I have a problem of a fixed/pinned beam. I have to account for the weight of the beam in finding the stress of the beam at the fixed end. It's stated to assume that the beam's weight is uniformly distributed along the span of the beam. I'm given the length of the beam 6.1 m and the area $0.01632255 m^2$. Also the density of $7870 kg/m^3$ and weight per unit length of $128 kg/m$.
I can calculate out the weight from the density, area, and length to get the weight. But what I'm confused about is the "uniformly distributed along the span" line. Should I assume that the problem as a uniformly distributed load of $128 kg/m$. But I would need that $N/m$ so I should multiply by $9.81 m/s^2$ to get $N/m$. Then I found an equation for the moment at the fixed end of a fixed/pinned beam with uniformly distributed load $$M=p*L^2/8.$$ $p$ is the distributed load which would be $128*9.81$ in my case. Then I know how to calculate the stress given the bending moment.
So if someone can help me figure out if I am correct in what I'm thinking or if I'm way off it would be greatly appreciated. Thanks.