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.