Lab #2 Report due TODAY Individual Data Processing and

Individual Write Up Lab #2 Report is due TODAY by

midnight Answer Multiple Choice Questions

ONLINE TODAY by midnight Answer Student Survey ONLINE TODAY

by midnight Submit the Lab Report #2 in the drawer

labeled “MECE204-Strength Lab” under M. E. Mail Folders

Torsion Testing Circular Cross-section Only Determine Material Properties in Torsion Draw Shear Stress-Strain Curve Ductile or Brittle Failure ? ASTM E-143 Test Method Compare results from Tensile, Poisson’s &

Torsion Test

Become familiar with Tinius Olsen Torsion Tester (10,000 in-lb capacity)

Sign Convention

Assumptions

Perfectly linear-elastic behavior Circular x-section (solid or hollow) Small rotations Constant length Constant diameter

No deformation A highly

deformable member

A circular x-section

A grid of parallel circles and longitudinal lines on the outer surface

After Deformation

Two torques are applied

Circles remain circles

Longitudinal lines become twisted

All angles are equal

End x-section remains flat

Angle of Twist A prismatic circular

member Fixed at x = 0 Other end is FREE Loaded by a torque

at the free end Angle (x) - angle

of twist It depends on x:

/x=constant

Shear Strain

Before After

9

Shear Strain Distribution

max = c• max - occurs on the

outer surface• = (/c) max

• Result valid also for circular tubes within the material

• Valid for plastic deformation also

Shear Strain Distribution

Shear Strain & Angle of Twist

= * / L

max = * D / 2 / L

12

Shear Stress Distribution - Elastic Deformation only

X-section: linear distribution Complimentary stresses in action Shear stress occur on axial planes (normal to the x-section

Shear Stress & Torque- Linear Elastic Deformation Only

= T * / J

max = T * D / 2 / J

Shear Stress-Strain Curve

max, rad

max, psi

Modulusof Rupture

Slope = = Shear Modulus, G

Figure 3.2 Typical shear stress-strain diagram from a Torsion Test

Linear Elastic Region – Shear Modulus

Failure Surface – Tensile Testing

Failure Surface – Torsion Test

Brittle Failure – Torsion Test

Stresses on an Inclined Plane in an Axially Loaded Member Seek for equilibrium after

cutting along the oblique plane

n

P

NV

t

2sin)2/(sincos

)2cos1)(2/(cos

: )/ that note (and plane inclined on the

ly,respectivestresses,shear and normal the

obtain to with V and N Normalize

)cos(

:is plane inclined theof Area

)sin(:0

)cos(:0

xxnt

x2

xn

x

AP

A

AA

PVF

PNF

n

n

t

n

x

Maximum Stress – Uniaxial Tension

Comparing Tensile vs. Torsion Results

Measuring Angle of TwistT=(R-R0)-(L-L0)

Torsion Data Sheet

Computing the Slip Angle

Manually Recorded Data

R0

L0

T=(R-R0)-(L-L0)

slip= H-(LH/LT)T

cor = H - slip

Shear Strain and Stress

=Radians(cor)*D/2/LH

=16T//D3

Integrating Computer Data

slip= constant

cor=H - slip

Selecting Computer Data

Head Angle = 30.00 deg

When Protractors taken OFF

Max Torque = 1931 in-lb

Entire Stress Strain Curve

Elastic Curve

Proportional Limit

=G*

Proportional Limit

Plot columns H, I, & J

Key Ideas - Torsion Shear strain formula is valid in both

elastic & plastic region Torque formula is valid in linear

elastic region ONLY Thus, shear stress formula is valid

until proportional limit After proportional limit, shear stress

formula overestimates stress.

Torsion Results

Comparing Tensile vs. Torsion Results

Comparing Lab 1, 2, & 3Experimental Results

Lab #2 Report due TODAY Individual Data Processing and

Individual Write Up Lab #2 Report is due TODAY by

midnight Answer Multiple Choice Questions

ONLINE TODAY by midnight Answer Student Survey ONLINE TODAY

by midnight Submit the Lab Report #2 in the drawer

labeled “MECE204-Strength Lab” under M. E. Mail Folders