Statics Session 3 Example 2 (ENGR5004)

Statics Session 3 Example 2TutorialCurrent spec2:28 min

ENGR5004 Statics session 3 worked example 2 (slides 13-14) official answers

A steel block ( $E = 200$ GPa, $\nu = 0.29$ ) is subjected to a uniform pressure $p$ on all its faces. Before the load is applied the edges of the block in the $x$ , $y$ and $z$ directions are $l_x = 100$ mm, $l_y = 50$ mm and $l_z = 75$ mm. Under the load, $l_x$ decreases by $\delta_x = 0.04$ mm.

Formulas you may need

Generalised Hooke's law: $\epsilon_x = \dfrac{\sigma_x}{E} - \dfrac{\nu\sigma_y}{E} - \dfrac{\nu\sigma_z}{E}$ (and cyclic) (learn this)
Bulk modulus: $k = \dfrac{E}{3(1-2\nu)}$ ; dilatation $e = \epsilon_x + \epsilon_y + \epsilon_z = -\dfrac{p}{k}$ under hydrostatic pressure (learn this)
Volume change $\Delta V = eV$ (learn this)

(a)
Determine the change in length of the other two edges.
delta_y =mm
delta_z =mm
(b)
Determine the pressure $p$ applied to the block faces.
p =MPa
(c)
Determine the overall volume change of the block.
Delta V =mm^3