from the moment diagram. Mm is at the midspan, or 6 ft to R2.