CE 334

1
CE 334

• EXPERIMENTAL ANALYSIS OF
• ENGINEERING MATERIALS
• Yan Xiao
• Chapter 6
• Stress Analysis

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Contents

• Introduction
• Review of stress and strain transformations
• Measurements of complicated strains
• Review of elastic beams
• Project

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Introduction

• Objectives of stress analysis
• To investigate stresses in bodies of complicated
  shapes, properties or under complex loading
  conditions, where no sophisticated and reliable
  analytical methods are available.
• Backups or validation of analysis
• Obtain mechanical properties
• Assessment of working (stress) condition. etc.

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General

• Measurement of surface strains at selected
  points
• Since only limited strains at limited points and
  limited directions are instrumented, analysis is
  needed to obtain strains in other directions,
  locations

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Strain transformation
Strain components in x-y coordinates,
Projecting strains from x-y system to x-y
system
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Equations for strain transformation
These equations are similar to those for
stresses, except exchanging normal stresses by
normal strains, and shear stress by shear strain
(i.e., 1/2 of the conventionally defined shear
strain gxy)
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Mohrs circle for strain and principle strains
Similar to stress Mohrs circle. From this, the
principal strains can be easily defined,
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Big Question???
Are the directions of principal stresses and
principal strains the same ? If so, under what
condition?
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Measurement of 2-D strains
To obtain the 3 independent strains (2 normal and
1 shear) at point can be done by measuring 3
normal strains in 3 know directions.
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Rosette
Principal strains and directions
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Commercial rosettes
Three-element 45-deg. rectangular rosettes
Two-element 90-deg. rectangular rosettes
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Plane-shear or Torque Gauge
As shown in the Mohrs circle, if A and B is
aligned in 45o to x-direction, then,
Torque gauges are made based on this concept to
directly measure shear strain.
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Experimental analysis of simple elements
Review of elastic beam theory Flexure
stresses the figure shown is based on 1. Plane
assumption 2. Elasticity.
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Shear stresses
Shear stress at position y from centroid,
For rectangular section,
Note shear stress thus defined VIOLATE the plane
assumption!!!!!
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Shear Stress in I-Shaped Sections
For flanges,
For web,
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Project 5 - stress analysis of simple beam
Requirements 1. Evaluate the plane assumption
for the mid-span section 2. Check principal
strains at the center point 3. Check principal
strains at point 1 and 2. 4. Assess Youngs
modulus. 5. Etc.