HW9_1: AXIAL AND TRANSVERSE STRAINS - THE POISSON'S RATIO

Question

When no loads are applied, the isotropic elastic block depicted below is a cube of side L0=200 mm.

When the distributed load (surface traction) q=200 MPa is applied as shown below, the side length along the direction of the applied load extends to measure La=210 mm, and the side lengths perpendicular to the direction of the applied load contract to measure Lt=196 mm.


HW9_1_1 : 40.0 POINTS

Obtain the numerical values for the Young's modulus (in GPa) and Poisson's ratio (dimensionless) of the material composing the block:

E=
GPa unanswered
ν=
unanswered
HW9_2: HOOKE'S LAW FOR NORMAL STRESSES AND STRAINS

When no loads are applied, an isotropic elastic block is a cube of side L0=100 mm with sides aligned with the Cartesian x, y, z axes. The modulus of the material is 30 GPa, and its Poisson's ratio is 0.4.


HW9_2_1 : 40.0 POINTS

If normal stresses σxx=−150MPa, σyy=−30MPa, and σzz=90MPa are applied to the faces of the block, obtain the numerical values (in mm) of the deformed side lengths Lx, Ly, and Lz of the block.

Note: these measurements will be very precise! You will need to provide your answer to the second decimal digit.

Lx=
mm unanswered
Ly=
mm unanswered
Lz=
mm unanswered

HW9_3: BLOCK BETWEEN RIGID WALLS

A cube L0×L0×L0 of isotropic linear elastic material (properties E, ν) is placed between two rigid frictionless walls at fixed distance L0 and compressed by a lateral pressure p along the x-axis, as indicated in the figure. No loads or constraints are acting along the z-axis. Under the effect of the applied lateral pressure, the cube elongates in the direction normal to the plane of the figure (z-direction) and the strain in this direction is measured to be ϵzz=ϵ0.


HW9_3_1 : 40.0 POINTS

Obtain symbolic expressions for the applied pressure p and for the constraining normal stress along the y direction σyy exerted by the walls on the block.

Write your expressions in terms of the measured strain along the z-axis, ϵ0 (enter as epsilon_0) and of the elastic properties E, ν (enter ν as nu).

p=
unanswered
σyy=
unanswered

Answer 1

9_1_1 4 &0.4
9_2_1 99.42,99.98,100.54
9_3_1 don't know...

Answer 2

9.1
a) 4
b) 0.4