Verifying Homework Equations: 4 Variables

[temaire]

Homework Statement

Homework Equations

\tau=\frac{4V}{3A}

\sigma_b=\frac{-Mc}{I}

\tau=\frac{Tr}{J}

J=\frac{\pi r^4}{2}

I=\frac{\pi r^4}{4}

The Attempt at a Solution

a)

-V(x) + R_y = 0
V(x) = R_y
V(x) = 1000

M(x) = \int V(x)dx
M(x) = 1000x

T(x) = P(0.4)
T(x) = 400

V(x) - 1000 = 0
V(x) = 1000

M(x) = \int V(x)dx
M(x) = 1000x

T(x) = 0

b)
\tau_{max} = \frac{4V}{3A}

\tau_{max} = \frac{4*1000}{3*\pi*0.12^2}

\tau_{max} = 29.5 KPa

Coordinates: From (0,-0.12,0)m to (0,0.12,0)m

c)
\sigma_b=\frac{Mc}{I}

\sigma_b=\frac{Mc}{\frac{\pi r^4}{4}}

\sigma_b=\frac{1000*0.4*0.12}{\frac{\pi * 0.12^4}{4}}

\sigma_b=294.7 KPa

\sigma_{Max,tensile}=294.7 KPa at (0,0,0.12)m

\sigma_{Max,compressive}=-294.7 KPa at (0,0,-0.12)m

d)
\tau=\frac{Tr}{J}

\tau=\frac{Tr}{\frac{\pi r^4}{2}}

\tau=\frac{1000*0.4*0.12}{\frac{\pi *0.12^4}{2}}

\tau=147.4 KPa

Coordinates: From (0,-0.12,0)m to (0,0.12,0)m


Is my work correct?

 

[temaire]

Guys, I have a final exam on this material tomorrow. Any help would be appreciated.