# Question: please answer the 2nd question the first is only for...

###### Question details

**Please answer the 2nd question, the first is only for
reference.**

1. Consider a cylinder of height h, diameter d, and wall
thickness t pressurized to an internal pressure P0 (gauge pressure,
relative to the external pressure). The cylinder consists of
material with Young’s modulus E, Poisson’s ratio ν, and density ρ.
Derive expressions for the axial and hoop strains of the cylinder
wall. You may assume plane stress conditions.

**2. (7 points) Continuing on Problem 1, assume a strain gage
is bonded to the cylinder wall surface in the direction of the hoop
strain. The strain gage has nominal resistance R0 and a Gage Factor
GF. It is connected in a Wheatstone bridge configuration where all
resistors have the same nominal resistance; the bridge has an input
voltage Vin. (The strain gage is bonded and the Wheatstone bridge
balanced with the vessel already pressurized.) Develop an
expression for the voltage change ΔV across the bridge if the
cylinder pressure changes by ΔP.**