   # - 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction? ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 7, Problem 7.7.26P
Textbook Problem
1 views

## - 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction? To determine

The stress along x-direction.

### Explanation of Solution

Given information:

The strain in gauge A is 1100×106, strain in gauge B is 1496×106and strain in gauge C is 39.44×106,.and the Poisson's ratio is 0.33and the Young modulus of the gauge is 70GPa.

Write the expression for transformation for plain strain.

ε=εx+εy2+εx+εy2cos2θ+γxy2sin2θ(I)

Here, strain in gauge is ε, strain along x direction is εx, strain along y-direction is εy, shear strain in x-y plane is γxy,and orientation of gauge is θ.

Write the expression for the stress along x-direction using Hooks law.

σx=E1ν(εx+νεy) (II)

Here, Young modulus is Eand the Poisson's ratio is ν.

Calculation:

Substitute 1100×106for εx, 0for εy, 0°for θin Equation (I) for gauge A.

ε=1100×106+02+1100×106+02cos2(0°)+γxy2sin2(0°)ε=εA=1100×106

Here, strain in gauge A is εA.

Substitute 1496×106for ε, 1100×106for εx, 40°for θin Equation (I) for gauge B.

εB=1100×106+εy2+1100×106+εy2cos2(40°)+γxy2sin2(40°)1496×106=1100×106+εy2+1100×106+εy2cos2(40°)+γxy2sin2(40°)1496×106=645.50×106+0.413εy+0.492γxy0.413εy+0.492γxy=8.5×104(III)

Substitute 39

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
Briefly describe the term sensitive drill press.

Precision Machining Technology (MindTap Course List)

What is connectivity? (Use a Crows Foot ERD to illustrate connectivity.)

Database Systems: Design, Implementation, & Management

Provide a brief history of the Internet.

Fundamentals of Information Systems

For a building located in Detroit, Michigan with annual heating degree-days (dd) of 6232, a heating load (heat ...

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

Determine the couple-vector that is equivalent to the two couples shown.

International Edition---engineering Mechanics: Statics, 4th Edition

5. Identify the main components of an information system. What is a mission-critical system?

Systems Analysis and Design (Shelly Cashman Series) (MindTap Course List)

What is meant by remote control?

Electric Motor Control

Distinguish among the web, a webpage, a website, and a web server.

Enhanced Discovering Computers 2017 (Shelly Cashman Series) (MindTap Course List)

What is the last weld bead on a multipass weld called?

Welding: Principles and Applications (MindTap Course List)

If your motherboard supports ECC DDR3 memory, can you substitute non-ECC DDR3 memory?

A+ Guide to Hardware (Standalone Book) (MindTap Course List) 